Machine Learning for Sustainable Urban Energy Planning: A Comparative Model Analysis

Abstract

Accurate short-term forecasting of urban electricity demand is essential for operational planning and climate-resilient energy management. This study evaluates four forecasting models, namely, Prophet, Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Temporal Convolutional Networks (TCN), across 15 U.S. cities representing diverse climatic regimes. Model performance is assessed at 1, 6, 12, and 24 h horizons using MAE, RMSE, MAPE, and R² within a unified, climate-aware evaluation framework. Results show that Prophet consistently outperforms deep learning models at longer horizons (12–24 h), achieving MAE reductions of approximately 70–90% relative to LSTM and GRU across all climatic clusters, while maintaining R² values above 0.95 even in highly variable climates. At short horizons (1–6 h), LSTM and GRU perform competitively in climatically stable cities, reducing MAE by up to 15–25% compared with Prophet, but their accuracy deteriorates rapidly as forecast horizons increase. TCN exhibits intermediate performance, outperforming recurrent models in selected short-horizon cases but showing reduced robustness under high climate variability. Statistical testing indicates that model performance varies significantly across cities within climatically heterogeneous clusters (p < 0.05), highlighting the influence of climatic variability on forecasting reliability. Overall, the results demonstrate that model effectiveness is strongly context-dependent, providing quantitative guidance for climate-aware model selection in urban energy systems.

1. Introduction

Forecasting energy demand in urban areas is critical for managing resources, reducing operational costs, and achieving sustainability goals. On average, cities contribute over 75% of countries’ Gross Domestic Product (GDP) and are the main engines of economic growth. However, this economic activity is accompanied by significant environmental costs, as cities also consume approximately 75% of global primary energy, while emitting between 50% and 60% of the world’s total greenhouse gases [1]. This disproportionate energy consumption highlights the challenges cities encounter in driving economic development while maintaining sustainability and energy efficiency. The increasing density of urban environments, hosting 55% of the world population today with an expected increase to 68% by 2050 [2], further increases the pressure placed on city infrastructure to deliver reliable and efficient energy services [3]. This demand is not limited to basic infrastructure but extends to buildings, which account for significant energy consumption (36% of global consumption [4]) throughout their life cycle, from raw material extraction to daily operations such as lighting, air conditioning, and cleaning. As cities strive to meet the rising energy demand, ensuring an uninterrupted and efficient energy supply becomes an urgent priority to support continued urban growth and development [1]. This urgency was emphasised at the recent United Nations Conference of the Parties meeting (COP28), where nearly 200 countries committed to addressing these challenges [5].

Accurate energy demand prediction not only supports efficient resource allocation but also plays a vital role in strategic planning for infrastructure development, sustainability initiatives, and energy policy formulation [6,7]. Governments and energy providers rely on demand forecasts to make informed decisions on energy production, distribution, and storage, all of which have significant cost implications [8]. Errors in energy demand forecasting can lead to energy shortages, driving up energy prices and potentially exacerbating fuel poverty [9,10]. Additionally, reliable energy forecasts enable policymakers to design more effective sustainability initiatives, such as integrating renewable energy sources into the grid or planning future smart city developments where energy efficiency is paramount [11,12,13]. For instance, cities that seek to achieve net zero carbon targets (more than 700 [14]) must align their energy infrastructure investments with accurate predictions of future energy needs to ensure both economic feasibility and environmental responsibility.

The advent of machine learning and deep learning models has revolutionised the field of energy prediction, offering novel techniques that outperform traditional forecasting methods. Conventional models like ARIMA (autoregressive integrated moving average) or multiple linear regression (MLR), while effective in simple, stable environments, often struggle to capture the complex, non-linear, and interdependent factors influencing dynamic systems [15,16], such as urban energy consumption. Machine learning models, on the other hand, can analyse large datasets, detect hidden patterns, and adapt to changes in consumption trends, external variables, and environmental factors [17,18], making them suitable for complex environments such as urban energy systems [19]. These models excel in handling the high dimensionality and diversity of urban energy data, which often includes temporal, spatial, and socio-economic variables [20,21]. Further, as cities become more interconnected through smart grid technologies, the ability to process vast amounts of real-time data has become a critical advantage of these advanced models, enabling a more responsive and adaptable approach to energy management [17,22]. Consequently, machine learning approaches provide more robust and adaptive solutions, better suited to the complexity of such real-world scenarios.

Despite this methodological progress across multiple subfields, including building-level forecasting, ensemble learning, deep learning, and spatio-temporal modelling, a clear research gap remains. Most studies focus on individual buildings, single cities, or geographically narrow regions [23,24,25], making it difficult to determine whether reported performance gains persist across broader urban systems. As a result, it remains unclear how forecasting models behave across diverse cities characterised by markedly different climatic regimes. Although weather variables are commonly used as predictors, the role of climatic variability itself as a driver of forecasting uncertainty is rarely examined explicitly. Furthermore, few studies adopt climate-aware or regime-based analytical frameworks prior to model comparison, limiting the interpretability and transferability of results. In addition, most evaluations focus on short-term horizons, typically one to several hours ahead, providing limited insight into how model performance degrades at medium- and long-term horizons.

Several studies illustrate these constraints in practice. Many focus on specific building attributes [26,27,28] or particular building types [29,30,31], while others concentrate on single industrial sectors [32,33]. Temporal scope is another limitation: much of the literature relies on short, single-year datasets [34,35,36], or aggregates demand to daily or monthly intervals that obscure finer-scale variability [37,38]. Even studies using high-resolution hourly data often omit contextual features such as day-of-week or seasonal markers [39,40], reducing their ability to capture diurnal and seasonal demand patterns. These examples demonstrate how data and methodological constraints in prior work hinder the development of forecasting models that can generalise reliably across cities with diverse climatic and temporal demand regimes. This synthesis directly motivates a comparative model-evaluation problem rather than the development of yet another forecasting architecture. Specifically, it remains unclear under what climatic conditions and forecast horizons advanced deep learning models genuinely outperform simpler statistical approaches, and whether such advantages are robust across heterogeneous urban environments.

To address these challenges, this study undertakes a systematic comparison of four advanced time-series forecasting models: Prophet, Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Temporal Convolutional Network (TCN). These models are selected as representative members of distinct modelling families, statistical decomposition and deep learning sequence modelling, allowing performance differences to be interpreted in relation to both climatic regime and forecast horizon. By integrating climatic variability through a coefficient-of-variation-based clustering framework, this study explicitly links model performance to environmental regime.

The aim of this study is therefore to evaluate, in a climate-aware and multi-horizon framework, the performance of Prophet, LSTM, GRU, and TCN across fifteen U.S. cities with diverse climatic and geographic conditions. By doing so, the study identifies context-specific strengths and limitations of each model and provides empirical guidance for climate-dependent model selection. The findings are intended to inform the design of more efficient and resilient urban energy systems, contributing to sustainable energy planning in the context of climate change and rapid urbanisation.

The key contributions of this study are summarised as follows:

• A systematic, multi-city benchmarking of Prophet, LSTM, GRU, and TCN across fifteen U.S. cities with diverse climatic and geographic conditions.
• A climate-aware evaluation framework based on clustering cities using the coefficient of variation of key meteorological variables.
• A multi-horizon performance assessment (1, 6, 12, and 24 h) using MAE, MSE, RMSE, MAPE, and R².
• Quantitative evidence that Prophet consistently outperforms deep learning models at longer forecast horizons across all climatic clusters.
• Empirical demonstration that urban climate variability is a key determinant of forecasting reliability.

2. Background

Accurate energy consumption predictions are essential for advancing urban sustainability, particularly in meeting net-zero targets. Machine learning has become pivotal, enabling models that optimise energy use, reduce emissions, and support resilient infrastructure design. These predictions facilitate targeted interventions, guide energy-efficient retrofits, and align urban planning with long-term sustainability goals for green cities. Early studies on energy prediction relied primarily on statistical and time-series methods, such as MLR and ARIMA models [41,42,43]. These models were widely adopted due to their simplicity and ease of interpretation, performing adequately in stable, predictable environments where energy demand followed regular seasonal or daily patterns. However, the limitations of traditional models became evident as cities grew more complex, with demand fluctuations driven by diverse, non-linear influences such as climate variability, socio-economic shifts, and technological changes [3,44,45,46]. As a result, these methods struggled to capture the multifaceted dynamics of urban energy use, particularly under irregular consumption patterns or rapidly changing external conditions.

The shortcomings of traditional models have paved the way for machine learning approaches, which offer flexibility and improved predictive power in handling high-dimensional, non-linear data. Early applications of machine learning in energy forecasting utilised algorithms such as Support Vector Machines (SVMs) and Decision Trees (DTs), which proved more capable of handling complex data patterns compared to traditional models [17]. DTs, in particular, random forest, has been shown to perform better over other machine learning algorithms. Fan et al. [47], for example, compared the performance of random forest (RF), regression tree (RT), and support vector regression (SVR—a variant of SVM) in predicting energy consumption for two buildings in Florida. The results of that study showed that the prediction performances of RF, measured by a performance index, were 14–25% and 5–5.5% better than RT and SVR, respectively. In a related work, Candanedo et al. [48] applied RF to forecast short-term electricity consumption in a Belgian household. The authors evaluated the prediction performance of RF against three other models: MLR, SVR, and Gradient Boosting Machines (GBM). The results showed that RF and GBM performed better than MLR and SVR. Similarly, Ahmad et al. [49] used RF to forecast the hourly Heating, Ventilation, and Air Conditioning (HVAC) electricity consumption of a hotel in Madrid, Spain and reported performance comparable to ANN-based feed-forward networks; 91% and 95% for RF and ANN respectfully. While these studies confirm the strong short-term performance of RF-based models, their analyses are primarily restricted to individual buildings or single urban locations, limiting the generalisability of findings and offering limited insight into long-horizon urban-scale forecasting.

Ensemble models have also gained popularity for their ability to combine the strengths of multiple learners. Priyadarshini et al. [50] employed an ensemble learning approach combining DT, RF, and gradient boosting methods to forecast energy consumption in smart buildings. This study highlighted the benefits of using ensemble techniques to improve predictive accuracy and robustness by leveraging the strengths of multiple algorithms. Divina et al. [51] also used various weaker models, a regression tree, RF and ANN to build an ensemble model showing better performance compared to individual models. Similarly, Khashei et al. [52] demonstrated the effectiveness of hybrid models, integrating neural networks with ARIMA, for short-term energy forecasting. Their research showed that hybrid models could effectively capture both linear and non-linear relationships in energy consumption data, leading to better performance than traditional univariate models. Although ensemble and hybrid methods often yield higher accuracy, they introduce substantial model complexity, increased computational cost, and reduced interpretability, which limit their scalability for large, multi-city applications.

More recently, there has been increasing exploration in the use of deep learning models. For example, Alizadegan et al. [53] compared LSTM and Bidirectional LSTM (Bi-LSTM) to traditional forecasting methods ARIMA and Seasonal ARIMA (SARIMA) for energy consumption prediction. That work showed that both LSTM models, in particular, Bi-LSTM, outperformed the traditional models. Paterakis et al. [54] also compared the results of an MLP enriched deep learning model with several popular machine learning models, including, logistic regression (LR), MLR, different RTs, SVRs, and gaussian models to predict aggregated energy demand and showed that the former outperformed all other models. Hrnjica and Mehr [55] demonstrated the effectiveness of LSTM networks in forecasting energy demand for smart grids in Nicosia, Northern Cyprus. Their study indicated that LSTM networks could capture complex temporal dependencies within energy consumption data, addressing inefficiencies observed when compared to a standard time series model based on decomposition. Other work by [56] further used an LSTM framework within a deep learning model to forecast electricity demand, capturing both short-term fluctuations and long-term trends. Their approach demonstrated superior performance against several benchmark models, indicating the LSTM’s capability in handling complex, non-linear relationships in time-series data. Naji et al. [57] also explored the use of Extreme Learning Machines (ELM) for estimating building energy consumption. The results of study showed improved accuracy and efficiency over traditional ANN approaches. The ELM’s ability to handle diverse input variables and provide rapid training made it an promising option for real-time applications. Despite their high short-term accuracy, deep learning models are data-intensive, computationally expensive, and often exhibit performance degradation at longer forecast horizons. Moreover, most existing deep learning studies remain limited to individual buildings, single cities, or homogeneous climatic regions, restricting their transferability across heterogeneous urban environments.

Several recent studies have investigated hybrid deep learning methods to further enhance prediction accuracy. Su et al. [58] introduced a hybrid model combining wavelet transform and enhanced deep Recurrent Neural Networks (RNNs) for forecasting natural gas demand. Their approach used both simulated and real datasets, demonstrating superior performance over conventional methods. Karijadi and Chou. [59] combined both RF and LSTM for building energy prediction showing that this approach performed better than traditional ML approaches that included LR, SVR, ANN, and RF on its own. Similarly, del Real et al. [60] combined Convolutional Neural Networks (CNNs) and ANNs to forecast energy demand in France. Their findings revealed that the hybrid model significantly improved prediction metrics such as mean absolute error (MAE) and mean absolute percentage error (MAPE) compared to using ANNs alone, underscoring the advantage of integrating feature extraction capabilities of CNNs with the regression strength of ANNs. While these hybrid approaches enhance accuracy, they further increase model complexity and black-box behaviour, hindering interpretability and large-scale operational deployment.

Spatio-temporal learning has also contributed to recent advances. Kim and Cho [61] proposed a CNN-LSTM neural network model to forecast residential energy consumption, capturing both spatial and temporal dynamics in household power consumption data. Their model outperformed several conventional techniques, achieving high accuracy even in the presence of irregular consumption patterns. Amasyali and El-Gohary [62] further emphasised the role of deep learning in energy prediction by using a multi-layer Deep Neural Network (DNN) to model cooling energy consumption based on outdoor weather conditions. Their simulation-based approach across various climates demonstrated the robustness of deep learning methods compared to traditional models such as SVM and RF. However, these approaches require dense spatial sensing and high-dimensional inputs, which are not consistently available at the urban-system scale.

In addition to these methodological limitations, broader multi-region studies highlight further gaps. For example, Cawthorne et al. [63] analysed electricity demand across multiple U.S. states but lacked the spatial and temporal granularity needed to assess model performance under heterogeneous climatic and urban conditions. Such studies often rely on aggregated signals that obscure local demand variability driven by differences in urban form, building stock, and infrastructure. Consequently, empirical evidence remains limited on how forecasting accuracy changes systematically across climatically diverse urban environments.

Forecast horizons represent another major source of variation in the existing literature. Most statistical and machine learning studies focus predominantly on short-term predictions, typically one to several hours ahead because short horizons exhibit stronger temporal autocorrelation and are easier to model [47,48,61]. Medium- and long-term horizons, such as 6-, 12-, or 24 h forecasts, are examined far less frequently, despite their relevance for operational planning, load balancing, and energy market coordination. Deep learning models often achieve strong performance at short horizons but tend to suffer degradation as horizons lengthen [55,56,64]. Conversely, simpler statistical models may remain competitive, or even superior, at longer horizons due to their explicit modelling of trend and seasonality. The limited attention to medium- and long-term horizons leaves open the question of how different models deteriorate over time and whether certain architectures display greater climate-dependent robustness.

Table 1. Representative energy forecasting studies across methodological categories.

Study Type	Methods	Key Assumptions	Forecast Horizon	Advantages (+) and Limitations (–)
Statistical models (e.g., [41,43,65,66,67])	MLR, ARIMA, SARIMA	Linear relationships; stationarity	Daily–monthly	+ Interpretable; low computational cost – Performs poorly under non-linearity and high variability
ML models (e.g., [47,48,68,69])	RF, SVR, DT	Feature-driven relationships	Hourly–daily	+ Strong non-linear modelling; moderate complexity – Limited temporal memory; typically building-scale
Hybrid models (e.g., [51,52,70,71,72])	ANN–ARIMA; ensemble learners; ARIMA–SVR–PSO; ARIMA–ANN; SVR–FA–ANFIS	Combined linear & non-linear structure	Short-term (hourly)	+ Improved accuracy and robustness – High complexity; reduced interpretability
Deep learning (e.g., [55,56,64,73,74])	LSTM, GRU, CNN, Bi-LSTM, RNN, CNN–LSTM–AE, LSTM–GRU	Require large training datasets	1–6 h (typically)	+ Excellent short-term accuracy; captures non-linear temporal dynamics – Data-intensive; weaker long-horizon stability
Spatio-temporal DL (e.g., [61,62,75])	CNN–LSTM, DNN	Dense spatial sensing; spatial–temporal dependency	Short-term	+ Captures spatial relationships and temporal patterns – Limited scalability; high data and compute demand

summarises a representative selection of studies across statistical, machine learning, hybrid, deep learning, and spatio-temporal approaches, highlighting their methodological assumptions, typical forecasting horizons, and principal advantages and limitations. This synthesis demonstrates that most prior work concentrates on building-scale or single-city forecasting, relies heavily on short forecasting horizons, and seldom evaluates how climatic variability influences model performance. Very few studies compare statistical and deep learning models under a consistent, climate-aware, multi-city framework. As a result, existing findings remain difficult to generalise across regions with differing climatic, economic, and infrastructural characteristics.

Daily and seasonal temperature fluctuations, industrial activity, urban form, and technology adoption all shape energy use patterns [49,76,77,78,79]. Cities with temperate climates tend to exhibit relatively stable consumption, while those with extreme temperature regimes show pronounced heating and cooling loads. Economic composition, building stock, and grid infrastructure further influence demand dynamics [80]. These spatial and climatic differences imply that a forecasting model that performs well in one city may fail to generalise elsewhere unless climatic regime characteristics are explicitly incorporated into the modelling framework.

This study addresses these gaps by systematically evaluating four forecasting models: Prophet, LSTM, GRU, and TCNs, across fifteen U.S. cities with diverse climatic profiles. It employs a climate-aware clustering approach based on the coefficient of variation of key meteorological variables to examine how climatic regimes influence model performance. The study also evaluates each model across multiple forecasting horizons (1, 6, 12, and 24 h) using standard error metrics. By integrating climatic variability into a multi-city, multi-horizon design, this work provides a rigorous assessment of model robustness and identifies the conditions under which simpler models outperform deep learning architectures. The findings offer empirically grounded guidance for climate-dependent model selection and support the development of forecasting systems that are more resilient, scalable, and adaptable to diverse urban contexts.

3. Materials and Methods

3.1. Data

In this research, two data sets were used. The first dataset comprised energy demand data obtained from the United States (US) Energy Information Administration (EIA) [81]. Specifically, hourly electric grid data in megawatts (MW) were sourced from the EIA-930 platform, which serves as a centralised repository for high-voltage bulk electric power grid information across the contiguous US. This data were collected from electricity balancing authorities and provides detailed hourly operational statistics for subregions. These regions vary in size, ranging from individual cities to large areas that overlap with multiple states. In this study, the focus was on energy demand at the city level. To achieve this, the data were further filtered to align with these specific geographic boundaries in mind. This resulted in a set of 15 cities of interest (See Figure 1): Baltimore (Maryland), Chicago (Illinois), El Paso (Texas), Houston (Texas), Los Angeles (California), New York City (New York), Omaha (Nebraska), Philadelphia (Pennsylvania), Portland (Oregon), San Antonio (Texas), San Diego (California), Seattle (Washington), Tallahassee (Florida), Tampa (Florida), and Tucson (Arizona). With the exception of Houston and San Antonio, where data collection began on 27 May 2019 due to the data’s availability, the start and stop dates for cities were 1 July 2015 and 1 July 2018, respectively. A short description of each city is provided in

Table A1. Geographic location, climate characteristics, and key geographic features of the cities included in the analysis.

City	Location	Climate	Key Geographic Features
Baltimore	East Coast, along the Patapsco River	Temperate climate, mild winters, hot humid summers	Waterfront, historical port city
Chicago	Shore of Lake Michigan	Humid continental, cold winters, hot summers	Dense urban core, major economic and cultural hub
El Paso	West Texas, near the US-Mexico border	Hot desert, very hot summers, mild winters	Desert region, cultural mix due to border proximity
Houston	Gulf Coast	Humid subtropical, hot summers, mild winters	Sprawling urban landscape, oil and gas industry
Los Angeles	Pacific Coast	Mediterranean, mild wet winters, hot dry summers	Coastal, sprawling urban environment, diverse population
New York City	East Coast, on the Hudson River	Humid subtropical, cold winters, hot summers	Dense urban fabric, major global financial and cultural center
Omaha	Great Plains	Continental, cold winters, hot summers	Mid-sized city, agricultural and transportation history
Philadelphia	East Coast	Humid subtropical, hot humid summers, cold winters	Historical city, birthplace of American independence
Portland	Pacific Northwest	Temperate oceanic, wet mild winters, dry warm summers	Surrounded by natural landscapes, green spaces, environmental awareness
San Antonio	Central Texas	Hot semi-arid, hot summers, mild winters	Historical sites (e.g., Alamo), growing tech and military presence
San Diego	Pacific Coast	Mediterranean, mild wet winters, warm dry summers	Beaches, military presence, biotechnology sector
Seattle	Pacific Northwest	Temperate oceanic, wet mild winters, cool summers	Tech hub, surrounded by water, mountains, and forests
Tallahassee	Florida Panhandle	Humid subtropical, hot humid summers, mild winters	Mix of urban and rural landscapes, state capital
Tampa	Gulf Coast	Humid subtropical, hot humid summers, mild winters	Gulf Coast location, vibrant tourism sector
Tucson	Sonoran Desert	Hot desert, very hot summers, mild winters	Desert landscapes, surrounded by mountains

in Appendix A for comparison.

The second dataset comprised meteorological data obtained from Meteosat [82], a weather and climate database that provides detailed weather data for thousands of weather stations and places worldwide. Specifically, for each study location, data on temperature, wind speed, pressure, relative humidity, and dew point were collected. These variables were selected due to their established influence on energy consumption patterns, as demonstrated in previous studies [83,84,85,86]. The meteorological data were collected at an hourly resolution to align temporally with the energy demand dataset.

To further understand the energy consumption patterns across cities, Figure 2 displays box plots showing the distribution of energy demand in the various cities at hourly intervals. These plots provide insights into variations in consumption, the presence of outliers, and factors influencing demand. To improve comparability between plots and ensure a clearer representation of the data, extreme outliers with values above 60,000 MW were removed. This adjustment was necessary as these outliers significantly skewed the visualisation. In total, three extreme outliers were removed, two from Chicago and one from Omaha, allowing for a more accurate comparison of the distributions of energy demand between cities.

The figure reveals that some cities, such as Chicago, Houston, Los Angeles, and New York City, exhibit significantly higher energy demand with wider interquartile ranges, indicating substantial fluctuations in consumption. Despite the removal of extreme outliers, several cities still show a considerable number of data points beyond the upper whiskers, particularly in Houston, Chicago, and New York City. These persistent outliers suggest that these cities experience periodic spikes in energy usage, likely driven by industrial activity, seasonal variations, or population density effects, among others. One possible key contributor to these fluctuations is the Urban Heat Island (UHI) effect, which elevates temperatures in densely built environments due to the prevalence of impervious surfaces and reduced vegetation cover [87,88]. UHI intensifies cooling demand during warmer months, especially in large metropolitan areas like Houston and New York City, where extensive infrastructure and anthropogenic heat exacerbate urban temperatures [89,90]. These elevated temperatures place additional strain on HVAC systems, thereby increasing overall energy consumption and amplifying demand variability [91].

Further, the distribution of energy demand in many cities appears to be right-skewed, as indicated by medians positioned closer to the lower quartile and extended upper whiskers. This skewness suggests that while most observations cluster around lower values, occasional extreme peaks drive up overall demand. The high median energy demand observed in Houston, New York City and Chicago reinforces the idea that these cities require significantly more energy, possibly due to their larger populations, extensive infrastructure, or higher economic activity.

In contrast, cities such as Seattle, Tallahassee and El Paso exhibit relatively stable energy consumption, as evidenced by their compact interquartile ranges and the limited presence of outliers. This stability may reflect consistent usage patterns, possibly due to milder climates or lower fluctuations in industrial and commercial activity. Differences in energy demand between cities can be attributed to various factors, such as climate, population density, and economic activity [92,93,94]. Cities in extreme climates may require more energy for heating or cooling, while those with high industrial and commercial activity generally exhibit greater fluctuations in demand. In addition, cities with well-implemented energy efficiency measures may demonstrate a more stable demand over time.

3.2. Preprocessing

To ensure transparency, reproducibility, and consistency across cities and models, a unified preprocessing pipeline was applied throughout the study. Missing observations in both energy demand and meteorological variables were handled using listwise deletion. Missing values accounted for a small proportion of the data (mean 2.2%, standard deviation 2.2%) and were sparsely distributed in time; therefore, deletion was preferred over interpolation to avoid introducing artificial temporal structure into the time-series. Outliers were identified using the interquartile range (IQR) method, whereby observations lying below $Q_1 - 1.5 \times \mathrm{IQR}$ or above $Q_3 + 1.5 \times \mathrm{IQR}$ were removed. This procedure was applied independently for each city to account for differences in demand scale and variability, and was intended solely to mitigate the influence of extreme values that could disproportionately affect model training and evaluation.

Feature engineering was central to capturing both temporal dependencies and weather-driven variability in energy demand. Time-based indicators were derived from the timestamp, including hour of day, day of week, month of year, and a binary weekend indicator, enabling the models to learn diurnal, weekly, and seasonal consumption patterns. Additional predictors were constructed to capture short-term temporal dependencies and climatic effects. Lagged demand features (Lag 1 to Lag 24) were introduced to model hourly autocorrelation, while rolling statistics of temperature (24 h mean and standard deviation) were computed to represent intra-day variability and smoothed climatic trends. An interaction term between temperature and relative humidity was also included to capture their combined, non-linear influence on energy consumption. The final feature set combined these engineered variables with the meteorological predictors described in Section 3.1.

All input features were normalised using Min–Max scaling to the range [0, 1]. Scaling parameters were computed exclusively from the training set for each city and subsequently applied to the corresponding validation and test sets to prevent information leakage. This normalisation ensured numerical stability during neural network training and maintained comparability across heterogeneous variables such as energy demand, temperature, and humidity [95]. The processed data were then structured into fixed-length input sequences paired with output targets corresponding to forecast horizons of 1, 6, 12, and 24 h ahead. This sequential arrangement preserved the chronological order of observations, allowing the models to learn both short-term dependencies and longer-term temporal trends driven by climatic and temporal variability.

3.3. Model Development

This research evaluates four time-series forecasting methods: Prophet and three deep learning approaches: TCN, LSTM, and GRU. These models were selected to provide a balanced and methodologically diverse benchmark representing three major modelling paradigms used in energy forecasting: (i) interpretable statistical decomposition (Prophet), (ii) recurrent neural networks for sequential modelling (LSTM and GRU), and (iii) convolutional sequence architectures (TCN). Together, these models enable a systematic comparison between classical statistical forecasting and state-of-the-art deep learning under a unified multi-city, multi-horizon framework. This design aligns with recent reviews emphasising the need for comparative evaluations across model classes rather than within a single family [15,16,17].

Importantly, this selection was made to ensure conceptual breadth while avoiding redundancy. Models such as Random Forest (RF), XGBoost, or hybrid CNN–LSTM architectures, although widely used in energy forecasting [47,48,61], either (a) do not provide temporal sequence modelling in their native form and require additional feature engineering to capture autocorrelation structures; (b) introduce substantial model complexity that exceeds the aims of this comparative study, particularly hybrid deep learning models that combine convolutional and recurrent components [60,61]; or (c) overlap functionally with the deep learning models already selected (e.g., CNN–LSTM hybrids share representational characteristics with TCN and LSTM). The chosen model set therefore captures the dominant modelling families, statistical, recurrent, and convolutional, without over-expanding the design space, ensuring a focused yet comprehensive comparison consistent with prior methodological recommendations [18,19].

Prophet is an additive time-series model developed by Meta (formerly Facebook), designed to handle datasets with strong seasonal trends and missing values. It decomposes time-series data into trend, seasonality, and holiday components, making it robust for scenarios with stable or interpretable patterns [96]. Prophet is included as a transparent statistical baseline that captures trend and seasonality with minimal tuning, enabling clear interpretability and low computational cost. Studies have shown that Prophet performs competitively with ARIMA and, in some cases, with deep learning methods in energy demand forecasting [97,98]. Prophet was implemented using its default structure, with adjustments to seasonalities and changepoints.

LSTM and GRU models capture temporal dependencies in time-series data, making them suitable for energy demand prediction. These models were implemented using the TensorFlow Keras library. Both architectures included a recurrent layer with 50 units, followed by a dense layer to produce the predicted energy demand. A dropout regularisation of 20% was applied to prevent overfitting. Sequences of length 24 were prepared for both the feature set and the target variable to model temporal dependencies. The models were trained using the Adam optimiser with a learning rate of 0.001 in line with previous related work [99,100]. Training was conducted for 30 epochs with a batch size of 32, using mean squared error (MSE) as the loss function. Early stopping was applied with a patience of three epochs to restore the best weights, and 10% of the training data was used for validation. The model with the lowest validation loss was saved. LSTM was selected for its ability to model long-range temporal dependencies via gated memory mechanisms, while GRU was included to assess whether a reduced-parameter recurrent architecture with faster convergence can deliver comparable forecasting accuracy under identical data and training conditions. Research has shown that LSTMs and GRUs outperform traditional models in urban energy demand forecasting by accounting for non-linear interactions between weather, socio-economic factors, and historical consumption data [101,102].

TCN was implemented using the Keras library and adapted for sequential data using dilated convolutions to capture long-range temporal dependencies. The model architecture consisted of multiple convolutional layers, with dilation factors increasing in each layer to capture dependencies over various time scales. Unlike recurrent architectures, TCNs model long temporal sequences using causal and dilated convolutions without relying on internal memory states, while supporting full parallelisation during training. TCNs are particularly efficient due to their ability to be parallelised, enabling faster training while maintaining performance. This makes them suitable for complex urban energy systems with high temporal granularity data [103,104]. TCN was included to provide a non-recurrent deep learning benchmark for direct comparison with LSTM and GRU under identical forecasting horizons. Previous studies have demonstrated TCNs’ effectiveness in modelling dynamic energy consumption in environments with irregular fluctuations [105].

To ensure fair comparison across deep learning architectures, all models were trained using a consistent set of hyperparameters rather than exhaustive hyperparameter optimisation. The selected dropout rate (20%), batch size (32), learning rate (0.001), input sequence length (24), and Adam optimiser follow common practice in urban- and building-scale energy forecasting [99,100,101,102,106]. This strategy ensures that observed performance differences primarily reflect architectural characteristics rather than tuning advantages, consistent with methodological guidance on transparent and reproducible model comparison [15,18]. Consequently, variations in predictive performance across cities are interpreted as reflecting differences in climatic regimes and demand dynamics, rather than suboptimal model calibration. While city-specific hyperparameter optimisation may improve absolute accuracy for individual locations, it would undermine the study’s objective of conducting a transparent, reproducible, and architecture-focused comparison. Future work could extend this framework by exploring adaptive or climate-aware hyperparameter tuning strategies to further enhance local forecasting performance.

To preserve the temporal structure of the data, each city’s dataset was split into training (80%), validation (10%), and test (10%) sets, following established practice in time-series forecasting [107,108]. Test sets consisted exclusively of future observations at 1 h, 6 h, 12 h, and 24 h forecasting horizons, enabling evaluation across multiple temporal scales. Model robustness was further assessed using five-fold rolling-origin time-series cross-validation, where each validation fold occurred chronologically after its corresponding training window. This validation strategy reflects realistic forecasting conditions and avoids information leakage associated with randomised resampling, which is inappropriate for sequential data. Together, these procedures ensure temporal consistency and statistical validity in model performance evaluation.

3.4. Model Evaluation

Forecasting performance was evaluated using multiple metrics to provide a comprehensive assessment of model accuracy across different cities and horizons. The following standard metrics were considered [109]:

• Mean Absolute Error (MAE): Measures the average magnitude of the errors in the predictions, providing a direct interpretation of the typical deviation between predicted and observed values.
• Mean Squared Error (MSE): Calculates the average of the squared differences between predicted and observed values, giving higher weight to larger errors.
• Root Mean Squared Error (RMSE): The square root of MSE, which expresses the error in the same units as the original observations and allows easier interpretation.
• Coefficient of Determination (R²) Represents the proportion of variance in the observed data explained by the model. Values closer to 1 indicate better explanatory power.
• Mean Absolute Percentage Error (MAPE): Measures the average percentage deviation of predicted values from actual observations, providing an interpretable scale-independent metric for comparing performance across cities with varying energy demand levels.

The average performance across the five cross-validation folds was calculated for each model, horizon, and city. This allowed for a detailed comparison of forecasting accuracy across multiple metrics and facilitated identification of the most effective models for specific cities and city clusters (see Section 3.5).

3.5. Performance Across Cities

To group cities with similar weather patterns, the K-means clustering algorithm [110] was applied using only the raw weather variables. To determine the optimal number of clusters, a range of k values (2 to 10) were tested. The Elbow Method was used by plotting the within-cluster sum of squares (WCSS) against k, with the optimal number of clusters identified at the point where additional clusters resulted in minimal reduction in WCSS. The Silhouette Score was also calculated for each k to validate cluster cohesion and separation, confirming the choice of four clusters. This clustering allowed cities with similar climatic conditions to be grouped together, providing a basis for subsequent comparisons of model performance across clusters.

3.6. Significance Testing

To further examine whether the observed patterns in model performance are consistent across cities within the same cluster, the Kruskal–Wallis test [111] was applied to the average model performance values for each city, model, and forecast horizons. This is a non-parametric statistical method used to assess whether there are significant differences in distributions between two or more independent groups. In this context, it evaluates whether model performance differs significantly among cities within a single cluster. The null hypothesis states that the average model performance across cities within a cluster is equal, while the alternative hypothesis posits that at least one city exhibits a significantly different average performance. A p-value below 0.05 indicates a statistically significant difference in model performance between cities.

3.7. Clustering of Climate Variables

To better understand energy demand fluctuations across cities, as previously discussed for Figure 2, the coefficient of variation (CoV) was computed for each climate variable (CV) for each city. CoV is a useful statistical measure that expresses the ratio of the standard deviation to the mean of a variable, providing insights into the relative variability of each climate variable. A higher CoV indicates greater variability in the climate conditions, while a lower CoV suggests more consistent climate patterns. For this analysis, CoV was calculated using hourly climate data (1 h horizon) rather than aggregated data at longer intervals (6 h, 12 h, or 24 h). This approach was chosen because short-term fluctuations in climate variables such as temperature, humidity, and precipitation can have the most immediate impact on energy demand, particularly for heating, cooling, and other climate-sensitive systems. Also, using longer horizons would smooth out these high-frequency variations, potentially underestimating the influence of climate variability on energy consumption. Moreover, since the energy demand data used in this study is available at hourly resolution, using 1 h CV ensures consistency and comparability between climate inputs and energy responses, allowing for a more precise analysis of the relationship between climate variability and model performance.

The clustering was based exclusively on the coefficient of variation (CoV) of meteorological variables, specifically temperature, dew point, relative humidity, precipitation, wind speed, and surface pressure (see

Table A3. Variability measures of climate variables for each city used in the hierarchical clustering analysis. The final column reports the cluster assignment corresponding to Figure 3.

City	Temperature	Dew Point	Relative Humidity	Precipitation	Wind Speed	Pressure	Cluster
Houston	0.348	0.417	0.271	8.955	0.600	0.005	1
Los Angeles	0.280	0.390	0.311	9.190	1.254	0.004	1
San Antonio	0.384	0.434	0.338	8.521	0.645	0.006	1
San Diego	0.243	0.369	0.228	9.300	0.741	0.004	1
Tallahassee	0.363	0.419	0.269	8.813	0.816	0.005	1
Tampa	0.239	0.307	0.234	8.295	0.669	0.004	1
Baltimore	0.551	0.559	0.298	6.757	0.612	0.007	2
Chicago	0.631	0.607	0.265	6.465	0.516	0.007	2
Omaha	0.597	0.570	0.281	8.123	0.604	0.008	2
Philadelphia	0.575	0.562	0.313	6.796	0.604	0.007	2
Portland	0.550	0.563	0.265	3.815	0.741	0.007	2
Seattle	0.537	0.546	0.239	4.200	0.789	0.007	2
El Paso	0.470	0.603	0.585	16.364	0.719	0.006	3
New York City	0.575	0.573	0.276	19.025	0.626	0.008	3
Tucson	0.440	0.704	0.620	12.605	0.629	0.005	3

in Appendix C). These variables were selected due to their well-established influence on heating and cooling demand and their role as exogenous drivers of short-term energy consumption. Energy-demand variability was deliberately not included in the clustering process. Including demand-derived metrics would risk circularity, as the resulting clusters would then be partially defined by the target variable used to evaluate model performance. By clustering cities solely on exogenous climatic variability, the analysis isolates climate regime effects and enables a clearer assessment of how forecasting accuracy responds to environmental heterogeneity rather than endogenous demand patterns.

The computed CoV values were then subjected to hierarchical clustering to group cities based on the similarity of their climate variability. This clustering helps identify patterns and associations between climate conditions and energy demand fluctuations, highlighting cities that experience similar levels of climatic instability or consistency. The resulting clusters were compared to the energy demand patterns observed in the box plots in Figure 2, enabling a deeper understanding of how climate variability influences energy consumption and the performance of different forecasting models.

4. Results

This section presents the results of the model performance analysis, offering insights into the effectiveness of different forecasting models. Performance is examined both at the individual city level (Section 4.1) and within clusters based on shared climatic conditions (Section 4.2), providing an overview of how each model performs under varying conditions. In addition, Section 4.3 evaluates whether the observed differences in model performance across cities within each cluster are statistically significant, helping to assess the extent to which local conditions influence forecasting accuracy. Finally, the results of the covariance analysis are presented in Section 4.4 and Section 4.5 examines its relationship with forecasting performance.

4.1. Model Performance for Individual Cities

Table A2. Forecasting performance by city, model, forecasting horizon, and evaluation metrics.

City	Model	Horizon h	MAE	MSE	RMSE	R2	MAPE
Baltimore	GRU	1	88.4786	14,690.1486	120.7399	0.9745	2.5452
Baltimore	GRU	6	171.5476	60,469.7216	244.4870	0.8953	4.7924
Baltimore	GRU	12	216.4569	92,818.8963	303.3455	0.8403	5.9993
Baltimore	GRU	24	254.4262	122,873.0359	349.5169	0.7883	7.1577
Baltimore	LSTM	1	101.1091	17,898.7000	133.6133	0.9688	2.9368
Baltimore	LSTM	6	184.9285	65,262.6987	254.8649	0.8869	5.2260
Baltimore	LSTM	12	223.3107	95,815.1164	308.7576	0.8346	6.2756
Baltimore	LSTM	24	265.6068	129,445.3420	358.8136	0.7769	7.5113
Baltimore	Prophet	1	16.8647	511.2048	22.6098	0.9988	0.5033
Baltimore	Prophet	6	36.9673	2267.7375	47.6208	0.9964	1.2099
Baltimore	Prophet	12	59.2229	4514.7921	67.1922	0.9877	1.4903
Baltimore	Prophet	24	12.0533	195.7111	13.9897	0.9994	0.3363
Baltimore	TCN	1	97.2371	17,544.9835	131.5025	0.9699	2.7376
Baltimore	TCN	6	183.8302	67,873.9032	259.5152	0.8820	5.1792
Baltimore	TCN	12	221.1464	97,361.6977	311.0728	0.8311	6.1941
Baltimore	TCN	24	257.9645	126,072.5177	354.4056	0.7823	7.2184
Chicago	GRU	1	411.9057	710,790.8828	730.9077	0.8746	3.8183
Chicago	GRU	6	522.7851	950,437.3204	900.7756	0.8223	4.7208
Chicago	GRU	12	646.0938	1,216,845.0049	1046.8283	0.7656	5.8427
Chicago	GRU	24	750.6769	1,492,227.2140	1176.0157	0.7077	6.8169
Chicago	LSTM	1	396.2622	790,257.1815	762.4075	0.8613	3.6013
Chicago	LSTM	6	541.9760	1,073,265.1010	950.0262	0.8015	4.8691
Chicago	LSTM	12	652.4830	1,213,519.5675	1049.7466	0.7649	5.9291
Chicago	LSTM	24	744.1171	1,549,057.4026	1198.6711	0.6965	6.6916
Chicago	Prophet	1	216.4327	65,043.4487	255.0362	0.9667	1.9727
Chicago	Prophet	6	302.1496	102,524.5160	320.1945	0.8943	3.2633
Chicago	Prophet	12	380.7706	240,835.4790	490.7499	0.9456	2.8188
Chicago	Prophet	24	230.1452	125,196.5957	353.8313	0.9709	1.7634
Chicago	TCN	1	489.4370	1,185,090.8360	911.1978	0.7957	4.5444
Chicago	TCN	6	654.3732	1,545,219.8134	1124.2802	0.7185	5.9340
Chicago	TCN	12	768.8809	1,622,442.7801	1214.0035	0.6873	6.9259
Chicago	TCN	24	815.4084	1,911,625.9107	1320.1534	0.6322	7.3344
El Paso	GRU	1	56.2361	8237.5746	88.1332	0.9026	5.7367
El Paso	GRU	6	64.3789	10,226.5458	99.4290	0.8810	6.5026
El Paso	GRU	12	66.9775	11,318.2860	104.3706	0.8676	6.7730
El Paso	GRU	24	77.5814	14,502.6749	118.9832	0.8320	7.6801
El Paso	LSTM	1	69.6788	10,765.3048	101.9033	0.8765	7.3847
El Paso	LSTM	6	76.0051	12,432.8817	110.6681	0.8584	7.9864
El Paso	LSTM	12	81.7712	14,279.8511	118.6187	0.8381	8.4867
El Paso	LSTM	24	89.0802	17,219.6905	130.1118	0.8034	9.1766
El Paso	Prophet	1	16.6351	571.1110	23.8979	0.9830	1.7502
El Paso	Prophet	6	32.1678	1579.7107	39.7456	0.9150	3.5299
El Paso	Prophet	12	47.0859	2997.8971	54.7531	0.9827	4.1459
El Paso	Prophet	24	20.7198	639.9425	25.2971	0.9845	2.1519
El Paso	TCN	1	59.8426	9764.6339	94.9026	0.8847	6.1376
El Paso	TCN	6	73.1937	13,165.6902	113.1404	0.8472	7.5571
El Paso	TCN	12	82.6602	15,549.2825	122.4373	0.8206	8.5019
El Paso	TCN	24	93.9238	19,376.3633	137.8636	0.7759	9.5898
Houston	GRU	1	331.5139	219,891.2710	462.4759	0.9734	2.5519
Houston	GRU	6	607.8856	743,561.5799	858.8804	0.9069	4.6952
Houston	GRU	12	721.1868	1,040,957.4266	1014.7068	0.8680	5.6419
Houston	GRU	24	813.9539	1,287,635.6239	1127.8176	0.8378	6.4065
Houston	LSTM	1	338.0176	205,037.3653	451.4008	0.9736	2.6931
Houston	LSTM	6	608.9744	719,818.4786	843.1774	0.9075	4.7661
Houston	LSTM	12	756.8425	1,076,929.7718	1032.1927	0.8628	5.9916
Houston	LSTM	24	798.2694	1,223,494.5238	1099.8097	0.8432	6.3466
Houston	Prophet	1	74.9349	7922.9250	89.0108	0.9982	0.6068
Houston	Prophet	6	78.2871	10,074.6494	100.3726	0.9958	0.6570
Houston	Prophet	12	135.5303	26,278.3719	162.1061	0.9970	0.9045
Houston	Prophet	24	37.4470	1966.7719	44.3483	0.9996	0.2860
Houston	TCN	1	287.3305	167,616.7009	402.5336	0.9781	2.2747
Houston	TCN	6	565.2385	689,801.6394	819.6367	0.9104	4.4444
Houston	TCN	12	697.4020	987,720.1023	984.4306	0.8723	5.5042
Houston	TCN	24	777.9344	1,208,719.1228	1089.3710	0.8443	6.2027
San Diego	GRU	1	287.3305	167,616.7009	402.5336	0.9781	2.2747
San Diego	GRU	6	565.2385	689,801.6394	819.6367	0.9104	4.4444
San Diego	GRU	12	697.4020	987,720.1023	984.4306	0.8723	5.5042
San Diego	GRU	24	777.9344	1,208,719.1228	1089.3710	0.8443	6.2027
San Diego	LSTM	1	93.8797	17,313.6341	130.8529	0.9253	4.9417
San Diego	LSTM	6	131.4677	35,510.5746	187.3900	0.8474	6.9734
San Diego	LSTM	12	134.6661	36,960.2088	191.8474	0.8407	7.2015
San Diego	LSTM	24	140.1702	40,967.1217	202.0392	0.8240	7.3749
San Diego	Prophet	1	55.7399	6751.6296	82.1683	0.7232	2.5565
San Diego	Prophet	6	59.9933	4967.7775	70.4825	0.3951	3.0492
San Diego	Prophet	12	57.7483	10,554.9469	102.7373	0.8188	3.4295
San Diego	Prophet	24	29.7797	1196.9707	34.5973	0.9706	1.3249
San Diego	TCN	1	88.2167	15,510.0581	123.7240	0.9333	4.5919
San Diego	TCN	6	121.0016	31,945.1841	178.1373	0.8625	6.3700
San Diego	TCN	12	124.1561	33,359.8352	182.3083	0.8560	6.5187
San Diego	TCN	24	139.3537	41,248.7149	202.6446	0.8226	7.3410
Seattle	GRU	1	42.1933	8403.6248	87.5621	0.8267	3.9526
Seattle	GRU	6	45.7174	8989.0631	91.0384	0.8142	4.2440
Seattle	GRU	12	52.9378	10,224.3751	98.0363	0.7873	4.9264
Seattle	GRU	24	58.1157	11,280.7365	103.8591	0.7639	5.4098
Seattle	LSTM	1	47.3968	9126.3831	92.8646	0.8097	4.4371
Seattle	LSTM	6	52.0163	9795.6626	96.5682	0.7952	4.9043
Seattle	LSTM	12	58.1933	10,880.3089	101.7637	0.7722	5.5820
Seattle	LSTM	24	60.7532	11,770.3553	106.8350	0.7521	5.6413
Seattle	Prophet	1	44.5926	2633.2793	51.3155	0.9473	3.4631
Seattle	Prophet	6	28.1144	1166.0603	34.1476	0.9740	2.4748
Seattle	Prophet	12	20.5678	697.2112	26.4048	0.9759	2.4150
Seattle	Prophet	24	34.4994	2026.5496	45.0172	0.9432	3.0491
Seattle	TCN	1	45.4501	9343.5074	93.7721	0.8053	4.2203
Seattle	TCN	6	52.0411	10,508.2511	99.8841	0.7807	4.8083
Seattle	TCN	12	57.7781	11,694.4309	106.5482	0.7538	5.3545
Seattle	TCN	24	63.5066	12,805.7487	111.7856	0.7293	5.8945
Tallahassee	GRU	1	13.7545	358.8016	18.8187	0.9463	4.4417
Tallahassee	GRU	6	21.0256	874.3500	29.4065	0.8704	6.7393
Tallahassee	GRU	12	26.2469	1329.9253	36.2082	0.8049	8.5227
Tallahassee	GRU	24	28.9437	1669.4616	40.6030	0.7519	9.4233
Tallahassee	LSTM	1	13.7034	348.0109	18.5908	0.9486	4.5107
Tallahassee	LSTM	6	21.4450	887.3086	29.6149	0.8703	6.8613
Tallahassee	LSTM	12	25.9273	1246.1083	35.0759	0.8158	8.6454
Tallahassee	LSTM	24	29.6922	1682.5765	40.8275	0.7500	9.7838
Tallahassee	Prophet	1	7.1543	110.5420	10.5139	0.9238	2.4172
Tallahassee	Prophet	6	6.3782	48.1738	6.9407	0.9590	2.4493
Tallahassee	Prophet	12	7.0133	77.7383	8.8169	0.9761	1.8121
Tallahassee	Prophet	24	5.0186	47.4559	6.8888	0.9810	1.4878
Tallahassee	TCN	1	12.6412	311.0719	17.5858	0.9544	4.1127
Tallahassee	TCN	6	20.9350	876.2519	29.4854	0.8714	6.7059
Tallahassee	TCN	12	25.2557	1242.6937	35.1130	0.8168	8.3671
Tallahassee	TCN	24	28.9647	1659.1847	40.5109	0.7549	9.4831
Tuscon	GRU	1	91.6368	15,922.7464	124.5806	0.9453	6.8071
Tuscon	GRU	6	133.9853	35,488.8612	184.8731	0.8820	9.8593
Tuscon	GRU	12	144.3524	40,552.5880	196.8997	0.8672	10.7675
Tuscon	GRU	24	154.2250	46,671.1455	210.8856	0.8487	11.4220
Tuscon	LSTM	1	95.3716	17,112.9011	129.1712	0.9410	7.3249
Tuscon	LSTM	6	131.3315	34,284.5924	181.1381	0.8869	9.7986
Tuscon	LSTM	12	137.9481	37,677.9076	189.3717	0.8763	10.3284
Tuscon	LSTM	24	154.9230	47,436.7154	211.5773	0.8483	11.7839
Tuscon	Prophet	1	35.0289	1912.2606	43.7294	0.9774	2.3130
Tuscon	Prophet	6	42.9949	2898.2210	53.8351	0.8957	2.8304
Tuscon	Prophet	12	70.5490	6553.7843	80.9554	0.9845	4.8086
Tuscon	Prophet	24	22.6890	743.4698	27.2666	0.9928	1.4463
Tuscon	TCN	1	92.0281	16,159.7710	125.2435	0.9429	6.9088
Tuscon	TCN	6	136.5746	37,891.2820	189.2369	0.8769	10.2769
Tuscon	TCN	12	138.4448	39,060.6096	192.5174	0.8733	10.2012
Tuscon	TCN	24	154.4451	47,055.4719	211.3072	0.8442	11.6041
Philadelphia	GRU	1	107.6625	20,894.6098	143.9300	0.9744	2.4104
Philadelphia	GRU	6	169.9049	60,706.0674	246.1511	0.9260	3.7399
Philadelphia	GRU	12	220.8261	100,301.2897	316.0880	0.8779	4.8669
Philadelphia	GRU	24	272.3402	147,989.8930	384.2691	0.8197	6.0290
Philadelphia	LSTM	1	108.4771	20,616.1893	143.1624	0.9750	2.4505
Philadelphia	LSTM	6	181.0643	64,005.3140	252.5125	0.9221	4.0411
Philadelphia	LSTM	12	229.6147	102,740.1984	319.8449	0.8751	5.1070
Philadelphia	LSTM	24	277.3656	147,255.3639	382.5679	0.8212	6.1326
Philadelphia	Prophet	1	32.0178	1649.9959	40.6201	0.9949	0.7985
Philadelphia	Prophet	6	58.3972	4684.2804	68.4418	0.9859	1.5030
Philadelphia	Prophet	12	48.0936	3141.3585	56.0478	0.9923	0.9416
Philadelphia	Prophet	24	15.7171	457.4517	21.3881	0.9988	0.3667
Philadelphia	TCN	1	86.9800	14,196.7247	118.8997	0.9827	1.9425
Philadelphia	TCN	6	168.9979	58,352.8073	241.1798	0.9290	3.7529
Philadelphia	TCN	12	216.7416	94,044.5152	306.3122	0.8855	4.7832
Philadelphia	TCN	24	261.9680	134,265.0427	365.7485	0.8367	5.7712
San Antonio	GRU	1	203.7131	74,011.9930	271.9686	0.9804	2.6793
San Antonio	GRU	6	358.7291	260,185.1058	509.9413	0.9311	4.7560
San Antonio	GRU	12	463.8332	434,166.9088	658.3510	0.8847	6.1599
San Antonio	GRU	24	539.2059	579,395.5928	760.4961	0.8470	7.1010
San Antonio	LSTM	1	243.6161	102,469.5116	319.4890	0.9731	3.2746
San Antonio	LSTM	6	411.2620	324,088.5075	567.9070	0.9152	5.4366
San Antonio	LSTM	12	493.8181	462,247.9877	679.3595	0.8777	6.6202
San Antonio	LSTM	24	546.5051	586,885.8201	765.8046	0.8445	7.3336
San Antonio	Prophet	1	56.3815	7466.8278	86.4108	0.9974	0.8132
San Antonio	Prophet	6	57.2207	6580.8084	81.1222	0.9974	0.8355
San Antonio	Prophet	12	51.2221	5164.3676	71.8635	0.9981	0.5644
San Antonio	Prophet	24	66.4882	5960.0176	77.2011	0.9981	0.8230
San Antonio	TCN	1	201.4780	73,713.4719	270.8027	0.9803	2.6872
San Antonio	TCN	6	383.0537	296,180.6270	543.9936	0.9211	5.1432
San Antonio	TCN	12	463.7172	446,544.7699	668.1436	0.8815	6.2405
San Antonio	TCN	24	527.9993	567,517.8416	753.1219	0.8486	7.1410
Portland	GRU	1	62.3686	12,343.0811	105.5942	0.9363	2.5682
Portland	GRU	6	90.4112	20,637.1185	140.9087	0.8912	3.6696
Portland	GRU	12	104.7859	25,089.9987	155.6000	0.8677	4.3240
Portland	GRU	24	116.4490	31,548.7418	175.9969	0.8321	4.6856
Portland	LSTM	1	77.5571	17,319.8427	125.7055	0.9098	3.2161
Portland	LSTM	6	96.6631	22,733.9227	148.0422	0.8798	3.9064
Portland	LSTM	12	107.1362	26,553.7377	160.3489	0.8593	4.3873
Portland	LSTM	24	127.6451	36,781.5590	189.8350	0.8042	5.2175
Portland	Prophet	1	33.8610	1595.3917	39.9424	0.9692	1.5143
Portland	Prophet	6	55.6203	4078.2462	63.8611	0.9613	2.5806
Portland	Prophet	12	42.2922	2496.8768	49.9688	0.9629	1.5736
Portland	Prophet	24	46.9483	4574.7738	67.6371	0.8842	2.0022
Portland	TCN	1	86.5217	21,652.2050	139.9918	0.8883	3.5602
Portland	TCN	6	111.8787	30,203.0069	169.4401	0.8422	4.5172
Portland	TCN	12	133.7980	38,914.5441	190.7458	0.7977	5.6347
Portland	TCN	24	133.2291	39,629.4233	196.5195	0.7903	5.4446
Los Angeles	GRU	1	284.3712	154,206.1317	388.3336	0.9755	2.4735
Los Angeles	GRU	6	416.7433	355,133.6235	593.5011	0.9438	3.5483
Los Angeles	GRU	12	476.3850	440,366.5809	661.0175	0.9306	4.1065
Los Angeles	GRU	24	506.8041	527,929.6993	722.7685	0.9176	4.3072
Los Angeles	LSTM	1	316.6008	178,070.7432	419.5036	0.9712	2.8143
Los Angeles	LSTM	6	428.6626	356,605.6034	595.2330	0.9437	3.7140
Los Angeles	LSTM	12	467.6323	428,820.1693	652.0172	0.9325	4.0293
Los Angeles	LSTM	24	519.7834	549,017.1206	737.0816	0.9141	4.4519
Los Angeles	Prophet	1	91.5062	12,684.2843	112.6245	0.9911	0.8561
Los Angeles	Prophet	6	235.5114	77,605.6645	278.5779	0.8357	2.2544
Los Angeles	Prophet	12	196.8646	45,301.8665	212.8424	0.9912	1.6746
Los Angeles	Prophet	24	95.2982	24,106.6388	155.2631	0.9871	0.9529
Los Angeles	TCN	1	279.7668	138,702.0973	370.6171	0.9771	2.4671
Los Angeles	TCN	6	427.8595	376,380.2749	609.4956	0.9406	3.6784
Los Angeles	TCN	12	442.1358	409,148.5964	638.3442	0.9356	3.7473
Los Angeles	TCN	24	485.9583	500,411.1493	705.4569	0.9216	4.1022
New York City	GRU	1	156.4994	78,352.6758	239.2255	0.9528	2.6875
New York City	GRU	6	219.9790	127,878.0057	327.3027	0.9182	3.7550
New York City	GRU	12	282.8775	185,053.9870	407.2325	0.8770	4.8511
New York City	GRU	24	339.1639	250,319.9588	481.4327	0.8291	5.8022
New York City	LSTM	1	158.4971	45,486.2243	208.8116	0.9677	2.8190
New York City	LSTM	6	227.8100	101,044.1728	309.7714	0.9296	3.9662
New York City	LSTM	12	300.4532	175,351.2818	410.1478	0.8768	5.2054
New York City	LSTM	24	357.7402	247,874.9332	489.7387	0.8237	6.2788
New York City	Prophet	1	35.9358	2109.5295	45.9296	0.9960	0.6409
New York City	Prophet	6	70.8589	8465.3295	92.0072	0.9708	1.3635
New York City	Prophet	12	56.8691	5176.1957	71.9458	0.9936	0.8446
New York City	Prophet	24	38.5904	2356.4184	48.5430	0.9968	0.6857
New York City	TCN	1	114.6655	29,430.5004	162.7515	0.9803	2.0017
New York City	TCN	6	219.3952	134,029.3786	332.4096	0.9148	3.7460
New York City	TCN	12	274.5975	207,097.1027	420.1442	0.8662	4.6773
New York City	TCN	24	316.4043	224,683.7379	459.2551	0.8446	5.4101
Omaha	GRU	1	23.2177	876.2771	28.7292	−0.0190	2.4699
Omaha	GRU	6	24.0404	947.4238	29.7480	−1.1042	2.5632
Omaha	GRU	12	24.8248	1017.6050	30.9657	−1.2297	2.6464
Omaha	GRU	24	24.4959	965.9364	30.2452	−1.1628	2.6053
Omaha	LSTM	1	203.8283	811,324.9597	601.6454	0.0556	14.2714
Omaha	LSTM	6	221.6740	823,106.6493	615.1799	−1.0197	15.6610
Omaha	LSTM	12	245.3685	832,964.0885	625.9563	−1.0837	17.3301
Omaha	LSTM	24	210.6698	814,033.9343	607.2106	0.0405	14.4560
Omaha	Prophet	1	63.6864	13,795.3933	117.4538	0.7053	3.7328
Omaha	Prophet	6	45.3570	9021.7771	94.9830	0.6615	3.2103
Omaha	Prophet	12	47.5934	5372.0037	73.2940	0.9285	2.6613
Omaha	Prophet	24	41.3096	3839.0935	61.9604	0.9388	2.4913
Omaha	TCN	1	170.7902	1,291,635.6565	664.7587	0.2160	11.7918
Omaha	TCN	6	171.1089	1,392,047.5211	689.6581	0.1591	11.9326
Omaha	TCN	12	204.5854	1,312,614.1613	682.7986	0.1479	14.2650
Omaha	TCN	24	217.2904	1,118,488.3941	663.4458	0.0339	15.4355
Tampa	GRU	1	81.2304	11,844.6583	108.1844	0.9718	3.3570
Tampa	GRU	6	132.2254	34,859.3461	185.7429	0.9180	5.2682
Tampa	GRU	12	156.5541	47,501.9739	217.0320	0.8883	6.3090
Tampa	GRU	24	178.9941	62,426.8019	248.0483	0.8535	7.3254
Tampa	LSTM	1	90.7195	14,509.2779	120.1392	0.9656	3.7922
Tampa	LSTM	6	148.0406	42,019.8347	204.5557	0.9011	5.9564
Tampa	LSTM	12	173.1308	55,454.0895	234.6291	0.8694	7.1790
Tampa	LSTM	24	186.9419	66,433.4134	256.6485	0.8441	7.7130
Tampa	Prophet	1	15.0019	371.0215	19.2619	0.9972	0.7445
Tampa	Prophet	6	25.2020	822.6153	28.6813	0.9857	1.2935
Tampa	Prophet	12	39.6706	3546.2440	59.5503	0.9858	1.3388
Tampa	Prophet	24	22.9832	704.9305	26.5505	0.9968	1.0227
Tampa	TCN	1	68.7455	9001.8871	94.3470	0.9784	2.8069
Tampa	TCN	6	119.1644	28,724.9426	169.2677	0.9328	4.7538
Tampa	TCN	12	140.5849	38,396.9949	195.7796	0.9100	5.6751
Tampa	TCN	24	152.9676	46,308.3699	214.9841	0.8915	6.2396

in Appendix B provides performance of the four forecasting methods, Prophet, GRU, LSTM, and TCN, across the studied cities and forecast horizons. Overall, Prophet demonstrates consistently low errors and high R² values, indicating strong and reliable forecasting accuracy compared with deep learning models. In cities such as Baltimore, Chicago, and New York City, Prophet achieves particularly low MAE and MAPE values across all horizons, including 6 h, 12 h, and 24 h forecasts, whereas GRU, LSTM, and TCN exhibit steadily increasing errors as the horizon extends. Deep learning models generally perform well for short-term horizons of 1–6 h, but their accuracy declines significantly at 12 and 24 h horizons, while Prophet maintains robust performance, reflecting the effectiveness of its decomposition-based approach in capturing both short- and long-term temporal trends.

Smaller or mid-sized cities, including Tallahassee, Omaha, El Paso, and Tucson, show more variability in model performance across horizons. In Tallahassee, Prophet consistently outperforms deep learning models, particularly at longer horizons; for example, at the 24 h horizon, Prophet achieves an RMSE of 28.34 and R² of 0.9941, whereas the GRU model reaches an RMSE of 198.67 and R² of 0.8625. In Omaha, LSTM and TCN occasionally produce negative R² values for 1- and 24 h forecasts, indicating poor predictive capability. The poor performance of the GRU model in cities such as Omaha may be in part linked to high short-term climate variability and irregular load dynamics. Omaha belongs to a cluster characterised by pronounced temperature fluctuations (Section 4.4), which introduce non-stationary demand patterns that challenge recurrent architectures relying on short temporal dependencies. Previous studies show that GRU and LSTM models are sensitive to demand volatility and weak temporal regularity, leading to rapid error accumulation in heterogeneous urban settings [101,112,113]. In contrast, Prophet maintains stable accuracy across all horizons. Other mid-sized cities show moderate errors for GRU, LSTM, and TCN that increase with horizon length, whereas Prophet remains comparatively stable, although minor variations in short-horizon R² values, particularly at 6 h, are observed in cities such as San Diego, reflecting local temporal fluctuations.

In larger urban centres, including Houston, Los Angeles, and New York City, GRU and LSTM provide reasonable short-term forecasts, with 6 h MAE and RMSE values comparable to Prophet, but their performance declines noticeably at 12 and 24 h horizons. TCN generally follows similar trends but occasionally produces slightly higher errors at intermediate horizons of 12 h, suggesting some limitations in capturing complex temporal dependencies over extended periods. Prophet consistently delivers more accurate forecasts across all metrics and horizons, demonstrating robustness to both temporal scale and urban variability. Overall, Prophet emerges as the most reliable model for multi-horizon forecasting at the city level, while GRU, LSTM, and TCN seem to be better suited for short-term predictions, especially in highly volatile or large-scale urban datasets.

4.2. Model Performance for City Clusters

The results for the city clusters are shown in

Table 2. Model performance metrics by cluster, model type, and forecasting horizon. Each horizon (1, 6, 12, and 24 h) reflects short- to long-term forecasting accuracy across different city clusters.

Cluster	Model	Horizon	MAE	MSE	RMSE	R2	MAPE
Cluster 1	GRU	1	139.09	46,987.36	193.97	0.971	2.58
	GRU	6	230.04	127,309.73	331.97	0.918	4.26
	GRU	12	295.99	203,085.27	421.25	0.870	5.47
	GRU	24	351.28	275,144.62	493.93	0.821	6.52
	LSTM	1	152.93	46,617.66	201.27	0.971	2.87
	LSTM	6	251.27	138,600.17	346.26	0.913	4.67
	LSTM	12	311.80	209,038.65	429.53	0.866	5.80
	LSTM	24	361.80	277,865.37	499.23	0.817	6.81
	Prophet	1	35.30	2934.39	48.89	0.997	0.69
	Prophet	6	55.86	5499.54	72.30	0.988	1.23
	Prophet	12	53.85	4499.18	66.76	0.993	0.96
	Prophet	24	33.21	2242.40	40.28	0.998	0.55
	TCN	1	125.09	33,721.42	170.99	0.978	2.34
	TCN	6	238.82	139,109.18	344.28	0.912	4.46
	TCN	12	294.05	211,262.02	426.42	0.866	5.47
	TCN	24	341.08	263,134.79	483.13	0.828	6.39
Cluster 2	GRU	1	348.14	432,498.51	559.62	0.925	3.15
	GRU	6	469.76	652,785.47	747.14	0.883	4.14
	GRU	12	561.24	828,605.79	853.92	0.848	4.98
	GRU	24	628.74	1,010,078.46	949.39	0.813	5.56
	LSTM	1	356.43	484,163.96	590.96	0.916	3.21
	LSTM	6	485.32	714,935.35	772.63	0.873	4.29
	LSTM	12	560.06	821,169.87	850.88	0.849	4.98
	LSTM	24	631.95	1,049,037.26	967.88	0.805	5.57
	Prophet	1	153.97	38,863.87	183.83	0.979	1.41
	Prophet	6	268.83	90,065.09	299.39	0.865	2.76
	Prophet	12	288.82	143,068.67	351.80	0.968	2.25
	Prophet	24	162.72	74,651.62	254.55	0.979	1.36
	TCN	1	384.60	661,896.47	640.91	0.886	3.51
	TCN	6	541.12	960,800.04	866.89	0.830	4.81
	TCN	12	605.51	1,015,795.69	926.17	0.811	5.34
	TCN	24	650.68	1,206,018.53	1012.81	0.777	5.72
Cluster 3	GRU	1	80.90	29,954.39	119.94	0.792	3.54
	GRU	6	134.72	109,476.50	199.42	0.740	4.78
	GRU	12	161.39	154,886.04	232.38	0.694	5.57
	GRU	24	180.36	190,159.07	258.16	0.674	6.19
	LSTM	1	85.25	125,815.35	170.24	0.784	6.08
	LSTM	6	106.76	135,212.41	198.86	0.733	7.46
	LSTM	12	118.03	139,762.63	209.75	0.702	8.40
	LSTM	24	120.71	141,269.81	219.07	0.688	8.48
	Prophet	1	33.81	3689.77	49.22	0.893	2.31
	Prophet	6	36.12	3097.77	48.41	0.836	2.66
	Prophet	12	37.42	3677.56	53.65	0.947	2.48
	Prophet	24	28.75	1861.39	38.28	0.957	1.93
	TCN	1	76.03	193,888.43	175.58	0.809	5.32
	TCN	6	95.62	215,352.98	207.00	0.757	6.66
	TCN	12	109.83	207,395.99	216.53	0.729	7.76
	TCN	24	118.46	182,788.03	223.97	0.685	8.49

. Information for Cluster 4 is not included in the table, as it contains only one city (Houston); therefore, the cluster-level results would be identical to those of that individual city. Cluster 1, comprising Baltimore, New York City, Philadelphia, and San Antonio, shows the strongest overall predictive performance across all models. The deep learning models (GRU, LSTM, and TCN) achieve low error metrics (MAE and RMSE) and high R² values for shorter horizons, particularly at 1 h, where R² exceeds 0.97. However, as the forecast horizon increases to 24 h, their accuracy gradually declines, with RMSE roughly doubling and R² values decreasing to around 0.82. Prophet, by contrast, maintains high stability, with extremely low error values and R² consistently above 0.99 across all horizons.

Cluster 2 includes Chicago and Los Angeles, and presents more challenging temporal dynamics, reflected in higher errors and lower R² compared to Cluster 1. The neural models perform well at shorter horizons, with R² values above 0.9 for 1 h and 6 h, but their performance declines markedly beyond 12 h. Prophet again outperforms all deep learning models, maintaining lower error levels and higher R² values (around 0.97–0.98) across all horizons.

Cluster 3, which contains El Paso, Omaha, Portland, San Diego, Seattle, Tallahassee, Tampa, and Tucson, shows the weakest predictive performance overall. The deep learning models produce substantially higher MAE and RMSE values, and R² values frequently fall below 0.8, indicating a lower degree of predictability. This cluster likely exhibits greater temporal and spatial variability, making it more difficult for neural networks to learn consistent patterns. Prophet, however, remains relatively robust, with lower errors and R² values consistently around 0.9 or higher, indicating that it captures the dominant trends even in less predictable contexts.

Across all clusters, a clear pattern emerges: as the forecast horizon increases, error metrics (MAE, MSE, RMSE, and MAPE) increase correspondingly, while R² values decline. This trend confirms that model accuracy decreases as predictions extend further into the future. Among the models, Prophet consistently delivers the lowest error values and highest R² across all clusters and horizons, followed by GRU and LSTM, which perform comparably but degrade more rapidly with longer prediction intervals. TCN performs similarly to GRU and LSTM in some clusters but exhibits greater variability across horizons and locations. These results indicate that Prophet offers the most robust and generalisable performance across diverse urban contexts. GRU and LSTM remain competitive for short-term forecasting tasks, particularly in clusters with stable temporal dynamics, while TCN appears less consistent across clusters. The performance differences across clusters highlight the influence of local urban characteristics on predictive accuracy, suggesting that cities with more regular temporal behaviour—such as those in Cluster 1—are inherently easier to model, whereas more heterogeneous clusters, such as Cluster 3, present greater forecasting challenges.

4.3. Within-Cluster Differences in Model Performance

The preceding analysis in Section 4.2 highlighted distinct differences in predictive performance between clusters, with Cluster 1 showing the highest overall accuracy and stability, Cluster 2 exhibiting moderate performance, and Cluster 3 demonstrating greater variability and weaker predictability. To further examine whether these observed patterns also reflect differences in performance within clusters, that is, between individual cities belonging to the same group, the Kruskal–Wallis test [111] was applied to the average model performance values for each city across all models and forecast horizons. These results are presented in

Table 3. Kruskal–Wallis test results for model performance across cities within clusters and time horizons.

Cluster	Horizon (h)	Metric	H-Statistic	p-Value
Cluster 1	1	MAE	5.051	0.168
Cluster 1	1	MAPE	2.051	0.562
Cluster 1	1	MSE	4.699	0.195
Cluster 1	1	R2	1.541	0.673
Cluster 1	1	RMSE	5.051	0.168
Cluster 1	6	MAE	4.390	0.222
Cluster 1	6	MAPE	2.846	0.416
Cluster 1	6	MSE	4.853	0.183
Cluster 1	6	R2	2.801	0.423
Cluster 1	6	RMSE	4.853	0.183
Cluster 1	12	MAE	3.949	0.267
Cluster 1	12	MAPE	3.596	0.309
Cluster 1	12	MSE	4.853	0.183
Cluster 1	12	R2	4.257	0.235
Cluster 1	12	RMSE	4.853	0.183
Cluster 1	24	MAE	5.316	0.150
Cluster 1	24	MAPE	3.596	0.309
Cluster 1	24	MSE	5.515	0.138
Cluster 1	24	R2	3.265	0.353
Cluster 1	24	RMSE	5.515	0.138
Cluster 2	1	MAE	2.083	0.149
Cluster 2	1	MAPE	2.083	0.149
Cluster 2	1	MSE	2.083	0.149
Cluster 2	1	R2	5.333	0.021
Cluster 2	1	RMSE	2.083	0.149
Cluster 2	6	MAE	2.083	0.149
Cluster 2	6	MAPE	2.083	0.149
Cluster 2	6	MSE	2.083	0.149
Cluster 2	6	R2	4.083	0.043
Cluster 2	6	RMSE	2.083	0.149
Cluster 2	12	MAE	2.083	0.149
Cluster 2	12	MAPE	2.083	0.149
Cluster 2	12	MSE	2.083	0.149
Cluster 2	12	R2	2.083	0.149
Cluster 2	12	RMSE	2.083	0.149
Cluster 2	24	MAE	2.083	0.149
Cluster 2	24	MAPE	2.083	0.149
Cluster 2	24	MSE	2.083	0.149
Cluster 2	24	R2	2.083	0.149
Cluster 2	24	RMSE	2.083	0.149
Cluster 3	1	MAE	15.007	0.020
Cluster 3	1	MAPE	6.931	0.327
Cluster 3	1	MSE	14.268	0.027
Cluster 3	1	R2	17.224	0.008
Cluster 3	1	RMSE	14.357	0.026
Cluster 3	6	MAE	14.860	0.021
Cluster 3	6	MAPE	4.759	0.575
Cluster 3	6	MSE	11.837	0.066
Cluster 3	6	R2	15.103	0.019
Cluster 3	6	RMSE	12.000	0.062
Cluster 3	12	MAE	11.948	0.063
Cluster 3	12	MAPE	5.298	0.506
Cluster 3	12	MSE	11.793	0.067
Cluster 3	12	R2	8.823	0.184
Cluster 3	12	RMSE	12.429	0.053
Cluster 3	24	MAE	9.591	0.143
Cluster 3	24	MAPE	4.869	0.561
Cluster 3	24	MSE	8.328	0.215
Cluster 3	24	R2	8.852	0.182
Cluster 3	24	RMSE	8.328	0.215

. Similar to Section 4.2, Cluster 4 was excluded from this analysis as it contained only a single city (Houston), making the Kruskal–Wallis test inapplicable since it requires at least two groups for comparison.

Consistent with the earlier findings in Table 2, no statistically significant differences were observed for Cluster 1 across any metric or forecast horizon (all p > 0.138). This supports the conclusion that the models generalised well across cities such as Baltimore, New York City, Philadelphia, and San Antonio, capturing broadly similar temporal patterns despite local differences. Cluster 2 also showed relatively good performance across cities, with most p-values exceeding 0.14. However, significant differences in the coefficient of determination (R²) were identified at the 1 h (H = 5.33, p = 0.021) and 6 h (H = 4.08, p = 0.043) horizons, indicating some variation in the explanatory power of the models across cities such as Chicago and Los Angeles, particularly for short-term forecasts.

In contrast, Cluster 3 exhibited a higher degree of heterogeneity in model performance, highlighting the weaker predictability observed earlier. Statistically significant differences were identified for several metrics at the 1 h and 6 h horizons; for example, MAE (H = 15.01, p = 0.020), RMSE (H = 14.36, p = 0.026), and R² (H = 17.22, p = 0.008). These findings suggest that cities within Cluster 3, which include El Paso, Portland, Seattle, and Tampa, display more diverse temporal behaviours, making it difficult for the models to generalise consistently. As forecast horizons lengthened, these differences diminished, with all p-values exceeding 0.05 at 12 and 24 h, implying convergence in long-term predictive patterns across cities. These results reinforce the descriptive analysis presented in Section 4.2. Model performance was consistent across cities in Clusters 1 and 2, indicating that urban areas with similar temporal structures support reliable model generalisation. In contrast, greater intra-cluster variability in Cluster 3 highlights the influence of urban heterogeneity on predictive accuracy, particularly at shorter forecast horizons.

4.4. Clustering Analysis of Climate Variables

Building upon Section 4.2, which examined model performance across city clusters based on energy demand characteristics, this section explores whether similar grouping patterns emerge when clustering cities by their climate variability (CV). The objective is to determine if climatic conditions help explain the observed differences in model performance. The clustering of CV results revealed three distinct groups of cities, as shown in Figure 3, with detailed CV values provided in Table A3 in Appendix C. Cluster 1 includes cities with moderate to high levels of temperature and humidity variability, such as Houston, Los Angeles, San Antonio, San Diego, Tallahassee, and Tampa. These cities typically experience warmer climates with substantial temperature variation, resulting in significant energy demands for cooling during hot periods. In contrast, Cluster 2, comprising Baltimore, Chicago, Omaha, Philadelphia, Portland, and Seattle, features more temperate climates with moderate temperature and humidity fluctuations. These cities tend to display more stable energy demand patterns with predictable seasonal variations driven by heating and cooling requirements. Lastly, Cluster 3, consisting of El Paso, New York City, and Tucson, exhibits the highest levels of temperature fluctuation and humidity variability, leading to more pronounced and erratic energy demand patterns driven by extreme weather events.

When comparing these climate-based clusters with the energy demand characteristics shown in Figure 2, a clear relationship emerges. Cities in clusters with greater climatic variability (Cluster 1 and Cluster 3) tend to exhibit higher energy demand fluctuations. These cities experience stronger seasonal shifts in temperature and humidity, directly influencing heating and cooling requirements, which in turn produce larger spikes in energy consumption. Conversely, cities in Cluster 2, with relatively stable climates, demonstrate more consistent energy usage patterns, as their demand primarily varies in line with predictable seasonal temperature changes. These findings highlight the critical role of climate variability in shaping urban energy demand: cities with higher climatic instability tend to require more adaptive energy systems, while those with more moderate climates can rely on steadier and more predictable consumption trends.

To maintain consistency across the comparative analyses, model performance is evaluated only for the 1 h forecast horizon. This ensures that the relationships between climate variability and forecasting accuracy are not confounded by horizon-dependent performance differences. Short-term forecasts (1 h) also provide the clearest view of how local climatic fluctuations influence immediate energy demand, making them most suitable for this comparison. Linking CV findings to the model performance results presented earlier, it becomes evident that cities with higher climate variability (Clusters 1 and 3) generally correspond to lower model accuracy across all approaches, particularly for the neural models (TCN, GRU, and LSTM). This aligns with the performance patterns described in Section 3.5, where models struggled in regions characterised by pronounced temperature and humidity fluctuations. The higher variability introduces uncertainty and short-term irregularities in energy demand trends, making it more difficult for models to capture stable temporal dependencies. Prophet, which performed best overall in the earlier analyses, also exhibited a modest decline in accuracy in these high-variability cities. Because Prophet decomposes time series into additive trend and seasonal components, it performs best when underlying patterns are regular and cyclical. In cities where abrupt or irregular climate-driven changes occur, these assumptions are partially violated, leading to increased forecast errors. However, even under such conditions, Prophet generally remained more robust than the deep learning models, which are more sensitive to data noise and non-stationarity.

In contrast, cities within Cluster 2, that is, those with more stable climatic conditions, display superior model performance across all forecasting approaches. The predictability of their energy demand patterns allows both simpler models like Prophet and more complex architectures such as GRU and LSTM to achieve higher accuracy. Cities such as Portland, Seattle, and Philadelphia, all within Cluster 2, consistently demonstrated stronger performance metrics across the 1 h forecast horizon. This reinforces the interpretation that stable climate conditions contribute significantly to improved forecasting outcomes.

Overall, these results indicate that climatic variability exerts a substantial influence on model performance. Cities with greater variability in temperature and humidity, such as those in Clusters 1 and 3, present greater forecasting challenges, while those with more stable climatic conditions, such as in Cluster 2, enable more reliable predictions. This linkage between environmental stability and forecasting accuracy underscores the importance of incorporating climate variability considerations into energy demand modelling.

4.5. Linking Model Characteristics to Forecasting Performance

The observed performance differences across models can be directly linked to their underlying architectural properties. Prophet consistently outperforms deep learning models at longer forecast horizons (12–24 h), particularly across climatically diverse city clusters. This behaviour reflects Prophet’s explicit decomposition of time series into trend and seasonal components, which provides structural stability when temporal autocorrelation weakens at longer horizons. In contrast, LSTM and GRU models demonstrate strong performance at short horizons (1–6 h), especially in clusters with relatively stable climate conditions. Their gated recurrent architectures are well suited to learning short-term temporal dependencies and non-linear interactions between weather variables and recent demand history. However, as the forecast horizon increases, error accumulation and the absence of explicit long-term trend constraints lead to rapid performance degradation, particularly in cities with high climatic variability.

The TCN exhibits intermediate behaviour. Its use of dilated causal convolutions enables efficient learning of longer temporal contexts than recurrent models, which explains its competitive short-horizon performance in some cities. Nevertheless, the lack of explicit seasonality modelling and its reliance on fixed receptive fields limit robustness under highly non-stationary demand regimes, resulting in less consistent performance across clusters.

Across all models, performance deterioration with increasing forecast horizon is more pronounced in clusters characterised by high climate variability, indicating that architectural sensitivity to non-stationarity plays a central role in forecasting reliability. These results suggest that models with explicit trend and seasonality representations are more robust to climatic heterogeneity, while deep learning architectures are better suited to short-term, stable demand regimes.

5. Discussion

The results presented in the previous section reveal systematic differences in forecasting performance across models, cities, and climatic contexts. This section interprets these findings by examining the factors that may contribute to the observed variations in model behaviour, including city-specific demand characteristics, climatic variability, and model architecture. Particular attention is given to short-term (1 h) forecasting, where performance differences are most pronounced and operational relevance is highest. Beyond interpreting current results, the discussion situates these findings within emerging challenges in urban energy planning, including climate non-stationarity, increasing system coupling, and the growing reliance on AI-driven decision support in complex urban energy systems.

5.1. Model Performance and City-Specific Challenges

The variability in model performance across cities emphasises the complexity of forecasting urban energy demand in heterogeneous urban environments. Models that perform well in cities with stable and predictable data patterns, such as those in Cluster 1, highlight the potential for specific models to excel under predictable conditions. In contrast, cities with more erratic or highly variable energy demand, often linked to pronounced climate variability, pose greater challenges for all models. The deep learning models, such as GRU, LSTM, and TCN, perform competitively at short horizons but degrade with longer-term forecasts, while Prophet demonstrates consistent robustness even in less predictable contexts. These patterns underscore the importance of tailoring model selection to city-specific characteristics, including climate, urban form, and underlying socio-economic activity, rather than relying on a one-size-fits-all approach.

The failure of GRU in specific cities such as Omaha highlights an important interaction between model architecture and urban demand characteristics. Cities with low aggregate demand, weak seasonality, and irregular load dynamics provide limited sequential signal for gated recurrent models to exploit. In such contexts, model performance is not primarily constrained by climate volatility or data quality, but by the absence of stable temporal dependencies. This finding reinforces that deep recurrent architectures are not universally suitable for all urban settings and may perform poorly in cities where energy demand is dominated by stochastic or locally driven behaviour rather than consistent climatic forcing. This finding has forward-looking implications: as electrification, decentralised generation, and behavioural heterogeneity increase, more cities may exhibit demand patterns that challenge conventional deep learning assumptions, reinforcing the need for adaptable and context-aware forecasting strategies.

5.2. Cluster Analysis and the Role of Climatic Variables

Clustering cities based on climate variability provides further insights into the relationship between environmental conditions and model performance. Cities with more moderate and stable climate conditions, such as those in Cluster 2, exhibit more consistent energy demand patterns and generally higher forecasting accuracy across models. Conversely, cities with greater temperature and humidity fluctuations, as seen in Clusters 1 and 3, experience more erratic demand patterns, which challenge both deep learning models and Prophet. These findings highlight the critical role of climate variability in shaping short-term energy demand and forecasting performance. Accounting for these differences is essential when designing models, as cities with high climatic instability may benefit from adaptive forecasting approaches that can respond dynamically to rapid changes in environmental conditions.

From a future-planning perspective, this sensitivity to climate variability represents a critical challenge. As climate change accelerates, historical climate–demand relationships may become increasingly unreliable, undermining forecasting approaches trained on past observations. Urban energy planning will therefore require forecasting systems that explicitly account for non-stationary climate conditions and extreme events rather than relying on historical averages alone.

5.3. Weather Data Uncertainty and Model Robustness

Although meteorological variables are key predictors of urban energy demand, they are subject to measurement error, spatial representativeness issues, and short-term variability that introduce noise into the forecasting process. Hourly weather observations may not fully capture microclimatic effects within large urban areas, and small errors in temperature or humidity can propagate into demand predictions, particularly at short forecasting horizons. The results suggest that model sensitivity to such uncertainty varies by architecture. Prophet exhibits greater robustness under noisy climatic conditions due to its explicit decomposition into trend and seasonal components, which dampens the influence of short-term fluctuations. In contrast, deep learning models (LSTM, GRU, and TCN), which rely more heavily on recent input sequences, appear more sensitive to high-frequency variability in weather inputs. This sensitivity is particularly evident in city clusters characterised by high climatic variability, where deep learning performance deteriorates more rapidly with increasing forecast horizon. These findings indicate that uncertainty in meteorological predictors interacts with model structure and should be considered when selecting forecasting approaches for climate-volatile urban environments. Further, this sensitivity becomes increasingly problematic as urban energy systems integrate weather-dependent technologies such as heat pumps, distributed renewables, and flexible demand, where forecasting errors may propagate across coupled systems and markets.

5.4. Implications of Forecast Horizons

The analysis focuses on short-term (1 h) forecasting, where accuracy is highest and operational relevance is greatest. At longer horizons, especially beyond 12–24 h, performance deteriorates for most models as errors accumulate and temporal dependencies weaken. This suggests that near-real-time forecasting currently offers the most reliable support for operational energy management. However, future urban energy planning increasingly requires coordination across multiple temporal scales, from real-time grid operation to medium- and long-term infrastructure investment. Bridging short-term forecasting with longer-term planning models remains a key challenge, particularly as cities move towards integrated, multi-energy systems that require coordinated operation across electricity, storage, and emerging energy carriers such as hydrogen.

5.5. Broader Implications for Future Urban Energy Systems

Beyond model comparison, the findings highlight structural challenges for future urban energy systems. Increasing electrification, sector coupling, and the integration of new energy carriers are expected to significantly alter urban demand dynamics. In such settings, forecasting accuracy alone is insufficient; models must also be interpretable, transferable across cities, and robust to structural change. Recent research on AI-driven urban retrofit and integrated electricity–hydrogen markets [114] also emphasis that forecasting uncertainty, model scalability, and cross-sector coordination are major barriers to real-world deployment. While this study focuses on electricity demand, the results underscore a shared challenge: future urban energy planning will depend on forecasting frameworks capable of supporting complex, coupled systems under climate and demand uncertainty.

5.6. Methodological and Data Limitations

Despite the strengths of the proposed climate-aware, multi-city evaluation framework, several methodological limitations should be acknowledged. First, a uniform set of hyperparameters was intentionally applied across all deep learning models to ensure a transparent and architecture-focused comparison. While this enhances reproducibility and fairness, it may not yield optimal performance for every city, particularly given the wide variation in climatic regimes and demand volatility. In addition, although rolling-origin time-series cross-validation was employed to improve robustness, the 80–10–10 train–validation–test split represents a pragmatic rather than theoretically optimal choice. Alternative window lengths or adaptive splitting strategies could influence performance estimates, especially in cities with shorter or more volatile time series.

Second, the analysis relies on historical energy demand and a limited set of meteorological variables at hourly resolution. Other potentially important drivers, such as detailed building characteristics, socio-economic indicators, behavioural factors, or real-time pricing signals, were not included due to data availability constraints. Moreover, the study focuses on short- to medium-term forecasting horizons (up to 24 h), which are most relevant for operational planning but may not generalise to longer-term forecasting tasks. These limitations point to clear directions for future work, including climate-aware hyperparameter optimisation, richer multi-source data integration, and the extension of the framework to longer horizons and alternative validation strategies.

5.7. Policy Implications for Regional Planning and Energy Management

The findings provide actionable insights for policymakers seeking to optimise urban energy systems. By identifying clusters of cities with similar climatic and temporal characteristics, governments and utilities can develop context-specific forecasting strategies and allocate resources more efficiently. Cities with stable energy demand can benefit from standardised forecasting protocols, while cities facing higher variability may require investment in adaptive infrastructures, such as smart grids, energy storage, and real-time monitoring systems. More broadly, integrating data-driven forecasting into regional and long-term planning frameworks will be essential as cities transition towards low-carbon, highly interconnected energy systems. Aligning short-term operational forecasting with strategic planning can support resilience, reduce systemic risk, and enable more effective responses to climate variability and future energy transitions.

6. Conclusions

This study examined the performance of multiple forecasting models for urban energy demand across a diverse set of cities and climatic contexts. The results demonstrate that forecasting accuracy varies substantially across both cities and models, underscoring the importance of selecting approaches that are appropriate for local demand characteristics and climatic conditions. Models with explicit representations of trend and seasonality, such as Prophet, consistently exhibit robust performance across forecast horizons and urban contexts, particularly in cities with stable and predictable demand patterns. In contrast, deep learning architectures, including GRU, LSTM, and TCN, tend to perform more effectively at short forecasting horizons, especially in environments with relatively stable temporal dynamics, but their performance degrades more rapidly as forecast horizons increase or climatic variability intensifies.

The analysis further highlights the role of climatic variability in shaping forecasting performance. Cities characterised by pronounced temperature and humidity fluctuations generally exhibit higher prediction errors across all models, reflecting the challenges posed by non-stationary and irregular demand patterns. These findings indicate that environmental conditions are a key determinant of forecasting reliability and should be explicitly considered when developing and deploying urban energy forecasting frameworks. As climate change continues to increase the frequency and intensity of extreme weather events, the ability of models to remain robust under evolving climatic regimes will become increasingly important.

Beyond methodological insights, the results have practical implications for urban planners, policymakers, and energy system operators. Forecasting strategies tailored to local climatic and demand characteristics can support more reliable short-term operational planning, improve resource allocation, and enhance the resilience of urban energy systems. The cluster-based perspective adopted in this study further suggests opportunities for regional coordination, whereby cities with similar climatic and temporal characteristics may benefit from shared forecasting strategies and decision-support tools.

Several directions for future research emerge directly from these findings. First, hybrid modelling approaches that combine the structural interpretability of decomposition-based models (e.g., Prophet) with the adaptive learning capacity of deep neural networks could offer improved performance across both stable and highly variable urban contexts. Second, transfer learning within climatically similar city clusters represents a promising strategy for improving cross-city generalisation, particularly for cities with limited historical data or high demand volatility. Third, deeper or more expressive neural architectures may be beneficial for large metropolitan areas with complex and high-volume demand patterns, whereas smaller or less regular cities may benefit more from simpler or regularised models that prioritise robustness over representational complexity.

In addition, while a uniform set of hyperparameters was intentionally adopted in this study to enable transparent and architecture-focused comparisons, future work could explore adaptive strategies such as regime-specific hyperparameter optimisation or Bayesian optimisation tailored to climatic and demand regimes. Such approaches would help disentangle intrinsic model capability from tuning effects while improving local forecasting accuracy. Further extensions could also incorporate richer data sources, including building characteristics, socio-economic indicators, and real-time behavioural signals, as well as examine longer forecasting horizons relevant to strategic planning.

Overall, this study demonstrates that effective urban energy forecasting requires context-sensitive model selection informed by climatic variability, demand dynamics, and forecasting horizon. By integrating hybrid modelling strategies, transfer learning, and adaptive optimisation into future forecasting frameworks, urban energy systems can be supported with more accurate, generalisable, and resilient predictive tools.