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55 pages, 28544 KB  
Article
Spatial Flows of Information Entropy as Indicators of Climate Variability and Extremes
by Bernard Twaróg
Entropy 2025, 27(11), 1132; https://doi.org/10.3390/e27111132 (registering DOI) - 31 Oct 2025
Abstract
The objective of this study is to analyze spatial entropy flows that reveal the directional dynamics of climate change—patterns that remain obscured in traditional statistical analyses. This approach enables the identification of pathways for “climate information transport”, highlights associations with atmospheric circulation types, [...] Read more.
The objective of this study is to analyze spatial entropy flows that reveal the directional dynamics of climate change—patterns that remain obscured in traditional statistical analyses. This approach enables the identification of pathways for “climate information transport”, highlights associations with atmospheric circulation types, and allows for the localization of both sources and “informational voids”—regions where entropy is dissipated. The analytical framework is grounded in a quantitative assessment of long-term climate variability across Europe over the period 1901–2010, utilizing Shannon entropy as a measure of atmospheric system uncertainty and variability. The underlying assumption is that the variability of temperature and precipitation reflects the inherently dynamic character of climate as a nonlinear system prone to fluctuations. The study focuses on calculating entropy estimated within a 70-year moving window for each calendar month, using bivariate distributions of temperature and precipitation modeled with copula functions. Marginal distributions were selected based on the Akaike Information Criterion (AIC). To improve the accuracy of the estimation, a block bootstrap resampling technique was applied, along with numerical integration to compute the Shannon entropy values at each of the 4165 grid points with a spatial resolution of 0.5° × 0.5°. The results indicate that entropy and its derivative are complementary indicators of atmospheric system instability—entropy proving effective in long-term diagnostics, while its derivative provides insight into the short-term forecasting of abrupt changes. A lag analysis and Spearman rank correlation between entropy values and their potential supported the investigation of how circulation variability influences the occurrence of extreme precipitation events. Particularly noteworthy is the temporal derivative of entropy, which revealed strong nonlinear relationships between local dynamic conditions and climatic extremes. A spatial analysis of the information entropy field was also conducted, revealing distinct structures with varying degrees of climatic complexity on a continental scale. This field appears to be clearly structured, reflecting not only the directional patterns of change but also the potential sources of meteorological fluctuations. A field-theory-based spatial classification allows for the identification of transitional regions—areas with heightened susceptibility to shifts in local dynamics—as well as entropy source and sink regions. The study is embedded within the Fokker–Planck formalism, wherein the change in the stochastic distribution characterizes the rate of entropy production. In this context, regions of positive divergence are interpreted as active generators of variability, while sink regions function as stabilizing zones that dampen fluctuations. Full article
(This article belongs to the Special Issue 25 Years of Sample Entropy)
19 pages, 4172 KB  
Article
Balancing Efficiency and Cost: A Technical and Economic Analysis of Condensed Maintenance
by Jan Schatzl and Stefan Marschnig
Appl. Sci. 2025, 15(21), 11688; https://doi.org/10.3390/app152111688 (registering DOI) - 31 Oct 2025
Abstract
In Europe’s changing transport landscape, railways are experiencing a renaissance, driven by environmental advantages, cost efficiency, growing demand, and political support. Yet this growth also exposes major challenges, especially regarding network capacity, infrastructure availability, maintainability, and the cost-effectiveness of maintenance. This study focuses [...] Read more.
In Europe’s changing transport landscape, railways are experiencing a renaissance, driven by environmental advantages, cost efficiency, growing demand, and political support. Yet this growth also exposes major challenges, especially regarding network capacity, infrastructure availability, maintainability, and the cost-effectiveness of maintenance. This study focuses on these aspects, analyzing their interdependence and their impact on building a more resilient and efficient rail system. A prediction model, based on historical measurement data, is developed to forecast track behavior and assess an alternative maintenance strategy. This maintenance strategy uses novel approaches to define maintenance-triggering intervention values. The overarching goal of this work is to contribute to the improvement of predictive maintenance approaches. Findings show no technical or economic justification for the continual reduction of section lengths, a practice common in heavily used networks. Instead, results demonstrate that with improved planning and long-section tamping, both track quality and service life can at least be kept at the same level or even be enhanced. Longer section lengths positively influence performance by lowering running meter costs and potentially reducing operational downtime in the long run. To validate these interrelationship, future research will integrate a model that explicitly considers the costs of operational hindrances. Full article
34 pages, 2025 KB  
Review
EV and Renewable Energy Integration in Residential Buildings: A Global Perspective on Deep Learning, Strategies, and Challenges
by Ahmad Mohsenimanesh, Christopher McNevin and Evgueniy Entchev
World Electr. Veh. J. 2025, 16(11), 603; https://doi.org/10.3390/wevj16110603 (registering DOI) - 31 Oct 2025
Abstract
Charging electric vehicles (EVs) and integrating renewable energy sources (RESs) are becoming key aspects of residential energy systems. However, the variability of RES generation, combined with uncontrolled EV charging, poses challenges for reliability, power quality, and supply-demand balancing within communities. The challenges only [...] Read more.
Charging electric vehicles (EVs) and integrating renewable energy sources (RESs) are becoming key aspects of residential energy systems. However, the variability of RES generation, combined with uncontrolled EV charging, poses challenges for reliability, power quality, and supply-demand balancing within communities. The challenges only grow when considering other electrified building loads as well. Accurate forecasting of power demand and renewable generation is essential for efficient and sustainable grid operation, optimal use of RESs, and effective energy trading within communities. Deep learning (DL), including supervised, unsupervised, and reinforcement learning (RL), has emerged as a promising solution for predicting consumer demand, renewable generation, and managing energy flows in residential environments. This paper provides a comprehensive review of the development and application of these methods for forecasting and energy management in residential communities. Evaluation metrics across studies indicate that supervised learning can achieve highly accurate forecasting results, especially when integrated with unsupervised K-means clustering and data decomposition. These methods help uncover patterns and relationships within the data while reducing noise, thereby enhancing prediction accuracy. RL shows significant potential in control applications, particularly for charging strategies. Similarly to how V2G-simulators model individual EV usage and simulate large fleets to generate grid-scale predictions, RL can be applied to various aspects of EV fleet management, including vehicle dispatching, smart scheduling, and charging coordination. Traditional methods are also used across different applications and help utilities with planning. However, these methods have limitations and may not always be completely accurate. Our review suggests that integrating hybrid supervised-unsupervised learning methods with RL can significantly improve the sustainability and resilience of energy systems. This approach can improve demand and generation forecasting while enabling smart charging coordination and scheduling for scalable EV fleets integrated with building electrification measures. Furthermore, the review introduces a unifying conceptual framework that links forecasting, optimization, and policy coupling through hierarchical deep learning layers, enabling scalable coordination of EV charging, renewable generation, and building energy management. Despite methodological advances, real-world deployment of hybrid and deep learning frameworks remains constrained by data-privacy restrictions, interoperability issues, and computational demands, highlighting the need for explainable, privacy-preserving, and standardized modeling approaches. To be effective in practice, these methods require robust data acquisition, optimized forecasting and control models, and integrated consideration of transport, building, and grid domains. Furthermore, deployment must account for data privacy regulations, cybersecurity safeguards, model interpretability, and economic feasibility to ensure resilient, scalable, and socially acceptable solutions. Full article
(This article belongs to the Section Energy Supply and Sustainability)
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17 pages, 826 KB  
Article
Climate Change, Factor Inputs and Cotton Yield Growth: Evidence from the Main Cotton Producing Areas in China
by Honghong Yang, Wenwen Ma, Hua Li and Qi Li
Agriculture 2025, 15(21), 2271; https://doi.org/10.3390/agriculture15212271 (registering DOI) - 31 Oct 2025
Abstract
Increasing the yield per unit area is crucial for achieving stable growth in China’s cotton production. Based on the transcendental logarithmic production function model and using panel data from eight major cotton-producing provinces in China from 1990 to 2022, this paper measures the [...] Read more.
Increasing the yield per unit area is crucial for achieving stable growth in China’s cotton production. Based on the transcendental logarithmic production function model and using panel data from eight major cotton-producing provinces in China from 1990 to 2022, this paper measures the elasticity of climate factors and factor inputs and calculates the contribution rate of each factor influencing cotton yield increase. The results show that accumulated temperature positively impacts cotton yield, while precipitation and sunshine duration have negative effects. Climate factors contribute 7.95% to yield growth. Among input factors, agricultural machinery and labor inputs positively affect yield, whereas fertilizer input negatively affects it. Factor inputs contribute 44.21% to yield improvement. Technological progress also plays a role in enhancing cotton yield. Finally, the paper suggests improving meteorological disaster forecasting, optimizing input structures, and promoting agricultural research and technology services based on local conditions. Full article
(This article belongs to the Section Ecosystem, Environment and Climate Change in Agriculture)
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23 pages, 2577 KB  
Article
A Hybrid STL-Based Ensemble Model for PM2.5 Forecasting in Pakistani Cities
by Moiz Qureshi, Atef F. Hashem, Hasnain Iftikhar and Paulo Canas Rodrigues
Symmetry 2025, 17(11), 1827; https://doi.org/10.3390/sym17111827 (registering DOI) - 31 Oct 2025
Abstract
Air pollution, outstanding particulate matter (PM2.5), poses severe risks to human health and the environment in densely populated urban areas. Accurate short-term forecasting of PM2.5 concentrations is therefore crucial for timely public health advisories and effective mitigation strategies. This work [...] Read more.
Air pollution, outstanding particulate matter (PM2.5), poses severe risks to human health and the environment in densely populated urban areas. Accurate short-term forecasting of PM2.5 concentrations is therefore crucial for timely public health advisories and effective mitigation strategies. This work proposes a hybrid approach that combines machine learning models with STL decomposition to provide precise short-term PM2.5 predictions. Daily PM2.5 series from four major Pakistani cities—Islamabad, Lahore, Karachi, and Peshawar—are first pre-processed to handle missing values, outliers, and variance instability. The data are then decomposed via seasonal-trend decomposition using Loess (STL), which explicitly exploits the symmetric and recurrent structure of seasonal patterns. Each decomposed component (trend, seasonality, and remainder) is modeled independently using an ensemble of statistical and machine learning approaches. Forecasts are combined through a weighted aggregation scheme that balances bias–variance trade-offs and preserves the distributional consistency. The final recombined forecasts provide one-day-ahead PM2.5 predictions with associated uncertainty measures. The model evaluation employs multiple statistical accuracy metrics, distributional diagnostics, and out-of-sample validation to assess its performance. The results demonstrate that the proposed framework consistently outperforms conventional benchmark models, yielding robust, interpretable, and probabilistically coherent forecasts. This study demonstrates how periodic and recurrent seasonal structure decomposition and probabilistic ensemble methods enhance the statistical modeling of environmental time series, offering actionable insights for urban air quality management. Full article
(This article belongs to the Special Issue Unlocking the Power of Probability and Statistics for Symmetry)
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9 pages, 7778 KB  
Proceeding Paper
Adaptive IoT-Based Platform for CO2 Forecasting Using Generative Adversarial Networks: Enhancing Indoor Air Quality Management with Minimal Data
by Alessandro Leone, Andrea Manni, Andrea Caroppo and Gabriele Rescio
Eng. Proc. 2025, 110(1), 3; https://doi.org/10.3390/engproc2025110003 - 30 Oct 2025
Abstract
Monitoring indoor air quality is vital for health, as CO2 is a major pollutant. An automated system that accurately forecasts CO2 levels can optimize HVAC management, preventing sudden increases and reducing energy waste while maintaining occupant comfort. Traditionally, such systems require [...] Read more.
Monitoring indoor air quality is vital for health, as CO2 is a major pollutant. An automated system that accurately forecasts CO2 levels can optimize HVAC management, preventing sudden increases and reducing energy waste while maintaining occupant comfort. Traditionally, such systems require extensive datasets collected over months to train algorithms, making them computational expensive and inefficient. To address this limitation, an adaptive IoT-based platform has been developed, leveraging a limited set of recent data to forecast CO2 trends. Tested in a real-world setting, the system analyzed parameters such as physical activity, temperature, humidity, and CO2 to ensure accurate predictions. Data acquisition was performed using the Smartex WWS T-shirt for physical activity data and the UPSense UPAI3-CPVTHA environmental sensor for other measurements. The chosen sensor devices are wireless and minimally invasive, while data processing was carried out on a low-power embedded PC. The proposed forecasting model adopts an innovative approach. After a 5-day training period, a Generative Adversarial Network enhances the dataset by simulating a 10-day training period. The model utilizes a Generative Adversarial Network with a Long Short-Term Memory network as the generator to predict future CO2 values based on historical data, while the discriminator, also a Long Short-Term Memory network, distinguishes between actual and generated CO2 values. This approach, based on Conditional Generative Adversarial Networks, effectively captures data distributions, enabling more accurate multi-step probabilistic forecasts. In this way, the framework maintains a Root Mean Square Error of approximately 8 ppm, matching the performance of our previous approach, while reducing the need for real training data from 10 to just 5 days. Furthermore, it achieves accuracy comparable to other state-of-the-art methods that typically requires weeks or even months of training. This advancement significantly enhances computational efficiency and reduces data requirements for model training, improving the system’s practicality for real-world applications. Full article
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28 pages, 6469 KB  
Article
Outlier Detection in Hydrological Data Using Machine Learning: A Case Study in Lao PDR
by Chung-Soo Kim, Cho-Rong Kim and Kah-Hoong Kok
Water 2025, 17(21), 3120; https://doi.org/10.3390/w17213120 - 30 Oct 2025
Abstract
Ensuring the quality of hydrological data is critical for effective flood forecasting, water resource management, and disaster risk reduction, especially in regions vulnerable to typhoons and extreme weather. This study presents a framework for quality control and outlier detection in rainfall and water [...] Read more.
Ensuring the quality of hydrological data is critical for effective flood forecasting, water resource management, and disaster risk reduction, especially in regions vulnerable to typhoons and extreme weather. This study presents a framework for quality control and outlier detection in rainfall and water level time series data using both supervised and unsupervised machine learning algorithms. The proposed approach is capable of detecting outliers arising from sensor malfunctions, missing values, and extreme measurements that may otherwise compromise the reliability of hydrological datasets. Supervised learning using XGBoost was trained on labeled historical data to detect known outlier patterns, while the unsupervised Isolation Forest algorithm was employed to identify unknown or rare outliers without the need for prior labels. This established framework was evaluated using hydrological datasets collected from Lao PDR, one of the member countries of the Typhoon Committee. The results demonstrate that the adopted machine learning algorithms effectively detected real-world outliers, thereby enhancing real-time monitoring and supporting data-driven decision-making. The Isolation Forest model yielded 1.21 and 12 times more false positives and false negatives, respectively, than the XGBoost model, demonstrating that XGBoost achieved superior outlier detection performance when labeled data were available. The proposed framework is designed to assist member countries in shifting from manual, human-dependent processes to AI-enabled, data-driven hydrological data management. Full article
(This article belongs to the Section Hydrology)
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18 pages, 1154 KB  
Article
Explainable AI-Driven Wildfire Prediction in Australia: SHAP and Feature Importance to Identify Environmental Drivers in the Age of Climate Change
by Zina Abohaia, Abeer Elkhouly, May El Barachi and Obada Al-Khatib
Fire 2025, 8(11), 421; https://doi.org/10.3390/fire8110421 - 30 Oct 2025
Viewed by 25
Abstract
This study develops an explainable machine learning framework for wildfire prediction across Australia, integrating region-specific models and feature attribution to identify key environmental drivers. Three wildfire indicators, Estimated Fire Area (FA), Mean Fire Brightness Temperature (FBT), and Fire Radiative Power (FRP), were modeled [...] Read more.
This study develops an explainable machine learning framework for wildfire prediction across Australia, integrating region-specific models and feature attribution to identify key environmental drivers. Three wildfire indicators, Estimated Fire Area (FA), Mean Fire Brightness Temperature (FBT), and Fire Radiative Power (FRP), were modeled using Lasso, Random Forest, LightGBM, and XGBoost. Performance metrics (RMSEC, RMSECV, RMSEP) confirmed strong calibration and generalization, with Tasmania and Queensland achieving the lowest prediction errors for FA and FRP, respectively. Feature importance and SHAP analyses revealed that soil moisture, solar radiation, precipitation, and humidity variability are dominant predictors. Extremes and variance-based measures proved more influential than mean climatic values, indicating that fire dynamics respond non-linearly to environmental fluctuations. Lasso models captured stable linear dependencies in arid regions, while ensemble models effectively represented complex interactions in tropical climates. The results highlight a hierarchical process where cumulative soil and radiation stress establish fire potential, and short-term meteorological variability drives ignition and spread. Projected climate shifts, declining soil water and increased radiative load, are likely to intensify these drivers. The framework supports interpretable, region-specific mitigation planning and paves the way for incorporating generative AI and multi-source data fusion to enhance real-time wildfire forecasting. Full article
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18 pages, 3428 KB  
Article
Farming on the Edge: The 10-Fold Deficit in Lombardy’s Agricultural Land
by Stefano Salata, Andrea Arcidiacono, Stefano Corsi, Chiara Mazzocchi, Alberto Fedalto and Domenico Riccobene
Land 2025, 14(11), 2112; https://doi.org/10.3390/land14112112 - 23 Oct 2025
Viewed by 371
Abstract
Lombardy is Italy’s leading region in primary agricultural production, yet it faces a significant decline in agricultural soil, primarily due to urban expansion. This land consumption largely affects arable areas, as land is repurposed for low-density residential developments, roads, logistics, and commercial or [...] Read more.
Lombardy is Italy’s leading region in primary agricultural production, yet it faces a significant decline in agricultural soil, primarily due to urban expansion. This land consumption largely affects arable areas, as land is repurposed for low-density residential developments, roads, logistics, and commercial or industrial hubs. The reduction in agricultural land threatens regional food security and increases dependency on external markets. This study determines the long-term sustainability of this trend by estimating the actual quantity of agricultural land required to satisfy the food demand of the region’s citizens. The research employed a two-part georeferenced analysis. First, a cross-tabulation matrix quantified the land consumption over two decades. Second, the Planning Forecasts Map was analyzed, coupled with new road projects, to estimate future potential land consumption embedded in Land Use Plans (PGT). Finally, food consumption was converted into the required hectares of agricultural land per capita and compared to the current stock of agricultural land to quantify the deficit by municipality. The dramatic spatial deficit confirms that the current trajectory of land consumption is unsustainable, leaving Lombardy’s food security highly dependent on imports. While regional laws have reduced planned urbanization, the limitation of land take remains far from the goals. The results highlight the urgent need for effective compensatory measures and mitigation strategies that account for the true magnitude and spatial distribution of the agricultural land deficit, particularly in the most critical urban and peri-urban areas. Full article
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22 pages, 3247 KB  
Article
Quantifying Field Soil Moisture, Temperature, and Heat Flux Using an Informer–LSTM Deep Learning Model
by Na Li, Xiaoxiao Sun, Peng Wang, Wenke Wang and Zhitong Ma
Agronomy 2025, 15(11), 2453; https://doi.org/10.3390/agronomy15112453 - 22 Oct 2025
Viewed by 335
Abstract
Understanding water and heat transport through soils is vital for managing soil and groundwater resources, agricultural irrigation, and ecosystem protection. This paper aims to explore the potential application of deep learning methods in simulating water and heat transport processes within soils. It also [...] Read more.
Understanding water and heat transport through soils is vital for managing soil and groundwater resources, agricultural irrigation, and ecosystem protection. This paper aims to explore the potential application of deep learning methods in simulating water and heat transport processes within soils. It also examines the interactions between soil hydrological processes and environmental factors, including meteorological conditions and groundwater levels. To achieve these, we develop a hybrid model Informer–LSTM by combining two powerful architectures: Informer, a Transformer-based model essentially designed for long-sequence time-series forecasting, and Long Short-Term Memory (LSTM), a neural network that is great at learning short-term patterns in sequential data. The model is applied to field measurements from Henan Township in Ordos, Inner Mongolia, China, for training and testing, to simulate three key variables: soil water content, temperature, and heat flux at different depths in two soil columns with different groundwater levels. Our results confirm that Informer–LSTM is highly effective at simulating the soil water and heat transport. Simultaneously, we evaluate its performance by incorporating various combinations of input data including meteorological data, soil hydrothermal dynamics, and groundwater level. This reveals the relationship between soil hydrothermal processes and meteorological data, as well as coupled processes of soil water and heat transport. Moreover, employing SHapley Additive exPlanations (SHAP) analysis, we identify the most influential factors for predicting heat flux in shallow soils. This research demonstrates that deep learning models are a viable and valuable tool for simulating soil hydrothermal processes in arid and semi-arid regions. Full article
(This article belongs to the Special Issue Agroclimatology and Crop Production: Adapting to Climate Change)
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21 pages, 6150 KB  
Article
A Hybrid Frequency Decomposition–CNN–Transformer Model for Predicting Dynamic Cryptocurrency Correlations
by Ji-Won Kang, Daihyun Kwon and Sun-Yong Choi
Electronics 2025, 14(21), 4136; https://doi.org/10.3390/electronics14214136 - 22 Oct 2025
Viewed by 375
Abstract
This study proposes a hybrid model that integrates Wavelet frequency decomposition, convolutional neural networks (CNNs), and Transformers to predict correlation structures among eight major cryptocurrencies. The Wavelet module decomposes asset time series into short-, medium-, and long-term components, enabling multi-scale trend analysis. CNNs [...] Read more.
This study proposes a hybrid model that integrates Wavelet frequency decomposition, convolutional neural networks (CNNs), and Transformers to predict correlation structures among eight major cryptocurrencies. The Wavelet module decomposes asset time series into short-, medium-, and long-term components, enabling multi-scale trend analysis. CNNs capture localized correlation patterns across frequency bands, while the Transformer models long-term temporal dependencies and global relationships. Ablation studies with three baselines (Wavelet–CNN, Wavelet–Transformer, and CNN–Transformer) confirm that the proposed Wavelet–CNN–Transformer (WCT) consistently outperforms all alternatives across regression metrics (MSE, MAE, RMSE) and matrix similarity measures (Cosine Similarity and Frobenius Norm). The performance gap with the Wavelet–Transformer highlights CNN’s critical role in processing frequency-decomposed features, and WCT demonstrates stable accuracy even during periods of high market volatility. By improving correlation forecasts, the model enhances portfolio diversification and enables more effective risk-hedging strategies than volatility-based approaches. Moreover, it is capable of capturing the impact of major events such as policy announcements, geopolitical conflicts, and corporate earnings releases on market networks. This capability provides a powerful framework for monitoring structural transformations that are often overlooked by traditional price prediction models. Full article
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20 pages, 3517 KB  
Article
On the Use of Machine Learning Methods for EV Battery Pack Data Forecast Applied to Reconstructed Dynamic Profiles
by Joaquín de la Vega, Jordi-Roger Riba and Juan Antonio Ortega-Redondo
Appl. Sci. 2025, 15(20), 11291; https://doi.org/10.3390/app152011291 - 21 Oct 2025
Viewed by 259
Abstract
Lithium-ion batteries are essential to electric vehicles, so it is crucial to continuously monitor and control their health. However, since today’s battery packs consist of hundreds or thousands of cells, monitoring all of them is challenging. Additionally, the performance of the entire battery [...] Read more.
Lithium-ion batteries are essential to electric vehicles, so it is crucial to continuously monitor and control their health. However, since today’s battery packs consist of hundreds or thousands of cells, monitoring all of them is challenging. Additionally, the performance of the entire battery pack is often limited by the weakest cell. Therefore, developing effective monitoring techniques that can reliably forecast the remaining time to depletion (RTD) of lithium-ion battery cells is essential for safe and efficient battery management. However, even in robust systems, this data can be lost due to electromagnetic interference, microcontroller malfunction, failed contacts, and other issues. Gaps in voltage measurements compromise the accuracy of data-driven forecasts. This work systematically evaluates how different voltage reconstruction methods affect the performance of recurrent neural network (RNN) forecast models trained to predict RTD through quantile regression. The paper uses experimental battery pack data based on the behavior of an electric vehicle under dynamic driving conditions. Artificial gaps of 500 s were introduced at the beginning, middle, and end of each discharge phase, resulting in over 4300 reconstruction cases. Four reconstruction methods were considered: a zero-order hold (ZOH), an autoregressive integrated moving average (ARIMA) model, a gated recurrent unit (GRU) model, and a hybrid unscented Kalman filter (UKF) model. The results presented here reveal that the UKF model, followed by the GRU model, outperform alternative reconstruction methods. These models minimize signal degradation and provide forecasts similar to the original past data signal, thus achieving the highest coefficient of determination and the lowest error indicators. The reconstructed signals were fed into LSTM and GRU RNNs to estimate RTD, which produced confidence intervals and median values for decision-making purposes. Full article
(This article belongs to the Special Issue AI-Based Machinery Health Monitoring)
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17 pages, 680 KB  
Article
Stochastic SO(3) Lie Method for Correlation Flow
by Yasemen Ucan and Melike Bildirici
Symmetry 2025, 17(10), 1778; https://doi.org/10.3390/sym17101778 - 21 Oct 2025
Viewed by 234
Abstract
It is very important to create mathematical models for real world problems and to propose new solution methods. Today, symmetry groups and algebras are very popular in mathematical physics as well as in many fields from engineering to economics to solve mathematical models. [...] Read more.
It is very important to create mathematical models for real world problems and to propose new solution methods. Today, symmetry groups and algebras are very popular in mathematical physics as well as in many fields from engineering to economics to solve mathematical models. This paper introduces a novel methodological framework based on the SO(3) Lie method to estimate time-dependent correlation matrices (correlation flows) among three variables that have chaotic, entropy, and fractal characteristics, from 11 April 2011 to 31 December 2024 for daily data; from 10 April 2011 to 29 December 2024 for weekly data; and from April 2011 to December 2024 for monthly data. So, it develops the stochastic SO(2) Lie method into the SO(3) Lie method that aims to obtain the correlation flow for three variables with chaotic, entropy, and fractal structure. The results were obtained at three stages. Firstly, we applied entropy (Shannon, Rényi, Tsallis, Higuchi) measures, Kolmogorov–Sinai complexity, Hurst exponents, rescaled range tests, and Lyapunov exponent methods. The results of the Lyapunov exponents (Wolf, Rosenstein’s Method, Kantz’s Method) and entropy methods, and KSC found evidence of chaos, entropy, and complexity. Secondly, the stochastic differential equations which depend on S2 (SO(3) Lie group) and Lie algebra to obtain the correlation flows are explained. The resulting equation was numerically solved. The correlation flows were obtained by using the defined covariance flow transformation. Finally, we ran the robustness check. Accordingly, our robustness check results showed the SO(3) Lie method produced more effective results than the standard and Spearman correlation and covariance matrix. And, this method found lower RMSE and MAPE values, greater stability, and better forecast accuracy. For daily data, the Lie method found RMSE = 0.63, MAE = 0.43, and MAPE = 5.04, RMSE = 0.78, MAE = 0.56, and MAPE = 70.28 for weekly data, and RMSE = 0.081, MAE = 0.06, and MAPE = 7.39 for monthly data. These findings indicate that the SO(3) framework provides greater robustness, lower errors, and improved forecasting performance, as well as higher sensitivity to nonlinear transitions compared to standard correlation measures. By embedding time-dependent correlation matrix into a Lie group framework inspired by physics, this paper highlights the deep structural parallels between financial markets and complex physical systems. Full article
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27 pages, 3255 KB  
Article
Hourly Photovoltaic Power Forecasting Using Exponential Smoothing: A Comparative Study Based on Operational Data
by Dmytro Matushkin, Artur Zaporozhets, Vitalii Babak, Mykhailo Kulyk and Viktor Denysov
Solar 2025, 5(4), 48; https://doi.org/10.3390/solar5040048 - 20 Oct 2025
Viewed by 251
Abstract
The accurate forecasting of solar power generation is becoming increasingly important in the context of renewable energy integration and intelligent energy management. The variability of solar radiation, caused by changing meteorological conditions and diurnal cycles, complicates the planning and control of photovoltaic systems [...] Read more.
The accurate forecasting of solar power generation is becoming increasingly important in the context of renewable energy integration and intelligent energy management. The variability of solar radiation, caused by changing meteorological conditions and diurnal cycles, complicates the planning and control of photovoltaic systems and may lead to imbalances in supply and demand. This study aims to identify the most effective exponential smoothing approach for real-world PV power forecasting using actual hourly generation data from a 9 MW solar power plant in the Kyiv region, Ukraine. Four exponential smoothing techniques are analysed: Classic, a Modified classic adapted to daily generation patterns, Holt’s linear trend method, and the Holt–Winters seasonal method. The models were implemented in Microsoft Excel (Microsoft 365, version 2408) using real measurement data collected over six months. Forecasts were generated one hour ahead, and optimal smoothing constants were identified via RMSE minimisation using the Solver Add-in. Substantial differences in forecasting accuracy were observed. The Classic simple exponential smoothing model performed worst, with an RMSE of 1413.58 kW and nMAE of 9.22%. Holt’s method improved trend responsiveness (RMSE = 1052.79 kW, nMAE = 5.96%), but still lacked seasonality modelling. Holt–Winters, which incorporates both trend and seasonality, achieved a strong balance (RMSE = 1031.00 kW, nMAE = 3.7%). The best performance was observed with the modified simple exponential smoothing method, which captured the daily cycle more effectively (RMSE = 166.45 kW, nMAE = 0.84%). These results pertain to a one-step-ahead evaluation on a single plant and an extended validation window; accuracy is dependent on meteorological conditions, with larger errors during rapid cloud transi. The study identifies forecasting models that combine high accuracy with structural simplicity, intuitive implementation, and minimal parameter tuning—features that make them well-suited for integration into lightweight real-time energy control systems, despite not being evaluated in terms of runtime or memory usage. The modified simple exponential smoothing model, in particular, offers a high degree of precision and interpretability, supporting its integration into operational PV forecasting tools. Full article
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16 pages, 9307 KB  
Article
Projected Heat-Stress in Sheep and Cattle in Greece Under Future Climate Change Scenarios
by Dimitris K. Papanastasiou, Athanasios I. Gelasakis, Giorgos Papadopoulos, Dimitrios Melas, Kostas Douvis, Ioannis Faraslis, Stavros Keppas, Ioannis Stergiou, Anastasia Poupkou, Dimitris Voloudakis, Athena Progiou, John Kapsomenakis and Nikolaos Katsoulas
Agriculture 2025, 15(20), 2141; https://doi.org/10.3390/agriculture15202141 - 15 Oct 2025
Viewed by 333
Abstract
It is well established that exposure to heat-stress conditions significantly impacts the physiology, health, welfare, and productivity of both sheep and cattle. The aim of this study was to apply the Temperature Humidity Index (THI) in order to assess the impact of future [...] Read more.
It is well established that exposure to heat-stress conditions significantly impacts the physiology, health, welfare, and productivity of both sheep and cattle. The aim of this study was to apply the Temperature Humidity Index (THI) in order to assess the impact of future climate conditions on the thermal stress exposure of sheep and cattle in Greece. The Weather Research and Forecasting (WRF) model was used as a high-resolution regional climate model to simulate climate conditions for two decades in Greece at a 10 Km spatial resolution and a 1 h temporal resolution. The WRF model was applied to two emission scenarios, namely SSP2-4.5 (intermediate) and SSP5-8.5 (worst-case). Projections were made for the near-future decade (2046–2055), with the decade (2005–2014) serving as the reference period for comparative analysis. The data analysis indicated that under the SSP2-4.5 emission scenario, the mean temperature is projected to increase by 1.2–1.4 °C and 1.4–1.6 °C across 38% and 58% of the country’s territory, respectively. Increases higher than 1.6 °C are projected across 32% of the Greek territory under the SSP5-8.5 emission scenario. The mean THI (sheep) and mean THI (adj) (cattle) are projected to increase by 5–10% and by 4% across 74% and 82% of the Greek territory, respectively, when considering the SSP2-4.5 emission scenario. Slightly more severe mean heat-stress conditions were projected when considering the SSP5-8.5 emission scenario. The analysis of the hourly THI values showed that sheep and cattle are expected to experience heat-stress conditions during extended periods in the future, in which hot weather will prevail. Specifically, the number of severe/danger heat-stress hours is projected to double in the greater part of the country. To mitigate the adverse effects of climate-change-induced thermal stress on animal productivity, health, and welfare, the implementation of adaptation measures and best management practices is strongly recommended for sheep and cattle farmers. These measures encompass improvements in breeding strategies, livestock housing and microclimate management, nutritional interventions, and the adoption of precision livestock farming technologies. Given the outstanding economic, social, and environmental importance of sheep and cattle farming in Greece, effective adaptation to and mitigation of climate change impacts represent urgent priorities to ensure the long-term sustainability and resilience of the livestock sector. Full article
(This article belongs to the Special Issue The Threats Posed by Environmental Factors to Farm Animals)
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