Search Results (131)

Accurate and high-resolution spatio-temporal prediction of PM_2.5 concentrations remains a significant challenge for air pollution early warning and prevention. Advanced artificial intelligence (AI) technologies, however, offer promising solutions to this problem. A spatio-temporal prediction model is designed in this study, which is built upon a seq2seq architecture. This model employs an improved graph convolutional neural network to capture spatially dependent features, integrates time-series information through a gated recurrent unit, and incorporates an attention mechanism to achieve PM_2.5 concentration prediction. Benefiting from high-resolution satellite remote sensing data, the regional, multi-step and high-resolution prediction of PM_2.5 concentration in Beijing has been performed. To validate the model’s performance, ablation experiments are conducted, and the model is compared with other advanced prediction models. The experimental results show our proposed Spatio-Temporal Graph Convolutional Network with Attention Mechanism (STGCA) outperforms comparison models in multi-step forecasting, achieving root mean squared error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) of 4.21, 3.11 and 11.41% for the first step, respectively. For subsequent steps, the model also shows significant improvements. For subsequent steps, the model also shows significant improvements, with RMSE, MAE and MAPE values of 5.08, 3.69 and 13.34% for the second step and 6.54, 4.61 and 16.62% for the third step, respectively. Additionally, STGCA achieves the index of agreement (IA) values of 0.98, 0.97 and 0.95, as well as Theil’s inequality coefficient (TIC) values of 0.06, 0.08 and 0.10 proving its superiority. These results demonstrate that the proposed model offers an efficient technical approach for smart air pollution forecasting and warning in the future. Full article

Time-series forecasting is widely recognized as essential for integrating renewable energy, managing emissions, and optimizing demand across energy and environmental applications. Initially, traditional forecasting methods are hindered by limitations including poor interpretability, limited generalization to diverse scenarios, and substantial computational demands. Consequently, a novel minimum-variance self-tuning (MVST) method is proposed, grounded in adaptive control theory, to overcome these challenges. The method utilizes recursive least squares with self-tuning parameter updates, delivering high prediction accuracy, rapid computation, and robust multi-step forecasting without pre-training requirements. Testing is performed on CO₂ emissions (annual), transformer load (15 min), and building electric load (hourly) datasets, comparing MVST against LSTM, ARDL, fixed-PID, XGBoost, and Prophet across varied scales and contexts. Significant improvements are observed, with prediction errors reduced by 3–8 times and computational time decreased by up to 2000 times compared to these methods. Finally, these advancements facilitate real-time power system dispatch, enhance energy planning, and support carbon emission management, demonstrating substantial research and practical value. Full article

During the steam reforming of methane (SRM) process, elevated CH₄ levels after the reaction often signify inadequate heat supply or incomplete reactions within the reformer, jeopardizing process stability. In this paper, a novel multi-step forecasting method using a Trans-GRU network was proposed for predicting the methane content outlet of the SRM reformer. First, a novel feature selection based on the maximal information coefficient (MIC) was applied to identify critical input variables and determine their optimal input order. Additionally, the Trans-GRU network enables the simultaneous capture of multivariate correlations and the learning of global sequence representations. The experimental results based on time-series data from a real SRM process demonstrate that the proposed approach significantly improves the accuracy of multi-step methane content prediction. Compared to benchmark models, including the TCN, Transformer, GRU, and CNN-LSTM, the Trans-GRU consistently achieves the lowest root mean squared error (RMSE) and mean absolute error (MAE) values across all prediction steps (1–6). Specifically, at the one-step horizon, it yields an RMSE of 0.0120 and an MAE of 0.0094. This high performance remains robust across the 2–6-step predictions. The improved predictive capability supports the stable operation and predictive optimization strategies of the steam reforming process in hydrogen production. Full article

The spread of COVID-19 is influenced by multiple factors, including control policies, virus characteristics, individual behaviors, and environmental conditions, exhibiting highly complex nonlinear dynamic features. The time series of new confirmed cases shows significant nonlinearity and non-stationarity. Traditional prediction methods that rely solely on one-dimensional case data struggle to capture the multi-dimensional features of the data and are limited in handling nonlinear and non-stationary characteristics. Their prediction accuracy and generalization capabilities remain insufficient, and most existing studies focus on single-step forecasting, with limited attention to multi-step prediction. To address these challenges, this paper proposes a multi-module fusion prediction model—TSMixer-BiKSA network—that integrates multi-feature inputs, Variational Mode Decomposition (VMD), and a dual-branch parallel architecture for 1- to 3-day-ahead multi-step forecasting of new COVID-19 cases. First, variables highly correlated with the target sequence are selected through correlation analysis to construct a feature matrix, which serves as one input branch. Simultaneously, the case sequence is decomposed using VMD to extract low-complexity, highly regular multi-scale modal components as the other input branch, enhancing the model’s ability to perceive and represent multi-source information. The two input branches are then processed in parallel by the TSMixer-BiKSA network model. Specifically, the TSMixer module employs a multilayer perceptron (MLP) structure to alternately model along the temporal and feature dimensions, capturing cross-time and cross-variable dependencies. The BiGRU module extracts bidirectional dynamic features of the sequence, improving long-term dependency modeling. The KAN module introduces hierarchical nonlinear transformations to enhance high-order feature interactions. Finally, the SA attention mechanism enables the adaptive weighted fusion of multi-source information, reinforcing inter-module synergy and enhancing the overall feature extraction and representation capability. Experimental results based on COVID-19 case data from Italy and the United States demonstrate that the proposed model significantly outperforms existing mainstream methods across various error metrics, achieving higher prediction accuracy and robustness. Full article

This study presents a deep learning-based approach for forecasting Sentinel-1 displacement time series, with particular attention to irregular temporal patterns—an aspect often overlooked in previous works. Displacement data were generated using the Parallel Small BAseline Subset (P-SBAS) technique via the Geohazard Thematic Exploitation Platform (G-TEP). Initial experiments on a regular dataset from Lombardy employed Long Short-Term Memory (LSTM) models to forecast multiple future time steps. Empirical analysis determined that optimal forecasting is achieved with a 50-time-step input sequence, and that predicting 10% of the input sequence length strikes a balance between temporal coverage and accuracy. The investigation then extended to irregular datasets from Lisbon and Washington, comparing two preprocessing strategies: imputation and the inclusion of time intervals as a second feature. While imputation improved one-step predictions, it was inadequate for multi-step forecasting. To address this, a Time-Gated LSTM (TG-LSTM) was implemented. TG-LSTM outperformed standard LSTM for irregular data in one-step prediction but faced limitations in handling heteroscedasticity and computational cost during multi-step forecasting. These issues were effectively resolved using Temporal Fusion Transformers (TFT), which achieved the best performance, with RMSE values of 1.71 mm/year (Lisbon) and 1.26 mm/year (Washington). A key contribution of this work is the development of a GIS-integrated forecasting toolbox that incorporates LSTM models for regular sequences and TG-LSTM/TFT models for irregular ones. The toolbox enables both single- and multi-step displacement predictions, offering a scalable solution for geohazard monitoring and early warning applications. Full article

Sustainable copper extraction presents significant challenges due to waste generation and environmental impacts, requiring advanced predictive methodologies to optimize production processes. This study addresses a gap in applying deep learning to forecast hydrometallurgical copper production by comparing six recurrent neural network architectures: Vanilla LSTM, Stacked LSTM, Bidirectional LSTM, GRU, CNN-LSTM, and Attention LSTM. Using time-series data from a full-scale industrial operation, we implemented a data augmentation approach to overcome data scarcity limitations. The models were evaluated through rigorous metrics and multi-step forecasting tests. The results demonstrated remarkable performance from five architectures, with Bidirectional LSTM and Attention LSTM achieving the highest accuracy (RMSE < 0.004, R² > 0.999, MAPE < 1%). These models successfully captured and reproduced complex cyclical patterns in copper mass production for up to 500 time steps ahead. The findings validate our data augmentation strategy for enabling models to learn complex known cyclical patterns from limited initial data and establish a promising foundation for implementing AI-driven predictive systems that can enhance process control, reduce waste, and advance sustainability in hydrometallurgical operations. However, these performance metrics reflect the models’ ability to reproduce patterns inherent in the augmented dataset derived from a single operational cycle; validation on entirely independent operational data is crucial for assessing true generalization and is a critical next step. Full article

There is a lack of a systematic comparison framework that can assess models in both single-step and multi-step forecasting situations while balancing accuracy, training efficiency, and prediction horizon. This study aims to evaluate the predictive capabilities of machine learning and deep learning models in water quality time series forecasting. It made use of 22-month data with a 4 h interval from two monitoring stations located in a tributary of the Pearl River. Six models, specifically Support Vector Regression (SVR), XGBoost, K-Nearest Neighbors (KNN), Recurrent Neural Network (RNN), Long Short-Term Memory (LSTM) Network, Gated Recurrent Unit (GRU), and PatchTST, were employed in this study. In single-step forecasting, LSTM Network achieved superior accuracy for a univariate feature set and attained an overall 22.0% (Welch’s t-test, p = 3.03 × 10⁻⁷) reduction in Mean Squared Error (MSE) compared with the machine learning models (SVR, XGBoost, KNN), while RNN demonstrated significantly reduced training time. For a multivariate feature set, the deep learning models exhibited comparable accuracy but with no model achieving a significant increase in accuracy compared to the univariate scenario. The KNN model underperformed across error evaluation metrics, with the lowest accuracy, and the XGBoost model exhibited the highest computational complexity. In multi-step forecasting, the direct multi-step PatchTST model outperformed the iterated multi-step models (RNN, LSTM, GRU), with a reduced time-delay effect and a slower decrease in accuracy with increasing prediction length, but it still required specific adjustments to be better suited for the task of river water quality time series forecasting. The findings provide actionable guidelines for model selection, balancing predictive accuracy, training efficiency, and forecasting horizon requirements in environmental time series analysis. Full article

As a core strategy for carbon emission reduction, carbon trading plays a critical role in policy guidance and market stability. Accurate forecasting of carbon prices is essential, yet remains challenging due to the nonlinear, non-stationary, noisy, and uncertain nature of carbon price time series. To address this, this paper proposes a novel hybrid deep learning framework that integrates dual-mode decomposition and a TKMixer-BiGRU-SA model for carbon price prediction. First, external variables with high correlation to carbon prices are identified through correlation analysis and incorporated as inputs. Then, the carbon price series is decomposed using Variational Mode Decomposition (VMD) and Empirical Wavelet Transform (EWT) to extract multi-scale features embedded in the original data. The core prediction model, TKMixer-BiGRU-SA Net, comprises three integrated branches: the first processes the raw carbon price and highly relevant external time series, and the second and third process multi-scale components obtained from VMD and EWT, respectively. The proposed model embeds Kolmogorov–Arnold Networks (KANs) into the Time-Series Mixer (TSMixer) module, replacing the conventional time-mapping layer to form the TKMixer module. Each branch alternately applies the TKMixer along the temporal and feature-channel dimensions to capture dependencies across time steps and variables. Hierarchical nonlinear transformations enhance higher-order feature interactions and improve nonlinear modeling capability. Additionally, the BiGRU component captures bidirectional long-term dependencies, while the Self-Attention (SA) mechanism adaptively weights critical features for integrated prediction. This architecture is designed to uncover global fluctuation patterns in carbon prices, multi-scale component behaviors, and external factor correlations, thereby enabling autonomous learning and the prediction of complex non-stationary and nonlinear price dynamics. Empirical evaluations using data from the EU Emission Allowance (EUA) and Hubei Emission Allowance (HBEA) demonstrate the model’s high accuracy in both single-step and multi-step forecasting tasks. For example, the e_MAPE of EUA predictions for 1–4 step forecasts are 0.2081%, 0.5660%, 0.8293%, and 1.1063%, respectively—outperforming benchmark models and confirming the proposed method’s effectiveness and robustness. This study provides a novel approach to carbon price forecasting with practical implications for market regulation and decision-making. Full article

With the growing demand for global energy transition, integrated energy systems (IESs) have emerged as a key pathway for sustainable development due to their deep coupling of multi-energy flows. Accurate load forecasting is crucial for IES optimization and scheduling, yet conventional methods struggle with complex spatio-temporal correlations and long-term dependencies. This study proposes ST-ScaleFusion, a multi-scale time–frequency complementary hybrid model to enhance comprehensive energy load forecasting accuracy. The model features three core modules: a multi-scale decomposition hybrid module for fine-grained extraction of multi-time-scale features via hierarchical down-sampling and seasonal-trend decoupling; a frequency domain interpolation forecasting (FI) module using complex linear projection for amplitude-phase joint modeling to capture long-term patterns and suppress noise; and an FI sub-module extending series length via frequency domain interpolation to adapt to non-stationary loads. Experiments on 2021–2023 multi-energy load and meteorological data from the Arizona State University Tempe campus show that ST-ScaleFusion achieves 24 h forecasting MAE values of 667.67 kW for electric load, 1073.93 kW/h for cooling load, and 85.73 kW for heating load, outperforming models like TimesNet and TSMixer. Robust in long-step (96 h) forecasting, it reduces MAE by 30% compared to conventional methods, offering an efficient tool for real-time IES scheduling and risk decision-making. Full article

In this paper, a size-biased Lindley (SBL) first-order autoregressive (AR(1)) process is proposed, the so-called SBL-AR(1). Some probabilistic and statistical properties of the proposed process are determined, including the distribution of its innovation process, the Laplace transformation function, multi-step-ahead conditional measures, autocorrelation, and spectral density function. In addition, the unknown parameters of the model are estimated via the conditional least squares and Gaussian estimation methods. The performance and behavior of the estimators are checked through some numerical results by a Monte Carlo simulation study. Additionally, two real-world datasets are utilized to examine the model’s applicability, and goodness-of-fit statistics are used to compare it to several pertinent non-Gaussian AR(1) models. The findings reveal that the proposed SBL-AR(1) model exhibits key theoretical properties, including a closed-form innovation distribution, multi-step conditional measures, and an exponentially decaying autocorrelation structure. Parameter estimation via conditional least squares and Gaussian methods demonstrates consistency and efficiency in simulations. Real-world applications to inflation expectations and water quality data reveal a superior fit over competing non-Gaussian AR(1) models, evidenced by lower values of the AIC and BIC statistics. Forecasting comparisons show that the classical conditional expectation method achieves accuracy comparable to some modern machine learning techniques, underscoring its practical utility for skewed and fat-tailed time series. Full article

Forecasting macroeconomic variables is essential to macroeconomics, financial economics, and monetary policy analysis. Due to the high dimensionality of the macroeconomic dataset, it is challenging to forecast efficiently and accurately. Thus, this study provides a comprehensive analysis of predicting macroeconomic variables by comparing various vector autoregressive models followed by different estimation techniques. To address this, this paper proposes a novel hybrid model based on a smoothly clipped absolute deviation estimation method and a vector autoregression model that combats the curse of dimensionality and simultaneously produces reliable forecasts. The proposed hybrid model is applied to the U.S. quarterly macroeconomic data from the first quarter of 1959 to the fourth quarter of 2023, yielding multi-step-ahead forecasts (one-, three-, and six-step ahead). The multi-step-ahead out-of-sample forecast results (root mean square error and mean absolute error) for the considered data suggest that the proposed hybrid model yields a highly accurate and efficient gain. Additionally, it is demonstrated that the proposed models outperform the baseline models. Finally, the authors believe the proposed hybrid model may be expanded to other countries to assess its efficacy and accuracy. Full article

Accurate energy consumption forecasting is essential for efficient power grid management, yet existing deep learning models struggle with the multi-scale nature of energy consumption patterns. Contemporary approaches like LSTM and GRU networks process raw time series directly, failing to distinguish between distinct frequency components that represent different physical phenomena in household energy usage. This study presents a novel methodological method that systematically decomposes energy consumption signals into low-frequency components representing gradual trends and daily routines and high-frequency components capturing transient events, such as appliance switching, before applying predictive modeling. Our approach employs computationally efficient convolution-based filters—uniform and binomial—with varying window sizes to separate these components for specialized processing. Experiments on two real-world datasets at different temporal resolutions (1 min and 15 min) demonstrate significant improvements over state-of-the-art methods. For the Smart House dataset, our optimal configuration achieved an R² of 0.997 and RMSE of 0.034, substantially outperforming previous models with R² values of 0.863. Similarly, for the Mexican Household dataset, our approach yielded an R² of 0.994 and RMSE of 13.278, compared to previous RMSE values exceeding 82.488. These findings establish frequency decomposition as a crucial preprocessing step for energy forecasting as it significantly improve the prediction in smart grid applications. Full article

Accurate prediction of Global Navigation Satellite System-derived precipitable water vapor (GNSS-PWV), which is a crucial indicator for climate change monitoring, holds significant scientific value for climate disaster prevention and mitigation. In the study of GNSS-PWV prediction, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm within a decomposition–integration framework effectively addresses the non-stationarity and complexity of PWV sequences, enhancing prediction accuracy. However, residual noise and pseudo-modes from decomposition can distort signals, reducing the predictor system’s reliability. Additionally, independent modeling of all decomposed components decreases computational efficiency. To address these challenges, this paper proposes a hybrid model combining the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), autoregressive integrated moving average (ARIMA), and long short-term memory (LSTM) networks. Enhanced by local mean optimization and adaptive noise regulation, the ICEEMDAN algorithm effectively suppresses pseudo-modes and minimizes residual noise, enabling its decomposed intrinsic mode functions (IMFs) to more accurately capture the multi-scale features of GNSS-PWV. Sample entropy (SE) is used to quantify the complexity of IMFs, and components with similar entropy values are reconstructed into the following three sub-sequences: high-frequency, low-frequency, and trend. This process significantly reduces modeling complexity and improves computational efficiency. We propose different modeling strategies tailored to the dynamics of various subsequences. For the nonlinear and non-stationary high-frequency components, the LSTM network is used to effectively capture their complex patterns. The LSTM’s gating mechanism and memory cell design proficiently address the long-term dependency issue. For the stationary and weakly nonlinear low-frequency and trend components, linear patterns are extracted using ARIMA. Differencing eliminates trends and moving average operations capture random fluctuations, effectively addressing periodicity and trends in the time series. Finally, the prediction results of the three components are linearly combined to obtain the final prediction value. To validate the model performance, experiments were conducted using measured GNSS-PWV data from several stations in Hong Kong. The results demonstrate that the proposed model reduces the root mean square error by 56.81%, 37.91%, and 13.58% at the 1 h scale compared to the LSTM, EMD-LSTM, and ICEEMDAN-SE-LSTM benchmark models, respectively. Furthermore, it exhibits strong robustness in cross-month forecasts (accounting for seasonal influences) and multi-step predictions over the 1–6 h period. By improving the accuracy and efficiency of PWV predictions, this model provides reliable technical support for the real-time monitoring and early warning of extreme weather events in Hong Kong while offering a universal methodological reference for multi-scale modeling of geophysical parameters. Full article

Time-series forecasting is a cornerstone of decision making in domains such as finance, energy management, and meteorology, where precise predictions drive both economic and operational efficiency. However, traditional time-domain methods often struggle to capture the intricate symmetries and hierarchical dependencies inherent in complex multivariate time-series data. These methods frequently fail to distinguish between global trends and localized fluctuations, limiting their ability to model the multifaceted temporal dynamics that arise across different time scales. To address these challenges, we propose a novel dual-component framework that explicitly leverages the symmetry between long-term trends and short-term fluctuations. Inspired by the principles of signal decomposition, we partition time-series data into a low-frequency stabilization component and a high-frequency fluctuation component. The stabilization component captures inter-variable relationships and global frequency-domain component dependencies through Fourier-transformed frequency-domain representations, variable-oriented attention mechanisms, and dilated causal convolutions. Meanwhile, the fluctuation component models localized dynamics using a multi-granularity structure and time-step attention mechanisms to enhance the sensitivity and robustness to transient variations. By integrating these complementary perspectives, our approach provides a more holistic representation of time-series dynamics. Comprehensive experiments on benchmark datasets from electricity, transportation, and weather domains demonstrate that our method consistently outperforms state-of-the-art models, achieving superior accuracy. Beyond predictive performance, our framework offers a deeper interpretability of temporal behaviors, highlighting its potential for practical applications in complex systems. This work underscores the importance of symmetry-aware modeling in advancing time-series forecasting methodologies. Full article

Maintaining stable prices is one of the goals of monetary policy makers. Since its formation, inflation has been a key issue and priority for every Pakistani government; it is a fundamental macroeconomic variable that plays a significant role in a nation’s economic progress and development. This research investigates the predictive capabilities of different univariate and multivariate models. The study considers autoregressive models, autoregressive neural networks, autoregressive moving average models, and other nonparametric autoregressive models within the univariate category. In contrast, the multivariate models include factor models that utilize Minimax Concave Penalty, Elastic-Smoothly Clipped Absolute Deviation, Principal Component Analysis, and Partial Least Squares. We conducted an empirical analysis using a well-established macroeconomic dataset from Pakistan. This dataset covers the period from January 2013 to December 2020 and consists of 79 variables recorded at that frequency. To evaluate the forecasting accuracy of the models for multiple steps ahead in the post-sample period, an analysis was performed using data extracted from January 2013 to February 2019 for model estimation and then another set from March 2019 to December 2020. The predictability of the univariate models following the sample period is compared with that of the multivariate models using statistical accuracy measurements, specifically root mean square error and mean absolute error. Additionally, the Diebold–Mariano test has been employed to evaluate the accuracy of the average errors statistically. The results indicated that the factor approach based on Partial Least Squares delivers significantly more effective outcomes than its competing methods. Full article