Search Results (3,820)

Neural ordinary differential equations (Neural ODEs) describe the feature evolution of deep networks by continuous-time dynamical systems and enable end-to-end learning through differentiable numerical solvers. Nevertheless, in closed-loop rolling prediction for small-sample time series, conventional Neural ODEs remain vulnerable to error accumulation and numerical instability. To improve the controllability of long-term evolution, this study proposes a neural ordinary differential equation framework based on fractional-order operators. Rather than directly introducing full-history convolution kernels into the governing dynamics, the proposed approach constructs a fractional effective step size from the closed-form expression of the Riemann–Liouville fractional integral of a constant function and consistently embeds it into all sub-steps of a fourth-order Runge–Kutta solver. In this way, the scale of continuous-depth propagation is regulated by a single tunable parameter. Combined with a residual output structure, the method preserves the interpretability of continuous dynamics while effectively suppressing trajectory drift in closed-loop prediction and improving training stability. To investigate the impact of the fractional-order parameter on fitting and extrapolation, particle swarm optimization is employed to search automatically for the optimal order. Experimental evaluations on the linear spiral system and Lorenz continuous dynamical systems and on a small-sample provincial annual electricity-consumption dataset show that the proposed model achieves lower prediction errors across multiple tasks and exhibits superior trajectory preservation and robustness under long-horizon forecasting. Full article

This study addresses the critical need for accurate sea wind speed predictions to support ocean wind farm operations, equipment maintenance, and maritime navigation safety. To enhance prediction accuracy for any location within target sea areas, we propose a short-to-medium-term wind speed prediction method that effectively explores spatiotemporal correlations in ocean reanalysis grid data. The method involves collecting and reanalyzing data, as well as spatial processing, to reconstruct the historical wind speed sequence at the target point. Finally, a future wind speed time series is generated using an LSTM network and a Transformer encoder. Test results validated against NOAA buoy data demonstrate the effectiveness of our spatiotemporal prediction model, achieving RMSE values of 1.161 m/s, 1.500 m/s, and 1.854 m/s for 1 h, 6 h, and 12 h predictions, respectively, outperforming comparative methods. The conclusions are threefold: (1) The proposed hybrid model effectively captures spatiotemporal dependencies and achieves more accurate spatiotemporal predictions compared to the benchmark model; (2) taking into account seasonal factors and forecasting time periods, the method proposed in this paper maintains good stability; (3) this framework provides a reliable technical approach for generating operational references in maritime navigation and wind power maintenance, with potential applications in wind farm siting and resource assessment. Full article

This research paper examines the spatial and time variation of demographic dependency in Europe in a 30-year horizon of the evolution of the demographic dividend regarding the economic dependency ratio (ADR1). We used the Curve Fit Forecast tool to estimate the trends of ADR1 in each of the EU Member States using data on Eurostat projections and a sophisticated geostatistical analysis tool developed in ArcGIS Pro 3.2.2. The findings indicate that the dependency in all countries has increased significantly in a statistically significant manner as the Gompertz function has appeared as the best curve in a third of the cases. It is an S-shaped asymptotic behaviour of this function that effectively describes the nonlinear patterns of acceleration and saturation of demographic ageing. As indicated in the analysis, the European regions are increasingly moving apart, with the southern and eastern nations such as Romania demonstrating the most alarming decline in ADR1. These trends highlight the need to reform labour market policies and social protection mechanisms to an ageing population. The paper combines the curve-fitting, descriptive statistics (median, skewness, interquartile range (IQR)) with time clustering (value, correlation, and Fourier) to provide an effective, replicable approach to early warning and policy prioritisation. Overall, the results highlight the importance of integrating predictive spatial modelling and demographic economics to support anticipatory and evidence-based policy decisions. The proposed approach proves to be a robust and transferable framework, applicable to a wide range of socio-economic phenomena characterised by inertia and structural change. Future research should extend the analysis to subnational levels, incorporate additional explanatory variables, and develop scenario-based simulations, including multivariate Gompertz-type models, to further enhance both predictive accuracy and policy relevance in the context of emerging structural labour scarcity. Full article

To address the degradation of zenith tropospheric delay (ZTD) prediction accuracy caused by time-varying noise and error accumulation in multi-step forecasting, this study proposes an integrated prediction model, named IBX, which combines improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), bidirectional long short-term memory (BiLSTM), and extreme gradient boosting (XGBoost). In the proposed framework, ICEEMDAN is first used to decompose the original ZTD series into components at different temporal scales. A three-criterion reconstruction strategy based on the Pearson correlation coefficient, dominant period, and sample entropy is then applied to obtain high-, medium-, and low-frequency subsequences with clearer physical meanings. BiLSTM and XGBoost are used to predict the reconstructed components, and their outputs are fused through a root mean square error (RMS)-based weighting strategy to improve forecasting robustness. Hourly ZTD data from 27 global navigation satellite system (GNSS) stations in China from 2011 to 2020 were used for model validation under 1–12 h rolling forecasting horizons. The results show that IBX achieves the best overall performance among the tested models. Its mean RMS and mean absolute error (MAE) over the 1–12 h horizons are 14.17 mm and 10.24 mm, respectively, which are 22.5% and 21.4% lower than those of the baseline BiLSTM model. Spatial and climate-region-based analyses further indicate that ZTD prediction accuracy is strongly affected by altitude, regional moisture conditions, and climate type. The proposed IBX model shows stable error suppression across heterogeneous station environments, especially in the temperate monsoon region and low-altitude regions with complex water vapor variability. These results demonstrate that IBX provides a reliable and physically interpretable approach for short- to medium-term ZTD forecasting and real-time atmospheric delay correction. Full article

Predicting long-term anaerobic digestion (AD) performance for food waste remains challenging because of substrate variability, process disturbance, and limited routine monitoring data. This study developed a practical framework that combines biomethane potential (BMP) test results with time-series analyses to estimate methane production during steady-state long-term AD operation. Ten paired batch and long-term datasets from three research groups were analysed. Among four BMP kinetic models, the Cone model gave the best fit in eight of 10 datasets. For long-term prediction, a 3-day sliding-window method and two Kalman filter approaches were compared. The one-dimensional Kalman filter achieved the best overall predictive accuracy, while the two-dimensional Kalman filter, which incorporated substrate conversion efficiency, provided clearer identification of persistent abnormal deviations associated with potential inhibition. The proposed framework offers a simple and localised decision support tool for methane forecasting, noise reduction, and early warning of instability when only BMP data and routine methane measurements are available. Full article

Short-term wind power forecasting is considered a critical challenge in smart grid management due to the nonlinear, unstable, and multi-scale noise characteristics of wind signals. Although recent advances in hybrid deep learning have improved the accuracy of short-term wind power forecasting, many state-of-the-art models usually consider signal denoising, residual decomposition, and attention mechanisms as independent modules without providing a unified solution. This paper proposes an end-to-end solution, W-HiTS-Attention (Wavelet Transform, N-stacked Hierarchical Interpolation for Time Series, Attention), which coherently integrates wavelet denoising, hierarchical residual learning from N-HiTS (Neural Hierarchical Interpolation), and an in-block self-attention mechanism. The proposed solution outperforms 21 benchmarks in accuracy, including state-of-the-art baselines such as N-BEATS, N-HiTS, TCN, Informer, Autoformer, LSTM, BiLSTM, GRU, and Prophet, achieving an RMSE of 55.56 W and an R² of 0.9918. Furthermore, the results show that the proposed solution is efficient in terms of parameter count (0.033M), latency (0.0036 ms/sample), and training time, making it promising for low-latency inference in resource-constrained environments. The results show that the coherent integration of frequency preprocessing, hierarchical residual forecasting, and attention-based temporal refinement provides a robust, explainable, and deployable solution for short-term wind power forecasting. Full article

Background/Objective: Emergency Departments (EDs) face persistent challenges with overcrowding, unpredictable patient arrivals, and difficulty forecasting short-term demand. Precise hourly arrival predictions are crucial for effective staffing, optimal resource management, and minimizing entry delays. Methods: This paper develops and evaluates a forecasting framework comparing six approaches (a Seasonal Naive baseline, Exponential Smoothing (ETS), Ridge Regression, LightGBM, a hybrid Temporal Convolutional Network (TCN), and a hybrid Long Short-Term Memory (LSTM) network) using de-identified hourly patient arrival records from an ED in Madinah, Saudi Arabia, covering January–November 2024. A set of 183 engineered features is constructed from cyclical time encodings, weekend and public-holiday indicators, structured autoregressive lags, and volatility measures, with all lag-based features verified to use strictly retrospective information. Models are optimized using Bayesian hyperparameter search and trained under an asymmetric loss function that penalizes underprediction to reflect operational risk. Results: Results on a 14-day hold-out test set show that Ridge Regression achieves the lowest MAE (3.75, R² = 0.52), with TCN and LSTM essentially tied (MAE 3.80 and 3.85). Diebold–Mariano tests confirm that Ridge, TCN, and LSTM are statistically indistinguishable from one another and that Ridge is marginally significantly better than LightGBM ($p=0.028$); all four ML models significantly outperform ETS and the Seasonal Naive baseline ($p<0.001$). On the asymmetric metric, TCN achieves the best AsymRMSE (5.59), reflecting its tendency to err on the safe side of staffing decisions. Robustness is confirmed through sensitivity analysis across penalty factors, feature ablation demonstrating the contribution of each feature group without overfitting, expanding-window cross-validation across three independent monthly test periods, and conformal prediction intervals achieving well-calibrated coverage. Conclusions: These results demonstrate that combining engineered temporal features with either a lightweight linear model or a hybrid sequence model yields accurate hourly ED arrival forecasts; whether the achieved accuracy is operationally sufficient for staffing decisions remains a site-specific question that requires clinical validation beyond the scope of this single-center study. Full article

A probabilistic data-driven framework for voltage quality forecasting in distribution transformers based on Gaussian process regression and high-resolution field measurements is presented. Voltage time series acquired under real operating conditions were modeled using composite covariance functions designed to capture long-term trends and stochastic multi-scale fluctuations. The proposed approach enables simultaneous prediction and uncertainty quantification, allowing direct compliance assessment with voltage quality standards. The additive Gaussian process models achieved coefficients of determination above 0.75 and produced statistically uncorrelated residuals, indicating an adequate representation of the intrinsic temporal structure. However, the predictive intervals exhibit a certain level of undercoverage, indicating that, while uncertainty is effectively quantified, there is still room for improvement in calibration. The selected kernel structures revealed distinct physical regimes in the voltage dynamics, including smooth steady operation, moderately irregular behavior associated with localized disturbances, and multi-scale stochastic variability. For benchmarking purposes, results were compared with those obtained from a stochastic damped harmonic oscillator with restoring force, a naive model, a seasonal naive model and an Autoregressive Integrated Moving Average model. The oscillator model, the naive model, the seasonal naive model, and the Autoregressive Integrated Moving Average model generated strongly autocorrelated residuals, whereas the Gaussian process models yielded consistent white-noise residuals that outperformed all the other models. These findings demonstrate that probabilistic Gaussian process modeling provides an interpretable, scalable, and uncertainty-aware alternative for predictive voltage quality assessment in modern distribution systems. Full article

Artificial intelligence development offers new solutions for enhancing corporate carbon performance and is crucial for promoting sustainable business practices. This study investigates the dynamic impact of artificial intelligence (AI) policy on corporate carbon performance using time series panel data of Chinese A-share listed companies from 2010 to 2024. Leveraging the staggered establishment of the National New Generation Artificial Intelligence Innovation Development Pilot Zones as a quasi-natural experiment, we develop a multi-period difference-in-differences framework with time-varying treatment. Our time series-based identification strategy addresses serial correlation and time-varying confounding factors through robust clustering and event study specifications. The findings reveal that AI policy significantly improves corporate carbon performance, a conclusion that remains robust after rigorous endogeneity tests, placebo checks, and counterfactual analyses. Using dynamic panel models, this study traces the temporal evolution of policy effects and demonstrates that AI exerts indirect effects through three time-lagged pathways: micro-level technological diffusion, future industry development, and the progressive accumulation of digital infrastructure and computing resources. Heterogeneity analysis reveals differentiated impacts across micro- and macro-levels, providing granular insights for forecasting heterogeneous treatment effects. By integrating panel time series econometrics with causal inference, this study contributes to the literature on corporate carbon performance while expanding analytical frameworks for understanding AI’s enabling effects. The findings offer policy insights and empirical benchmarks for forecasting green transition trajectories, with direct implications for green finance and sustainable economic development. Full article

Interferometric Synthetic Aperture Radar (InSAR) enables regional monitoring of ground deformation, but operational geohazard analysis remains challenged by atmospheric artefacts, temporal decorrelation, and the need for scalable interpretation of multi-temporal products. A systematic review was conducted through searches in Scopus and Web of Science, resulting in 135 peer-reviewed scientific articles on the integration of Machine Learning (ML) and Deep Learning (DL) with multi-temporal InSAR (MT-InSAR). The literature is dominated by applications to landslides and land subsidence, with additional studies addressing volcanic unrest and other deformation-related hazards. Persistent Scatterer (PS) and Small-Baseline Subset (SBAS) approaches are frequently used to derive deformation time series, which are then coupled with ML/DL for the detection and mapping of active phenomena and for short-horizon forecasting. Convolutional architectures, such as Convolutional Neural Networks (CNNs), are commonly reported for spatial recognition tasks, while recurrent models like Long Short-Term Memory (LSTM) networks are often applied to time-series prediction. Reported benefits include improved automation and predictive performance, although sensitivity to noise sources remains a challenge. Overall, the evidence supports AI-enabled InSAR workflows for scalable geohazard monitoring, while highlighting the need for standardized benchmarks and systematic transferability assessment. This review provides a roadmap for transitioning from research prototypes to operational early-warning systems. Full article

Stock trend forecasting remains challenging in real financial markets because data distributions evolve over time, and models trained under static settings often degrade during online deployment. Recent studies have introduced incremental and meta-incremental learning into stock forecasting, yet effective sequential adaptation remains constrained by two issues: financial multivariate time series require stronger representation modeling before downstream prediction, and repeated online updates may lead to forgetting and parameter drift. To address these issues, we propose ProAdapt, a bi-level meta-incremental learning framework for stock trend forecasting in non-stationary markets. ProAdapt contains two key components. The first is a Structural Spectral-Temporal Feature Adapter (SSTFA), which enhances financial time series representations by modeling non-uniform temporal importance and selective cross-factor interactions through adaptive soft window temporal encoding, frequency-domain structure modeling, and feature refinement. The second is online Elastic Weight Consolidation (EWC), which is incorporated into the outer-loop optimization to regularize sequential parameter updates and improve the balance between adaptation and stability. We evaluate ProAdapt on the CSI300 and CSI500 benchmarks under an incremental forecasting setting with sequential task updates. Experimental results across multiple backbones show that ProAdapt generally achieves favorable forecasting results relative to the compared baselines, with relatively clearer gains on CSI500. Additional ablation and analysis results further support the effectiveness of SSTFA and online EWC. Overall, the results suggest that combining explicit representation enhancement with stability-aware sequential updating is beneficial for incremental stock forecasting in evolving market environments. Full article

Accurate simulation of karst spring discharge is critical for sustainable water resource management, yet it remains a significant challenge due to the inherent complexity, heterogeneity, and non-linearity of karst systems. While machine learning models have been increasingly applied to this problem, standalone algorithms often struggle to simultaneously capture complex temporal dependencies and maintain robust generalization. This study provides a comprehensive comparative assessment of five state-of-the-art machine learning (ML) models for forecasting the daily discharge of the Jósva Spring, located in the World Heritage Aggtelek karst area. The main goal of the study is to determine which modern machine learning approach can most accurately forecast the daily discharge of the Jósva Spring using meteorological data and the discharge of a hydraulically connected upstream spring. This is motivated by the need for a reliable operational prediction tool for complex karst aquifers, the improved water-resource management in a climate-sensitive region, and a lack of comparative studies evaluating multiple ML paradigms on the same karst system. The study also aimed at comparing the predictive performance of five state-of-the-art ML models to identify the most accurate and robust model and to understand the predictability of the karst system by analyzing feature importance, lag effects, and temporal dependencies. Three tree-based ensemble models (Random Forest, XGBoost, and Extra Trees) and two deep learning architectures (a Bidirectional Long Short-Term Memory network, BiLSTM, and a novel Hybrid XGBoost–BiLSTM model) were trained using a five-year (2015–2019) daily dataset comprising rainfall, temperature, and upstream discharge. The modeling framework was designed for synchronous simulation (lead time = 0 days), estimating concurrent downstream discharge using upstream and meteorological measurements from the same time step. A rigorous feature-engineering workflow was implemented based on statistical characterization, correlation analysis, and time-series diagnostics. Models were trained on 80% of the dataset and evaluated on an independent 20% test set. The results demonstrate that the proposed Hybrid XGBoost-BiLSTM model achieved the highest predictive accuracy on the unseen test data (R² = 0.74, NSE = 0.74, RMSE = 716.35 L/min). While the standalone tree-based models, particularly XGBoost (R² = 0.66), also exhibited strong and competitive performance, the hybrid architecture provided a consistent and measurable improvement across all evaluation metrics. The hybrid model’s success is attributed to its synergistic design, which leverages the powerful feature extraction and refinement capabilities of XGBoost to provide a more informative input space for the BiLSTM, thereby enhancing its ability to capture complex temporal dependencies while mitigating overfitting. Feature importance analysis confirmed that upstream discharge at a 3-day lag was the most critical predictor, highlighting the system’s hydraulic connectivity. This research provides clear, evidence-based guidance showing that hybrid machine learning architectures, which integrate the strengths of different modeling paradigms, represent the most effective approach for developing robust and reliable operational prediction tools for complex karst aquifers. Full article

Self-contained local forecasting of wind and solar series can improve operational planning of wind farms and photovoltaic (PV) plant day-cycles in addition to numerical models, which are mostly behind time due to high simulation costs. Unstable electricity production requires balancing the availability of renewable energy (RE) with unpredictable user consumption to achieve effective usage. Artificial intelligence (AI) predictive modelling can minimise the intermittent uncertainty in wind and solar resources by trying to eliminate specific problems in RE-detached system reliability and optimal utilisation. The proposed 24 h day-training and prediction scheme comprises the starting detection and the following similarity re-assessment of sampling day-series intervals. Two-point professional weather stations record standard meteorological variables, of which the most relevant are selected as optimal model inputs. Automatic two-layer altitude observation captures key relationships between hill- and lowland-level data, which comply with pattern progress. New biologically inspired differential learning (DfL) is designed and developed to integrate adaptive neurocomputing (evolving node tree components) with customised numerical procedures of operator calculus (OC) based on derivative transforms. DfL enables the representation of uncertain dynamics related to local weather patterns. Angular and frequency data (wind azimuth, temperature, irradiation) are processed together with the amplitudes to solve simple 2-variable partial differential equations (PDEs) in binomial nodes. Differentiated data provide the fruitful information necessary to model upcoming changes in mid-term day horizons. Additional PDE components in periodic form improve the modelling of hidden complex patterns in cycle data. The DfL efficiency was proved in statistical experiments, compared to a variety of elaborated AI techniques, enhanced by selective difference input preprocessing. Successful LSTM-deep and stochastic tree learning shows little inferior model performances, notably in day-ahead estimation of chaotic 24 h wind series, and slightly better approximation of alterative 8 h solar cycles. Free parametric C++ software with the applied archive data is available for additional comparative and reproducible experiments. Full article

Retail demand forecasting for fast-moving consumer goods (FMCGs) presents significant challenges due to high product variety, demand intermittency, and uncertainty, which prevent any single model from capturing the diverse demand patterns. To address these challenges, this study proposes a hybrid clustering framework that integrates rule-based (Syntetos–Boylan Classification) and machine learning (ML) approaches, combining time-series embeddings with unsupervised learning to segment products by demand structure. Building on this framework, forecasting is conducted through a two-phase methodology: selecting optimal baseline algorithms per cluster (Phase 1), then enhancing them with embedding-based hybrid models (Phase 2). The effectiveness of this approach is demonstrated using a large-scale real-world dataset comprising over 3.8 million weekly sales records from 12,661 products across 691 stores. Results show that the proposed method improves forecasting accuracy by approximately 5–15% compared to conventional models. Furthermore, model performance varies with demand volatility, as different model–embedding combinations perform best under different conditions. Finally, the proposed diagnostic heuristic reduces experimental effort by 25–50%. Comparative analysis reveals that ML-based clustering outperforms rule-based methods under stable demand, whereas rule-based clustering is superior under high demand uncertainty, confirming that no single clustering paradigm is universally optimal. These findings demonstrate the practical value of adaptive hybrid frameworks for FMCGs demand forecasting. Full article

High-frequency volatility and extreme tail risks in offshore wind power pose severe challenges to grid stability and economic operation. Conventional storage planning often relies on deterministic profiles or static allocation rules, failing to capture the non-stationary temporal dynamics of marine wind resources. To bridge this gap, this paper proposes a closed-loop framework that integrates ultra-short-term probabilistic forecasting with dynamic hybrid energy storage optimization. A novel Dual-Channel Residual Network is developed to provide well-calibrated predictive uncertainty quantification, which explicitly drives a Prediction-Guided Dynamic Hybrid Storage Optimization Framework. By dynamically coordinating lithium-ion batteries and liquid air energy storage based on evidential predictive variance, the proposed approach achieves superior synergy between short-term power response and long-duration energy shifting. Case studies on an offshore wind farm validate that the framework significantly reduces the Levelized Cost of Energy and loss-of-load risks while enhancing frequency regulation capabilities compared to state-of-the-art benchmarks. Full article