Probabilistic Multi-Regional Solar Power Forecasting with Any-Quantile Recurrent Neural Networks

The increasing penetration of photovoltaic (PV) generation introduces significant uncertainty into power system operation, necessitating forecasting approaches that extend beyond deterministic point predictions. This paper proposes an any-quantile probabilistic forecasting framework for multi-regional PV power generation based on the Any-Quantile Recurrent Neural Network (AQ-RNN). The model integrates an any-quantile forecasting paradigm with a dual-track recurrent architecture that jointly processes series-specific and cross-regional contextual information, supported by dilated recurrent cells, patch-based temporal modeling, and a dynamic ensemble mechanism. The proposed framework enables the estimation of calibrated conditional quantiles at arbitrary probability levels within a single trained model and effectively exploits spatial dependencies to enhance robustness at the system level. The approach is evaluated using 30 years of hourly PV generation data from 259 European regions and compared against established statistical and neural probabilistic baselines. The results demonstrate consistent improvements in forecast accuracy, calibration, and prediction interval quality, underscoring the suitability of the proposed method for uncertainty-aware energy management and operational decision-making in renewable-dominated power systems.

MoDEx: Mixture of Depth-specific Experts for Multivariate Long-term Time Series Forecasting

Multivariate long-term time series forecasting (LTSF) supports critical applications such as traffic-flow management, solar-power scheduling, and electricity-transformer monitoring. The existing LTSF paradigms follow a three-stage pipeline of embedding, backbone refinement, and long-horizon prediction. However, the behaviors of individual backbone layers remain underexplored. We introduce layer sensitivity, a gradient-based metric inspired by GradCAM and effective receptive field theory, which quantifies both positive and negative contributions of each time point to a layer's latent features. Applying this metric to a three-layer MLP backbone reveals depth-specific specialization in modeling temporal dynamics in the input sequence. Motivated by these insights, we propose MoDEx, a lightweight Mixture of Depth-specific Experts, which replaces complex backbones with depth-specific MLP experts. MoDEx achieves state-of-the-art accuracy on seven real-world benchmarks, ranking first in 78 percent of cases, while using significantly fewer parameters and computational resources. It also integrates seamlessly into transformer variants, consistently boosting their performance and demonstrating robust generalizability as an efficient and high-performance LTSF framework.

SolARED: Solar Active Region Emergence Dataset for Machine Learning Aided Predictions

The development of accurate forecasts of solar eruptive activity has become increasingly important for preventing potential impacts on space technologies and exploration. Therefore, it is crucial to detect Active Regions (ARs) before they start forming on the solar surface. This will enable the development of early-warning capabilities for upcoming space weather disturbances. For this reason, we prepared the Solar Active Region Emergence Dataset (SolARED). The dataset is derived from full-disk maps of the Doppler velocity, magnetic field, and continuum intensity, obtained by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). SolARED includes time series of remapped, tracked, and binned data that characterize the evolution of acoustic power of solar oscillations, unsigned magnetic flux, and continuum intensity for 50 large ARs before, during, and after their emergence on the solar surface, as well as surrounding areas observed on the solar disc between 2010 and 2023. The resulting ML-ready SolARED dataset is designed to support enhancements of predictive capabilities, enabling the development of operational forecasts for the emergence of active regions. The SolARED dataset is available at https://sun.njit.edu/sarportal/, through an interactive visualization web application.

SolarGPT-QA: A Domain-Adaptive Large Language Model for Educational Question Answering in Space Weather and Heliophysics

Solar activity, including solar flares, coronal mass ejections (CMEs), and geomagnetic storms, can significantly impact satellites, aviation, power grids, data centers, and space missions. Extreme solar events can cause substantial economic damage if not predicted in advance, highlighting the importance of accurate forecasting and effective education in space science. Although large language models (LLMs) perform well on general tasks, they often lack domain-specific knowledge and pedagogical capability to clearly explain complex space science concepts. We introduce SolarGPT-QA, a question answering system based on a domain-adapted large language model built on the LLaMA-3 base model. The model is trained using scientific literature and large-scale question-answer data generated with GPT-4 and refined using Grok-3 in a student-friendly storytelling style. Human pairwise evaluations show that SolarGPT-QA outperforms general-purpose models in zero-shot settings and achieves competitive performance compared to instruction-tuned models for educational explanations in space weather and heliophysics. A small pilot student comprehension study further suggests improved clarity and accessibility of the generated explanations. Ablation experiments indicate that combining domain-adaptive pretraining with pedagogical fine-tuning is important for balancing scientific accuracy and educational effectiveness. This work represents an initial step toward a broader SolarGPT framework for space science education and forecasting.

Physics-Guided Counterfactual Explanations for Large-Scale Multivariate Time Series: Application in Scalable and Interpretable SEP Event Prediction

Accurate prediction of solar energetic particle events is vital for safeguarding satellites, astronauts, and space-based infrastructure. Modern space weather monitoring generates massive volumes of high-frequency, multivariate time series (MVTS) data from sources such as the Geostationary perational Environmental Satellites (GOES). Machine learning (ML) models trained on this data show strong predictive power, but most existing methods overlook domain-specific feasibility constraints. Counterfactual explanations have emerged as a key tool for improving model interpretability, yet existing approaches rarely enforce physical plausibility. This work introduces a Physics-Guided Counterfactual Explanation framework, a novel method for generating counterfactual explanations in time series classification tasks that remain consistent with underlying physical principles. Applied to solar energetic particles (SEP) forecasting, this framework achieves over 80% reduction in Dynamic Time Warping (DTW) distance increasing the proximity, produces counterfactual explanations with higher sparsity, and reduces runtime by nearly 50% compared to state-of-the-art baselines such as DiCE. Beyond numerical improvements, this framework ensures that generated counterfactual explanations are physically plausible and actionable in scientific domains. In summary, the framework generates counterfactual explanations that are both valid and physically consistent, while laying the foundation for scalable counterfactual generation in big data environments.

Intraday spatiotemporal PV power prediction at national scale using satellite-based solar forecast models

We present a novel framework for spatiotemporal photovoltaic (PV) power forecasting and use it to evaluate the reliability, sharpness, and overall performance of seven intraday PV power nowcasting models. The model suite includes satellite-based deep learning and optical-flow approaches and physics-based numerical weather prediction models, covering both deterministic and probabilistic formulations. Forecasts are first validated against satellite-derived surface solar irradiance (SSI). Irradiance fields are then converted into PV power using station-specific machine learning models, enabling comparison with production data from 6434 PV stations across Switzerland. To our knowledge, this is the first study to investigate spatiotemporal PV forecasting at a national scale. We additionally provide the first visualizations of how mesoscale cloud systems shape national PV production on hourly and sub-hourly timescales. Our results show that satellite-based approaches outperform the Integrated Forecast System (IFS-ENS), particularly at short lead times. Among them, SolarSTEPS and SHADECast deliver the most accurate SSI and PV power predictions, with SHADECast providing the most reliable ensemble spread. The deterministic model IrradianceNet achieves the lowest root mean square error, while probabilistic forecasts of SolarSTEPS and SHADECast provide better-calibrated uncertainty. Forecast skill generally decreases with elevation. At a national scale, satellite-based models forecast the daily total PV generation with relative errors below 10% for 82% of the days in 2019-2020, demonstrating robustness and their potential for operational use.

Disentangling Aleatoric and Epistemic Uncertainty in Physics-Informed Neural Networks. Application to Insulation Material Degradation Prognostics

Physics-Informed Neural Networks (PINNs) provide a framework for integrating physical laws with data. However, their application to Prognostics and Health Management (PHM) remains constrained by the limited uncertainty quantification (UQ) capabilities. Most existing PINN-based prognostics approaches are deterministic or account only for epistemic uncertainty, limiting their suitability for risk-aware decision-making. This work introduces a heteroscedastic Bayesian Physics-Informed Neural Network (B-PINN) framework that jointly models epistemic and aleatoric uncertainty, yielding full predictive posteriors for spatiotemporal insulation material ageing estimation. The approach integrates Bayesian Neural Networks (BNNs) with physics-based residual enforcement and prior distributions, enabling probabilistic inference within a physics-informed learning architecture. The framework is evaluated on transformer insulation ageing application, validated with a finite-element thermal model and field measurements from a solar power plant, and benchmarked against deterministic PINNs, dropout-based PINNs (d-PINNs), and alternative B-PINN variants. Results show that the proposed B-PINN provides improved predictive accuracy and better-calibrated uncertainty estimates than competing approaches. A systematic sensitivity study further analyzes the impact of boundary-condition, initial-condition, and residual sampling strategies on accuracy, calibration, and generalization. Overall, the findings highlight the potential of Bayesian physics-informed learning to support uncertainty-aware prognostics and informed decision-making in transformer asset management.

Accounting for Optimal Control in the Sizing of Isolated Hybrid Renewable Energy Systems Using Imitation Learning

Decarbonization of isolated or off-grid energy systems through phase-in of large shares of intermittent solar or wind generation requires co-installation of energy storage or continued use of existing fossil dispatchable power sources to balance supply and demand. The effective CO2 emission reduction depends on the relative capacity of the energy storage and renewable sources, the stochasticity of the renewable generation, and the optimal control or dispatch of the isolated energy system. While the operations of the energy storage and dispatchable sources may impact the optimal sizing of the system, it is challenging to account for the effect of finite horizon, optimal control at the stage of system sizing. Here, we present a flexible and computationally efficient sizing framework for energy storage and renewable capacity in isolated energy systems, accounting for uncertainty in the renewable generation and the optimal feedback control. To this end, we implement an imitation learning approach to stochastic neural model predictive control (MPC) which allows us to relate the battery storage and wind peak capacities to the emissions reduction and investment costs while accounting for finite horizon, optimal control. Through this approach, decision makers can evaluate the effective emission reduction and costs of different storage and wind capacities at any price point while accounting for uncertainty in the renewable generation with limited foresight. We evaluate the proposed sizing framework on a case study of an offshore energy system with a gas turbine, a wind farm and a battery energy storage system (BESS). In this case, we find a nonlinear, nontrivial relationship between the investment costs and reduction in gas usage relative to the wind and BESS capacities, emphasizing the complexity and importance of accounting for optimal control in the design of isolated energy systems.

Electricity Price Forecasting: Bridging Linear Models, Neural Networks and Online Learning

Precise day-ahead forecasts for electricity prices are crucial to ensure efficient portfolio management, support strategic decision-making for power plant operations, enable efficient battery storage optimization, and facilitate demand response planning. However, developing an accurate prediction model is highly challenging in an uncertain and volatile market environment. For instance, although linear models generally exhibit competitive performance in predicting electricity prices with minimal computational requirements, they fail to capture relevant nonlinear relationships. Nonlinear models, on the other hand, can improve forecasting accuracy with a surge in computational costs. We propose a novel multivariate neural network approach that combines linear and nonlinear feed-forward neural structures. Unlike previous hybrid models, our approach integrates online learning and forecast combination for efficient training and accuracy improvement. It also incorporates all relevant characteristics, particularly the fundamental relationships arising from wind and solar generation, electricity demand patterns, related energy fuel and carbon markets, in addition to autoregressive dynamics and calendar effects. Compared to the current state-of-the-art benchmark models, the proposed forecasting method significantly reduces computational cost while delivering superior forecasting accuracy (12-13% RMSE and 15-18% MAE reductions). Our results are derived from a six-year forecasting study conducted on major European electricity markets.

Efficient Deep Learning for Short-Term Solar Irradiance Time Series Forecasting: A Benchmark Study in Ho Chi Minh City

Reliable forecasting of Global Horizontal Irradiance (GHI) is essential for mitigating the variability of solar energy in power grids. This study presents a comprehensive benchmark of ten deep learning architectures for short-term (1-hour ahead) GHI time series forecasting in Ho Chi Minh City, leveraging high-resolution NSRDB satellite data (2011-2020) to compare established baselines (e.g. LSTM, TCN) against emerging state-of-the-art architectures, including Transformer, Informer, iTransformer, TSMixer, and Mamba. Experimental results identify the Transformer as the superior architecture, achieving the highest predictive accuracy with an R^2 of 0.9696. The study further utilizes SHAP analysis to contrast the temporal reasoning of these architectures, revealing that Transformers exhibit a strong "recency bias" focused on immediate atmospheric conditions, whereas Mamba explicitly leverages 24-hour periodic dependencies to inform predictions. Furthermore, we demonstrate that Knowledge Distillation can compress the high-performance Transformer by 23.5% while surprisingly reducing error (MAE: 23.78 W/m^2), offering a proven pathway for deploying sophisticated, low-latency forecasting on resource-constrained edge devices.