Physics-Constrained Latent Dynamics for Solar PV Forecasting via Interpretable Deep Learning

As solar photovoltaic (PV) generation becomes increasingly central to global renewable energy systems, cloud-induced intermittency of solar irradiance remains a major challenge for power system stability and economic dispatch. Due to the sparse spatial coverage of ground-based measurements, high-resolution geostationary satellite imagery (e.g., Himawari-8/9) has become essential for real-time solar forecasting. However, satellite observations provide only two-dimensional projections of integrated atmospheric optical effects, lacking explicit information on cloud vertical structure and microphysics, which fundamentally complicates the inference of physically meaningful irradiance dynamics. Despite recent advances, deep learning–based satellite forecasting methods continue to face three key limitations: limited interpretability due to black-box model structures, excessive parameterization that constrains real-time or edge deployment, and strong sensitivity to quasi-static background signals embedded in satellite imagery. To address these challenges, we propose a Physics-Constrained Latent Dynamics Framework that reframes image reconstruction as an auxiliary constraint governing latent dynamical evolution rather than a prediction target. By minimizing reconstruction errors between predicted and observed satellite images, the framework guides neural physical operators to learn physically consistent cloud motion in latent space. Inspired by PhyDNet, the model decomposes prediction into two parallel pathways: a physics-based branch that governs latent state evolution through neural physical operators, and a data-driven residual branch that compensates for non-physical visual components beyond simplified physical representations. The framework comprises three core components: (i) neural physical operators that approximate partial differential equations (PDEs) via architectural constraints in latent space, enforcing conservation and temporal continuity; (ii) a clear-sky background representation to isolate deterministic irradiance patterns; and (iii) a Global Horizontal Irradiance (GHI) prediction head. In parallel, a ConvLSTM-based residual branch captures cloud formation and dissipation, illumination variability, and sensor noise, forming a dual-branch architecture that integrates physics-based structure with data-driven flexibility. To further decouple stochastic cloud variability from quasi-static background signals, a bootstrap-based extreme-quantile method is employed to construct clear-sky deviation maps, enabling more effective separation of dynamic cloud processes. Preliminary experiments using multiple ground stations in Tokyo, Japan, demonstrate that, without direct irradiance inputs, the proposed framework achieves an R² of 0.801 and a mean absolute error of 0.5 MJ m^-2 for one-hour-ahead GHI forecasts. Analysis of the learned higher-order PDE coefficients suggests that the latent dynamics capture nonlinear physical behaviors beyond simple translational motion. Ablation studies further show that, compared with a pure ConvLSTM baseline, the proposed decoupled architecture reduces parameter counts by approximately 30% while improving forecasting performance by about 12%. While autoregressive frame-based prediction remains susceptible to error accumulation at longer horizons, ongoing work explores replacing the autoregressive formulation with Neural Ordinary Differential Equations to model temporal evolution as continuous dynamical flows, aiming to mitigate long-horizon error growth and establish a more robust foundation for physics-informed solar forecasting and dynamical analysis.