Weakly Informative Priors Flow Matching for Probabilistic Regional Solar Irradiance Forecasting

Probabilistic forecasting of regional surface solar irradiance provides critical technical support for the reliable operation and grid integration of large-scale and distributed photovoltaic power systems. However, stochastic fluctuations driven by cloud dynamics substantially complicate the characterization of solar irradiance uncertainty at the regional scale, thereby posing significant challenges to probabilistic regional forecasting. To address this, we propose WIP-Flow, a novel Weakly Informative Priors Flow Matching framework that leverages satellite-derived historical irradiance fields and cloud optical thickness to capture complex spatio-temporal dynamics. Central to WIP-Flow is an unsupervised autoregressive integrated correction algorithm, which combines optical flow with multi-scale decomposition to generate a physically informed initial distribution based on cloud advection. Furthermore, a Flow Matching model with a stochastic interpolation path is introduced to correct boundary distortions and characterize stochastic cloud formation, diffusion, and dissipation processes. Experimental validation on a satellite derived regional solar irradiance dataset demonstrates that WIP Flow generates physically coherent probabilistic forecasts and achieves competitive or superior performance across marginal and multivariate evaluation metrics. Notably, WIP-Flow achieves a root mean square error of 104.3 W/m² and a continuous ranked probability score of 47.81 W/m² in 4-hour-ahead forecasts, indicating its potential value for uncertainty-aware solar power grid integration.