Physics-Informed State Space Models for Reliable Solar Irradiance Forecasting in Off-Grid Systems

The stable operation of off-grid photovoltaic systems requires accurate, computationally efficient solar forecasting. Contemporary deep learning models often suffer from massive computational overhead and physical blindness, generating impossible predictions. This paper introduces the Physics-Informed State Space Model (PISSM) to bridge the gap between efficiency and physical accuracy for edge-deployed microcontrollers. PISSM utilizes a dynamic Hankel matrix embedding to filter stochastic sensor noise by transforming raw meteorological sequences into a robust state space. A Linear State Space Model replaces heavy attention mechanisms, efficiently modeling temporal dependencies for parallel processing. Crucially, a novel Physics-Informed Gating mechanism leverages the Solar Zenith Angle and Clearness Index to structurally bound outputs, ensuring predictions strictly obey diurnal cycles and preventing nocturnal errors. Validated on a multi-year dataset for Omdurman, Sudan, PISSM achieves superior accuracy with fewer than 40,000 parameters, establishing an ultra-lightweight benchmark for real-time off-grid control.

Thermodynamic Liquid Manifold Networks: Physics-Bounded Deep Learning for Solar Forecasting in Autonomous Off-Grid Microgrids

The stable operation of autonomous off-grid photovoltaic systems requires solar forecasting algorithms that respect atmospheric thermodynamics. Contemporary deep learning models consistently exhibit critical anomalies, primarily severe temporal phase lags during cloud transients and physically impossible nocturnal power generation. To resolve this divergence between data-driven modeling and deterministic celestial mechanics, this research introduces the Thermodynamic Liquid Manifold Network. The methodology projects 22 meteorological and geometric variables into a Koopman-linearized Riemannian manifold to systematically map complex climatic dynamics. The architecture integrates a Spectral Calibration unit and a multiplicative Thermodynamic Alpha-Gate. This system synthesizes real-time atmospheric opacity with theoretical clear-sky boundary models, structurally enforcing strict celestial geometry compliance. This completely neutralizes phantom nocturnal generation while maintaining zero-lag synchronization during rapid weather shifts. Validated against a rigorous five-year testing horizon in a severe semi-arid climate, the framework achieves an RMSE of 18.31 Wh/m2 and a Pearson correlation of 0.988. The model strictly maintains a zero-magnitude nocturnal error across all 1826 testing days and exhibits a sub-30-minute phase response during high-frequency optical transients. Comprising exactly 63,458 trainable parameters, this ultra-lightweight design establishes a robust, thermodynamically consistent standard for edge-deployable microgrid controllers.