PING: physics informed graph neural network for advection-diffusion processes with applications to solar power forecasting

Short-term forecasting of cloud-induced power ramps across a network of distributed photovoltaic (PV) or irradiance sensors is a recognised pain point for grid operators. A natural idea is to make the graph neural network (GNN) advection-aware: connect each site to the sites upwind of it, with edge time-lags set by the cloud-motion vector (CMV), so that a ramp is propagated forward before it physically arrives. Using a controlled synthetic testbed with a known wind field, we show that (i) with a realistic cross-correlation CMV estimate, an explicit advection graph does not beat a plain static or learned-adjacency spatiotemporal GNN; (ii) roughly half of the benefit available from a perfect CMV comes simply from providing an accurate motion vector as an input feature, not from graph structure; and (iii) advection helps only when the advective displacement over the forecast horizon, v*H, fits inside the sensor network. Motivated by (ii), we introduce a small self-supervised cloud-motion estimator -- a position-aware encoder trained only on a multi-lag optical-flow reconstruction objective with an annealed kernel -- that recovers the true wind vector to 2-4 degrees median angular error, 2-4x better than the classical cross-correlation method across every wind regime. Freezing this estimator and feeding its vector to the forecaster closes about 60% of the oracle-CMV RMSE gap at moderate wind (8-15% RMSE reduction over no advection), with no external wind data. We also report a negative result for a spatially-coherent probabilistic head. All claims are established on a single synthetic simulator; we discuss why real-network validation is the necessary next step and outline it.

Accurate photovoltaic (PV) power forecasting is essential for reliable grid dispatch and renewable energy integration, yet it remains challenging because PV generation is jointly shaped by weather variability, day-night transitions, regime-dependent dynamics, and strict physical constraints. We propose PARA-PV, a Physics-Aware Retrieval-Augmented framework that embeds physical knowledge throughout the forecasting process. The framework first encodes multivariate PV observations into patch-level representations and, through a physics-aware retrieval-augmented learner, retrieves historical patches and analog trajectories that are consistent with the current window in temporal shape, power level, PV operating state, and intra-day period; this yields a physically grounded base forecast. To supplement local memory with broader temporal knowledge, the base forecast is then calibrated against a frozen Chronos time-series foundation-model prior through a lightweight residual adapter, so that general temporal regularities are adapted to PV-specific dynamics without overriding the physically grounded prediction. Because residual conditional distribution shifts persist when weather and diurnal regimes change, a physics-aware distribution shift correction module subsequently adjusts the preliminary forecast using power, weather, timestamp, and day/night conditions, applying gated mean-shift and scale corrections selectively. Finally, a physics-constrained loss function partitions the samples into peak, ramping, night-time, and regular regimes and adaptively reweights their error contributions, preventing the dominant regular regime from suppressing learning of operationally critical states. Our code is available at https://github.com/weican1103/PARA-PV.

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.