PhyTTA: Physics-Informed Test-Time Adaptation of Foundation Models for Regional Drought Prediction

摘要

Drought prediction is crucial for disaster mitigation, yet it remains challenging because regional droughts reflect nonlinear interactions among precipitation supply, evaporative demand, and slowly varying land atmosphere states. Although time series foundation models (TSFMs) have shown strong zero shot performance in general forecasting tasks, they can exhibit systematic sensitivity mismatch in the prediction of regional precipitation and temperature anomalies in the Standardized Precipitation Evapotranspiration Index (SPEI). We introduce PhyTTA, a physics informed test time adaptation framework that keeps the TSFM backbone frozen and corrects the predictable part of its one step residual through three components: a dynamic forcing correction, a static tracker of slowly varying background bias, and a conditional confidence gate that applies the correction only in supported regimes. Our analysis shows that, when frozen model residuals contain a component predictable from local forcing changes or slowly varying background bias, correcting this component reduces expected squared error in the population setting. PhyTTA implements this principle through a conservative online ridge EMA correction with regime support gating. Across four foundation backbones on three South Australian locations and TimesFM on three cross regional regions, PhyTTA reduces MSE by up to 19.78%. With the TimesFM backbone it gives consistent 12.3% to 15.1% MSE reductions across the three South Australian locations.