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

Abstract

Drought prediction is crucial for disaster mitigation, yet it remains challenging due to the complexity and variability of drought events. Although time series foundation models (TSFMs) have shown great potential in general time series forecasting problems, they struggle to adapt to regional hydrological information. They often underestimate the impact of regional precipitation or temperature anomalies on drought indices like SPEI. This problem arises because general pretraining captures averaged time series patterns, which do not account for the unique climatic and hydrological characteristics of specific regions. To bridge this gap, we introduce Phy-TTA, a physics-informed adaptation framework designed to restore the physical consistency of drought forecasts. Rather than updating model parameters, which might overfit random weather noise, Phy-TTA corrects prediction errors by explicitly modeling the causal link between physical forcing (e.g., rainfall deficits) and drought. Our theoretical analysis highlights the critical role of incorporating physics-driven information to enhance the accuracy and reliability of drought predictions. Experiments across multiple regions demonstrate that Phy-TTA consistently improves performance.