PIER: Physics-Informed Environmental Retrieval for Time-Series Modeling

Shiyuan Luo, Runlong Yu, Chonghao Qiu, Yue Qin, Rahul Ghosh, Robert Ladwig, Paul C. Hanson, Yiqun Xie, Xiaowei Jia

Accurate modeling of environmental systems is fundamental to scientific understanding and decision-making, yet remains challenging because observations are limited and physical dynamics vary across systems. Retrieval-augmented approaches offer a natural path to transfer knowledge across systems, but standard embedding-based retrieval does not guarantee consistency of underlying physical processes, since scenarios with similar embeddings may arise from different underlying mechanisms. We propose Physics-Informed Environmental Retrieval (PIER), a model-agnostic framework that augments embedding-based retrieval with a physics-aware stream that scores candidates by flux-response consistency with the target, using local verifiers trained on physics-derived flux features. A weight adjustment mechanism then learns per-scenario weights that adaptively balance the two retrieval streams based on diagnostic features summarizing physics-stream reliability. Experiments on 356 lakes across the Midwestern United States spanning 41 years show that PIER consistently outperforms baselines for water temperature and dissolved oxygen prediction, and serves as a general augmentation strategy across diverse backbones.