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

2026-07-22

AI Summary

Environmental system modeling faces significant challenges due to sparse observations and heterogeneous physical mechanisms, which hinder cross-system knowledge transfer and compromise the physical consistency of traditional embedding-based retrieval approaches. To address this, this work proposes PIER—the first retrieval-augmented paradigm that explicitly incorporates physical consistency constraints into environmental time-series modeling. PIER integrates embedding similarity retrieval with a physics-aware retrieval stream, and employs a local validator to assess the physical consistency between candidate scenarios and the target system in terms of flux–response relationships. A learnable dynamic weighting mechanism adaptively fuses information from both streams. Evaluated on 41 years of data from 356 lakes across the U.S. Midwest, PIER significantly outperforms baseline methods in water temperature and dissolved oxygen prediction tasks and demonstrates compatibility with diverse backbone models, confirming its effectiveness and generalizability.

Abstract

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.

Problem

• environmental systems
• time-series modeling
• physics consistency
• retrieval-augmented learning
• knowledge transfer

Innovation

• physics-informed retrieval
• flux-response consistency
• retrieval-augmented modeling
• environmental time-series
• model-agnostic framework