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

arXiv: https://arxiv.org/abs/2607.20230 · HTML: https://mlsanity.com/paper/2607.20230/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 39 references that are in the map.
- First posted on arXiv 22 Jul 2026.

## Builds on (most cited first, 20 of 20)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [Graph Retrieval-Augmented Generation: A Survey](https://mlsanity.com/paper/2408.08921/) (2024)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [A Comprehensive Survey of Retrieval-Augmented Generation (RAG): Evolution, Current Landscape and Future Directions](https://mlsanity.com/paper/2410.12837/) (2024)
- [Towards Learning Universal, Regional, and Local Hydrological Behaviors via Machine-Learning Applied to Large-Sample Datasets](https://mlsanity.com/paper/1907.08456/) (2019)
- [Physics Guided RNNs for Modeling Dynamical Systems: A Case Study in Simulating Lake Temperature Profiles](https://mlsanity.com/paper/1810.13075/) (2018)
- [Retrieval Augmented Time Series Forecasting](https://mlsanity.com/paper/2411.08249/) (2024)
- [Retrieval-Augmented Diffusion Models for Time Series Forecasting](https://mlsanity.com/paper/2410.18712/) (2024)
- [RAG and RAU: A Survey on Retrieval-Augmented Language Model in Natural Language Processing](https://mlsanity.com/paper/2404.19543/) (2024)
- [Predicting Water Temperature Dynamics of Unmonitored Lakes with Meta Transfer Learning](https://mlsanity.com/paper/2011.05369/) (2020)
- [Physics-Guided Foundation Model for Scientific Discovery: An Application to Aquatic Science](https://mlsanity.com/paper/2502.06084/) (2025)
- [Adaptive Process-Guided Learning: An Application in Predicting Lake DO Concentrations](https://mlsanity.com/paper/2411.12973/) (2024)
- [RAG for Geoscience: What We Expect, Gaps and Opportunities](https://mlsanity.com/paper/2508.11246/) (2025)
- [Learning to Retrieve for Environmental Knowledge Discovery: An Augmentation-Adaptive Self-Supervised Learning Framework](https://mlsanity.com/paper/2509.14563/) (2025)
- [GREAT: Generalizable Representation Enhancement via Auxiliary Transformations for Zero-Shot Environmental Prediction](https://mlsanity.com/paper/2511.13469/) (2025)

## Abstract (arXiv)

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.