Lake Temperature Forecasting
Physics-Informed Neural Networks for Multi-Depth Lake Water Temperature Modeling
A physics-informed neural network combining Koopman operator embeddings with LSTM recurrent networks for long-horizon, multi-depth forecasting of lake water temperature — a problem that matters both for climate-change attribution (lake temperature is a sentinel signal of regional warming) and for managing freshwater drinking supplies, fisheries, and aquatic-ecosystem habitats.
The problem
Conventional recurrent neural networks (LSTMs) learn temperature dynamics directly from observations. They produce accurate short-term forecasts but accumulate error at multi-month horizons because they have no mechanism for the underlying physics — heat diffusion, vertical stratification, seasonal mixing. Long-horizon multi-depth lake-temperature forecasting demands both learning flexibility and the inductive bias of physical structure.
Our approach
We combine two ideas:
- Koopman operator embeddings lift the nonlinear thermal dynamics into a higher-dimensional space where they become approximately linear, providing a physics-grounded representation that generalizes across temperature regimes and depths. The Koopman embeddings are jointly learned end-to-end with the rest of the network, building on prior Koopman-based dynamics modelling (Takeishi et al., MLPS 2017; Lusch et al., Nat. Commun. 2018).
- LSTM recurrent networks learn the residual lake-specific dynamics that the Koopman linearization cannot capture.
The resulting hybrid model takes multi-depth temperature time series as input and produces multi-depth temperature forecasts at long horizons.
Evaluation
We evaluate the model on a benchmark of 450 lakes across the U.S. Midwest spanning 40 years (1980–2019) of multi-depth temperature observations. It significantly outperforms a conventional LSTM baseline on long-horizon multi-depth forecasting.
Publication
Peer-reviewed and published at the ICLR 2025 Workshop on Tackling Climate Change with Machine Learning — the dedicated climate-AI workshop co-located with the International Conference on Learning Representations — Singapore, April 2025.
Co-authors
- Trieu H. Vo (lead author) — PhD Student, Florida International University
- Prof. Cuong V. Nguyen — Assistant Professor, Department of Mathematical Sciences, Durham University, United Kingdom
- Prof. Dongsheng Luo — Assistant Professor, Knight Foundation School of Computing and Information Sciences, Florida International University
- Prof. Leonardo Bobadilla — Associate Professor, Knight Foundation School of Computing and Information Sciences, Florida International University
Funding
The NSF AI Institute for Research on Trustworthy AI in Weather, Climate, and Coastal Oceanography (AI2ES) funds this research via the FIU–AI2ES ExpandAI partnership.
Paper
Full paper, slides, and poster are available open-access from the Climate Change AI workshop archive.