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Physics-Guided Foundation Model for Scientific Discovery: An Application to Aquatic Science
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Proposes PGFM, a physics-guided foundation model pre-trained on simulated lake data via evolution-based feature-interaction search and fine-tuned with energy- and mass-conservation losses to predict lake water temperature and dissolved oxygen.
Problem
Physics-guided ML models are tailored to isolated, simple tasks and struggle with multiple coupled processes and scarce observations, so they fail to generalize and violate physical laws when predicting lake water temperature and dissolved oxygen.
Approach
Pre-train an LSTM-based model on a simulated lake environment labeled by physics-based models (GLM and a DO model), selecting feature interactions with an evolutionary search (mutation and crossover over operations), then fine-tune with observations plus energy and DO mass conservation penalties, and feed predicted temperature into the DO model.
Key results
- PGFM achieves the lowest water temperature RMSE in summer (1.953) and fall-to-spring (1.365), versus 2.795 and 1.624 for the physics-based model.
- PGFM achieves summer epilimnion DO RMSE of 2.077 and hypolimnion DO RMSE of 2.162, outperforming the physics-based model (2.277, 2.367).
- Pre-training with the foundation model improves LSTM and Transformer: FM+LSTM reaches 2.003 summer water temperature RMSE versus 3.841 for plain LSTM.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add physics-guided fine-tuning to the foundation model | PGFM · Water temperature, summer | RMSE: 2.003 (0.011) -> 1.953 (0.126) | Helped |
| Add physics-guided fine-tuning to the foundation model | PGFM · Water temperature, fall to spring | RMSE: 1.578 (0.030) -> 1.365 (0.200) | Helped |
| Add physics-guided fine-tuning to the foundation model | PGFM · DO concentration, summer epilimnion | RMSE: 2.117 (0.012) -> 2.077 (0.111) | Helped |
| Add physics-guided fine-tuning to the foundation model | PGFM · DO concentration, summer hypolimnion | RMSE: 2.292 (0.008) -> 2.162 (0.114) | Helped |
| Add physics-guided fine-tuning to the foundation model | PGFM · DO concentration, fall to spring | RMSE: 2.264 (0.352) -> 2.258 (0.288) | Helped |
| Add pre-training (ablation) | PGFM · Water temperature, summer | RMSE: 3.578 (0.938) -> 1.953 (0.126) | Helped |
| Add pre-training (ablation) | PGFM · Water temperature, fall to spring | RMSE: 3.044 (0.939) -> 1.365 (0.200) | Helped |
| Add pre-training (ablation) | PGFM · DO concentration, summer epilimnion | RMSE: 2.772 (0.242) -> 2.077 (0.111) | Helped |
| Add pre-training (ablation) | PGFM · DO concentration, summer hypolimnion | RMSE: 2.725 (0.226) -> 2.162 (0.114) | Helped |
| Add pre-training (ablation) | PGFM · DO concentration, fall to spring | RMSE: 2.833 (0.291) -> 2.258 (0.288) | Helped |
| Include predicted water temperature in DO model inputs (ablation) | PGFM · DO concentration, summer epilimnion | RMSE: 2.104 (0.126) -> 2.077 (0.111) | Helped |
| Include predicted water temperature in DO model inputs (ablation) | PGFM · DO concentration, summer hypolimnion | RMSE: 2.170 (0.106) -> 2.162 (0.114) | Helped |
Surprising findings
- Physics-based models generally outperform plain ML models in this limited-data setting.
- PGFM without pre-training performs worse than the physics-based model on summer water temperature (3.578 vs 2.795 RMSE).
Limitations
- Evaluated only on lakes in the Midwestern USA with a single model family (LSTM) for the main PGFM method.
- Physical loss tolerance thresholds and heat/mass flux estimation rely on input drivers and may be affected by meteorological observation errors.
Experimental setup
Datasets: simulated lake environmental system (GLM and DO model outputs) observed lake water temperature and DO data for 117 Midwestern US lakes (1979-2019)
Benchmarks: lake water temperature prediction (observed data, 117 lakes) dissolved oxygen prediction (summer epilimnion, summer hypolimnion, fall-to-spring)
Metrics: RMSE energy inconsistency mass inconsistency
Baselines: Physics-based models LSTM EA-LSTM Transformer iTransformer LSTM (w/ pre-train) PGFM (w/o pre-train) PGFM (w/o T̂)
Builds on: LSTM General Lake Model (GLM) regularized dual averaging optimizer EA-LSTM iTransformer
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