Physically-constrained evapotranspiration models with machine learning parameterization outperform pure machine learning: Critical role of domain knowledge
Bibliographic record
Abstract
Physics-informed machine learning techniques have emerged to tackle challenges inherent in pure machine learning (ML) approaches. One such technique, the hybrid approach, has been introduced to estimate terrestrial evapotranspiration (ET), a crucial variable linking water, energy, and carbon cycles. A key advantage of these hybrid ET models is their improved performance, particularly under extreme conditions, compared to ET estimates relying solely on ML. However, the mechanisms driving their improved performance are not well understood. To address this gap, we developed six hybrid approaches based on different physical formulations of ET and compared them with a pure ML model. All models employed the random forest algorithm and were trained on daily-scale ET observations, in-situ meteorological data and satellite remote sensing. We found a strong correlation (r = 0.93) between the sensitivity of ET estimates to machine-learned parameters and model error (root-mean-square error; RMSE), indicating that reduced sensitivity minimizes error propagation and improves performance. Notably, the most accurate hybrid model (RMSE = 17.8 W m-2 in energy unit) utilized a novel empirical parameter, which is relatively stable due to land-atmosphere equilibrium, outperforming both the pure ML model and hybrid models requiring conventional parameters (e.g., surface conductance). These results imply that conventional parameterizations may require reevaluated to effectively integrate physical models with machine learning, as conventional choices may not be optimal for this new, hybrid, paradigm. This study underscores the critical role of domain knowledge in setting up hybrid models, potentially guiding future hybrid model developments beyond ET estimation.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".