Physics-informed, Differentiable Hydrologic Models for Capturing Unseen Extreme Events
Bibliographic record
Abstract
Recently, a hybrid framework combining deep learning (DL) and process-based equations, termed differentiable modeling, has shown comparable accuracy to DL models while offering enhanced interpretability and spatial generalizability. However, it remains unclear how well hybrid models generalize to extreme floods outside of the range of training data, and whether optimizing models for extreme events jeopardize spatial generalizability and the physical significance of internal variables. Here we evaluated multiple versions of a differentiable model (δHBV1.1p) for predicting unseen extreme events, and benchmarked them against the widely applied long short-term memory (LSTM) model on the CAMELS dataset. We find that both LSTM and δHBV models performed well, and δHBV1.1p outperformed LSTM for events with a return period of 5 years or more. This advantage was more pronounced as the return period increased (0.06 higher median Nash-Sutcliffe efficiency and lower peak flow errors for 80% of the 50-year or rarer events). Loss functions can have a larger impact on δHBV1.1p than on LSTM, and using the proper loss can lead to δHBV models that further surpass LSTM in different performance aspects. Furthermore, allowing more dynamic parameters improved the extreme metrics, had no negative impact on spatial generalization, and exerted a minimal influence on the untrained variables. We hypothesize that δHBV’s mass balance and first-order exchange terms help to constrain and inform its responses to mitigate the underestimation of peaks compared to LSTM. We conclude that adopting interpretable structural priors can improve generalizability to unseen cases.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 teacher head, 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".