A hierarchical transformer and graph neural network model for high-accuracy watershed nitrate prediction
Bibliographic record
Abstract
Non-point source pollution from agricultural activities poses a significant threat to water quality by introducing excess nutrients like nitrogen into aquatic ecosystems, leading to issues such as eutrophication and groundwater contamination. In agricultural watersheds, nitrate transport involves intricate physical, chemical, and biological processes influenced by meteorological conditions, hydrological features, and spatial topologies, making accurate short-term predictions challenging. Traditional data-driven deep learning models often fail to incorporate physical constraints and complex spatiotemporal dynamics, limiting their interpretability and predictive accuracy. Here we show a hierarchical transformer and graph neural network model that accurately predicts watershed nitrate concentrations by integrating multi-source data and simulating pollutant migration. The model captures nonlinear multivariate temporal patterns through hierarchical transformers, fuses global meteorological and local hydrological features via neural networks, and models runoff topologies with physically constrained graph neural networks. For predicting the concentration changes of pollutants discharged from watersheds, it outperforms baselines like multi-layer perceptrons, recurrent neural networks, and long short-term memory networks, with state-of-the-art performance in root mean square error, mean absolute error, and R 2 . Ablation studies confirm the essential roles of multi-source data integration and watershed topological modeling in enhancing performance. This method of directly modeling physical processes by leveraging the characteristics of different neural network architectures opens up a new path for addressing the interpretability problem in neural earth system modeling, apart from the process-guided deep learning and differentiable modelling methods.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".