Deep neural networks in surrogate hydrogeological modeling : an application for transient groundwater flow combined with a geostatistical spectral algorithm for inverse problem-solving
Bibliographic record
Abstract
ABSTRACT: Characterizing groundwater flow parameters is crucial for understanding complex aquifer systems. Inverse techniques are key for modeling hydrogeological parameters and assessing uncertainties. However, using a flow simulator can be time-consuming, especially with many model parameters. To address this, surrogate models are proposed, increasingly leveraging deep learning. However, their training relies on a large database of models, often lacking diversity and requiring significant time. A recent proposal suggests replacing the transient groundwater flow model with a U-Net encoder-decoder architecture. This reduces execution time and enables uncertainty quantification with geostatistical methods. The substitute is trained using limited forward model evaluations to understand the physical relationship between hydraulic conductivity fields and transient hydraulic heads measured on-site. Physical principles, like boundary conditions and source terms, are mapped as inputs to enhance the model's understanding of transient groundwater flow equations. We explore the possibility of generating drawdowns at any given time by training a U-Net architecture on a subset of the spatiotemporal drawdown series. We propose a methodology to reduce training times while maintaining good emulation quality. Mapping boundary conditions and source terms introduce the physical knowledge of the problem. The novelty pertains to the introduction of an estimation map to mimic the pumping area. Once the model is trained, we use a spectral geostatistical method to solve the inverse problem using the surrogate model to estimate uncertainties associated with hydraulic conductivity and boundary conditions. Our study demonstrates that the U-Net accurately reproduces the drawdown inside the training range, and in terms of computational demand, using U-Net as a substitution model reduces the required calculation time by about an order of magnitude for the defined field. The proposed approach provides an efficient and accurate method for characterizing groundwater flow parameters. The quantification of uncertainties in complex aquifer systems is thus determined more rapidly.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".