A New Inverse Modeling Approach for Hydraulic Conductivity Estimation Based on Gaussian Mixtures
Bibliographic record
Abstract
Abstract This study proposes a new inverse algorithm to estimate the hydraulic conductivity (K) distribution based on a Gaussian Mixture Model that significantly reduces the number of parameters to be estimated during the inversion process. Moreover, a new objective function that increases the sensitivity of parameters using the spatial derivatives of hydraulic heads is introduced, and the algorithm is further improved by including a Bayes estimator that takes advantage of different possible solutions. The developed approach is tested through multiple synthetic experiments consisting of 250 randomly generated K fields resulting in different levels of heterogeneity and the use of different number of pumping tests, with a total of 1,000 cases of two‐dimensional configuration. A large number of cases are considered to ensure that our findings and conclusions are not based on a single realization. Results revealed significant improvements to K estimates, computational time, and predictions of independently conducted tests not used in the calibration effort when compared to a geostatistical inverse approach. Overall, our results reveal that the Gaussian Mixture inversion approach is able to achieve similar or higher levels of accuracy using half of the pumping tests and 20% of the computational time compared to a geostatistical inversion approach.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 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) | 0.001 | 0.001 |
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".