A full-Bayesian approach to the inverse problem for steady-state groundwater flow and heat transport
Bibliographic record
Abstract
The full (hierarchal) Bayesian approach proposed by Woodbury & Ulrych and Jiang et al. is extended to the inverse problem for 2-D steady-state groundwater flow and heat transport. A stochastic conceptual framework for the heat flow and groundwater flow is adopted. A perturbation of both the groundwater flow and the advection-conduction heat transport equations leads to a linear formulation between heads, temperature and logarithm transmissivity [denoted as ln (T)]. A Bayesian updating procedure similar to that of Woodbury & Ulrych can then be performed. This new algorithm is examined against a generic example through simulations. The prior mean, variance and integral scales of ln (T) (hyperparameters) are treated as random variables and their pdfs are determined from maximum entropy considerations. It is also assumed that the statistical properties of the noise in the hydraulic head and temperature measurements are also uncertain. Uncertainties in all pertinent hyperparameters are removed by marginalization. It is found that the use of temperature measurements is showed to further improve the ln (T) estimates for the test case in comparison to the updated ln (T) field conditioned on ln (T) and head data; the addition of temperature data without hydraulic head data to the update also aids refinement of the ln (T) field compared to simply interpolating ln (T) data alone these results suggest that temperature measurements are a promising data source for site characterization for heterogeneous aquifer, which can be accomplished through the full-Bayesian methodology.
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".