Kriging-based surrogate models for convergence acceleration of Markov chains: An example of magnetotellurics-dix joint inversion
Bibliographic record
Abstract
A probabilistic model is presented to jointly invert magnetotelluric data and root mean square (RMS) velocities using a reduced model space based on kriging surrogates. Under the assumption that the resistivity and velocity models are smooth fields that a Gaussian process can represent, we select a reduced representation of the original model space to perform Bayesian inference. The surrogate models were later used to perform probabilistic joint inversion using a petrophysical constraint. The petrophysical constraint corresponds to a Multivariate Normal Distribution based on Faust’s equation built using uncertainty propagation. It allows the creation of a Markov Chain from a reduced model space, where the velocity-resistivity covariance is depth-dependent. The model fields reconstructed with kriging are generally smooth. Therefore, the required burn-in to go from the initial model to smooth models is significantly reduced, which helps reach a stationary chain with fewer iterations. The posterior sampling is done based on the Metropolis-Hastings rule. A synthetic example that exhibits a hidden resistive layer is chosen to test the workflow. Models extracted from the posterior explain the observed data within the expected tolerance levels while also satisfying the selected petrophysical coupling function. The results are encouraging since they show that a reduced representation of the model space can be used to effectively explore complex posterior probability distributions to solve multiphysics problems that are highly non-unique.
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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) | 0.000 | 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".