Using MMD GANs to correct physics models and improve Bayesian parameter estimation
Bibliographic record
Abstract
Bayesian parameter estimation methods are robust techniques for quantifying properties of physical systems which cannot be observed directly. In estimating such parameters, one first requires a physics model of the phenomenon to be studied. Often, such a model follows a series of assumptions to make parameter inference feasible. When simplified models are used for inference, however, systematic differences between model predictions and observed data may propagate throughout the parameter estimation process, biasing inference results. In this work, we use generative adversarial networks (GANs) based on the maximum mean discrepancy (MMD) to learn small stochastic corrections to physics models in order to minimize inference bias. We further propose a hybrid training procedure utilizing both the MMD and the standard GAN objective functionals. We demonstrate the ability to learn stochastic model corrections and eliminate inference bias on a toy problem wherein the true data distribution is known. Subsequently, we apply these methods to a mildly ill-posed inference problem in magnetic resonance imaging (MRI), showing improvement over an established inference method. Finally, because 3D MRI images often contain millions of voxels which would each require parameter inference, we train a conditional variational autoencoder (CVAE) network on the corrected MRI physics model to perform fast inference and make this approach practical.
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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 | 0.001 |
| 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".