High performance computing methods for nonlinear Bayesian uncertainty quantification
Bibliographic record
Abstract
Bayesian uncertainty quantification (UQ) for nonlinear inverse problems requires the application of numerical integration (sampling) to estimate the posterior probability density since no closed-form expressions exist. Nonlinear problems are common in geophysics, in particular, in applications of studying the seabed with sound. The computational cost of applying UQ can be daunting and we present several approaches that improve efficiency for large inverse problems. Fundamentally, Bayesian sampling includes both fine-grained parallelism in the forward model (data prediction) as well as coarse grained parallelism in the sampling. Fine grained parallelism can be addressed efficiently by implementation on massively parallel accelerators, such as graphics processing units, and application to reflection coefficient computation is shown. The coarse grained parallelism of sampling is ideally addressed by traditional parallelization with message passing across a cluster of computers. We consider implementation of parallel sampling algorithms that scale efficiently to 103 computer cores. Finally, computational efficiency is closely tied to parametrization efficiency, which is addressed by self-adapting parametrizations of unknown complexity that lead to parsimonious representations of complex environments with few parameters. These three aspects of efficiency will be illustrated for several inverse and imaging problems in seabed acoustics and seismology. [Funded by the Natural Sciences and Engineering Research Council of Canada.]
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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 | 0.003 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".