PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers
Researchers release PosteriorBench, a benchmark testing whether generative inverse solvers recover full reference posteriors across four physics-based inverse problems.
PosteriorBench evaluates distributional accuracy of generative inverse solvers on Darcy flow inversion, Poisson source recovery, carbon capture and storage, and light transport material inference. High-fidelity reference posteriors are built with rejection sampling and Markov chain Monte Carlo, paired with a five-metric suite including posterior-mean error, maximum mean discrepancy, and sliced Wasserstein distance. Experiments reveal substantial distribution-matching gaps in current solvers, while neural operators improve resolution robustness and guidance weights and generation noise are key to posterior-variance calibration.
- Targets mode collapse and overconfident uncertainty that pointwise metrics miss
- Covers Darcy flow, Poisson recovery, carbon storage, and material inference
- Reference posteriors built via rejection sampling and Markov chain Monte Carlo
- Five-metric suite includes MMD, sliced Wasserstein, and power-spectrum error
- Tags
- benchmarkevaluationgenerative-modelsinverse-problemsscientific-machine-learninguncertainty-quantification
- AI models
- PosteriorBench
From the original article
1 min read at arxiv.orgGenerative models are increasingly used to solve scientific inverse problems, but existing evaluations still focus primarily on whether a method can produce a single plausible reconstruction. This is insufficient for ill-posed problems, where multiple solutions may be consistent with the same sparse or noisy observations.
By Jiachen Yao · arxiv.org
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