Sampling from Neural Operator Priors to Solve Partial Differential Equations

Abstract:Guided sampling with sparse observations and PDE residuals has recently been combined with neural operator priors to solve partial differential equations in function space, their natural setting. We pair such a prior with pseudo-bootstrap sequential Monte Carlo (pBS SMC), a guided sampling framework that accommodates proposals without tractable densities, and introduce a new proposal by adapting the DPM++ algorithm to the guidance setting. Across five benchmark PDE systems this proposal attains the best error--time trade-off at every step count tested, and wrapping it in pBS gives the lowest error on most inverse-problem settings, with the largest gains when few sampling steps are used.

Machine Learning (cs.LG)

arXiv:2610.16396 [cs.LG]

(or arXiv:2610.16396v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.16396 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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