Model Releases
Sampling from Neural Operator Priors to Solve Partial Differential Equations
arXiv:2610.16396v1 Announce Type: new Abstract: Guided sampling with sparse observations and PDE residuals has recently been combined with neural operator priors to solve partial differential equation
arXiv:2610.16396v1 Announce Type: new 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.
Related
- Modelling Gas-Phase Reaction Kinetics with Guided Particle Diffusion Sampling
- Physics-informed neural networks by Gradient-Guided Gaussian Adaptive Sampling (3GAS-PINNs)
- Particle-Guided Diffusion Models for Partial Differential Equations
Source: arXiv cs.LG | 2026-10-14