mlsanityData to 14 Oct 2026

Sampling from Neural Operator Priors to Solve Partial Differential Equations

arXiv 2610.16396 ↗First posted 12 Oct 2026cs.LGcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 16 of its 27 references that are in the map. First posted on arXiv 12 Oct 2026.

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References · 16

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  2. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
  3. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  4. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,416
  5. 2022DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Modelscited by 938
  6. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 527
  7. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 232
  8. 2022U-NO: U-shaped Neural Operatorscited by 230
  9. 2024DiffusionPDE: Generative PDE-Solving Under Partial Observationcited by 108
  10. 2023SA-Solver: Stochastic Adams Solver for Fast Sampling of Diffusion Modelscited by 72
  11. 2023Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulationcited by 71
  12. 2024On conditional diffusion models for PDE simulationscited by 60
4 more
  1. 2025Guided Diffusion Sampling on Function Spaces with Applications to PDEscited by 36
  2. 2023A Denoising Diffusion Model for Fluid Field Predictioncited by 32
  3. 2024Conditional sampling within generative diffusion modelscited by 19
  4. 2026Particle-Guided Diffusion Models for Partial Differential Equationscited by 5

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