Particle-Guided Diffusion Models for Partial Differential Equations
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911723948081152 |
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| author | Millard, Andrew Lindsten, Fredrik Zhao, Zheng |
| author_facet | Millard, Andrew Lindsten, Fredrik Zhao, Zheng |
| contents | We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples remain physically admissible. We embed this sampling procedure within a new Sequential Monte Carlo (SMC) framework, yielding a scalable generative PDE solver. Across multiple benchmark PDE systems as well as multiphysics and interacting PDE systems, our method produces solution fields with lower numerical error than existing state-of-the-art generative methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_23262 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Particle-Guided Diffusion Models for Partial Differential Equations Millard, Andrew Lindsten, Fredrik Zhao, Zheng Machine Learning We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples remain physically admissible. We embed this sampling procedure within a new Sequential Monte Carlo (SMC) framework, yielding a scalable generative PDE solver. Across multiple benchmark PDE systems as well as multiphysics and interacting PDE systems, our method produces solution fields with lower numerical error than existing state-of-the-art generative methods. |
| title | Particle-Guided Diffusion Models for Partial Differential Equations |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2601.23262 |