Diffusion models as probabilistic neural operators for recovering unobserved states of dynamical systems

arXiv:2405.07097v1 Announce Type: new
Abstract: This paper explores the efficacy of diffusion-based generative models as neural operators for partial differential equations (PDEs). Neural operators are neural networks that learn a mapping from the parameter space to the solution space of PDEs from data, and they can also solve the inverse problem of estimating the parameter from the solution. Diffusion models excel in many domains, but their potential as neural operators has not been thoroughly explored. In this work, we show …

abstract arxiv cs.ai cs.lg data differential diffusion diffusion models generative generative models learn mapping networks neural networks operators paper solution space systems type