Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models release_wxywkpvzfbavjkc2ewbcltgbum

by Ling Guo, Hao Wu, Tao Zhou

Released as a article .

2021  

Abstract

We introduce in this work the normalizing field flows (NFF) for learning random fields from scattered measurements. More precisely, we construct a bijective transformation (a normalizing flow characterizing by neural networks) between a Gaussian random field with the Karhunen-Lo\`eve (KL) expansion structure and the target stochastic field, where the KL expansion coefficients and the invertible networks are trained by maximizing the sum of the log-likelihood on scattered measurements. This NFF model can be used to solve data-driven forward, inverse, and mixed forward/inverse stochastic partial differential equations in a unified framework. We demonstrate the capability of the proposed NFF model for learning Non Gaussian processes and different types of stochastic partial differential equations.
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Type  article
Stage   submitted
Date   2021-09-07
Version   v2
Language   en ?
arXiv  2108.12956v2
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