Normalizing Field Flows: Solving forward and inverse stochastic differential equations using Physics-Informed flow model

• URL: http://arxiv.org/abs/2108.12956v1
• Date: Mon, 30 Aug 2021 01:58:01 GMT
• Title: Normalizing Field Flows: Solving forward and inverse stochastic differential equations using Physics-Informed flow model
• Authors: Ling Guo, Hao Wu, Tao Zhou
• Abstract summary: We introduce in this work the normalizing field flows (NFF) for learning random fields from scattered measurements. We demonstrate the capability of the proposed NFF model for learning Non Gaussian processes, mixed Gaussian processes, and forward & inverse partial differential equations.
• Score: 8.455584500599807
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 reference random field (say, a Gaussian random field with the Karhunen-Lo\`eve 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, mixed Gaussian processes, and forward & inverse stochastic partial differential equations.

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