CAM seminar——Normalizing field flow: Solving forward and inverse stochastic differential equations using physics-informed flow model
报告人：周涛 (中科院计算数学与科学工程计算研究所)
时间：2022-03-08 10:30-11:30
地点：Room 1560, Sciences Building No. 1
Abstract:
We introduce 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 (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, mixed Gaussian processes, and forward \& inverse stochastic partial differential equations.
