Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models
release_wxywkpvzfbavjkc2ewbcltgbum
by
Ling Guo, Hao Wu, Tao Zhou
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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