Deep Probabilistic Models for Forward and Inverse Problems in Parametric PDEs. (arXiv:2208.04856v1 [stat.ML])

We formulate a class of physics-driven deep latent variable models (PDDLVM)
to learn parameter-to-solution (forward) and solution-to-parameter (inverse)
maps of parametric partial differential equations (PDEs). Our formulation
leverages the finite element method (FEM), deep neural networks, and
probabilistic modeling to assemble a deep probabilistic framework in which the
forward and inverse maps are approximated with coherent uncertainty
quantification. Our probabilistic model explicitly incorporates a parametric
PDE-based density and a trainable solution-to-parameter network while the
introduced amortized variational family postulates a …

arxiv deep probabilistic models ml parametric