![]() ![]() ![]() The proposed framework further allows for a seamless integration of observed data for solving inverse problems and building generative models. Furthermore, the proposed methodology does not require any expensive PDE solves and is physics-informed only at training time, which allows real-time emulation of PDEs and generation of inverse problem solutions after training, bypassing the need for FEM solve operations with comparable accuracy to FEM solutions. 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 parameter-to-solution network, all of which are jointly trained. 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. 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). ![]()
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