Solving PDE-based inverse problems with learned surrogates and constraints

TitleSolving PDE-based inverse problems with learned surrogates and constraints
Publication TypePresentation
Year of Publication2023
AuthorsZiyi Yin, Rafael Orozco, Mathias Louboutin, Felix J. Herrmann
Keywordsdeep learning, Fourier neural operators, Inverse problems, learned constraints, learned surrogates, multiphysics, Normalizing flows, PDE

In this presentation, I will introduce a learned inversion algorithm for solving inverse problems with computationally expensive forward operators. We tackle this challenge by combining learned surrogates (Fourier neural operators) with learned constraints (normalizing flows). After jointly training these networks with the same samples, the learned surrogates lead to computationally efficient surrogate-assisted inversion. Meanwhile, the learned constraints safeguard the accuracy of the surrogates by forcing the model iterates to remain in-distribution. By combining the two, we come up with a homotopy / continuation scheme where the constraints are relaxed slowly so that the data misfit objective can be minimized while the model iterates always remain in the statistical distribution on which the surrogates are trained. We demonstrate the efficacy of our learned inversion algorithm through carefully selected experiments centered around the problem of geological carbon storage monitoring.



Citation Keyyin2023HOTCSEspi