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Neural Operators offer a powerful, data-driven tool for solving parametricPDEs as they can represent maps between infinite-dimensional function spaces.In this work, we employ physics-informed Neural Operators in the context ofhigh-dimensional, Bayesian inverse problems. Traditional solution strategiesnecessitate an enormous, and frequently infeasible, number of forward modelsolves, as well as the computation of parametric derivatives. In order toenable efficient solutions, we extend Deep Operator Networks (DeepONets) byemploying a RealNVP architecture which yields an invertible and differentiablemap between the parametric input and the branch-net output. This allows us toconstruct accurate approximations of the full posterior, irrespective of thenumber of observations and the magnitude of the observation noise, without anyneed for additional forward solves nor for cumbersome, iterative samplingprocedures. We demonstrate the efficacy and accuracy of the proposedmethodology in the context of inverse problems for three benchmarks: ananti-derivative equation, reaction-diffusion dynamics and flow through porousmedia.

Semi-supervised Invertible Neural Operators for Bayesian Inverse Problems