BiLO: Bilevel Local Operator Learning for PDE inverse problems

arXiv:2404.17789v1 Announce Type: new
Abstract: We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to locally approximate the PDE solution operator in the neighborhood of a given set of PDE parameters, which enables an accurate approximation of …

abstract arxiv cs.lg cs.na data data loss differential loss math.na math.oc network neural network optimization parameters type