A GAN based solver of black-box inverse problems

Michael Gillhofer, Hubert Ramsauer, Johannes Brandstetter, Bernhard Schäfl, Sepp Hochreiter

Keywords: GAN

Abstract: We propose a GAN based approach to solve inverse problems which have non-differential or non-continuous forward relations. In the standard sense, an inverse problem is interpreted as the process of calculating factors that produce observations. We reformulate the inverse problem such that the discriminator is a binary classifier and the generator is used to produce samples in a local region of the input domain of the forward relation. Our GAN based approach solves inverse problems by using adversarial training but without relying on the gradients of the original problem formulation. We prove the efficacy of our approach by applying it to an artificially generated topology optimization problem. We demonstrate that despite not having access to derivatives of f our method leads to similar results than more traditional topology optimization methods.