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The solution of probabilistic inverse problems for which the correspondingforward problem is constrained by physical principles is challenging. This isespecially true if the dimension of the inferred vector is large and the priorinformation about it is in the form of a collection of samples. In this work, anovel deep learning based approach is developed and applied to solving thesetypes of problems. The approach utilizes samples of the inferred vector drawnfrom the prior distribution and a physics-based forward model to generatetraining data for a conditional Wasserstein generative adversarial network(cWGAN). The cWGAN learns the probability distribution for the inferred vectorconditioned on the measurement and produces samples from this distribution. ThecWGAN developed in this work differs from earlier versions in that its criticis required to be 1-Lipschitz with respect to both the inferred and themeasurement vectors and not just the former. This leads to a loss term with thefull (and not partial) gradient penalty. It is shown that this rather simplechange leads to a stronger notion of convergence for the conditional densitylearned by the cWGAN and a more robust and accurate sampling strategy. Throughnumerical examples it is shown that this change also translates to betteraccuracy when solving inverse problems. The numerical examples consideredinclude illustrative problems where the true distribution and/or statistics areknown, and a more complex inverse problem motivated by applications inbiomechanics.

Solution of physics-based inverse problems using conditional generative adversarial networks with full gradient penalty