Methods and systems for solving inverse problems arising in systems described by a physics-based forward propagation model use a Bayesian approach to model the uncertainty in the realization of model parameters. A Generative Adversarial Network (“GAN”) architecture along with heuristics and statistical learning is used. This results in a more reliable point estimate of the desired model parameters. In some embodiments, the disclosed methodology may be applied to automatic inversion of physics-based modeling of pipelines.