Solving inverse problems in stochastic models using deep neural networks and adversarial training

Inverse problems associated with stochastic models constitute a significant portion of scientific and engineering applications. In such cases the unknown quantities are distributions. The applicability of traditional methods is limited because of their demanding assumptions or prohibitive computational consumption; for example, maximum likelihood methods require closed-form density functions, and Markov Chain Monte Carlo needs a large number of simulations. We propose a new method that estimates the unknown distribution by matching the statistical properties between observed and simulated random processes. We leverage the expressive power of neural networks to approximate the unknown distribution and use a discriminative neural network for computing the statistical discrepancies between the observed and simulated random processes. We demonstrated numerically that the proposed methods can estimate both the model parameters and learn complicated unknown distributions. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

Inverse problems associated with stochastic models, where the unknown quantities are distributions, often face limitations with traditional methods that require closed-form density functions or a large number of simulations. A new method is proposed in this study which utilizes neural networks to approximate the unknown distribution and compute statistical discrepancies. Numerical experiments demonstrate the effectiveness of the proposed method in estimating model parameters and learning complex unknown distributions.