Adversarial Numerical Analysis for Inverse Problems

TL;DR

This paper introduces adversarial numerical analysis, a novel approach that estimates unknown distributions in inverse problems by minimizing discrepancies using neural networks, overcoming limitations of traditional methods.

Contribution

It proposes a new adversarial approach for inverse problems that estimates distributions without requiring closed-form densities or extensive simulations.

Findings

Successfully estimates complex unknown distributions

Demonstrates effectiveness in parameter estimation

Uses neural networks to measure distribution discrepancies

Abstract

Many scientific and engineering applications are formulated as inverse problems associated with stochastic models. In such cases the unknown quantities are distributions. The applicability of traditional methods is limited because of their demanding assumptions or prohibitive computational consumptions; for example, maximum likelihood methods require closed-form density functions, and Markov Chain Monte Carlo needs a large number of simulations. We introduce adversarial numerical analysis, which estimates the unknown distributions by minimizing the discrepancy of statistical properties between observed random process and simulated random process. The discrepancy metric is computed with a discriminative neural network. We demonstrated numerically that the proposed methods can estimate the underlying parameters and learn complicated unknown distributions.