  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.
