Adversarial Numerical Analysis for Inverse Problems

Kailai Xu, Eric Darve
10/15/2019
math.NA

Official code: kailaix/ADCME.jl (319 stars, MIT, TensorFlow, last commit 2023-10-18).

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.

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Code Implementations(1)

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Automatic Differentiation Library for Computational and Mathematical Engineering

31963Julia, DockerfileJun 2, 20193 years agoMIT
automatic-differentiationmachine-learningneural-networksnumerical-pdesoptimization+2 more

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Cite this paper

@article{xu2019adversarial,
  title  = {Adversarial Numerical Analysis for Inverse Problems},
  author = {Kailai Xu and Eric Darve},
  year   = {2019},
  eprint = {1910.06936},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/1910.06936}
}

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