{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/adversarial-numerical-analysis-for-inverse","title":"Adversarial Numerical Analysis for Inverse Problems","arxiv_id":"1910.06936","date":"2019-10-15","proceeding":null,"authors":["Kailai Xu","Eric Darve"],"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.","url_abs":"https://arxiv.org/abs/1910.06936v1","url_pdf":"https://arxiv.org/pdf/1910.06936v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"adversarial-numerical-analysis-for-inverse","repo_url":"https://github.com/kailaix/ADCME.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"adversarial-numerical-analysis-for-inverse","repo_url":"https://github.com/UnofficialJuliaMirror/ADCME.jl-07b341a0-ce75-57c6-b2de-414ffdc00be5","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"adversarial-numerical-analysis-for-inverse","repo_url":"https://github.com/UnofficialJuliaMirrorSnapshots/ADCME.jl-07b341a0-ce75-57c6-b2de-414ffdc00be5","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}