{"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/forward-backward-stochastic-neural-networks","title":"Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations","arxiv_id":"1804.07010","date":"2018-04-19","proceeding":null,"authors":["Maziar Raissi"],"abstract":"Classical numerical methods for solving partial differential equations suffer\nfrom the curse dimensionality mainly due to their reliance on meticulously\ngenerated spatio-temporal grids. Inspired by modern deep learning based\ntechniques for solving forward and inverse problems associated with partial\ndifferential equations, we circumvent the tyranny of numerical discretization\nby devising an algorithm that is scalable to high-dimensions. In particular, we\napproximate the unknown solution by a deep neural network which essentially\nenables us to benefit from the merits of automatic differentiation. To train\nthe aforementioned neural network we leverage the well-known connection between\nhigh-dimensional partial differential equations and forward-backward stochastic\ndifferential equations. In fact, independent realizations of a standard\nBrownian motion will act as training data. We test the effectiveness of our\napproach for a couple of benchmark problems spanning a number of scientific\ndomains including Black-Scholes-Barenblatt and Hamilton-Jacobi-Bellman\nequations, both in 100-dimensions.","url_abs":"http://arxiv.org/abs/1804.07010v1","url_pdf":"http://arxiv.org/pdf/1804.07010v1.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":"abstracts"},"code_links":[{"paper_slug":"forward-backward-stochastic-neural-networks","repo_url":"https://github.com/maziarraissi/FBSNNs","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"forward-backward-stochastic-neural-networks","repo_url":"https://github.com/Shine119/FBSNNs_pytorch","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"forward-backward-stochastic-neural-networks","repo_url":"https://github.com/batuhanguler/Deep-BSDE-Solver","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1804.07010","atlas_url":"https://app.syntology.ai/?focus=1804.07010","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1804.07010"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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