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This\npaper introduces a deep learning-based approach that can handle general\nhigh-dimensional parabolic PDEs. To this end, the PDEs are reformulated using\nbackward stochastic differential equations and the gradient of the unknown\nsolution is approximated by neural networks, very much in the spirit of deep\nreinforcement learning with the gradient acting as the policy function.\nNumerical results on examples including the nonlinear Black-Scholes equation,\nthe Hamilton-Jacobi-Bellman equation, and the Allen-Cahn equation suggest that\nthe proposed algorithm is quite effective in high dimensions, in terms of both\naccuracy and cost. This opens up new possibilities in economics, finance,\noperational research, and physics, by considering all participating agents,\nassets, resources, or particles together at the same time, instead of making ad\nhoc assumptions on their inter-relationships.","url_abs":"http://arxiv.org/abs/1707.02568v3","url_pdf":"http://arxiv.org/pdf/1707.02568v3.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":"solving-high-dimensional-partial-differential","repo_url":"https://github.com/davidzhou9/DeepVol","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}},{"paper_slug":"solving-high-dimensional-partial-differential","repo_url":"https://github.com/frankhan91/DeepBSDE","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}},{"paper_slug":"solving-high-dimensional-partial-differential","repo_url":"https://github.com/huisun317/snn","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"solving-high-dimensional-partial-differential","repo_url":"https://github.com/kousun12/TFDE","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"solving-high-dimensional-partial-differential","repo_url":"https://github.com/mindspore-ai/models/tree/master/research/hpc/deepbsde","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"mindspore","reach":null},{"paper_slug":"solving-high-dimensional-partial-differential","repo_url":"https://github.com/yangyucheng000/deepbsde","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"mindspore","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"},{"task_slug":"deep-reinforcement-learning","task_name":"Deep Reinforcement Learning"},{"task_slug":"reinforcement-learning","task_name":"Reinforcement Learning"},{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1707.02568","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1707.02568"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+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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