{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:16:41Z","timestamp":1787329001333,"version":"build-2736575974"},"reference-count":56,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100018625","name":"Science and Technology Innovation Plan of Shanghai Science and Technology Commission","doi-asserted-by":"crossref","award":["20JC1414200"],"award-info":[{"award-number":["20JC1414200"]}],"id":[{"id":"10.13039\/501100018625","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271367"],"award-info":[{"award-number":["12271367"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["92470119"],"award-info":[{"award-number":["92470119"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundations of Hainan Province of China","award":["121MS001"],"award-info":[{"award-number":["121MS001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2025,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We propose a deep learning algorithm for solving high-dimensional parabolic integro-differential equations (PIDEs) and high-dimensional forward-backward stochastic differential equations with jumps (FBSDEJs), where the jump-diffusion process is derived by a Brownian motion and an independent compensated Poisson random measure. In this novel algorithm, a pair of deep neural networks for the approximations of the gradient and the integral kernel is introduced in a crucial way based on the deep FBSDE method. To derive the error estimates for this deep learning algorithm, the convergence of Markovian iteration, the error bound of Euler time discretization, and the simulation error of deep learning algorithm are investigated. It is also shown that the approximation error converges to zero given the universal approximation capability of neural networks. Three numerical examples are provided to show the efficiency of this proposed algorithm.<\/jats:p>\n                  <jats:p>Reproducibility of computational results. This paper has been awarded the s\u201cSIAM Reproducibility Badge: Code and Data Available\u201d as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https:\/\/github.com\/yezaijun\/DeepFBSDEJ and in the supplementary materials ( DeepFBSDEJ-main.zip [8.75KB]), linked from the main article webpage. 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