{"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/pde-net-learning-pdes-from-data","title":"PDE-Net: Learning PDEs from Data","arxiv_id":"1710.09668","date":"2017-10-26","proceeding":"ICML 2018 7","authors":["Zichao Long","Yiping Lu","Xianzhong Ma","Bin Dong"],"abstract":"In this paper, we present an initial attempt to learn evolution PDEs from\ndata. Inspired by the latest development of neural network designs in deep\nlearning, we propose a new feed-forward deep network, called PDE-Net, to\nfulfill two objectives at the same time: to accurately predict dynamics of\ncomplex systems and to uncover the underlying hidden PDE models. The basic idea\nof the proposed PDE-Net is to learn differential operators by learning\nconvolution kernels (filters), and apply neural networks or other machine\nlearning methods to approximate the unknown nonlinear responses. Comparing with\nexisting approaches, which either assume the form of the nonlinear response is\nknown or fix certain finite difference approximations of differential\noperators, our approach has the most flexibility by learning both differential\noperators and the nonlinear responses. A special feature of the proposed\nPDE-Net is that all filters are properly constrained, which enables us to\neasily identify the governing PDE models while still maintaining the expressive\nand predictive power of the network. These constrains are carefully designed by\nfully exploiting the relation between the orders of differential operators and\nthe orders of sum rules of filters (an important concept originated from\nwavelet theory). We also discuss relations of the PDE-Net with some existing\nnetworks in computer vision such as Network-In-Network (NIN) and Residual\nNeural Network (ResNet). Numerical experiments show that the PDE-Net has the\npotential to uncover the hidden PDE of the observed dynamics, and predict the\ndynamical behavior for a relatively long time, even in a noisy environment.","url_abs":"http://arxiv.org/abs/1710.09668v2","url_pdf":"http://arxiv.org/pdf/1710.09668v2.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":"pde-net-learning-pdes-from-data","repo_url":"https://github.com/Slowpuncher24/pde-net-in-tf","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"pde-net-learning-pdes-from-data","repo_url":"https://github.com/ZichaoLong/aTEAM","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"pde-net-learning-pdes-from-data","repo_url":"https://github.com/agrundner24/pde-net-in-tf","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"pde-net-learning-pdes-from-data","repo_url":"https://github.com/isds-neu/percnn","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"pde-net-learning-pdes-from-data","repo_url":"https://github.com/yangyucheng000/papercode-2/tree/main/PDOC_mindspore-main","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"mindspore","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1710.09668","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1710.09668"}},"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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