{"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/multistep-neural-networks-for-data-driven","title":"Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems","arxiv_id":"1801.01236","date":"2018-01-04","proceeding":null,"authors":["Maziar Raissi","Paris Perdikaris","George Em. Karniadakis"],"abstract":"The process of transforming observed data into predictive mathematical models\nof the physical world has always been paramount in science and engineering.\nAlthough data is currently being collected at an ever-increasing pace, devising\nmeaningful models out of such observations in an automated fashion still\nremains an open problem. In this work, we put forth a machine learning approach\nfor identifying nonlinear dynamical systems from data. Specifically, we blend\nclassical tools from numerical analysis, namely the multi-step time-stepping\nschemes, with powerful nonlinear function approximators, namely deep neural\nnetworks, to distill the mechanisms that govern the evolution of a given\ndata-set. We test the effectiveness of our approach for several benchmark\nproblems involving the identification of complex, nonlinear and chaotic\ndynamics, and we demonstrate how this allows us to accurately learn the\ndynamics, forecast future states, and identify basins of attraction. In\nparticular, we study the Lorenz system, the fluid flow behind a cylinder, the\nHopf bifurcation, and the Glycoltic oscillator model as an example of\ncomplicated nonlinear dynamics typical of biological systems.","url_abs":"http://arxiv.org/abs/1801.01236v1","url_pdf":"http://arxiv.org/pdf/1801.01236v1.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":"multistep-neural-networks-for-data-driven","repo_url":"https://github.com/maziarraissi/MultistepNNs","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"multistep-neural-networks-for-data-driven","repo_url":"https://github.com/aiqing-zhu/imde-lmm","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1801.01236","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}