{"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/tangent-space-regularization-for-neural","title":"Tangent-Space Regularization for Neural-Network Models of Dynamical Systems","arxiv_id":"1806.09919","date":"2018-06-26","proceeding":null,"authors":["Fredrik Bagge Carlson","Rolf Johansson","Anders Robertsson"],"abstract":"This work introduces the concept of tangent space regularization for\nneural-network models of dynamical systems. The tangent space to the dynamics\nfunction of many physical systems of interest in control applications exhibits\nuseful properties, e.g., smoothness, motivating regularization of the model\nJacobian along system trajectories using assumptions on the tangent space of\nthe dynamics. Without assumptions, large amounts of training data are required\nfor a neural network to learn the full non-linear dynamics without overfitting.\nWe compare different network architectures on one-step prediction and\nsimulation performance and investigate the propensity of different\narchitectures to learn models with correct input-output Jacobian. Furthermore,\nthe influence of $L_2$ weight regularization on the learned Jacobian eigenvalue\nspectrum, and hence system stability, is investigated.","url_abs":"http://arxiv.org/abs/1806.09919v1","url_pdf":"http://arxiv.org/pdf/1806.09919v1.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":"tangent-space-regularization-for-neural","repo_url":"https://github.com/baggepinnen/JacProp.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}