{"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/forward-invariance-in-neural-network","title":"Forward Invariance in Neural Network Controlled Systems","arxiv_id":"2309.09043","date":"2023-09-16","proceeding":null,"authors":["Akash Harapanahalli","Saber Jafarpour","Samuel Coogan"],"abstract":"We present a framework based on interval analysis and monotone systems theory to certify and search for forward invariant sets in nonlinear systems with neural network controllers. The framework (i) constructs localized first-order inclusion functions for the closed-loop system using Jacobian bounds and existing neural network verification tools; (ii) builds a dynamical embedding system where its evaluation along a single trajectory directly corresponds with a nested family of hyper-rectangles provably converging to an attractive set of the original system; (iii) utilizes linear transformations to build families of nested paralleletopes with the same properties. The framework is automated in Python using our interval analysis toolbox $\\texttt{npinterval}$, in conjunction with the symbolic arithmetic toolbox $\\texttt{sympy}$, demonstrated on an $8$-dimensional leader-follower system.","url_abs":"https://arxiv.org/abs/2309.09043v2","url_pdf":"https://arxiv.org/pdf/2309.09043v2.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":"forward-invariance-in-neural-network","repo_url":"https://github.com/gtfactslab/harapanahalli_lcss2024","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}