{"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/the-lyapunov-neural-network-adaptive","title":"The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems","arxiv_id":"1808.00924","date":"2018-08-02","proceeding":null,"authors":["Spencer M. Richards","Felix Berkenkamp","Andreas Krause"],"abstract":"Learning algorithms have shown considerable prowess in simulation by allowing\nrobots to adapt to uncertain environments and improve their performance.\nHowever, such algorithms are rarely used in practice on safety-critical\nsystems, since the learned policy typically does not yield any safety\nguarantees. That is, the required exploration may cause physical harm to the\nrobot or its environment. In this paper, we present a method to learn accurate\nsafety certificates for nonlinear, closed-loop dynamical systems. Specifically,\nwe construct a neural network Lyapunov function and a training algorithm that\nadapts it to the shape of the largest safe region in the state space. The\nalgorithm relies only on knowledge of inputs and outputs of the dynamics,\nrather than on any specific model structure. We demonstrate our method by\nlearning the safe region of attraction for a simulated inverted pendulum.\nFurthermore, we discuss how our method can be used in safe learning algorithms\ntogether with statistical models of dynamical systems.","url_abs":"http://arxiv.org/abs/1808.00924v2","url_pdf":"http://arxiv.org/pdf/1808.00924v2.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":"the-lyapunov-neural-network-adaptive","repo_url":"https://github.com/befelix/safe_learning","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1808.00924","atlas_url":"https://app.syntology.ai/?focus=1808.00924","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1808.00924"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/befelix/safe_learning","reach":null}],"summary":{"unverified":1},"by_repo_kind":{},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":1,"samples":[{"code_sha256_prefix":"8a5fdb040f931560","entry":"perturb_actions","repo":null,"repo_kind":null,"path":null,"file_url":null,"link_basis":"identical_code_first_harvested_elsewhere","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":null,"inline_ok":false,"mcp_get_code":{"code_sha256":"8a5fdb040f931560"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}