{"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/dysmho-data-driven-discovery-of-governing","title":"DySMHO: Data-Driven Discovery of Governing Equations for Dynamical Systems via Moving Horizon Optimization","arxiv_id":"2108.00069","date":"2021-07-30","proceeding":null,"authors":["Fernando Lejarza","Michael Baldea"],"abstract":"Discovering the governing laws underpinning physical and chemical phenomena is a key step towards understanding and ultimately controlling systems in science and engineering. We introduce Discovery of Dynamical Systems via Moving Horizon Optimization (DySMHO), a scalable machine learning framework for identifying governing laws in the form of differential equations from large-scale noisy experimental data sets. DySMHO consists of a novel moving horizon dynamic optimization strategy that sequentially learns the underlying governing equations from a large dictionary of basis functions. The sequential nature of DySMHO allows leveraging statistical arguments for eliminating irrelevant basis functions, avoiding overfitting to recover accurate and parsimonious forms of the governing equations. Canonical nonlinear dynamical system examples are used to demonstrate that DySMHO can accurately recover the governing laws, is robust to high levels of measurement noise and that it can handle challenges such as multiple time scale dynamics.","url_abs":"https://arxiv.org/abs/2108.00069v1","url_pdf":"https://arxiv.org/pdf/2108.00069v1.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":"dysmho-data-driven-discovery-of-governing","repo_url":"https://github.com/Baldea-Group/DySMHO","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2108.00069","atlas_url":"https://app.syntology.ai/?focus=2108.00069","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2108.00069"}},"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/Baldea-Group/DySMHO","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":5},"by_repo_kind":{"official":{"samples":5,"ran":0,"repositories":1}},"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":0,"samples":[{"code_sha256_prefix":"d41b8c2d4c834a71","entry":"data_interp","repo":"Baldea-Group/DySMHO","repo_kind":"official","path":"DySMHO/model/utils.py","file_url":"https://github.com/Baldea-Group/DySMHO/blob/HEAD/DySMHO/model/utils.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"d41b8c2d4c834a71"}},{"code_sha256_prefix":"ef7734d96aa800aa","entry":"optim_solve","repo":"Baldea-Group/DySMHO","repo_kind":"official","path":"DySMHO/model/utils.py","file_url":"https://github.com/Baldea-Group/DySMHO/blob/HEAD/DySMHO/model/utils.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"ef7734d96aa800aa"}},{"code_sha256_prefix":"d653cb548207b619","entry":"optim_solve","repo":"Baldea-Group/DySMHO","repo_kind":"official","path":"DySMHO/model/utils_3D.py","file_url":"https://github.com/Baldea-Group/DySMHO/blob/HEAD/DySMHO/model/utils_3D.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"d653cb548207b619"}},{"code_sha256_prefix":"f339be2263c1a63e","entry":"time_scale_conversion","repo":"Baldea-Group/DySMHO","repo_kind":"official","path":"DySMHO/model/utils.py","file_url":"https://github.com/Baldea-Group/DySMHO/blob/HEAD/DySMHO/model/utils.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"f339be2263c1a63e"}},{"code_sha256_prefix":"5ee6491d1012bc7d","entry":"time_scale_conversion","repo":"Baldea-Group/DySMHO","repo_kind":"official","path":"DySMHO/model/utils_3D.py","file_url":"https://github.com/Baldea-Group/DySMHO/blob/HEAD/DySMHO/model/utils_3D.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"5ee6491d1012bc7d"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}