{"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/discovering-sparse-interpretable-dynamics","title":"Discovering Sparse Interpretable Dynamics from Partial Observations","arxiv_id":"2107.10879","date":"2021-07-22","proceeding":null,"authors":["Peter Y. Lu","Joan Ariño","Marin Soljačić"],"abstract":"Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. We propose a machine learning framework for discovering these governing equations using only partial observations, combining an encoder for state reconstruction with a sparse symbolic model. Our tests show that this method can successfully reconstruct the full system state and identify the underlying dynamics for a variety of ODE and PDE systems.","url_abs":"https://arxiv.org/abs/2107.10879v2","url_pdf":"https://arxiv.org/pdf/2107.10879v2.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":"discovering-sparse-interpretable-dynamics","repo_url":"https://github.com/peterparity/symder","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2107.10879","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2107.10879"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+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/peterparity/symder","reach":null}],"summary":{"ran_draft_wrong":1,"unverified":2},"by_repo_kind":{"official":{"samples":3,"ran":1,"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":"f6cad340caf3a795","entry":"get_model_apply","repo":"peterparity/symder","repo_kind":"official","path":"symder/symder.py","file_url":"https://github.com/peterparity/symder/blob/HEAD/symder/symder.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"f6cad340caf3a795"}},{"code_sha256_prefix":"27141289006aae18","entry":"generate_dataset","repo":"peterparity/symder","repo_kind":"official","path":"data/lorenz.py","file_url":"https://github.com/peterparity/symder/blob/HEAD/data/lorenz.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":"27141289006aae18"}},{"code_sha256_prefix":"5f99e041a0bd1107","entry":"get_symder_apply","repo":"peterparity/symder","repo_kind":"official","path":"symder/symder.py","file_url":"https://github.com/peterparity/symder/blob/HEAD/symder/symder.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":"5f99e041a0bd1107"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}