{"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/deep-learning-and-symbolic-regression-for","title":"Deep Learning and Symbolic Regression for Discovering Parametric Equations","arxiv_id":"2207.00529","date":"2022-07-01","proceeding":null,"authors":["Michael Zhang","Samuel Kim","Peter Y. Lu","Marin Soljačić"],"abstract":"Symbolic regression is a machine learning technique that can learn the governing formulas of data and thus has the potential to transform scientific discovery. However, symbolic regression is still limited in the complexity and dimensionality of the systems that it can analyze. Deep learning on the other hand has transformed machine learning in its ability to analyze extremely complex and high-dimensional datasets. We propose a neural network architecture to extend symbolic regression to parametric systems where some coefficient may vary but the structure of the underlying governing equation remains constant. We demonstrate our method on various analytic expressions, ODEs, and PDEs with varying coefficients and show that it extrapolates well outside of the training domain. The neural network-based architecture can also integrate with other deep learning architectures so that it can analyze high-dimensional data while being trained end-to-end. To this end we integrate our architecture with convolutional neural networks to analyze 1D images of varying spring systems.","url_abs":"https://arxiv.org/abs/2207.00529v2","url_pdf":"https://arxiv.org/pdf/2207.00529v2.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":"deep-learning-and-symbolic-regression-for","repo_url":"https://github.com/samuelkim314/parametric-eql","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"},{"task_slug":"deep-learning","task_name":"Deep Learning"},{"task_slug":"symbolic-regression","task_name":"Symbolic Regression"},{"task_slug":"regression-1","task_name":"regression"},{"task_slug":"scientific-discovery","task_name":"scientific discovery"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2207.00529","atlas_url":"https://app.syntology.ai/?focus=2207.00529","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2207.00529"}},"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/samuelkim314/parametric-eql","reach":null}],"summary":{"ran_draft_wrong":3},"by_repo_kind":{"official":{"samples":3,"ran":3,"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":3,"samples":[{"code_sha256_prefix":"eac25a00bed20d9b","entry":"f1_parser","repo":"samuelkim314/parametric-eql","repo_kind":"official","path":"utils/plotters.py","file_url":"https://github.com/samuelkim314/parametric-eql/blob/HEAD/utils/plotters.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"eac25a00bed20d9b"}},{"code_sha256_prefix":"e46175203698c74b","entry":"id_parser","repo":"samuelkim314/parametric-eql","repo_kind":"official","path":"utils/plotters.py","file_url":"https://github.com/samuelkim314/parametric-eql/blob/HEAD/utils/plotters.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"e46175203698c74b"}},{"code_sha256_prefix":"e9e43c2c24a8a4cc","entry":"sinfreq_parser","repo":"samuelkim314/parametric-eql","repo_kind":"official","path":"utils/plotters.py","file_url":"https://github.com/samuelkim314/parametric-eql/blob/HEAD/utils/plotters.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"e9e43c2c24a8a4cc"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}