{"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/self-supervised-learning-with-lie-symmetries","title":"Self-Supervised Learning with Lie Symmetries for Partial Differential Equations","arxiv_id":"2307.05432","date":"2023-07-11","proceeding":"NeurIPS 2023 11","authors":["Grégoire Mialon","Quentin Garrido","Hannah Lawrence","Danyal Rehman","Yann Lecun","Bobak T. Kiani"],"abstract":"Machine learning for differential equations paves the way for computationally efficient alternatives to numerical solvers, with potentially broad impacts in science and engineering. Though current algorithms typically require simulated training data tailored to a given setting, one may instead wish to learn useful information from heterogeneous sources, or from real dynamical systems observations that are messy or incomplete. In this work, we learn general-purpose representations of PDEs from heterogeneous data by implementing joint embedding methods for self-supervised learning (SSL), a framework for unsupervised representation learning that has had notable success in computer vision. Our representation outperforms baseline approaches to invariant tasks, such as regressing the coefficients of a PDE, while also improving the time-stepping performance of neural solvers. We hope that our proposed methodology will prove useful in the eventual development of general-purpose foundation models for PDEs. Code: https://github.com/facebookresearch/SSLForPDEs.","url_abs":"https://arxiv.org/abs/2307.05432v2","url_pdf":"https://arxiv.org/pdf/2307.05432v2.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":"self-supervised-learning-with-lie-symmetries","repo_url":"https://github.com/facebookresearch/sslforpdes","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[{"task_slug":"representation-learning","task_name":"Representation Learning"},{"task_slug":"self-supervised-learning","task_name":"Self-Supervised Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2307.05432","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2307.05432"}},"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":"deterministic:regex_extraction","url":"https://github.com/facebookresearch/SSLForPDEs","reach":{"status":"ok","spdx":"NOASSERTION"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/facebookresearch/sslforpdes","reach":{"status":"ok","spdx":"NOASSERTION"}}],"summary":{"ran_draft_wrong":2,"ran_fixture":1,"ran":1},"by_repo_kind":{"official":{"samples":4,"ran":4,"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":4,"samples":[{"code_sha256_prefix":"2ce7b58fb0badce0","entry":"Projector","repo":"facebookresearch/SSLForPDEs","repo_kind":"official","path":"navier_stokes.py","file_url":"https://github.com/facebookresearch/SSLForPDEs/blob/HEAD/navier_stokes.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":"NOASSERTION","inline_ok":false,"mcp_get_code":{"code_sha256":"2ce7b58fb0badce0"}},{"code_sha256_prefix":"3ebdb43028393e63","entry":"lie_trotter_exp","repo":"facebookresearch/SSLForPDEs","repo_kind":"official","path":"transformations.py","file_url":"https://github.com/facebookresearch/SSLForPDEs/blob/HEAD/transformations.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"NOASSERTION","inline_ok":false,"mcp_get_code":{"code_sha256":"3ebdb43028393e63"}},{"code_sha256_prefix":"d8fe2e49736074c4","entry":"lie_trotter_exp_2","repo":"facebookresearch/SSLForPDEs","repo_kind":"official","path":"transformations.py","file_url":"https://github.com/facebookresearch/SSLForPDEs/blob/HEAD/transformations.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"NOASSERTION","inline_ok":false,"mcp_get_code":{"code_sha256":"d8fe2e49736074c4"}},{"code_sha256_prefix":"2b0f2e01325010f3","entry":"relative_error","repo":"facebookresearch/sslforpdes","repo_kind":"official","path":"utils.py","file_url":"https://github.com/facebookresearch/sslforpdes/blob/HEAD/utils.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"NOASSERTION","inline_ok":false,"mcp_get_code":{"code_sha256":"2b0f2e01325010f3"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}