{"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/learning-dynamical-systems-an-example-from","title":"Learning dynamical systems: an example from open quantum system dynamics","arxiv_id":"2211.06678","date":"2022-11-12","proceeding":null,"authors":["Pietro Novelli"],"abstract":"Machine learning algorithms designed to learn dynamical systems from data can be used to forecast, control and interpret the observed dynamics. In this work we exemplify the use of one of such algorithms, namely Koopman operator learning, in the context of open quantum system dynamics. We will study the dynamics of a small spin chain coupled with dephasing gates and show how Koopman operator learning is an approach to efficiently learn not only the evolution of the density matrix, but also of every physical observable associated to the system. Finally, leveraging the spectral decomposition of the learned Koopman operator, we show how symmetries obeyed by the underlying dynamics can be inferred directly from data.","url_abs":"https://arxiv.org/abs/2211.06678v2","url_pdf":"https://arxiv.org/pdf/2211.06678v2.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":"learning-dynamical-systems-an-example-from","repo_url":"https://github.com/CSML-IIT-UCL/kooplearn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"operator-learning","task_name":"Operator learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2211.06678","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2211.06678"}},"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/CSML-IIT-UCL/kooplearn","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":16},"by_repo_kind":{"official":{"samples":16,"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":"c2199443c77a8fa1","entry":"assemble_operators_1d","repo":"CSML-IIT-UCL/kooplearn","repo_kind":"official","path":"src/kooplearn/datasets/_overdamped_langevin_generator.py","file_url":"https://github.com/CSML-IIT-UCL/kooplearn/blob/HEAD/src/kooplearn/datasets/_overdamped_langevin_generator.py","link_basis":"harvester_set","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":"c2199443c77a8fa1"}},{"code_sha256_prefix":"3108d99f4689babb","entry":"assemble_operators_2d","repo":"CSML-IIT-UCL/kooplearn","repo_kind":"official","path":"src/kooplearn/datasets/_overdamped_langevin_generator.py","file_url":"https://github.com/CSML-IIT-UCL/kooplearn/blob/HEAD/src/kooplearn/datasets/_overdamped_langevin_generator.py","link_basis":"harvester_set","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":"3108d99f4689babb"}},{"code_sha256_prefix":"68ad10e8ef37d022","entry":"build_cosine_basis_1d","repo":"CSML-IIT-UCL/kooplearn","repo_kind":"official","path":"src/kooplearn/datasets/_overdamped_langevin_generator.py","file_url":"https://github.com/CSML-IIT-UCL/kooplearn/blob/HEAD/src/kooplearn/datasets/_overdamped_langevin_generator.py","link_basis":"harvester_set","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":"68ad10e8ef37d022"}},{"code_sha256_prefix":"fad015dcf69a86cf","entry":"compute_transition_matrix","repo":"CSML-IIT-UCL/kooplearn","repo_kind":"official","path":"src/kooplearn/datasets/_logistic_map.py","file_url":"https://github.com/CSML-IIT-UCL/kooplearn/blob/HEAD/src/kooplearn/datasets/_logistic_map.py","link_basis":"harvester_set","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":"fad015dcf69a86cf"}},{"code_sha256_prefix":"29532cdf3f0299d4","entry":"covariance","repo":"CSML-IIT-UCL/kooplearn","repo_kind":"official","path":"src/kooplearn/_linalg.py","file_url":"https://github.com/CSML-IIT-UCL/kooplearn/blob/HEAD/src/kooplearn/_linalg.py","link_basis":"harvester_set","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":"29532cdf3f0299d4"}},{"code_sha256_prefix":"fc5e0c22ee0c97e4","entry":"directed_hausdorff_distance","repo":"CSML-IIT-UCL/kooplearn","repo_kind":"official","path":"src/kooplearn/metrics.py","file_url":"https://github.com/CSML-IIT-UCL/kooplearn/blob/HEAD/src/kooplearn/metrics.py","link_basis":"harvester_set","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":"fc5e0c22ee0c97e4"}},{"code_sha256_prefix":"21ca10017842e559","entry":"find_complex_conjugates","repo":"CSML-IIT-UCL/kooplearn","repo_kind":"official","path":"src/kooplearn/_utils.py","file_url":"https://github.com/CSML-IIT-UCL/kooplearn/blob/HEAD/src/kooplearn/_utils.py","link_basis":"harvester_set","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":"21ca10017842e559"}},{"code_sha256_prefix":"9e63dcf31d16723c","entry":"fuzzy_parse_complex","repo":"CSML-IIT-UCL/kooplearn","repo_kind":"official","path":"src/kooplearn/_utils.py","file_url":"https://github.com/CSML-IIT-UCL/kooplearn/blob/HEAD/src/kooplearn/_utils.py","link_basis":"harvester_set","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":"9e63dcf31d16723c"}},{"code_sha256_prefix":"144f7c9df1753a93","entry":"logistic_map","repo":"CSML-IIT-UCL/kooplearn","repo_kind":"official","path":"src/kooplearn/datasets/_logistic_map.py","file_url":"https://github.com/CSML-IIT-UCL/kooplearn/blob/HEAD/src/kooplearn/datasets/_logistic_map.py","link_basis":"harvester_set","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":"144f7c9df1753a93"}},{"code_sha256_prefix":"7e5917ad9b7d91d6","entry":"make_duffing","repo":"CSML-IIT-UCL/kooplearn","repo_kind":"official","path":"src/kooplearn/datasets/_samples_generator.py","file_url":"https://github.com/CSML-IIT-UCL/kooplearn/blob/HEAD/src/kooplearn/datasets/_samples_generator.py","link_basis":"harvester_set","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":"7e5917ad9b7d91d6"}},{"code_sha256_prefix":"eb5b8263066395a5","entry":"make_linear_system","repo":"CSML-IIT-UCL/kooplearn","repo_kind":"official","path":"src/kooplearn/datasets/_samples_generator.py","file_url":"https://github.com/CSML-IIT-UCL/kooplearn/blob/HEAD/src/kooplearn/datasets/_samples_generator.py","link_basis":"harvester_set","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":"eb5b8263066395a5"}},{"code_sha256_prefix":"b59e7e8dc93e917e","entry":"make_lorenz63","repo":"CSML-IIT-UCL/kooplearn","repo_kind":"official","path":"src/kooplearn/datasets/_samples_generator.py","file_url":"https://github.com/CSML-IIT-UCL/kooplearn/blob/HEAD/src/kooplearn/datasets/_samples_generator.py","link_basis":"harvester_set","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":"b59e7e8dc93e917e"}},{"code_sha256_prefix":"38721ec99a7c41f6","entry":"noise_features","repo":"CSML-IIT-UCL/kooplearn","repo_kind":"official","path":"src/kooplearn/datasets/_logistic_map.py","file_url":"https://github.com/CSML-IIT-UCL/kooplearn/blob/HEAD/src/kooplearn/datasets/_logistic_map.py","link_basis":"harvester_set","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":"38721ec99a7c41f6"}},{"code_sha256_prefix":"a92bd87a7d27826d","entry":"spd_neg_pow","repo":"CSML-IIT-UCL/kooplearn","repo_kind":"official","path":"src/kooplearn/_linalg.py","file_url":"https://github.com/CSML-IIT-UCL/kooplearn/blob/HEAD/src/kooplearn/_linalg.py","link_basis":"harvester_set","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":"a92bd87a7d27826d"}},{"code_sha256_prefix":"fc4666aeadf8fcdb","entry":"stable_topk","repo":"CSML-IIT-UCL/kooplearn","repo_kind":"official","path":"src/kooplearn/_utils.py","file_url":"https://github.com/CSML-IIT-UCL/kooplearn/blob/HEAD/src/kooplearn/_utils.py","link_basis":"harvester_set","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":"fc4666aeadf8fcdb"}},{"code_sha256_prefix":"bd99f93761bae48d","entry":"weighted_norm","repo":"CSML-IIT-UCL/kooplearn","repo_kind":"official","path":"src/kooplearn/_linalg.py","file_url":"https://github.com/CSML-IIT-UCL/kooplearn/blob/HEAD/src/kooplearn/_linalg.py","link_basis":"harvester_set","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":"bd99f93761bae48d"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}