{"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-stochastic-dynamics-from-snapshots","title":"Learning stochastic dynamics from snapshots through regularized unbalanced optimal transport","arxiv_id":"2410.00844","date":"2024-10-01","proceeding":null,"authors":["Zhenyi Zhang","Tiejun Li","Peijie Zhou"],"abstract":"Reconstructing dynamics using samples from sparsely time-resolved snapshots is an important problem in both natural sciences and machine learning. Here, we introduce a new deep learning approach for solving regularized unbalanced optimal transport (RUOT) and inferring continuous unbalanced stochastic dynamics from observed snapshots. Based on the RUOT form, our method models these dynamics without requiring prior knowledge of growth and death processes or additional information, allowing them to be learned directly from data. Theoretically, we explore the connections between the RUOT and Schr\\\"odinger bridge problem and discuss the key challenges and potential solutions. The effectiveness of our method is demonstrated with a synthetic gene regulatory network, high-dimensional Gaussian Mixture Model, and single-cell RNA-seq data from blood development. Compared with other methods, our approach accurately identifies growth and transition patterns, eliminates false transitions, and constructs the Waddington developmental landscape. Our code is available at: https://github.com/zhenyiizhang/DeepRUOT.","url_abs":"https://arxiv.org/abs/2410.00844v5","url_pdf":"https://arxiv.org/pdf/2410.00844v5.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-stochastic-dynamics-from-snapshots","repo_url":"https://github.com/zhenyiizhang/deepruot","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2410.00844","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2410.00844"}},"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. 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odels.py","file_url":"https://github.com/zhenyiizhang/deepruot/blob/HEAD/DeepRUOT/models.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"163395a4fd44c11f"}},{"code_sha256_prefix":"dd9e8b103b5851ca","entry":"to_np","repo":"zhenyiizhang/DeepRUOT","repo_kind":"official","path":"DeepRUOT/utils.py","file_url":"https://github.com/zhenyiizhang/DeepRUOT/blob/HEAD/DeepRUOT/utils.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"dd9e8b103b5851ca"}},{"code_sha256_prefix":"1e1c0b70144ee8a6","entry":"velocityNet","repo":"zhenyiizhang/deepruot","repo_kind":"official","path":"DeepRUOT/models.py","file_url":"https://github.com/zhenyiizhang/deepruot/blob/HEAD/DeepRUOT/models.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"1e1c0b70144ee8a6"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}