{"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/distributional-gradient-matching-for-learning","title":"Distributional Gradient Matching for Learning Uncertain Neural Dynamics Models","arxiv_id":"2106.11609","date":"2021-06-22","proceeding":"NeurIPS 2021 12","authors":["Lenart Treven","Philippe Wenk","Florian Dörfler","Andreas Krause"],"abstract":"Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the adjoint method, many downstream tasks such as active learning, exploration in reinforcement learning, robust control, or filtering require accurate estimates of predictive uncertainties. In this work, we propose a novel approach towards estimating epistemically uncertain neural ODEs, avoiding the numerical integration bottleneck. Instead of modeling uncertainty in the ODE parameters, we directly model uncertainties in the state space. Our algorithm - distributional gradient matching (DGM) - jointly trains a smoother and a dynamics model and matches their gradients via minimizing a Wasserstein loss. Our experiments show that, compared to traditional approximate inference methods based on numerical integration, our approach is faster to train, faster at predicting previously unseen trajectories, and in the context of neural ODEs, significantly more accurate.","url_abs":"https://arxiv.org/abs/2106.11609v2","url_pdf":"https://arxiv.org/pdf/2106.11609v2.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":"distributional-gradient-matching-for-learning","repo_url":"https://github.com/lenarttreven/dgm","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","reach":null}],"tasks":[{"task_slug":"active-learning","task_name":"Active Learning"},{"task_slug":"numerical-integration","task_name":"Numerical Integration"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2106.11609","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2106.11609"}},"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/lenarttreven/dgm","reach":null}],"summary":{"ran_honours":1,"unverified":1},"by_repo_kind":{"official":{"samples":2,"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":"c09c97df5a1d2228","entry":"make_positive","repo":"lenarttreven/dgm","repo_kind":"official","path":"dgm/dynamics/dynamics_model.py","file_url":"https://github.com/lenarttreven/dgm/blob/HEAD/dgm/dynamics/dynamics_model.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":null,"behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"c09c97df5a1d2228"}},{"code_sha256_prefix":"36ae9760eaecade1","entry":"create_get_dynamics_moments","repo":"lenarttreven/dgm","repo_kind":"official","path":"dgm/dynamics/dynamics_model.py","file_url":"https://github.com/lenarttreven/dgm/blob/HEAD/dgm/dynamics/dynamics_model.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":"36ae9760eaecade1"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}