{"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-potential-recovering-the-gravitational-1","title":"Deep Potential: Recovering the gravitational potential from a snapshot of phase space","arxiv_id":"2205.02244","date":"2022-05-04","proceeding":null,"authors":["Gregory M. Green","Yuan-Sen Ting","Harshil Kamdar"],"abstract":"One of the major goals of the field of Milky Way dynamics is to recover the gravitational potential field. Mapping the potential would allow us to determine the spatial distribution of matter - both baryonic and dark - throughout the Galaxy. We present a novel method for determining the gravitational field from a snapshot of the phase-space positions of stars, based only on minimal physical assumptions, which makes use of recently developed tools from the field of deep learning. We first train a normalizing flow on a sample of observed six-dimensional phase-space coordinates of stars, obtaining a smooth, differentiable approximation of the distribution function. Using the Collisionless Boltzmann Equation, we then find the gravitational potential - represented by a feed-forward neural network - that renders this distribution function stationary. This method, which we term \"Deep Potential,\" is more flexible than previous parametric methods, which fit restricted classes of analytic models of the distribution function and potential to the data. We demonstrate Deep Potential on mock datasets, and demonstrate its robustness under various non-ideal conditions. Deep Potential is a promising approach to mapping the density of the Milky Way and other stellar systems, using rich datasets of stellar positions and kinematics now being provided by Gaia and ground-based spectroscopic surveys.","url_abs":"https://arxiv.org/abs/2205.02244v1","url_pdf":"https://arxiv.org/pdf/2205.02244v1.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"deep-potential-recovering-the-gravitational-1","repo_url":"https://github.com/gregreen/deep-potential","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2205.02244","atlas_url":"https://app.syntology.ai/?focus=2205.02244","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2205.02244"}},"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/gregreen/deep-potential","reach":null}],"summary":{"ran_honours":1},"by_repo_kind":{"official":{"samples":1,"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":"d48dcaf0e1aacb89","entry":"calc_selfn_derivatives","repo":"gregreen/deep-potential","repo_kind":"official","path":"scripts/potential.py","file_url":"https://github.com/gregreen/deep-potential/blob/HEAD/scripts/potential.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"d48dcaf0e1aacb89"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}