{"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/neural-optimal-transport-with-lagrangian","title":"Neural Optimal Transport with Lagrangian Costs","arxiv_id":"2406.00288","date":"2024-06-01","proceeding":null,"authors":["Aram-Alexandre Pooladian","Carles Domingo-Enrich","Ricky T. Q. Chen","Brandon Amos"],"abstract":"We investigate the optimal transport problem between probability measures when the underlying cost function is understood to satisfy a least action principle, also known as a Lagrangian cost. These generalizations are useful when connecting observations from a physical system where the transport dynamics are influenced by the geometry of the system, such as obstacles (e.g., incorporating barrier functions in the Lagrangian), and allows practitioners to incorporate a priori knowledge of the underlying system such as non-Euclidean geometries (e.g., paths must be circular). Our contributions are of computational interest, where we demonstrate the ability to efficiently compute geodesics and amortize spline-based paths, which has not been done before, even in low dimensional problems. Unlike prior work, we also output the resulting Lagrangian optimal transport map without requiring an ODE solver. We demonstrate the effectiveness of our formulation on low-dimensional examples taken from prior work. The source code to reproduce our experiments is available at https://github.com/facebookresearch/lagrangian-ot.","url_abs":"https://arxiv.org/abs/2406.00288v1","url_pdf":"https://arxiv.org/pdf/2406.00288v1.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":"neural-optimal-transport-with-lagrangian","repo_url":"https://github.com/facebookresearch/lagrangian-ot","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2406.00288","atlas_url":"https://app.syntology.ai/?focus=2406.00288","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2406.00288"}},"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. 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