{"ID":5937280,"CreatedAt":"2026-07-07T03:14:33.014478982Z","UpdatedAt":"2026-07-09T07:20:22.971468815Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.04738","arxiv_id":"2607.04738","title":"Wasserstein Residuals: Learning Gradient Flows from Population Dynamics","abstract":"Reconstructing population dynamics is a central problem in the physical and data sciences. Often, the dynamics are modeled as a Wasserstein gradient flow (WGF): a curve of distributions driven by an energy functional. Though there are multiple mathematical characterizations of a WGF, the dominant algorithmic approach relies on the Jordan--Kinderlehrer--Otto (JKO) scheme. JKO-based methods are inflexible to time discretisation and require solving costly optimal transport problems. We take a residual approach, enforcing the continuity equations via a non-negative loss function whose minimum is the WGF. Combined with a data-fitting divergence, this gives a single global objective. This perspective unifies several existing methods and leads to a new particle-based method, stitching, that is simulation-free and robust to large gaps between observations. We demonstrate that the stitching method achieves state-of-the-art performance across trajectory inference benchmarks. For code see github.com/BasisResearch/wasserstein-residuals.","short_abstract":"Reconstructing population dynamics is a central problem in the physical and data sciences. Often, the dynamics are modeled as a Wasserstein gradient flow (WGF): a curve of distributions driven by an energy functional. Though there are multiple mathematical characterizations of a WGF, the dominant algorithmic approach r...","url_abs":"https://arxiv.org/abs/2607.04738","url_pdf":"https://arxiv.org/pdf/2607.04738v1","authors":"[\"Markus Heinonen\",\"Yair Shenfeld\",\"Ricardo Baptista\",\"Daniel Waxman\",\"Dmitry Batenkov\",\"Tim Cooijmans\",\"Eli Bingham\"]","published":"2026-07-06T07:20:30Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.AI\",\"cs.LG\"]","methods":"[]","has_code":false}