{"ID":3053267,"CreatedAt":"2026-06-04T04:41:36.695875263Z","UpdatedAt":"2026-06-05T22:02:57.54306338Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.04265","arxiv_id":"2606.04265","title":"Nonlocal Mean Field Schrödinger Bridge with Learned Interactions","abstract":"The Schrödinger Bridge Problem constructs a stochastic process that connects an initial distribution to a terminal distribution with minimum energy. This work considers its mean-field extension, the Mean-Field Schrödinger Bridge, for interacting particle systems. With nonlocal interactions, evaluating the resulting particle-dependent distributional terms can scale quadratically with the population size, which makes large-scale problems intractable. We address this bottleneck by approximating the nonlocal interactions with neural network surrogates. The resulting four-stage alternating algorithm reduces the per-step cost from quadratic to linear in the population size at inference. We also derive Grönwall-type stability bounds that show how surrogate errors propagate to the generated trajectories. In numerical experiments on navigation and opinion-dynamics tasks, the proposed method reproduces trajectories obtained with analytical evaluation and reduces training time.","short_abstract":"The Schrödinger Bridge Problem constructs a stochastic process that connects an initial distribution to a terminal distribution with minimum energy. This work considers its mean-field extension, the Mean-Field Schrödinger Bridge, for interacting particle systems. With nonlocal interactions, evaluating the resulting par...","url_abs":"https://arxiv.org/abs/2606.04265","url_pdf":"https://arxiv.org/pdf/2606.04265v1","authors":"[\"Daisuke Inoue\",\"Mathieu Laurière\",\"Dante Kalise\"]","published":"2026-06-02T22:30:46Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.LG\",\"math.NA\"]","methods":"[]","has_code":false}