Nonlocal Mean Field Schrödinger Bridge with Learned Interactions

• URL: http://arxiv.org/abs/2606.04265v1
• Date: Tue, 02 Jun 2026 22:30:46 GMT
• Title: Nonlocal Mean Field Schrödinger Bridge with Learned Interactions
• Abstract summary: This work considers its mean-field extension, the Mean-Field Schrdinger Bridge, for interacting particle systems.<n>We address this bottleneck by approximating the nonlocal interactions with neural network surrogates.<n>The resulting four-stage alternating algorithm reduces the per-step cost from quadratic to linear in the population size at inference.
• Score: 4.327576659466596
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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