Title: Entangled Schrödinger Bridge Matching
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Schrödinger Bridge Matching, transition path sampling, stochastic optimal control, molecular dynamics, generative modelling, trajectory inference, stochastic processes, probabilistic transport

Abstract: Simulating trajectories of multi-particle systems on complex energy landscapes and data manifolds is a central task in molecular dynamics (MD) and drug discovery, but remains challenging at scale due to computationally expensive and long simulations. Previous ML-based approaches for multi-particle simulation leverage techniques such as flow or Schrödinger bridge matching to implicitly learn joint trajectories through data snapshots. However, many systems, including biomolecular systems and heterogeneous cell populations, undergo *dynamic* interactions that evolve over their trajectory and cannot be captured through static snapshots. To close this gap, we introduce **Entangled Schrödinger Bridge Matching (EntangledSBM)**, a framework that learns the first- and second-order stochastic dynamics of interacting, multi-particle systems where the direction and magnitude of each particle's path depend dynamically on the paths of the other particles. We define the Entangled Schrödinger Bridge (EntangledSB) problem as solving a coupled system of bias potentials that *entangle* particle velocities. We show that our framework can accurately simulate trajectories of high-dimensional biomolecular systems and heterogeneous cell populations under perturbations that evolve dynamically through interacting forces.

TL;DR: We introduce Entangled Schrödinger Bridge Matching, a framework that learns the second-order Langevin dynamics of multi-particle systems where the direction and magnitude of each particle's path depend dynamically on the paths of the other particles.