Entangled Schrödinger Bridge Matching

Simulating trajectories of multi-particle systems on complex energy landscapes is a central task in molecular dynamics (MD) and drug discovery, but remains challenging at scale due to computationally expensive and long simulations. We introduce Entangled Schrödinger Bridge Matching (EntangledSBM), a novel framework that models 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 be applied to transition path sampling of high-dimensional biomolecular systems that evolve dynamically through interdependent constraints and forces.