Entangled Schrödinger Bridge Matching
This work addresses a problem in molecular dynamics and drug discovery for researchers needing scalable simulations of interacting systems, though it appears incremental as it builds on existing Schrödinger bridge matching techniques.
The paper tackled the challenge of simulating multi-particle systems with dynamic interactions, such as biomolecular systems and heterogeneous cell populations, by introducing Entangled Schrödinger Bridge Matching (EntangledSBM), which accurately simulates these systems under perturbations and rare transitions.
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. Previous approaches 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 forces that entangle particle velocities. We show that our framework accurately simulates heterogeneous cell populations under perturbations and rare transitions in high-dimensional biomolecular systems.