Entangled Schr""odinger Bridge Matching

2025-11-10

AI Summary

This work addresses the challenge of modeling dynamic trajectories of multi-particle systems navigating complex energy landscapes in molecular dynamics and drug discovery—particularly non-stationary, time-evolving interactions in biomolecules and heterogeneous cell populations. We propose the “Entangled Schrödinger Bridge,” a novel framework that explicitly models dynamic velocity dependencies among particles via coupled bias force fields, thereby unifying first- and second-order stochastic dynamics. Integrating normalizing flows with Schrödinger bridge optimal transport, we develop a stochastic differential equation–based method for trajectory generation and inference. Unlike conventional snapshot-driven approaches, our method fully respects temporal causality and continuity. It successfully reproduces perturbed heterogeneous cell population behaviors and rare transitions in high-dimensional biomolecular systems. Empirically, it achieves superior accuracy, generalization, and scalability to high dimensions compared to state-of-the-art methods.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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 Schr""odinger 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 Schr""odinger 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 Schr""odinger 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.

Problem

• Simulating multi-particle trajectories on complex energy landscapes efficiently
• Capturing dynamic interactions between particles that evolve over time
• Modeling coupled stochastic dynamics where particle paths depend on others

Innovation

• Learns first- and second-order stochastic dynamics
• Solves coupled system of bias forces
• Dynamically entangles multi-particle velocities