建模粒子间动态相互作用，提升复杂系统模拟精度
Entangled Schrödinger Bridge Matching
- 通过耦合偏置力建模粒子路径间的动态依赖关系
- 可准确模拟高维生物分子系统的罕见转变与细胞群体扰动
- 适合需要动态交互建模的分子动力学与药物发现场景
在复杂势能面上模拟多粒子系统的轨迹是分子动力学和药物发现的核心任务，但因计算成本高、模拟时间长而难以规模化。以往方法借助流模型或薛定谔桥匹配，通过数据快照隐式学习联合轨迹，但许多系统（如生物分子体系和异质细胞群体）在演化过程中存在随轨迹变化的动态相互作用，无法仅靠静态快照捕捉。为此，我们提出纠缠薛定谔桥匹配（EntangledSBM），一种学习相互作用多粒子系统一阶与二阶随机动力学的框架，其中每个粒子的运动方向与大小动态依赖于其他粒子的路径。我们将该问题定义为求解耦合偏置力的纠缠薛定谔桥（EntangledSB）问题。实验表明，该框架能精确模拟受扰动的异质细胞群体及高维生物分子系统中的罕见转变。
原文摘要 · Abstract (English)
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.
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