Generalized Flow Matching for Transition Dynamics Modeling
This addresses a fundamental problem in dynamical systems for researchers in fields like computational biology and chemistry, though it appears incremental as it builds on existing flow matching frameworks.
The paper tackles the challenge of simulating transition dynamics between metastable states in systems like protein folding by proposing a data-driven method to learn nonlinear interpolations from local dynamics, which reduces computational costs by sampling probable paths more efficiently, as validated on synthetic and real-world molecular systems.
Simulating transition dynamics between metastable states is a fundamental challenge in dynamical systems and stochastic processes with wide real-world applications in understanding protein folding, chemical reactions and neural activities. However, the computational challenge often lies on sampling exponentially many paths in which only a small fraction ends in the target metastable state due to existence of high energy barriers. To amortize the cost, we propose a data-driven approach to warm-up the simulation by learning nonlinear interpolations from local dynamics. Specifically, we infer a potential energy function from local dynamics data. To find plausible paths between two metastable states, we formulate a generalized flow matching framework that learns a vector field to sample propable paths between the two marginal densities under the learned energy function. Furthermore, we iteratively refine the model by assigning importance weights to the sampled paths and buffering more likely paths for training. We validate the effectiveness of the proposed method to sample probable paths on both synthetic and real-world molecular systems.