Generalized Flow Matching for Transition Dynamics Modeling

TMLR Paper4118 Authors

Abstract: 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 the kinetic energy or ``potential energy'' of the system 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 probable 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.

Submission Length: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission: N/A

Assigned Action Editor: ~Razvan_Pascanu1

Submission Number: 4118