TELD: Trajectory-Level Langevin Dynamics for Versatile Constrained Sampling

We introduce Trajectory Ensemble Langevin Dynamics (TELD), a method that applies Langevin dynamics to entire molecular trajectories. TELD formulates a trajectory probability distribution and derives a score function from it, incorporating energetic and dynamic information. This enables gradient-based sampling in the trajectory phase space. By shifting the perspective from conventional conformation-based MD to trajectory-level MD, TELD can impose diverse constraints on entire trajectories, such as fixing the start and end points in two distinct states, thereby sampling only the transition paths. Our advancements allow us to scale to higher-dimensional systems than previous similar approaches. Our implementation leverages automatic differentiation for computing the high-order derivatives needed for the trajectory probability score calculation, making it compatible with differentiable classical force fields and GNN-based neural network potentials. We validate TELD's performance on a molecular system, demonstrating its ability to accurately reproduce equilibrium properties, dynamics, and rare event statistics.