Towards accurate estimation of free-energy barriers and kinetic rates via Langevin inference on molecular dynamics trajectories

We propose a novel approach for estimating free-energy barriers and kinetic rates of physico-chemical processes, using only short, unbiased molecular dynamics trajectories. Our method focuses on correcting the likelihood function of underdamped Langevin models.

Rare events, such as phase transitions, biomolecular conformational changes, and chemical reactions, are critical in condensed matter systems. Analyzing these processes often involves projecting atomic dynamics onto a reduced space defined by one or more CVs, with the resulting dynamics approximately governed by generalized Langevin equations. Depending on the time resolution, these equations can be either overdamped, underdamped or generalized. Parametrizing overdamped models is relatively straightforward using statistical inference techniques, such as likelihood maximization, even when long ergodic trajectories are not available. However, the accurate parametrization of underdamped or non-Markovian models remains significantly more challenging due to the complexities introduced by inertia and acceleration effects.

Our contribution lies in rigorously addressing these challenges for underdamped Langevin models using short, non-equilibrium trajectories, such as those generated by transition path sampling. We present a correction to the likelihood function that analytically eliminates spurious correlations arising from finite-difference velocity estimation. These corrections enable more accurate and reliable characterization of free-energy landscapes and kinetics in systems where inertia plays a crucial role, thereby expanding the applicability of Langevin models to a broader range of physico-chemical processes.