Correcting systematic errors in the likelihood optimization of underdamped Langevin models of molecular dynamics trajectories

TL;DR

This paper introduces an analytical correction method for likelihood optimization in underdamped Langevin models, enabling more accurate inference of physical parameters from molecular dynamics trajectories.

Contribution

It presents a novel correction technique addressing velocity correlation issues, facilitating likelihood-based inference for underdamped Langevin equations from short trajectory data.

Findings

Improved accuracy in parameter inference demonstrated on benchmark systems.

Robustness of the correction method validated with realistic molecular systems.

Enables application of Langevin inference to activated chemical phenomena.

Abstract

Since Kramers' pioneering work in 1940, significant efforts have been devoted to studying Langevin equations applied to physical and chemical reactions projected onto few collective variables, with particular focus on the inference of their parameters. While the inference for overdamped Langevin equations is well-established and widely applied, a notable gap remains in the literature for underdamped Langevin equation. This gap arises from the challenge of accessing velocities solely through finite differences of positions, resulting in spurious correlations. In this letter, we propose an analytical correction for these correlations, specifically designed for a likelihood-maximization algorithm that exploits short, non-ergodic trajectories that can be obtained at reasonable numerical cost. The accuracy and robustness of our approach are tested on a benchmark case and a realistic system. This work paves the way for applying generalized Langevin equation inference to activated phenomena, such as chemical reactions, in several scientific domains.