Adaptive tensor train metadynamics for high-dimensional free energy exploration

TL;DR

This paper introduces TT-Metadynamics, a scalable method that compresses bias potentials into a tensor train format, enabling efficient exploration of high-dimensional free energy landscapes in molecular dynamics.

Contribution

The authors develop a tensor train-based compression technique for metadynamics, allowing efficient high-dimensional free energy exploration with linear scaling in the number of CVs.

Findings

Achieves accurate free energy calculations with up to 14 CVs.

Maintains computational efficiency and memory use over long simulations.

Outperforms standard metadynamics in high-barrier systems.

Abstract

A key challenge for molecular dynamics simulations is efficient exploration of free energy landscapes over relevant collective variables (CV). Common methods for enhancing sampling become prohibitively inefficient beyond only a few CVs; in the case of the widely-used metadynamics method, the computational cost of evaluating and storing the bias potential grows exponentially with the number of dimensions. Here, we introduce TT-Metadynamics, in which the accumulated sum of Gaussian functions in the original metadynamics method is periodically compressed into a low-rank tensor train (TT) representation. The TT enables efficient memory use and prevents the computational cost of evaluating the bias potential from increasing with simulation time. We present a "sketching" algorithm that allows us to construct the TT with linear scaling in the number of CVs. Applied to benchmark systems with up to 14 CVs, the accuracy of TT-Metadynamics matches or exceeds that of standard metadynamics in long simulations, particularly in systems with high barriers. These results establish TT-Metadynamics as a scalable and effective method for computing free energies that are functions of several CVs.