Adaptive Tensor Train Metadynamics for High-Dimensional Free Energy Exploration
Year: 2026
Type: article
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.
Institution: University of Chicago
Language: English
Subfield: Physical and Theoretical Chemistry
Field: Chemistry
Domain: Physical Sciences
Open Access status: green
Awards: CAREER: Towards a general recipe for fast high-dimensional scientific computing, Rare-event simulation and analysis for elucidating mechanisms of development and disease, NSF-Simons National Institute for Theory and Mathematics in Biology, MACHINE-LEARNING ACCELERATED SIMULATIONS FOR FORECASTING, DATA ASSIMILATION, AND EXTREME EVENTS, Divide-and-Conquer Approach for Strongly Interacting Systems via Convex Optimization, G648017143, MACHINE-LEARNING ACCELERATED SIMULATIONS FOR FORECASTING, DATA ASSIMILATION, AND EXTREME EVENTS
OpenAlex ID: W7162541862