Slow dynamical modes from static averages

Timothée Devergne; Vladimir Kostic; Massimiliano Pontil; Michele Parrinello

doi:10.1063/5.0246248

Slow dynamical modes from static averages

J Chem Phys. 2025 Mar 28;162(12):124108. doi: 10.1063/5.0246248.

Authors

Timothée Devergne^{1

2}, Vladimir Kostic^{2

3}, Massimiliano Pontil^{2

4}, Michele Parrinello¹

Affiliations

¹ Atomistic Simulations, Italian Institute of Technology, Genova, Italy.
² Computational Statistics and Machine Learning, Italian Institute of Technology, Genova, Italy.
³ Department of Mathematics and Informatics, University of Novi Sad, Novi Sad, Serbia.
⁴ AI Centre, Department of Computer Science, UCL, London, United Kingdom.

PMID: 40130793
DOI: 10.1063/5.0246248

Abstract

In recent times, efforts have been made to describe the evolution of a complex system not through long trajectories but via the study of probability distribution evolution. This more collective approach can be made practical using the transfer operator formalism and its associated dynamics generator. Here, we reformulate in a more transparent way the result of Devergne et al. [Adv. Neural Inform. Process. Syst. 37, 75495-75521 (2024)] and show that the lowest eigenfunctions and eigenvalues of the dynamics generator can be efficiently computed using data easily obtainable from biased simulations. We also show explicitly that the long time dynamics can be reconstructed by using the spectral decomposition of the dynamics operator.