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  • Open Access

Machine learning approach to fast thermal equilibration

Diego Rengifo*

Gabriel Téllez†

  • *Contact author: d.rengifo@uniandes.edu.co
  • †Contact author: gtellez@uniandes.edu.co
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Phys. Rev. E 111, 065311 – Published 23 June, 2025

DOI: https://doi.org/10.1103/q18f-yrm2

Abstract

We present a method to design driving protocols that achieve fast thermal equilibration of a system of interest using techniques inspired by machine learning training algorithms. For example, consider a Brownian particle manipulated by optical tweezers. The force on the particle can be controlled and adjusted over time, resulting in a driving protocol that transitions the particle from an initial state to a final state. Once the driving protocol has been completed, the system requires additional time to relax to thermal equilibrium. Designing driving protocols that bypass the relaxation period is of interest so that, at the end of the protocol, the system is either in thermal equilibrium or very close to it. Several studies have addressed this problem through reverse engineering methods, which involve prescribing a specific evolution for the probability density function of the system and then deducing the corresponding form of the driving protocol potential. Here we propose a new method that can be applied to more complex systems where reverse engineering is not feasible. We simulate the evolution of a large ensemble of trajectories while tracking the gradients with respect to a parametrization of the driving protocol. The final probability density function is compared to the target equilibrium one. Using machine learning libraries, the gradients are computed via backpropagation and the protocol is iteratively adjusted until the optimal protocol is achieved. We demonstrate the effectiveness of our approach with several examples.

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Phys. Rev. E 111, 065311– Published 23 June, 2025
  • Received 10 April 2025
  • Accepted 5 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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