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Yin R, Wang Q, Barkai E. Instability in the quantum restart problem. Phys Rev E 2024; 109:064150. [PMID: 39020895 DOI: 10.1103/physreve.109.064150] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2024] [Accepted: 06/06/2024] [Indexed: 07/20/2024]
Abstract
Repeatedly monitored quantum walks with a rate 1/τ yield discrete-time trajectories which are inherently random. With these paths the first-hitting time with sharp restart is studied. We find an instability in the optimal mean hitting time, which is not found in the corresponding classical random-walk process. This instability implies that a small change in parameters can lead to a rather large change of the optimal restart time. We show that the optimal restart time versus τ, as a control parameter, exhibits sets of staircases and plunges. The plunges, are due to the mentioned instability, which in turn is related to the quantum oscillations of the first-hitting time probability, in the absence of restarts. Furthermore, we prove that there are only two patterns of staircase structures, dependent on the parity of the distance between the target and the source in units of lattice constant. The global minimum of the hitting time is controlled not only by the restart time, as in classical problems, but also by the sampling time τ. We provide numerical evidence that this global minimum occurs for the τ minimizing the mean hitting time, given restarts taking place after each measurement. Last, we numerically show that the instability found in this work is relatively robust against stochastic perturbations in the sampling time τ.
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Blumer O, Reuveni S, Hirshberg B. Short-Time Infrequent Metadynamics for Improved Kinetics Inference. J Chem Theory Comput 2024; 20:3484-3491. [PMID: 38668722 PMCID: PMC11099961 DOI: 10.1021/acs.jctc.4c00170] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2024] [Revised: 04/02/2024] [Accepted: 04/02/2024] [Indexed: 05/15/2024]
Abstract
Infrequent Metadynamics is a popular method to obtain the rates of long time-scale processes from accelerated simulations. The inference procedure is based on rescaling the first-passage times of the Metadynamics trajectories using a bias-dependent acceleration factor. While useful in many cases, it is limited to Poisson kinetics, and a reliable estimation of the unbiased rate requires slow bias deposition and prior knowledge of efficient collective variables. Here, we propose an improved inference scheme, which is based on two key observations: (1) the time-independent rate of Poisson processes can be estimated using short trajectories only. (2) Short trajectories experience minimal bias, and their rescaled first-passage times follow the unbiased distribution even for relatively high deposition rates and suboptimal collective variables. Therefore, by basing the inference procedure on short time scales, we obtain an improved trade-off between speedup and accuracy at no additional computational cost, especially when employing suboptimal collective variables. We demonstrate the improved inference scheme for a model system and two molecular systems.
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Affiliation(s)
- Ofir Blumer
- School
of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Shlomi Reuveni
- School
of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
- The
Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
- The
Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Barak Hirshberg
- School
of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
- The
Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
- The
Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 6997801, Israel
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Blumer O, Reuveni S, Hirshberg B. Combining stochastic resetting with Metadynamics to speed-up molecular dynamics simulations. Nat Commun 2024; 15:240. [PMID: 38172126 PMCID: PMC10764788 DOI: 10.1038/s41467-023-44528-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2023] [Accepted: 12/18/2023] [Indexed: 01/05/2024] Open
Abstract
Metadynamics is a powerful method to accelerate molecular dynamics simulations, but its efficiency critically depends on the identification of collective variables that capture the slow modes of the process. Unfortunately, collective variables are usually not known a priori and finding them can be very challenging. We recently presented a collective variables-free approach to enhanced sampling using stochastic resetting. Here, we combine the two methods, showing that it can lead to greater acceleration than either of them separately. We also demonstrate that resetting Metadynamics simulations performed with suboptimal collective variables can lead to speedups comparable with those obtained with optimal collective variables. Therefore, applying stochastic resetting can be an alternative to the challenging task of improving suboptimal collective variables, at almost no additional computational cost. Finally, we propose a method to extract unbiased mean first-passage times from Metadynamics simulations with resetting, resulting in an improved tradeoff between speedup and accuracy. This work enables combining stochastic resetting with other enhanced sampling methods to accelerate a broad range of molecular simulations.
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Affiliation(s)
- Ofir Blumer
- School of Chemistry, Tel Aviv University, Tel Aviv, 6997801, Israel
| | - Shlomi Reuveni
- School of Chemistry, Tel Aviv University, Tel Aviv, 6997801, Israel
- The Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, 6997801, Israel
- The Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv, 6997801, Israel
| | - Barak Hirshberg
- School of Chemistry, Tel Aviv University, Tel Aviv, 6997801, Israel.
- The Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, 6997801, Israel.
- The Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv, 6997801, Israel.
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Kleiman DE, Nadeem H, Shukla D. Adaptive Sampling Methods for Molecular Dynamics in the Era of Machine Learning. J Phys Chem B 2023; 127:10669-10681. [PMID: 38081185 DOI: 10.1021/acs.jpcb.3c04843] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2023]
Abstract
Molecular dynamics (MD) simulations are fundamental computational tools for the study of proteins and their free energy landscapes. However, sampling protein conformational changes through MD simulations is challenging due to the relatively long time scales of these processes. Many enhanced sampling approaches have emerged to tackle this problem, including biased sampling and path-sampling methods. In this Perspective, we focus on adaptive sampling algorithms. These techniques differ from other approaches because the thermodynamic ensemble is preserved and the sampling is enhanced solely by restarting MD trajectories at particularly chosen seeds rather than introducing biasing forces. We begin our treatment with an overview of theoretically transparent methods, where we discuss principles and guidelines for adaptive sampling. Then, we present a brief summary of select methods that have been applied to realistic systems in the past. Finally, we discuss recent advances in adaptive sampling methodology powered by deep learning techniques, as well as their shortcomings.
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Affiliation(s)
- Diego E Kleiman
- Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Hassan Nadeem
- Department of Bioengineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Diwakar Shukla
- Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
- Department of Bioengineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
- Department of Plant Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
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Blumer O, Reuveni S, Hirshberg B. Stochastic Resetting for Enhanced Sampling. J Phys Chem Lett 2022; 13:11230-11236. [PMID: 36446130 PMCID: PMC9743203 DOI: 10.1021/acs.jpclett.2c03055] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2022] [Accepted: 11/23/2022] [Indexed: 06/16/2023]
Abstract
We present a method for enhanced sampling of molecular dynamics simulations using stochastic resetting. Various phenomena, ranging from crystal nucleation to protein folding, occur on time scales that are unreachable in standard simulations. They are often characterized by broad transition time distributions, in which extremely slow events have a non-negligible probability. Stochastic resetting, i.e., restarting simulations at random times, was recently shown to significantly expedite processes that follow such distributions. Here, we employ resetting for enhanced sampling of molecular simulations for the first time. We show that it accelerates long time scale processes by up to an order of magnitude in examples ranging from simple models to a molecular system. Most importantly, we recover the mean transition time without resetting, which is typically too long to be sampled directly, from accelerated simulations at a single restart rate. Stochastic resetting can be used as a standalone method or combined with other sampling algorithms to further accelerate simulations.
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Affiliation(s)
- Ofir Blumer
- School
of Chemistry, Tel Aviv University, Tel Aviv6997801, Israel
| | - Shlomi Reuveni
- School
of Chemistry, Tel Aviv University, Tel Aviv6997801, Israel
- The
Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv6997801, Israel
- The
Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv6997801, Israel
| | - Barak Hirshberg
- School
of Chemistry, Tel Aviv University, Tel Aviv6997801, Israel
- The
Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv6997801, Israel
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