Bringing discrete-time Langevin splitting methods into agreement with thermodynamics

Finkelstein, Joshua; Cheng, Chungho; Fiorin, Giacomo; Seibold, Benjamin; Grønbech‐Jensen, Niels

doi:10.1063/5.0066008

Cited by 6 publications

(7 citation statements)

References 48 publications

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“…For γ TC = 0, the algorithm in eq , with the given choice of c L , is a splitting formulation of the method by Grønbech–Jensen and Farago. , In fact, any of the recently derived one-parameter family of thermodynamically exact Grønbech–Jensen (GJ) methods ,, can be written using a similar splitting when an additional time-scaling factor is included. A detailed derivation and theoretical evaluation for the family of GJ integration schemes in splitting form, on which eq is based, is presented in ref . An alternative integration method, again based on this splitting formalism, is given in the Supporting Information.…”

Section: Canonical Qmd Simulations Using Tensor Coresmentioning

confidence: 99%

Quantum-Based Molecular Dynamics Simulations Using Tensor Cores

Finkelstein

Smith

Mniszewski

et al. 2021

J. Chem. Theory Comput.

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Tensor cores, along with tensor processing units, represent a new form of hardware acceleration specifically designed for deep neural network calculations in artificial intelligence applications. Tensor cores provide extraordinary computational speed and energy efficiency but with the caveat that they were designed for tensor contractions (matrix–matrix multiplications) using only low-precision floating-point operations. Despite this perceived limitation, we demonstrate how tensor cores can be applied with high efficiency to the challenging and numerically sensitive problem of quantum-based Born–Oppenheimer molecular dynamics, which requires highly accurate electronic structure optimizations and conservative force evaluations. The interatomic forces are calculated on-the-fly from an electronic structure that is obtained from a generalized deep neural network, where the computational structure naturally takes advantage of the exceptional processing power of the tensor cores and allows for high performance in excess of 100 Tflops on a single Nvidia A100 GPU. Stable molecular dynamics trajectories are generated using the framework of extended Lagrangian Born–Oppenheimer molecular dynamics, which combines computational efficiency with long-term stability, even when using approximate charge relaxations and force evaluations that are limited in accuracy by the numerically noisy conditions caused by the low-precision tensor core floating-point operations. A canonical ensemble simulation scheme is also presented, where the additional numerical noise in the calculated forces is absorbed into a Langevin-like dynamics.

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Section: Canonical Qmd Simulations Using Tensor Coresmentioning

confidence: 99%

Quantum-Based Molecular Dynamics Simulations Using Tensor Cores

Finkelstein

Smith

Mniszewski

et al. 2021

J. Chem. Theory Comput.

Self Cite

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“…The differences are found in, e.g., correlations to the configurational coordinate, r n ; see Eq. (34).…”

Section: Constructing Half-step Velocities With a Single Noise Value ...mentioning

confidence: 99%

Complete set of stochastic Verlet-type thermostats for correct Langevin simulations

Grønbech‐Jensen

2019

Molecular Physics

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We present the complete set of stochastic Verlet-type algorithms that can provide correct statistical measures for both configurational and kinetic sampling in discretetime Langevin systems. The approach is a brute-force general representation of the Verlet-algorithm with free parameter coefficients that are determined by requiring correct Boltzmann sampling for linear systems, regardless of time step. The result is a set of statistically correct methods given by one free functional parameter, which can be interpreted as the one-time-step velocity attenuation factor. We define the statistical characteristics of both true on-site v n and true half-step u n+ 1 2 velocities, and use these definitions for each statistically correct Størmer-Verlet method to find a unique associated half-step velocity expression, which yields correct kinetic Maxwell-Boltzmann statistics for linear systems. It is shown that no other similar, statistically correct on-site velocity exists. We further discuss the use and features of finite-difference velocity definitions that are neither true on-site, nor true halfstep. The set of methods is written in convenient and conventional stochastic Verlet forms that lend themselves to direct implementation for, e.g., Molecular Dynamics applications. We highlight a few specific examples, and validate the algorithms through comprehensive Langevin simulations of both simple nonlinear oscillators and complex Molecular Dynamics.To Appear in Molecular Physics: https://doi.

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“…Our simulations confirm that GSD/BAOA achieves the same high numerical accuracy as BAOAB for configurational properties. We remark that other Langevin integrators have been compared to BAOAB and also found to exhibit similar or equivalent configurational properties. ,,− …”

Section: Discussionmentioning

confidence: 74%

GROMACS Stochastic Dynamics and BAOAB Are Equivalent Configurational Sampling Algorithms

Kieninger

Keller

2022

J. Chem. Theory Comput.

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Two of the most widely used Langevin integrators for molecular dynamics simulations are the GROMACS Stochastic Dynamics (GSD) integrator and the splitting method BAOAB. In this letter, we show that the GROMACS Stochastic Dynamics integrator is equal to the less frequently used splitting method BAOA. It immediately follows that GSD and BAOAB sample the same configurations and have the same high configurational accuracy. Our numerical results indicate that GSD/BAOA has higher kinetic accuracy than BAOAB.

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Bringing discrete-time Langevin splitting methods into agreement with thermodynamics

Cited by 6 publications

References 48 publications

Quantum-Based Molecular Dynamics Simulations Using Tensor Cores

Quantum-Based Molecular Dynamics Simulations Using Tensor Cores

Complete set of stochastic Verlet-type thermostats for correct Langevin simulations

GROMACS Stochastic Dynamics and BAOAB Are Equivalent Configurational Sampling Algorithms

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