Multiple time step integrators in <i>ab initio</i> molecular dynamics

Luehr, Nathan; Markland, Thomas E.; Martı́nez, Todd J.

doi:10.1063/1.4866176

Cited by 34 publications

(32 citation statements)

References 55 publications

(55 reference statements)

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“…The non-local exchange term evidently makes the system more sensitive to errors, likely because the Hartree-Fock exchange contribution to the Fock matrix oscillates more rapidly in time as compared to other components of the exchange-correlation functional. 61,62 Meanwhile, the induced dipole diverges to unrealistically large values as errors accumulate; see Fig. S3 in the supplementary material.…”

Section: A Numerical Stabilitymentioning

confidence: 99%

Self-consistent predictor/corrector algorithms for stable and efficient integration of the time-dependent Kohn-Sham equation

Zhu

Herbert

2018

The Journal of Chemical Physics

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The "real time" formulation of time-dependent density functional theory (TDDFT) involves integration of the time-dependent Kohn-Sham (TDKS) equation in order to describe the time evolution of the electron density following a perturbation. This approach, which is complementary to the more traditional linear-response formulation of TDDFT, is more efficient for computation of broad-band spectra (including core-excited states) and for systems where the density of states is large. Integration of the TDKS equation is complicated by the time-dependent nature of the effective Hamiltonian, and we introduce several predictor/corrector algorithms to propagate the density matrix, one of which can be viewed as a self-consistent extension of the widely used modified-midpoint algorithm. The predictor/corrector algorithms facilitate larger time steps and are shown to be more efficient despite requiring more than one Fock build per time step, and furthermore can be used to detect a divergent simulation on-the-fly, which can then be halted or else the time step modified.

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Section: A Numerical Stabilitymentioning

confidence: 99%

Self-consistent predictor/corrector algorithms for stable and efficient integration of the time-dependent Kohn-Sham equation

Zhu

Herbert

2018

The Journal of Chemical Physics

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“…Consequently, in the next subsection, we consider two important approximations of the Schrödinger equation, namely, the adiabatic and the Born-Oppenheimer approximations, which aim to reduce such a complexity. These approximations, as well as those that later follow, reduce substantially the duration of the calculations allowing for larger molecular systems to be simulated and longer time-scales to be explored [8,9].…”

Section: Quantum Molecular Dynamics and The Schrödinger Equation: A Mmentioning

confidence: 99%

Computational Methods for Ab Initio Molecular Dynamics

Paquet

Viktor

2018

Advances in Chemistry

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Ab initio molecular dynamics is an irreplaceable technique for the realistic simulation of complex molecular systems and processes from first principles. This paper proposes a comprehensive and self-contained review of ab initio molecular dynamics from a computational perspective and from first principles. Quantum mechanics is presented from a molecular dynamics perspective. Various approximations and formulations are proposed, including the Ehrenfest, Born-Oppenheimer, and Hartree-Fock molecular dynamics. Subsequently, the Kohn-Sham formulation of molecular dynamics is introduced as well as the afferent concept of density functional. As a result, Car-Parrinello molecular dynamics is discussed, together with its extension to isothermal and isobaric processes. Car-Parrinello molecular dynamics is then reformulated in terms of path integrals. Finally, some implementation issues are analysed, namely, the pseudopotential, the orbital functional basis, and hybrid molecular dynamics.

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“…These explorations have inspired us to use ML to design an adaptive MD-based dynamical optimization framework that updates the simulation timestep and auto-tunes the virtual parameters characterizing the dynamics of ions near polarizable NPs to yield a more stable and efficient simulation. Related work in the area of adapting timestep in a simulation has involved using analytical approaches to multiple timestep integration (Luehr et al, 2014;Tuckerman et al, 1992). Recent work has also focused on adaptive ensemble simulations to enhance the computational efficiency of biomolecular simulations (Kasson and Jha, 2018).…”

Section: Parameter Prediction Using MLmentioning

confidence: 99%

Machine learning for parameter auto-tuning in molecular dynamics simulations: Efficient dynamics of ions near polarizable nanoparticles

Kadupitiya¹,

Fox²,

Jadhao

2020

The International Journal of High Performance Computing Applica

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Simulating the dynamics of ions near polarizable nanoparticles (NPs) using coarse-grained models is extremely challenging due to the need to solve the Poisson equation at every simulation timestep. Recently, a molecular dynamics (MD) method based on a dynamical optimization framework bypassed this obstacle by representing the polarization charge density as virtual dynamic variables, and evolving them in parallel with the physical dynamics of ions. We highlight the computational gains accessible with the integration of machine learning (ML) methods for parameter prediction in MD simulations by demonstrating how they were realized in MD simulations of ions near polarizable NPs. An artificial neural network based regression model was integrated with MD simulation and predicted the optimal simulation timestep and optimization parameters characterizing the virtual system with 94.3% success. The ML-enabled auto-tuning of parameters generated accurate dynamics of ions for ≈ 10 million steps while improving the stability of the simulation by over an order of magnitude. The integration of ML-enhanced framework with hybrid OpenMP/MPI parallelization techniques reduced the computational time of simulating systems with thousands of ions and induced charges from thousands of hours to tens of hours, yielding a maximum speedup of ≈ 3 from ML-only acceleration and a maximum speedup of ≈ 600 from the combination of ML and parallel computing methods. Extraction of ionic structure in concentrated electrolytes near oil-water emulsions demonstrates the success of the method. The approach can be generalized to select optimal parameters in other MD applications and energy minimization problems.

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Multiple time step integrators in ab initio molecular dynamics

Cited by 34 publications

References 55 publications

Self-consistent predictor/corrector algorithms for stable and efficient integration of the time-dependent Kohn-Sham equation

Self-consistent predictor/corrector algorithms for stable and efficient integration of the time-dependent Kohn-Sham equation

Computational Methods for Ab Initio Molecular Dynamics

Machine learning for parameter auto-tuning in molecular dynamics simulations: Efficient dynamics of ions near polarizable nanoparticles

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