Rational Construction of Stochastic Numerical Methods for Molecular Sampling

Abstract

In this article, we focus on the sampling of the configurational Gibbs-Boltzmann distribution, that is, the calculation of averages of functions of the position coordinates of a molecular $N$-body system modelled at constant temperature. We show how a formal series expansion of the invariant measure of a Langevin dynamics numerical method can be obtained in a straightforward way using the Baker-Campbell-Hausdorff lemma. We then compare Langevin dynamics integrators in terms of their invariant distributions and demonstrate a superconvergence property (4th order accuracy where only 2nd order would be expected) of one method in the high friction limit; this method, moreover, can be reduced to a simple modification of the Euler-Maruyama method for Brownian dynamics involving a non-Markovian (coloured noise) random process. In the Brownian dynamics case, 2nd order accuracy of the invariant density is achieved. All methods considered are efficient for molecular applications (requiring one force evaluation per timestep) and of a simple form. In fully resolved (long run) molecular dynamics simulations, for our favoured method, we observe up to two orders of magnitude improvement in configurational sampling accuracy for given stepsize with no evident reduction in the size of the largest usable timestep compared to common alternative methods.

References in corpus (3)

• Design of quasi-symplectic propagators for Langevin dynamics
• From ballistic to diffusive behavior in periodic potentials
• Discretization errors in molecular dynamics simulations with deterministic and stochastic thermostats

Cited by in corpus (41)

• Robust and efficient configurational molecular sampling via Langevin Dynamics
• Exciton diffusion in two-dimensional metal-halide perovskites
• Coarse Graining Molecular Dynamics with Graph Neural Networks
• A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat
• The computation of averages from equilibrium and nonequilibrium Langevin molecular dynamics
• Dielectric properties of nano-confined water: a canonical thermopotentiostat approach
• Galerkin Approximation of Dynamical Quantities using Trajectory Data
• A unified thermostat scheme for efficient configurational sampling for classical/quantum canonical ensembles via molecular dynamics
• Numerical Integration of the Extended Variable Generalized Langevin Equation with a Positive Prony Representable Memory Kernel
• New Langevin and Gradient Thermostats for Rigid Body Dynamics
• Dimension-free path-integral molecular dynamics without preconditioning
• Force-Field-Enhanced Neural Network Interactions: from Local Equivariant Embedding to Atom-in-Molecule properties and long-range effects
• A generalized class of strongly stable and dimension-free T-RPMD integrators
• Probing quantum coherence in ultrafast molecular processes: an ab initio approach to open quantum systems
• Routine Molecular Dynamics Simulations Including Nuclear Quantum Effects: from Force Fields to Machine Learning Potentials
• Stationary state distribution and efficiency analysis of the Langevin equation via real or virtual dynamics
• Path Integral Molecular Dynamics for Exact Quantum Statistics of Multi-Electronic-State Systems
• Non-Adiabatic Vibrational Damping of Molecular Adsorbates: Insights into Electronic Friction and the Role of Electronic Coherence
• Sampling the isothermal-isobaric ensemble by Langevin dynamics
• Frequency and field-dependent response of confined electrolytes from Brownian dynamics simulations
• FeNNol: an Efficient and Flexible Library for Building Force-field-enhanced Neural Network Potentials
• From Classical to Quantum and Back: Hamiltonian Adaptive Resolution Path Integral, Ring Polymer, and Centroid Molecular Dynamics
• Simulated Tempering Method in the Infinite Switch Limit with Adaptive Weight Learning
• Improved torque estimator for condensed-phase quasicentroid molecular dynamics
• Stability of velocity-Verlet- and Liouville-operator-derived algorithms to integrate non-Hamiltonian systems
• A systematic study of the dynamics of chain formation in electrorheological fluids
• Estimating time-correlation functions by sampling and unbiasing dynamically activated events
• Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions
• The Challenge of Stochastic Størmer-Verlet Thermostats Generating Correct Statistics
• Bringing discrete-time Langevin splitting methods into agreement with thermodynamics
• Computing Long Timescale Biomolecular Dynamics using Quasi-Stationary Distribution Kinetic Monte Carlo (QSD-KMC)
• Stochastic gradient descent and fast relaxation to thermodynamic equilibrium: a stochastic control approach
• Velocity Jumps for Molecular Dynamics
• On the Numerical Stationary Distribution of Overdamped Langevin Equation in Harmonic System
• Understanding the Sources of Error in MBAR through Asymptotic Analysis
• Combining multiple interface set path ensembles with MBAR reweighting
• Understanding Reaction Mechanisms from Start to Finish
• NQCDynamics.jl: A Julia Package for Nonadiabatic Quantum Classical Molecular Dynamics in the Condensed Phase
• GROMACS Stochastic Dynamics and BAOAB are equivalent configurational sampling algorithms
• Multimodal sampling via Schrödinger-Föllmer samplers with temperatures
• Faster Molecular Dynamics with Neural Network Potentials via Distilled Multiple Time-Stepping and Non-Conservative Forces