Theoretical and numerical comparison of some sampling methods for molecular dynamics

DOI10.1051/m2an:2007014zbMath1138.82341OpenAlexW2063939409MaRDI QIDQ5447907

Eric Cancès, Frédéric Legoll, Gabriel Stoltz

Publication date: 20 March 2008

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=M2AN_2007__41_2_351_0

Mathematics Subject Classification ID

Related Items (38)

LANGEVIN MOLECULAR DYNAMICS DERIVED FROM EHRENFEST DYNAMICS ⋮ HMC: reducing the number of rejections by not using leapfrog and some results on the acceptance rate ⋮ Connecting the Dots: Numerical Randomized Hamiltonian Monte Carlo with State-Dependent Event Rates ⋮ Equilibrium sampling from nonequilibrium dynamics ⋮ Efficient numerical evaluation of thermodynamic quantities on infinite (semi-)classical chains ⋮ Predictive coarse-graining ⋮ Convergence of nonequilibrium Langevin dynamics for planar flows ⋮ Geometric Ergodicity for Hamiltonian Monte Carlo on Compact Manifolds ⋮ Palindromic 3-stage splitting integrators, a roadmap ⋮ Hypocoercivity Properties of Adaptive Langevin Dynamics ⋮ Free energy computations by minimization of Kullback-Leibler divergence: An efficient adaptive biasing potential method for sparse representations ⋮ A patch that imparts unconditional stability to explicit integrators for Langevin-like equations ⋮ Convergence of unadjusted Hamiltonian Monte Carlo for mean-field models ⋮ Comparing the efficiencies of stochastic isothermal molecular dynamics methods ⋮ Weak backward error analysis for Langevin process ⋮ Optimal tuning of the hybrid Monte Carlo algorithm ⋮ Low temperature dynamics of the one-dimensional discrete nonlinear Schrödinger equation ⋮ On the rate of convergence to equilibrium of the Andersen thermostat in molecular dynamics ⋮ Mixing of Hamiltonian Monte Carlo on strongly log-concave distributions: continuous dynamics ⋮ Symmetrically Processed Splitting Integrators for Enhanced Hamiltonian Monte Carlo Sampling ⋮ Irreducibility and geometric ergodicity of Hamiltonian Monte Carlo ⋮ A stochastic phase-field model determined from molecular dynamics ⋮ An ergodic sampling scheme for constrained Hamiltonian systems with applications to molecular dynamics ⋮ Approximation of stationary statistical properties of dissipative dynamical systems: Time discretization ⋮ Adaptive Thermostats for Noisy Gradient Systems ⋮ Molecular Simulation in the Canonical Ensemble and Beyond ⋮ Path sampling with stochastic dynamics: some new algorithms ⋮ Extra chance generalized hybrid Monte Carlo ⋮ Finite-temperature coarse-graining of one-dimensional models: mathematical analysis and computational approaches ⋮ A Conjecture about Molecular Dynamics ⋮ Two-scale coupling for preconditioned Hamiltonian Monte Carlo in infinite dimensions ⋮ Geometric integrators and the Hamiltonian Monte Carlo method ⋮ On the geometric ergodicity of Hamiltonian Monte Carlo ⋮ Hybrid Monte Carlo methods for sampling probability measures on submanifolds ⋮ Metropolis Integration Schemes for Self-Adjoint Diffusions ⋮ Weighted L ²-contractivity of Langevin dynamics with singular potentials ⋮ Geometric Integration of Measure-Preserving Flows for Sampling ⋮ Numerical algorithms for stationary statistical properties of dissipative dynamical systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Markov chains and stochastic stability
• Molecular modeling and simulation. An interdisciplinary guide
• Non-ergodicity of the Nosé-Hoover thermostatted harmonic oscillator
• The Nosé-Poincaré method for constant temperature molecular dynamics
• A direct approach to conformational dynamics based on hybrid Monte Carlo
• An improved acceptance procedure for the hybrid Monte Carlo algorithm
• Exponential convergence of Langevin distributions and their discrete approximations
• Monte-Carlo methods for the transport and diffusion equations
• Isotropic hypoelliptic and trend to equilibrium for the Fokker-Planck equation with a high-degree potential
• Shadow hybrid Monte Carlo: an efficient propagator in phase space of macromolecules
• Rates of convergence of the Hastings and Metropolis algorithms
• Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise.
• Long-time averaging for integrable Hamiltonian dynamics
• Stability of Markovian processes II: continuous-time processes and sampled chains
• Simulating Hamiltonian Dynamics
• Discrete mechanics and variational integrators
• Second-order discretization schemes of stochastic differential systems for the computation of the invariant law
• Smooth Transition Densities for One-Dimensional Diffusions
• Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms
• Optimal Scaling of Discrete Approximations to Langevin Diffusions
• Backward Error Analysis for Numerical Integrators
• Splitting for Dissipative Particle Dynamics
• Quasi-symplectic methods for Langevin-type equations
• Sur quelques algorithmes récursifs pour les probabilités numériques
• A Hamiltonian Formulation for Recursive Multiple Thermostats in a Common Timescale
• Projection of diffusions on submanifolds: Application to mean force computation
• Geometric Numerical Integration
• The Targeted Shadowing Hybrid Monte Carlo (TSHMC) Method
• Monte Carlo sampling methods using Markov chains and their applications
• The Art of Molecular Dynamics Simulation
• Cost of the generalised hybrid Monte Carlo algorithm for free field theory
• Monte Carlo strategies in scientific computing

This page was built for publication: Theoretical and numerical comparison of some sampling methods for molecular dynamics