Hybrid Monte Carlo methods for sampling probability measures on submanifolds

DOI10.1007/s00211-019-01056-4zbMath1453.65027arXiv1807.02356OpenAlexW2962905242WikidataQ127622239 ScholiaQ127622239MaRDI QIDQ2326372

Mathias Rousset, Gabriel Stoltz, Tony Lelièvre

Publication date: 7 October 2019

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.02356

Mathematics Subject Classification ID

Numerical analysis or methods applied to Markov chains (65C40) Constrained dynamics, Dirac's theory of constraints (70H45) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)

Related Items

Random Points on an Algebraic Manifold ⋮ A Uniformly Accurate Scheme for the Numerical Integration of Penalized Langevin Dynamics ⋮ Constrained overdamped Langevin dynamics for symmetric multimarginal optimal transportation ⋮ Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds ⋮ Optimal Reaction Coordinates: Variational Characterization and Sparse Computation ⋮ Ergodic SDEs on submanifolds and related numerical sampling schemes ⋮ Randomized time Riemannian manifold Hamiltonian Monte Carlo ⋮ Computing the Hausdorff Boundary Measure of Semialgebraic Sets ⋮ Sampling from manifold-restricted distributions using tangent bundle projections ⋮ Coulomb Gases Under Constraint: Some Theoretical and Numerical Results ⋮ Normal-Bundle Bootstrap ⋮ NonReversible Sampling Schemes on Submanifolds ⋮ Geometric Integration of Measure-Preserving Flows for Sampling

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Approximate Bayesian computational methods
• RATTLE: A velocity version of the SHAKE algorithm for molecular dynamics calculations
• Exponential convergence of Langevin distributions and their discrete approximations
• Irreducibility and geometric ergodicity of Hamiltonian Monte Carlo
• The geometric foundations of Hamiltonian Monte Carlo
• An ergodic sampling scheme for constrained Hamiltonian systems with applications to molecular dynamics
• Langevin dynamics with constraints and computation of free energy differences
• Conservative stochastic differential equations: Mathematical and numerical analysis
• Simulating Hamiltonian Dynamics
• Pathwise accuracy and ergodicity of metropolized integrators for SDEs
• Optimal Scaling of Discrete Approximations to Langevin Diffusions
• Symplectic Integration of Constrained Hamiltonian Systems
• Monte Carlo on Manifolds: Sampling Densities and Integrating Functions
• Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods
• Langevin Dynamics With General Kinetic Energies
• Geometric Numerical Integration of Inequality Constrained, Nonsmooth Hamiltonian Systems
• Random Points on an Algebraic Manifold
• Equation of State Calculations by Fast Computing Machines
• Efficient molecular dynamics using geodesic integration and solvent–solute splitting
• Theoretical and numerical comparison of some sampling methods for molecular dynamics
• Geometric Numerical Integration
• Sampling from a Manifold
• Monte Carlo sampling methods using Markov chains and their applications