The penalty method for random walks with uncertain energies

We generalize the Metropolis et al. random walk algorithm to the situation where the energy is noisy and can only be estimated. Two possible applications are for long range potentials and for mixed quantum-classical simulations. If the noise is normally distributed, we are able to modify the acceptance probability by applying a penalty to the energy difference and thereby achieve exact sampling even with very strong noise. When one has to estimate the variance we have an approximate formula, good in the limit of a large number of independent estimates. We argue that the penalty method is nearly optimal. We also adapt an existing method by Kennedy and Kuti and compare to the penalty method on a one-dimensional double well.

• Publication year

  1998

• Venue

  Journal of Chemical Physics

• Publication date

  1998-12-18

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1063/1.478034arXiv physics/9812035
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• An Introduction to the Monte Carlo Method for Particle Simulations

  1999cited by this paper
• An ab initio path integral Monte Carlo simulation method for molecules and clusters: Application to Li4 and Li5+

  1998cited by this paper
• Superposition formulae for the discrete Ribaucour transformations of circular lattices

  1998cited by this paper
• Path integrals in the theory of condensed helium

  1995cited by this paper
• Structure and stability of molecular carbon: Importance of electron correlation.

  1995cited by this paper
• An optimized method for treating long-range potentials

  1995cited by this paper
• Decisions, decisions: Noise and its effects on integral Monte Carlo algorithms

  1994cited by this paper
• Computer Simulation of Liquids

  1988cited by this paper
• Rapid solution of integral equations of classical potential theory

  1985cited by this paper
• Bosonic lattice gauge theory with noise

  1985cited by this paper
• Unified approach for molecular dynamics and density-functional theory.

  1985cited by this paper
• Noise without noise: A new Monte Carlo method.

  1985cited by this paper
• Monte Carlo simulation of a many-fermion study

  1977cited by this paper
• Optimum Monte-Carlo sampling using Markov chains

  1973cited by this paper
• Monte Carlo calculations of the radial distribution functions for a proton-electron plasma

  1965cited by this paper

• Implementing advanced trial wave functions in fermion quantum Monte Carlo via stochastic sampling.

  2025cites this paper
• Efficient quantum thermal simulation

  2025cites this paper
• Impact of local field correction on transport and dynamic properties of warm dense matter

  2025cites this paper
• Revisiting the Broken Symmetry Phase of Solid Hydrogen: A Neural Network Variational Monte Carlo Study

  2025cites this paper
• Quantum Metropolis-Hastings algorithm

  2025cites this paper
• ALAAMEE: Open-source software for fitting autologistic actor attribute models

  2024cites this paper
• Quantum generalizations of Glauber and Metropolis dynamics

  2024cites this paper
• Toward first principles-based simulations of dense hydrogen

  2024cites this paper
• Perturbations of Markov Chains

  2024influential citation
• Re-use of samples in stochastic annealing

  2024cites this paper
• Analysing symbolic data by pseudo-marginal methods

  2024cites this paper
• Generating Synthetic Power Grids Using Exponential Random Graph Models

  2024cites this paper
• New network models facilitate analysis of biological networks

  2023cites this paper
• Generating synthetic power grids using exponential random graphs models

  2023influential citation
• Quantum computing for chemistry and physics applications from a Monte Carlo perspective.

  2023cites this paper
• DP-Fast MH: Private, Fast, and Accurate Metropolis-Hastings for Large-Scale Bayesian Inference

  2023influential citation
• A Correlated Pseudo-Marginal Approach to Doubly Intractable Problems

  2022cites this paper
• A deep variational free energy approach to dense hydrogen

  2022cites this paper
• When you can’t count, sample!

  2022cites this paper
• Non-reversible Parallel Tempering for Deep Posterior Approximation

  2022cites this paper
• Data Subsampling for Bayesian Neural Networks

  2022influential citation
• Deep Variational Free Energy Approach to Dense Hydrogen.

  2022cites this paper
• Differentially Private Hamiltonian Monte Carlo

  2021cites this paper
• Unitary block optimization for variational quantum algorithms

  2021cites this paper
• Monte Carlo Methods

  2021cites this paper
• A general perspective on the Metropolis-Hastings kernel

  2020cites this paper
• Probabilistic Programs with Stochastic Conditioning

  2020cites this paper
• Non-convex Learning via Replica Exchange Stochastic Gradient MCMC

  2020cites this paper
• Modeling of many-body interactions between elastic spheres through symmetry functions.

  2020cites this paper
• Efficient Langevin dynamics for "noisy" forces.

  2020cites this paper
• Exact MCMC with differentially private moves

  2019cites this paper
• A Simple Algorithm for Scalable Monte Carlo Inference

  2019influential citation
• Estimating reciprocal partition functions to enable design space sampling.

  2019cites this paper
• Peskun-Tierney ordering for Markov chain and process Monte Carlo: beyond the reversible scenario

  2019cites this paper
• Optimal Sampling for Simulated Annealing Under Noise

  2018influential citation
• Subsampling MCMC - an Introduction for the Survey Statistician

  2018influential citation
• Scalable Monte Carlo inference for state-space models

  2018influential citation
• Benchmarking vdW‐DF first‐principles predictions against Coupled Electron–Ion Monte Carlo for high‐pressure liquid hydrogen

  2018cites this paper
• Subsampling sequential Monte Carlo for static Bayesian models

  2018cites this paper
• Estimation of Noisy Cost Functions by Conventional and Adjusted Simulated Annealing Techniques

  2018influential citation
• Structural, electrical and optical properties of ZnO nanoparticle: combined experimental and theoretical study

  2018cites this paper
• Field‐programmable gate arrays and quantum Monte Carlo: Power efficient coprocessing for scalable high‐performance computing

  2018cites this paper
• The Correlated Pseudo-Marginal Method

  2018cites this paper
• MEXIT: Maximal un-coupling times for Markov processes

  2017cites this paper
• Projector Quantum Monte Carlo Methods for Linear and Non-linear Wavefunction Ansatzes

  2017cites this paper
• MEXIT: Maximal un-coupling times for stochastic processes

  2017cites this paper
• Hamiltonian Monte Carlo with Energy Conserving Subsampling

  2017cites this paper
• Stability and examples of some approximate MCMC algorithms.

  2017influential citation
• Development of a quasi-classical method and application to the infrared spectroscopy

  2016influential citation
• Thermodynamic integration methods, infinite swapping, and the calculation of generalized averages.

  2016cites this paper
• Near-optimal protocols in complex nonequilibrium transformations

  2016cites this paper
• Monte Carlo sampling for stochastic weight functions

  2016influential citation
• On the Use of Penalty MCMC for Differential Privacy

  2016influential citation
• Fermion sign problem in imaginary-time projection continuum quantum Monte Carlo with local interaction.

  2016cites this paper
• Inference for partial orders from random linear extensions

  2015cites this paper
• Speeding up MCMC by Delayed Acceptance and Data Subsampling

  2015influential citation
• Ab Initio Molecular Dynamics with Quantum Monte Carlo

  2015cites this paper
• On Markov chain Monte Carlo methods for tall data

  2015cites this paper
• The correlated pseudomarginal method

  2015cites this paper
• Gas phase infrared spectra from quasi-classical Kubo time correlation functions

  2015cites this paper
• SISSA Lecture notes on Numerical methods for strongly correlated electrons

  2015cites this paper
• On extended state-space constructions for Monte Carlo methods

  2015cites this paper
• Two Paths Diverged: Exploring Trajectories, Protocols, and Dynamic Phases

  2015cites this paper
• Ab initio molecular dynamics of water by quantum Monte Carlo

  2014cites this paper
• Speeding Up MCMC by Efficient Data Subsampling

  2014influential citation
• GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation

  2014cites this paper
• Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo.

  2014cites this paper
• Establishing some order amongst exact approximations of MCMCs

  2014cites this paper
• Spatial Averaging: Sampling Enhancement for Exploring Configurational Space of Atomic Clusters and Biomolecules.

  2014cites this paper
• Gas phase infrared spectra via the phase integration quasi-classical method

  2014cites this paper
• First Principles Methods: A Perspective from Quantum

  2014cites this paper
• Metallization and dissociation in high pressure liquid hydrogen by an efficient molecular dynamics with quantum Monte Carlo

  2014influential citation
• Ab initio molecular dynamics with noisy forces: validating the quantum Monte Carlo approach with benchmark calculations of molecular vibrational properties.

  2014cites this paper
• Computing thermal Wigner densities with the phase integration method.

  2014cites this paper
• First Principles Methods: A Perspective from Quantum Monte Carlo

  2013cites this paper
• Approximating Time-Dependent Quantum Statistical Properties

  2013influential citation
• On the efficiency of pseudo-marginal random walk Metropolis algorithms

  2013cites this paper
• Quantum Monte Carlo techniques and applications for warm dense matter

  2013cites this paper
• Quantum dynamical structure factor of liquid neon via a quasiclassical symmetrized method.

  2013cites this paper
• On nonnegative unbiased estimators

  2013cites this paper
• Coupled MCMC with a randomized acceptance probability

  2012influential citation
• Finite-temperature electronic simulations without the Born-Oppenheimer constraint.

  2012cites this paper
• The Properties of Hydrogen and Helium Under Extreme Conditions

  2011cites this paper
• Linearized symmetrized quantum time correlation functions calculation via phase pre-averaging

  2011cites this paper
• Evidence for a first-order liquid-liquid transition in high-pressure hydrogen from ab initio simulations

  2010cites this paper
• Algorithmic differentiation and the calculation of forces by quantum Monte Carlo.

  2010cites this paper
• Spatial averaging for small molecule diffusion in condensed phase environments.

  2010cites this paper
• An Overview of Quantum Monte Carlo Methods

  2010cites this paper
• A spatial averaging approach to rare-event sampling

  2009cites this paper
• Quantum Monte Carlo algorithms for electronic structure at the petascale; the Endstation project

  2008cites this paper
• Simulated annealing in the presence of noise

  2008influential citation
• 4.13 – De Novo Design

  2007cites this paper
• Quantum Monte Carlo method using a stochastic Poisson solver.

  2006cites this paper
• Quantum monte carlo with a stochastic potential solver

  2005cites this paper
• The Coupled Electron-Ion Monte Carlo Method

  2005influential citation
• Computational methods in coupled electron-ion Monte Carlo simulations.

  2005cites this paper
• Coupled Electron-Ion Monte Carlo calculations of atomic hydrogen

  2004cites this paper
• Correlated geminal wave function for molecules: an efficient resonating valence bond approach.

  2004cites this paper
• Coupled electron-ion monte carlo calculations of dense metallic hydrogen.

  2004cites this paper
• METHODS FOR COUPLED ELECTRONIC-IONIC MONTE CARLO

  2002cites this paper