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We point out that Monte Carlo simulations of theories with severe sign problems can be profitably performed over manifolds in complex space different from the one with fixed imaginary part of the action. We describe a family of such…
We investigate the performance of the hybrid Monte Carlo algorithm, the standard algorithm used for lattice QCD simulations involving fermions, in updating non-trivial global topological structures. We find that the hybrid Monte Carlo…
A new algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables which can be expressed in…
We introduce a new Monte Carlo method for pure gauge theories. It is not intended for use with dynamical fermions. It belongs to the class of Local Hybrid Monte Carlo (LHMC) algorithms, which make use of the locality of the action by…
This paper develops and analyzes an efficient numerical method for solving elliptic partial differential equations, where the diffusion coefficients are random perturbations of deterministic diffusion coefficients. The method is based upon…
The self-healing diffusion Monte Carlo algorithm (SHDMC) [Reboredo, Hood and Kent, Phys. Rev. B {\bf 79}, 195117 (2009); Reboredo, {\it ibid.} {\bf 80}, 125110 (2009)] is extended to study the ground and excited states of magnetic and…
In infinite-dimensional Hilbert spaces we device a class of strongly convergent primal-dual schemes for solving variational inequalities defined by a Lipschitz continuous and pseudomonote map. Our novel numerical scheme is based on Tseng's…
We describe a novel switching algorithm based on a ``reverse'' Monte Carlo method, in which the potential is stochastically modified before the system configuration is moved. This new algorithm facilitates a generalized formulation of…
By precisely writing down the matrix element of the local Boltzmann operator, we have proposed a new path integral formulation for quantum field theory and developed a corresponding Monte Carlo algorithm. With current formula, the…
We introduce a robust numerical method for determining intersection numbers of Lefschetz thimbles in multivariable settings. Our approach employs the multiple shooting method to solve the upward flow equations from the saddle points to the…
This paper addresses the problem of Monte Carlo approximation of posterior probability distributions. In particular, we have considered a recently proposed technique known as population Monte Carlo (PMC), which is based on an iterative…
An accurate algorithm is proposed to improve the prediction of a particle in collision with a moving wall within the direct simulation Monte Carlo (DSMC) framework for the simulation of unsteady rarefied flows. This algorithm is able to…
The path integral formulation of quantum mechanical problems including fermions is often affected by a severe numerical sign problem. We show how such a sign problem can be alleviated by a judiciously chosen constant imaginary offset to the…
We establish the geometric ergodicity of the preconditioned Hamiltonian Monte Carlo (HMC) algorithm defined on an infinite-dimensional Hilbert space, as developed in [Beskos et al., Stochastic Process. Appl., 2011]. This algorithm can be…
We present an implicit collision method with on-the-fly multiplicity adjustment based on the forward weight window methodology for efficient Dynamic Monte Carlo (MC) simulation of reactivity excursion transport problems. Test problems based…
The paper proposes a Riemannian Manifold Hamiltonian Monte Carlo sampler to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The…
Probability measures supported on submanifolds can be sampled by adding an extra momentum variable to the state of the system, and discretizing the associated Hamiltonian dynamics with some stochastic perturbation in the extra variable. In…
Coulomb and log-gases are exchangeable singular Boltzmann-Gibbs measures appearing in mathematical physics at many places, in particular in random matrix theory. We explore experimentally an efficient numerical method for simulating such…
We present the preliminary tests on two modifications of the Hybrid Monte Carlo (HMC) algorithm. Both algorithms are designed to travel much farther in the Hamiltonian phase space for each trajectory and reduce the autocorrelations among…
Many physical systems can be described in terms of matrix models that we often cannot solve analytically. Fortunately, they can be studied numerically in a straightforward way. Many commonly used algorithms follow the Monte Carlo method,…