Related papers: Monte Carlo approximations of the Neumann problem
We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such methods have concrete value in the statistics on Riemannian…
Conditional Monte Carlo refers to sampling from the conditional distribution of a random vector X given the value T(X) = t for a function T(X). Classical conditional Monte Carlo methods were designed for estimating conditional expectations…
In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte Carlo" approach to the standard problem of…
We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…
We establish elliptic regularity for nonlinear inhomogeneous Cauchy-Riemann equations under minimal assumptions, and give a counterexample in a borderline case. In some cases where the inhomogeneous term has a separable factorization, the…
We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such…
We present real-time inchworm quantum Monte Carlo results for single-site dynamical mean field theory on an infinite coordination number Bethe lattice. Our numerically exact results are obtained on the L-shaped Keldysh contour and, being…
We construct asymptotically Euclidean solutions of the vacuum Einstein constraint equations with an apparent horizon boundary condition. Specifically, we give sufficient conditions for the constant mean curvature conformal method to…
We consider the forward problem of uncertainty quantification for the generalised Dirichlet eigenvalue problem for a coercive second order partial differential operator with random coefficients, motivated by problems in structural…
Continuous level Monte Carlo is an unbiased, continuous version of the celebrated multilevel Monte Carlo method. The approximation level is assumed to be continuous resulting in a stochastic process describing the quantity of interest.…
We consider the "Method of particular solutions" for numerically computing eigenvalues and eigenfunctions of the Laplacian $\Delta$ on a smooth, bounded domain Omega in RR^n with either Dirichlet or Neumann boundary conditions. This method…
Quantitative long-time entropic convergence and short-time regularization are established for an idealized Hamiltonian Monte Carlo chain which alternatively follows an Hamiltonian dynamics for a fixed time and then partially or totally…
A simple-to-implement weak-sense numerical method to approximate reflected stochastic differential equations (RSDEs) is proposed and analysed. It is proved that the method has the first order of weak convergence. Together with the Monte…
Motivated mainly by applications to partial differential equations with random coefficients, we introduce a new class of Monte Carlo estimators, called Toeplitz Monte Carlo (TMC) estimator for approximating the integral of a multivariate…
In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the…
The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as an expected value of a random time process. Using the latter, we present an interesting numerical…
We study semi-linear elliptic PDEs with polynomial non-linearity and provide a probabilistic representation of their solution using branching diffusion processes. When the non-linearity involves the unknown function but not its derivatives,…
This work demonstrates algorithms to accurately compute solutions to thermal radiation transport problems using a reduced floating-point precision implementation of the Implicit Monte Carlo method. Several techniques falling into the…
We introduce an exact Monte Carlo approach to the statistics of discrete quantum systems which does not rely on the standard fragmentation of the imaginary time, or any small parameter. The method deals with discrete objects, kinks,…
We present a new approach to the study of equilibrium properties in many-body quantum physics. Our method takes inspiration from Density Matrix Quantum Monte Carlo and incorporates new crucial features. First of all, the dynamics is…