Related papers: Deflated Multigrid Multilevel Monte Carlo
We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element…
Multifidelity Monte Carlo methods rely on a hierarchy of possibly less accurate but statistically correlated simplified or reduced models, in order to accelerate the estimation of statistics of high-fidelity models without compromising the…
Polynomial approximations to the inverse of the fermion matrix are used to filter the dynamics of the upper energy scales in HMC simulations. The use of a multiple time-scale integration scheme allows the filtered pseudofermions to be…
Can Monte Carlo (MC) solvers be directly used in gradient-based methods for PDE-constrained optimization problems? In these problems, a gradient of the loss function is typically presented as a product of two PDE solutions, one for the…
Ground state properties of the Hubbard model on a two-dimensional square lattice are studied by the auxiliary-field quantum Monte Carlo method. Accurate results for energy, double occupancy, effective hopping, magnetization, and momentum…
This manuscript presents a framework for using multilevel quadrature formulae to compute the solution of optimal control problems constrained by random partial differential equations. Our approach consists in solving a sequence of optimal…
The bold diagrammatic Monte Carlo (BDMC) method performs an unbiased sampling of Feynman's diagrammatic series using skeleton diagrams. For lattice models the efficiency of BDMC can be dramatically improved by incorporating dynamic…
Multigrid methods were invented for the solution of discretized partial differential equations in ordered systems. The slowness of traditional algorithms is overcome by updates on various length scales. In this article we discuss…
Lattice QCD solvers encounter critical slowing down for fine lattice spacings and small quark mass. Traditional matrix eigenvalue deflation is one approach to mitigating this problem. However, to improve scaling we study the effects of…
We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. This setting is ubiquitous…
We propose a new framework for Hamiltonian Monte Carlo (HMC) on truncated probability distributions with smooth underlying density functions. Traditional HMC requires computing the gradient of potential function associated with the target…
Markov chain Monte Carlo (MCMC) methods provide powerful framework for sampling unknown probability measures across a wide range of scientific applications. In some settings, the target distribution is supported on a lower-dimensional…
I show how to avoid a two level nested conjugate gradient procedure in the context of Hybrid Monte Carlo with the overlap fermionic action. The resulting procedure is quite similar to Hybrid Monte Carlo with domain wall fermions, but is…
Due to its constrained support, the Dirichlet distribution is uniquely suited to many applications. The constraints that make it powerful, however, can also hinder practical implementations, particularly those utilizing Markov Chain Monte…
Knowledge of a machine tool axis to axis location errors allows compensation and correcting actions to be taken to enhance its volumetric accuracy. Several procedures exist, involving either lengthy individual test for each geometric error…
I consider the problem of integrating a function $f$ over the $d$-dimensional unit cube. I describe a multilevel Monte Carlo method that estimates the integral with variance at most $\epsilon^{2}$ in $O(d+\ln(d)d_{t}\epsilon^{-2})$ time,…
We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC) algorithm with piecewise-constant interpolation and a W-cycle, applied to the one-dimensional $O(4)$-symmetric nonlinear $\sigma$-model [= $SU(2)$ principal chiral…
We give a brief discussion of the recently developed Constrained-Path Monte Carlo Method. This method is a quantum Monte Carlo technique that eliminates the fermion sign problem plaguing simulations of systems of interacting electrons. The…
In high-energy particle physics, complex Monte Carlo (MC) simulations are needed to compare theory predictions to measurable quantities. Many and large MC samples are needed to be generated to take into account all the systematics.…
We show how the integrators used for the molecular dynamics step of the Hybrid Monte Carlo algorithm can be further improved. These integrators not only approximately conserve some Hamiltonian $H$ but conserve exactly a nearby shadow…