Related papers: Deflated Multigrid Multilevel Monte Carlo
A hybrid Monte Carlo (HMC) approach is employed to quantify the influence of inelastic deformation on the microstructural evolution of polycrystalline materials. This approach couples a time explicit material point method (MPM) for…
This review gives an overview on the research of algorithms for dynamical fermions used in large scale lattice QCD simulations. First a short overview on the state-of-the-art of ensemble generation at the physical point is given. Followed…
Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of…
We present a new trace estimator of the matrix whose explicit form is not given but its matrix multiplication to a vector is available. The form of the estimator is similar to the Hutchison stochastic trace estimator, but instead of the…
In Kuznetsov et al. (2011) a new Monte Carlo simulation technique was introduced for a large family of Levy processes that is based on the Wiener-Hopf decomposition. We pursue this idea further by combining their technique with the recently…
Multilevel Monte Carlo (MLMC) and unbiased estimators recently proposed by McLeish (Monte Carlo Methods Appl., 2011) and Rhee and Glynn (Oper. Res., 2015) are closely related. This connection is elaborated by presenting a new general class…
Sampling from a log-concave distribution function is one core problem that has wide applications in Bayesian statistics and machine learning. While most gradient free methods have slow convergence rate, the Langevin Monte Carlo (LMC) that…
We introduce Reflective Hamiltonian Monte Carlo (ReHMC), an HMC-based algorithm, to sample from a log-concave distribution restricted to a convex body. We prove that, starting from a warm start, the walk mixes to a log-concave target…
At low temperatures $T$ where $1/T=\beta\gg1$ the na\"ive implementation of determinant quantum Monte Carlo (DQMC) methods suffers from loss of precision and numerical instabilities when evaluating the fermion determinant. This instability…
This paper proposes a new multilevel Monte Carlo (MLMC) method for the ergodic SDEs which do not satisfy the contractivity condition. By introducing the change of measure technique, we simulate the path with contractivity and add the…
We investigate the applicability of Quasi-Monte Carlo methods to Euclidean lattice systems for quantum mechanics in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable…
I discuss the behaviour of algorithms for dynamical fermions as the sea-quark mass decreases. I focus on the Hybrid-Monte-Carlo (HMC) algorithm applied to two degenerate flavours of Wilson fermions. First, I briefly review the performance…
The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximations at different levels of accuracy using a hierarchy of…
A new method to perform numerical simulations of light-front Hamiltonians formulated on transverse lattices is introduced. The method is based on a DLCQ formulation for the (continuous) longitudinal directions. The hopping term in the…
In this article we review some of recent results on higher order quasi-Monte Carlo (HoQMC) methods. After a seminal work by Dick (2007, 2008) who originally introduced the concept of HoQMC, there have been significant theoretical progresses…
We introduce a near-linear complexity (geometric and meshless/algebraic) multigrid/multiresolution method for PDEs with rough ($L^\infty$) coefficients with rigorous a-priori accuracy and performance estimates. The method is discovered…
We consider a three-dimensional magnetic field produced by an arbitrary collection of dipoles. Assuming the magnetic vector or its gradient tensor field is measured above the earth surface, the inverse problem is to use the measurement data…
Modeling physical phenomena like heat transport and diffusion is crucially dependent on the numerical solution of partial differential equations (PDEs). A PDE solver finds the solution given coefficients and a boundary condition, whereas an…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
In this article we consider the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice,…