Related papers: High-degree Polynomial Noise Subtraction
When solving stochastic partial differential equations (SPDEs) driven by additive spatial white noise, the efficient sampling of white noise realizations can be challenging. Here, we present a new sampling technique that can be used to…
This paper introduces a versatile approach for computing the risk of collision specifically tailored for scenarios featuring low relative encounter velocities, but with potential applicability across a wide range of situations. The…
This paper provides a framework in which multilevel Monte Carlo and continuous level Monte Carlo can be compared. In continuous level Monte Carlo the level of refinement is determined by an exponentially distributed random variable, which…
In this paper, we tackle the parametric complete multiplicity problem for a univariate polynomial. Our approach to the parametric complete multiplicity problem has a significant difference from the classical method, which relies on repeated…
We report on coding and performance of our polynomial hybrid Monte Carlo program on the Earth Simulator. At present the entire program achieves 25--40% efficiency. An analysis of overheads shows that a tuning of inter-node communications is…
We propose a novel $hp$-multilevel Monte Carlo method for the quantification of uncertainties in the compressible Navier-Stokes equations, using the Discontinuous Galerkin method as deterministic solver. The multilevel approach exploits…
We consider the efficient construction of polynomial lattice rules, which are special cases of so-called quasi-Monte Carlo (QMC) rules. These are of particular interest for the approximate computation of multivariate integrals where the…
Efficiently estimating energy expectation values of quantum lattice systems on quantum computers is a crucial subroutine for various quantum algorithms, which can lead to significant overhead due to the high measurement shot numbers…
We present a fundamental improvement of a high polynomial degree time domain cell method recently introduced by the last three authors. The published work introduced a method featuring block-diagonal system matrices where the block size and…
High-probability analysis of stochastic first-order optimization methods under mild assumptions on the noise has been gaining a lot of attention in recent years. Typically, gradient clipping is one of the key algorithmic ingredients to…
We review the application of lattice QCD techniques, most notably the Hybrid Monte-Carlo (HMC) simulations, to first-principle study of tight-binding models of crystalline solids with strong inter-electron interactions. After providing a…
Calculating the expected information gain in optimal Bayesian experimental design typically relies on nested Monte Carlo sampling. When the model also contains nuisance parameters, which are parameters that contribute to the overall…
Many fields require computing the trace of the inverse of a large, sparse matrix. The typical method used for such computations is the Hutchinson method which is a Monte Carlo (MC) averaging over matrix quadratures. To improve its…
The subsurface flow is usually subject to uncertain porous media structures. In most cases, however, we only have partial knowledge about the porous media properties. A common approach is to model the uncertain parameters of porous media as…
The Rational Hybrid Monte Carlo (RHMC) algorithm extends the Hybrid Monte Carlo algorithm for lattice QCD simulations to situations involving fractional powers of the determinant of the quadratic Dirac operator. This avoids the updating…
We present results of a high statistics study (O(2000) configurations) of the quark masses in the MS-bar scheme from Lattice QCD in the quenched approximation at beta=6.0, beta=6.2 and beta=6.4 using both the Wilson and the tree-level…
We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…
We present new, explicit, volume-preserving vector fields for polynomial divergence-free vector fields of arbitrary degree (both positive and negative). The main idea is to decompose the divergence polynomial by means of an appropriate…
Discrepancies play an important role in the study of uniformity properties of point sets. Their probability distributions are a help in the analysis of the efficiency of the Quasi Monte Carlo method of numerical integration, which uses…
We present a Monte Carlo method that allows efficient and unbiased sampling of Hamiltonian walks on a cubic lattice. Such walks are self-avoiding and visit each lattice site exactly once. They are often used as simple models of globular…