相关论文: Reliable Adaptive Cubature Using Digital Sequences

Appropriately designing the proposal kernel of particle filters is an issue of significant importance, since a bad choice may lead to deterioration of the particle sample and, consequently, waste of computational power. In this paper we…

Deploying deep learning models in safety-critical applications remains a very challenging task, mandating the provision of assurances for the dependable operation of these models. Uncertainty quantification (UQ) methods estimate the model's…

Layer potentials represent solutions to partial differential equations in an integral equation formulation. When numerically evaluating layer potentials at evaluation points close to the domain boundary, specialized quadrature techniques…

Quasi-Monte Carlo methods have become the industry standard in computer graphics. For that purpose, efficient algorithms for low discrepancy sequences are discussed. In addition, numerical pitfalls encountered in practice are revealed. We…

Adaptive tomography has been widely investigated to achieve faster state tomography processing of quantum systems. Infidelity of the nearly pure states in a quantum information process generally scales as O(1/sqrt(N) ), which requires a…

A compression algorithm is introduced for multi-determinant wave functions which can greatly reduce the number of determinants that need to be evaluated in quantum Monte Carlo calculations. We have devised an algorithm with three levels of…

Adjusted similarity measures, such as Cohen's kappa for inter-rater reliability and the adjusted Rand index used to compare clustering algorithms, are a vital tool for comparing discrete labellings. These measures are intended to have the…

We propose a sampling-based simulation for fault-tolerant quantum error correction under coherent noise. A mixture of incoherent and coherent noise, possibly due to over-rotation, is decomposed into Clifford channels with a quasiprobability…

Standard quantum amplitude estimation algorithms provide quadratic speedup to Monte-Carlo simulations but require a circuit depth that scales as inverse of the estimation error. In view of the shallow depth in near-term devices, the…

We present optimized implementations of the weak-coupling continuous-time Monte Carlo method defined for nonequilibrium problems on the Keldysh contour. We describe and compare two methods of preparing the system before beginning the…

Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…

This paper studies the use of a machine learning-based estimator as a control variate for mitigating the variance of Monte Carlo sampling. Specifically, we seek to uncover the key factors that influence the efficiency of control variates in…

Accurate sensor calibration is crucial for autonomous systems, yet its uncertainty quantification remains underexplored. We present the first approach to integrate uncertainty awareness into online extrinsic calibration, combining Monte…

Many exact Markov chain Monte Carlo algorithms have been developed for posterior inference in Bayesian nonparametric models which involve infinite-dimensional priors. However, these methods are not generic and special methodology must be…

Gibbs measures, such as Coulomb gases, are popular in modelling systems of interacting particles. Recently, we proposed to use Gibbs measures as randomized numerical integration algorithms with respect to a target measure $\pi$ on $\mathbb…

We study numerical integration over bounded regions in $\mathbb{R}^s, s\ge1$ with respect to some probability measure. We replace random sampling with quasi-Monte Carlo methods, where the underlying point set is derived from deterministic…

We demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of Markov Chain Monte Carlo (MCMC) algorithms as a function of the target density and proposal density. The bound relies on…

Many problems require to approximate an expected value by some kind of Monte Carlo (MC) sampling, e.g. molecular dynamics (MD) or simulation of stochastic reaction models (also termed kinetic Monte Carlo (kMC)). Often, we are furthermore…

In this work we propose and analyze a numerical method for electrical impedance tomography of recovering a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a…

We employ unsupervised machine learning to enhance the accuracy of our recently presented scaling method for wave confinement analysis [1]. We employ the standard k-means++ algorithm as well as our own model-based algorithm. We investigate…