相关论文: Reliable Adaptive Cubature Using Digital Sequences

In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical…

In this paper, a novel hybrid-degree dual estimation approach based on cubature rules and cubature-based nonlinear filters is proposed for fault diagnosis of nonlinear systems through simultaneous state and time-varying parameter…

This paper contributes to the study of optimal experimental design for Bayesian inverse problems governed by partial differential equations (PDEs). We derive estimates for the parametric regularity of multivariate double integration…

We revisit the problem of computing submatrices of the Cram\'er-Rao bound (CRB), which lower bounds the variance of any unbiased estimator of a vector parameter $\vth$. We explore iterative methods that avoid direct inversion of the Fisher…

We study the convergence rate of the median estimator for affine matrix scrambled digital nets applied to integrands over the unit hypercube $[0, 1]^s$. By taking the median of $(2r-1)$ independent randomized quasi-Monte Carlo (RQMC)…

Several analog-to-digital conversion methods for bandlimited signals used in applications, such as Sigma Delta quantization schemes, employ coarse quantization coupled with oversampling. The standard mathematical model for the error accrued…

While the 3d Ising model has defied analytic solution, various numerical methods like Monte Carlo, MCRG and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff…

This article introduces a method of evaluating subsamples until any prescribed level of classification accuracy is attained, thus obtaining arbitrary accuracy. A logarithmic reduction in error rate is obtained with a linear increase in…

Kernel quadrature is widely used to approximate integrals of smooth functions, with worst-case error typically decaying at the minimax rate $n^{-\alpha/d}$ for smoothness $\alpha$ in dimension $d$. Existing rate-optimal methods often depend…

High order perturbation theory has seen an unexpected recent revival for controlled calculations of quantum many-body systems, even at strong coupling. We adapt integration methods using low-discrepancy sequences to this problem. They…

We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…

We consider the efficient use of an approximation within Markov chain Monte Carlo (MCMC), with subsequent importance sampling (IS) correction of the Markov chain inexact output, leading to asymptotically exact inference. We detail…

We consider the problem of computing an approximation to the integral $I=\int_{[0,1]^d}f(x) dx$. Monte Carlo (MC) sampling typically attains a root mean squared error (RMSE) of $O(n^{-1/2})$ from $n$ independent random function evaluations.…

Kernel quadrature can exploit RKHS spectral structure and outperform Monte Carlo on smooth integrands, but optimized quadrature weights are generally signed and may be numerically unstable. We study whether spectral acceleration remains…

Estimation of distribution algorithms are evolutionary algorithms that use extracted information from the population instead of traditional genetic operators to generate new solutions. This information is represented as a probabilistic…

Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties…

Edge intelligence enables low-latency inference via compact on-device models, but assuring reliability remains challenging. We study edge-cloud cascades that must preserve conditional coverage: whenever the edge returns a prediction set, it…

Atomistic/continuum coupling methods aim to achieve optimal balance between accuracy and efficiency. Adaptivity is the key for the efficient implementation of such methods. In this paper, we carry out a rigorous a posteriori analysis of the…

The efficient and accurate simulation of material systems with defects using atomistic- to-continuum (a/c) coupling methods is a topic of considerable interest in the field of computational materials science. To achieve the desired balance…

Precision theoretical predictions for high multiplicity scattering rely on the evaluation of increasingly complicated scattering amplitudes which come with an extremely high CPU cost. For state-of-the-art processes this can cause technical…