Related papers: Non-intrusive uncertainty quantification using red…

There are essentially three kinds of approaches to Uncertainty Quantification (UQ): (A) robust optimization, (B) Bayesian, (C) decision theory. Although (A) is robust, it is unfavorable with respect to accuracy and data assimilation. (B)…

Recently, the graph-accelerated non-intrusive polynomial chaos (NIPC) method has been proposed for solving uncertainty quantification (UQ) problems. This method leverages the full-grid integration-based NIPC method to address UQ problems…

Bosonic codes utilize the infinite-dimensional Hilbert space of harmonic oscillators to encode quantum information, offering a hardware-efficient approach to quantum error correction. Designing these codes requires precise geometric…

Archimedes' hat-box theorem states that uniform measure on a sphere projects to uniform measure on an interval. This fact can be used to derive Simpson's rule. We present various constructions of, and lower bounds for, numerical cubature…

We consider the problem of quantifying uncertainty regarding the output of an electromagnetic field problem in the presence of a large number of uncertain input parameters. In order to reduce the growth in complexity with the number of…

Probabilistic error cancellation is a quantum error mitigation technique capable of producing unbiased computation results but requires an accurate error model. Constructing this model involves estimating a set of parameters, which, in the…

We consider uncertainty quantification for the Poisson problem subject to domain uncertainty. For the stochastic parameterization of the random domain, we use the model recently introduced by Kaarnioja, Kuo, and Sloan (SIAM J. Numer. Anal.,…

A method is developed to compute analytically fully symmetric cubature rules on the triangle by using symmetric polynomials to express the two kinds of invariance inherent in these rules. Rules of degree up to 15, some of them new and of…

Quantifying uncertainty of machine learning model predictions is essential for reliable decision-making, especially in safety-critical applications. Recently, uncertainty quantification (UQ) theory has advanced significantly, building on a…

The possibility of using squeezed states in the recently suggested unidimensional continuous-variable quantum key distribution based on a single quadrature modulation is addressed. It is shown that squeezing of the signal states expands the…

In this article, we propose the use of partitioning and clustering methods as an alternative to Gaussian quadrature for stochastic collocation. The key idea is to use cluster centers as the nodes for collocation. In this way, we can extend…

This paper presents a convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less…

Many computational methods in ab initio quantum chemistry are formulated in terms of high-order tensor contractions, whose cost determines the size of system that can be studied. We introduce stochastic tensor contraction to perform such…

In this paper, we deal with several aspects of the universal Frolov cubature method, that is known to achieve optimal asymptotic convergence rates in a broad range of function spaces. Even though every admissible lattice has this favorable…

In this paper we introduce concepts from uncertainty quantification (UQ) and numerical analysis for the efficient evaluation of stochastic high dimensional Newton iterates. In particular, we develop complex analytic regularity theory of the…

We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…

Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…

We address the problem of uncertainty quantification and propose measures of total, aleatoric, and epistemic uncertainty based on a known decomposition of (strictly) proper scoring rules, a specific type of loss function, into a divergence…

Chance-constrained programming is a widely used framework for decision-making under uncertainty, yet its mixed-integer reformulations involve nonconvex mixing sets with a knapsack constraint, leading to weak relaxations and computational…

The purpose of this paper is to develop the anti-Gauss cubature rule for approximating integrals defined on the square whose integrand function may have algebraic singularities at the boundaries. An application of such a rule to the…