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For a large class of orthogonal basis functions, there has been a recent identification of expansion methods for computing accurate, stable approximations of a quantity of interest. This paper presents, within the context of uncertainty…

Computation · Statistics 2018-06-13 Jerrad Hampton , Alireza Doostan

Accelerating the learning of Partial Differential Equations (PDEs) from experimental data will speed up the pace of scientific discovery. Previous randomized algorithms exploit sparsity in PDE updates for acceleration. However such methods…

Machine Learning · Computer Science 2023-09-15 Md Nasim , Yexiang Xue

This paper considers sequential adaptive estimation of sparse signals under a constraint on the total sensing effort. The advantage of adaptivity in this context is the ability to focus more resources on regions of space where signal…

Methodology · Statistics 2013-04-03 Dennis Wei , Alfred O. Hero

This article considers the $\mathcal{H}_\infty$ static output-feedback control for linear time-invariant uncertain systems with polynomial dependence on probabilistic time-invariant parametric uncertainties. By applying polynomial chaos…

Systems and Control · Electrical Eng. & Systems 2021-03-02 Yiming Wan , Dongying E. Shen , Sergio Lucia , Rolf Findeisen , Richard D. Braatz

Efficient surrogate modelling is a key requirement for uncertainty quantification in data-driven scenarios. In this work, a novel approach of using Sparse Random Features for surrogate modelling in combination with self-supervised…

Machine Learning · Computer Science 2023-01-02 Maternus Herold , Anna Veselovska , Jonas Jehle , Felix Krahmer

Integrated sensing and communications (ISAC) is a key use case for sixth-generation (6G) wireless systems, where parametric channel estimation (PCE) plays a central role in enabling sensing, localization, and channel equalization in…

Signal Processing · Electrical Eng. & Systems 2026-05-26 Enrique T. R. Pinto , André L. F. de Almeida , Markku Juntti

Stochastic simulators are ubiquitous in many fields of applied sciences and engineering. In the context of uncertainty quantification and optimization, a large number of simulations is usually necessary, which becomes intractable for…

Computation · Statistics 2022-02-09 X. Zhu , B. Sudret

Efficiently solving the Fokker-Planck equation (FPE) is central to analyzing complex parameterized stochastic systems. However, current numerical methods lack parallel computation capabilities across varying conditions, severely limiting…

Computational Physics · Physics 2026-04-08 Xiaolong Wang , Jing Feng , Qi Liu , Chengli Tan , Yuanyuan Liu , Yong Xu

In this paper we explain how to use the Fast Fourier Transform (FFT) to solve partial differential equations (PDEs). We start by defining appropriate discrete domains in coordinate and frequency domains. Then describe the main limitation of…

Numerical Analysis · Mathematics 2025-07-31 Daniela Rodriguez-Lara , Ivan Alvarez-Rios , Francisco S. Guzman

We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…

Probability · Mathematics 2015-09-29 Konstantinos Spiliopoulos

The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…

Signal Processing · Electrical Eng. & Systems 2018-01-16 Shaogang Wang , Vishal M. Patel , Athina Petropulu

Fractional cumulative residual entropy (FCRE) is a powerful tool for the analysis of complex systems. Most of the theoretical results and applications related to the FCRE of the lifetime random variable are based on the distribution…

Statistics Theory · Mathematics 2025-02-04 Iona Ann Sebastian , S. M. Sunoj

Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…

Machine Learning · Statistics 2015-03-23 Yarin Gal , Richard Turner

Accurate modeling of radio wave propagation over irregular terrains is crucial for designing reliable wireless communication systems in such environments, yet uncertainties in the antenna configuration are not quantified within…

Signal Processing · Electrical Eng. & Systems 2026-03-04 Sicheng An , Luca Di Rienzo , Hao Qin , Xingqi Zhang , Lorenzo Codecasa

We propose a method for the approximation of solutions of PDEs with stochastic coefficients based on the direct, i.e., non-adapted, sampling of solutions. This sampling can be done by using any legacy code for the deterministic problem as a…

Numerical Analysis · Mathematics 2015-05-19 Alireza Doostan , Houman Owhadi

Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…

Machine Learning · Statistics 2019-08-21 Genevera I. Allen , Michael Weylandt

In this paper, we present an abstract framework to obtain convergence rates for the approximation of random evolution equations corresponding to a random family of forms determined by finite-dimensional noise. The full discretization error…

Functional Analysis · Mathematics 2024-12-19 Katharina Klioba , Christian Seifert

A ubiquitous challenge in design space exploration or uncertainty quantification of complex engineering problems is the minimization of computational cost. A useful tool to ease the burden of solving such systems is model reduction. This…

Numerical Analysis · Mathematics 2021-04-16 Felix Newberry , Jerrad Hampton , Kenneth Jansen , Alireza Doostan

In this work, we propose adaptive deep learning approaches based on normalizing flows for solving fractional Fokker-Planck equations (FPEs). The solution of a FPE is a probability density function (PDF). Traditional mesh-based methods are…

Machine Learning · Computer Science 2022-10-27 Li Zeng , Xiaoliang Wan , Tao Zhou

The present work addresses the issue of accurate stochastic approximations in high-dimensional parametric space using tools from uncertainty quantification (UQ). The basis adaptation method and its accelerated algorithm in polynomial chaos…

Numerical Analysis · Mathematics 2022-12-22 Xiaoshu Zeng , Roger Ghanem