English
Related papers

Related papers: A tree-based Polynomial Chaos expansion for surrog…

200 papers

We apply the Tensor Train (TT) approximation to construct the Polynomial Chaos Expansion (PCE) of a random field, and solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization. We compare two strategies of the…

Numerical Analysis · Mathematics 2014-06-12 Sergey Dolgov , Boris N. Khoromskij , Alexander Litvinenko , Hermann G. Matthies

In the field of computer experiments sensitivity analysis aims at quantifying the relative importance of each input parameter (or combinations thereof) of a computational model with respect to the model output uncertainty. Variance…

Computation · Statistics 2014-05-23 Bruno Sudret , Chu Van Mai

Polynomial chaos expansion is a popular way to develop surrogate models for stochastic systems with arbitrary random variables. Standard techniques such as Galerkin projection, stochastic collocation, and least squares approximation, are…

Optimization and Control · Mathematics 2019-09-10 Vedang M. Deshpande , Raktim Bhattacharya

This work introduces a method to equip data-driven polynomial chaos expansion surrogate models with intervals that quantify the predictive uncertainty of the surrogate. To that end, jackknife-based conformal prediction is integrated into…

Methodology · Statistics 2025-12-18 Dimitrios Loukrezis , Dimitris G. Giovanis

Sub-terahertz (subTHz) antennas will play an important role in the next generations of wireless communication systems. However, when comes to the subTHz frequency spectrum, the antenna fabrication tolerance needs to be accurately considered…

Information Theory · Computer Science 2024-04-09 Aristeides D. Papadopoulos , Yihan Ma , Qi Luo , George C. Alexandropoulos

An integrated optimization method based on the constrained multi-objective evolutionary algorithm (MOEA) and non-intrusive polynomial chaos expansion (PCE) is proposed, which solves robust multi-objective optimization problems under…

Neural and Evolutionary Computing · Computer Science 2022-09-29 Yuji Takubo , Masahiro Kanazaki

Polynomial chaos expansions (PCE) have seen widespread use in the context of uncertainty quantification. However, their application to structural reliability problems has been hindered by the limited performance of PCE in the tails of the…

Computation · Statistics 2018-08-10 S. Marelli , B. Sudret

Recent advancements in equivariant deep models have shown promise in accurately predicting atomic potentials and force fields in molecular dynamics simulations. Using spherical harmonics (SH) and tensor products (TP), these equivariant…

Machine Learning · Computer Science 2024-11-08 Zhao Xu , Haiyang Yu , Montgomery Bohde , Shuiwang Ji

Constructing accurate and generalizable approximators for complex physico-chemical processes exhibiting highly non-smooth dynamics is challenging. In this work, we propose new developments and perform comparisons for two promising…

Machine Learning · Computer Science 2023-02-17 Katiana Kontolati , Somdatta Goswami , Michael D. Shields , George Em Karniadakis

In this letter, we compare three polynomial chaos expansion (PCE)-based methods for ANCOVA (ANalysis of COVAriance) indices based global sensitivity analysis for correlated random inputs in two power system applications. Surprisingly, the…

Signal Processing · Electrical Eng. & Systems 2023-07-17 Xiaoting Wang , Rong-Peng Liu , Xiaozhe Wang , François Bouffard

Uncertainty quantification seeks to provide a quantitative means to understand complex systems that are impacted by parametric uncertainty. The polynomial chaos method is a computational approach to solve stochastic partial differential…

Numerical Analysis · Mathematics 2017-09-27 Melvin Leok , Gautam Wilkins

Polynomial chaos expansion (PCE) is an increasingly popular technique for uncertainty propagation and quantification in systems and control. Based on the theory of Hilbert spaces and orthogonal polynomials, PCE allows for a unifying…

Systems and Control · Electrical Eng. & Systems 2020-04-09 Tillmann Mühlpfordt , Frederik Zahn , Veit Hagenmeyer , Timm Faulwasser

We introduce a surrogate-based black-box optimization method, termed Polynomial-model-based optimization (PMBO). The algorithm alternates polynomial approximation with Bayesian optimization steps, using Gaussian processes to model the error…

Optimization and Control · Mathematics 2024-03-13 Janina Schreiber , Pau Batlle , Damar Wicaksono , Michael Hecht

Shapley-related techniques have gained attention as both global and local interpretation tools because of their desirable properties. However, their computation using conditional expectations is computationally expensive. Approximation…

Machine Learning · Statistics 2022-07-13 Zhipu Zhou , Jie Chen , Linwei Hu

Deep neural networks have shown exceptional performance in various tasks, but their lack of robustness, reliability, and tendency to be overconfident pose challenges for their deployment in safety-critical applications like autonomous…

Computer Vision and Pattern Recognition · Computer Science 2023-07-20 Steven Landgraf , Markus Hillemann , Kira Wursthorn , Markus Ulrich

Sequential model-based optimization sequentially selects a candidate point by constructing a surrogate model with the history of evaluations, to solve a black-box optimization problem. Gaussian process (GP) regression is a popular choice as…

Machine Learning · Statistics 2022-02-23 Jungtaek Kim , Seungjin Choi

Bayesian analysis enables combining prior knowledge with measurement data to learn model parameters. Commonly, one resorts to computing the maximum a posteriori (MAP) estimate, when only a point estimate of the parameters is of interest. We…

Machine Learning · Statistics 2024-08-08 Felix Schneider , Iason Papaioannou , Bruno Sudret , Gerhard Müller

Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpensively. We show, by analysis and example, that when the data…

Numerical Analysis · Mathematics 2015-06-19 Fei Lu , Matthias Morzfeld , Xuemin Tu , Alexandre J. Chorin

A spline chaos expansion, referred to as SCE, is introduced for uncertainty quantification analysis. The expansion provides a means for representing an output random variable of interest with respect to multivariate orthonormal basis…

Numerical Analysis · Mathematics 2019-11-12 Sharif Rahman

We apply the Tensor Train (TT) decomposition to construct the tensor product Polynomial Chaos Expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization, and to compute some…

Numerical Analysis · Mathematics 2015-03-12 Sergey Dolgov , Boris N. Khoromskij , Alexander Litvinenko , Hermann G. Matthies