English
Related papers

Related papers: Polynomial Chaos Surrogate Construction for Random…

200 papers

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

In recent years, increasingly complex computational models are being built to describe physical systems which has led to increased use of surrogate models to reduce computational cost. In problems related to Structural Health Monitoring…

Machine Learning · Computer Science 2024-07-08 Nicholas E. Silionis , Theodora Liangou , Konstantinos N. Anyfantis

As uncertainty and sensitivity analysis of complex models grows ever more important, the difficulty of their timely realizations highlights a need for more efficient numerical operations. Non-intrusive Polynomial Chaos methods are highly…

Numerical Analysis · Mathematics 2022-04-14 Konstantin Weise , Erik Müller , Lucas Poßner , Thomas R. Knösche

We present a bifidelity Karhunen-Lo\`eve expansion (KLE) surrogate model for field-valued quantities of interest (QoIs) under uncertain inputs. The approach combines the spectral efficiency of the KLE with polynomial chaos expansions (PCEs)…

Machine Learning · Statistics 2025-11-07 Aniket Jivani , Cosmin Safta , Beckett Y. Zhou , Xun Huan

Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional $\mathcal{O}(10^{\ge 2})$ stochastic inputs (e.g., forcing terms, boundary conditions,…

Machine Learning · Computer Science 2022-05-27 Katiana Kontolati , Dimitrios Loukrezis , Dimitris G. Giovanis , Lohit Vandanapu , Michael D. Shields

This work develops a novel basis-adaptive method for constructing anisotropic polynomial chaos expansions of multidimensional (vector-valued, multi-output) model responses. The adaptive basis selection is based on multivariate sensitivity…

Computational Engineering, Finance, and Science · Computer Science 2024-10-11 Dimitrios Loukrezis , Eric Diehl , Herbert De Gersem

Fatigue crack growth is one of the most common types of deterioration in metal structures with significant implications on their reliability. Recent advances in Structural Health Monitoring (SHM) have motivated the use of structural…

Machine Learning · Statistics 2023-10-12 Nicholas E. Silionis , Konstantinos N. Anyfantis

Metamodeling of complex numerical systems has recently attracted the interest of the mathematical programming community. Despite the progress in high performance computing, simulations remain costly, as a matter of fact, the assessment of…

Other Statistics · Statistics 2018-11-13 Soumaya Azzi , Yuanyuan Huang , Bruno Sudret , Joe Wiart

We propose a non-intrusive reduced-order modeling method based on proper orthogonal decomposition (POD) and polynomial chaos expansion (PCE) for stochastic representations in uncertainty quantification (UQ) analysis. Firstly, POD provides…

Computational Physics · Physics 2021-07-02 Xiang Sun , Xiaomin Pan , Jung-Il Choi

The Polynomial Chaos Expansion (PCE) technique recovers a finite second order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochas- tic quantity {\xi}, hence acting as a…

Computational Finance · Quantitative Finance 2016-10-31 Luca Di Persio , Michele Bonollo , Gregorio Pellegrini

We present an algorithm for computing sparse, least squares-based polynomial chaos expansions, incorporating both adaptive polynomial bases and sequential experimental designs. The algorithm is employed to approximate stochastic…

Computational Engineering, Finance, and Science · Computer Science 2020-01-13 Dimitrios Loukrezis , Armin Galetzka , Herbert De Gersem

The need to rapidly solve PDEs in engineering design workflows has spurred the rise of neural surrogate models. In particular, neural operator models provide a discretization-invariant surrogate by retaining the infinite-dimensional,…

Machine Learning · Computer Science 2026-02-12 Yash Patel , Ambuj Tewari

Polynomial chaos based methods enable the efficient computation of output variability in the presence of input uncertainty in complex models. Consequently, they have been used extensively for propagating uncertainty through a wide variety…

Optimization and Control · Mathematics 2020-09-18 Tuhin Sahai

The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide…

Numerical Analysis · Mathematics 2016-08-24 Katerina Konakli , Bruno Sudret

We present a probabilistic deep learning methodology that enables the construction of predictive data-driven surrogates for stochastic systems. Leveraging recent advances in variational inference with implicit distributions, we put forth a…

Machine Learning · Statistics 2019-01-16 Yibo Yang , Paris Perdikaris

Human exposure induced by wireless communication systems increasingly draws the public attention. Here, an indoor down-link scenario is concerned and the exposure level is statistically analyzed. The electromagnetic field (EMF) emitted by a…

Applications · Statistics 2020-04-14 Zicheng Liu , Dominique Lesselier , Bruno Sudret , Joe Wiart

Many physics and engineering applications demand Partial Differential Equations (PDE) property evaluations that are traditionally computed with resource-intensive high-fidelity numerical solvers. Data-driven surrogate models provide an…

Machine Learning · Computer Science 2023-12-18 Raphaël Pestourie , Youssef Mroueh , Chris Rackauckas , Payel Das , Steven G. Johnson

Polynomial Chaos Expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and non-trivial manipulation of the model,…

Computation · Statistics 2012-11-13 Lorenzo Fagiano , Mustafa Khammash

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

The quantification of uncertainties of computer simulations due to input parameter uncertainties is paramount to assess a model's credibility. For computationally expensive simulations, this is often feasible only via surrogate models that…

Methodology · Statistics 2021-08-30 Sascha Ranftl , Wolfgang von der Linden