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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

We present a hybrid sampling-surrogate approach for reducing the computational expense of uncertainty quantification in nonlinear dynamical systems. Our motivation is to enable rapid uncertainty quantification in complex mechanical systems…

Computation · Statistics 2022-01-27 Hang Yang , Yuji Fujii , K. W. Wang , Alex A. Gorodetsky

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

In this paper, we develop a numerical approach based on Chaos expansions to analyze the sensitivity and the propagation of epistemic uncertainty through a queueing systems with breakdowns. Here, the quantity of interest is the stationary…

Probability · Mathematics 2017-05-17 Katia Bachi , Cédric Chauvière , Hacène Djellout , Karim Abbas

The work presented here investigates the application of polynomial chaos expansion toward input shaper design in order to maintain robustness in dynamical systems subject to uncertainty. Furthermore, this work intends to specifically…

Systems and Control · Electrical Eng. & Systems 2026-02-05 Johannes Güttler , Karan Baker , Premjit Saha , James Warner , Adrian Stein

Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many…

Methodology · Statistics 2024-06-19 Joy N. Mueller , Khachik Sargsyan , Craig J. Daniels , Habib N. Najm

Stochastic unit commitment models typically handle uncertainties in forecast demand by considering a finite number of realizations from a stochastic process model for loads. Accurate evaluations of expectations or higher moments for the…

Systems and Control · Computer Science 2014-07-09 Cosmin Safta , Richard L. Chen , Habib N. Najm , Ali Pinar , Jean-paul watson

We present an approach to the simulation of quantum systems driven by classical stochastic processes that is based on the polynomial chaos expansion, a well-known technique in the field of uncertainty quantification. The polynomial chaos…

Quantum Physics · Physics 2013-12-17 Kevin C. Young , Matthew D. Grace

Fast and accurate predictions of uncertainties in the computed dose are crucial for the determination of robust treatment plans in radiation therapy. This requires the solution of particle transport problems with uncertain parameters or…

Medical Physics · Physics 2022-11-09 Pia Stammer , Lucas Burigo , Oliver Jäkel , Martin Frank , Niklas Wahl

In this work, we revisit the use of the virtual density method to model uniform geometrical perturbations. We propose a general algorithm in order to estimate explicitly the effect of geometrical perturbations in continuous-energy Monte…

Computational Physics · Physics 2026-02-05 Théophile Bonnet , Anuj Dubey , Eugene Shwageraus

Machine learning (ML) surrogate models are increasingly used in engineering analysis and design to replace computationally expensive simulation models, significantly reducing computational cost and accelerating decision-making processes.…

Machine Learning · Statistics 2025-07-22 Xiaoping Du

A surrogate model approximates a computationally expensive solver. Polynomial Chaos is a method to construct surrogate models by summing combinations of carefully chosen polynomials. The polynomials are chosen to respect the probability…

Numerical Analysis · Mathematics 2017-06-29 Thomas A. McCourt , Brodie Lawson , Fengde Zhou , Bevan Thompson , Stephen Tyson , Diane Donovan

Stochastic economic dispatch models address uncertainties in forecasts of renewable generation output by considering a finite number of realizations drawn from a stochastic process model, typically via Monte Carlo sampling. Accurate…

Computational Engineering, Finance, and Science · Computer Science 2015-08-24 Cosmin Safta , Richard L. -Y. Chen , Habib N. Najm , Ali Pinar , Jean-Paul Watson

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

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 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

This paper studies the utility of techniques within uncertainty quantification, namely spectral projection and polynomial chaos expansion, in reducing sampling needs for characterizing acoustic metamaterial dispersion band responses given…

Differential equations with random parameters have gained significant prominence in recent years due to their importance in mathematical modelling and data assimilation. In many cases, random ordinary differential equations (RODEs) are…

Dynamical Systems · Mathematics 2018-12-13 Maxime Breden , Christian Kuehn

Robustness analysis is very important in biology and neuroscience, to unravel behavioural patterns of systems that are conserved despite large parametric uncertainties. To make studies of probabilistic robustness more efficient and scalable…

Quantitative Methods · Quantitative Biology 2026-01-08 Uros Sutulovic , Daniele Proverbio , Rami Katz , Giulia Giordano

In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a…

Machine Learning · Statistics 2024-11-11 Dimitris G. Giovanis , Dimitrios Loukrezis , Ioannis G. Kevrekidis , Michael D. Shields
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