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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

We propose an algorithm for optimizations in which the gradients contain stochastic noise. This arises, for example, in structural optimizations when computations of forces and stresses rely on methods involving Monte Carlo sampling, such…

Materials Science · Physics 2022-11-30 Siyuan Chen , Shiwei Zhang

We propose a new algorithm for the solution of the robust multiple-load topology optimization problem. The algorithm can be applied to any type of problem, e.g., truss topology, variable thickness sheet or free material optimization. We…

Optimization and Control · Mathematics 2013-07-30 Michal Kocvara

Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with high-dimensional random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter,…

Probability · Mathematics 2015-06-22 Jerrad Hampton , Alireza Doostan

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

To tackle the curse of dimensionality and multicollinearity problems of polynomial chaos expansion for analyzing global sensitivity and reliability of models with high stochastic dimensions, this paper proposes a novel non-intrusive…

Numerical Analysis · Mathematics 2024-12-20 Ling-Ze Bu , Wei Zhao , Wei Wang

Polynomial chaos expansions (PCEs) have been used in many real-world engineering applications to quantify how the uncertainty of an output is propagated from inputs. PCEs for models with independent inputs have been extensively explored in…

Systems and Control · Electrical Eng. & Systems 2021-06-02 Zhanlin Liu , Youngjun Choe

In this paper we develop a novel, discrete-time optimal control framework for mechanical systems with uncertain model parameters. We consider finite-horizon problems where the performance index depends on the statistical moments of the…

Optimization and Control · Mathematics 2017-05-17 George I. Boutselis , Yunpeng Pan , Gerardo De La Tore , Evangelos A. Theodorou

Building surrogate models with uncertainty quantification capabilities is essential for many engineering applications where randomness, such as variability in material properties, is unavoidable. Polynomial Chaos Expansion (PCE) is widely…

Computational Engineering, Finance, and Science · Computer Science 2025-11-04 Bahador Bahmani , Ioannis G. Kevrekidis , Michael D. Shields

In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…

Computational Engineering, Finance, and Science · Computer Science 2024-05-14 Gabriel Garayalde , Matteo Torzoni , Matteo Bruggi , Alberto Corigliano

This paper presents a computational framework for the robust stiffness design of hyperelastic structures at finite deformations subject to various uncertain sources. In particular, the loading, material properties, and geometry…

Computational Engineering, Finance, and Science · Computer Science 2025-01-28 Nan Feng , Guodong Zhang , Kapil Khandelwal

Polynomial chaos expansion (PCE) is a classical and widely used surrogate modeling technique in physical simulation and uncertainty quantification. By taking a linear combination of a set of basis polynomials - orthonormal with respect to…

Machine Learning · Computer Science 2026-04-01 Johannes Exenberger , Sascha Ranftl , Robert Peharz

This paper proposes a novel computationally efficient dynamic bi-orthogonality based approach for calibration of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on a…

Computation · Statistics 2012-11-14 Piyush Tagade , Han-Lim Choi

This paper proposes an algorithm to find robust reliability-based topology optimized designs under a random-field material model. The initial design domain is made of linear elastic material whose property, i.e., Young's modulus, is modeled…

Optimization and Control · Mathematics 2022-01-04 Trung Pham , Christopher Hoyle

The application of polynomial chaos expansions (PCEs) to the propagation of uncertainties in stochastic dynamical models is well-known to face challenging issues. The accuracy of PCEs degenerates quickly in time. Thus maintaining a…

Methodology · Statistics 2016-04-27 C. V. Mai , M. D. Spiridonakos , E. N. Chatzi , B. Sudret

Presence of a high-dimensional stochastic parameter space with discontinuities poses major computational challenges in analyzing and quantifying the effects of the uncertainties in a physical system. In this paper, we propose a stochastic…

Numerical Analysis · Mathematics 2018-08-01 Anindya Bhaduri , Yanyan He , Michael D. Shields , Lori Graham-Brady , Robert M. Kirby

The work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a nonsmoothed…

Computational Engineering, Finance, and Science · Computer Science 2021-08-06 J. Oliver , D. Yago , J. Cante , O. Lloberas-Valls

Topology optimization under uncertainty or reliability-based topology optimization is usually numerically very expensive. This is mainly due to the fact that an accurate evaluation of the probabilistic model requires the system to be…

Optimization and Control · Mathematics 2024-10-28 Lukas Pflug , Michael Stingl , Andrian Uihlein

In this paper, approximation schemes are proposed for handling load uncertainty in compliance-based topology optimization problems, where the uncertainty is described in the form of a set of finitely many loading scenarios. Efficient…

Computational Engineering, Finance, and Science · Computer Science 2022-05-03 Mohamed Tarek , Tapabrata Ray

Physics-informed polynomial chaos expansions (PC$^2$) provide an efficient physically constrained surrogate modeling framework by embedding governing equations and other physical constraints into the standard data-driven polynomial chaos…

Machine Learning · Statistics 2025-12-12 Qitian Lu , Himanshu Sharma , Michael D. Shields , Lukáš Novák