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Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is…

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is…

This work is concerned with the propagation of uncertainty across coupled domain problems with high-dimensional random inputs. A stochastic model reduction approach based on low-rank separated representations is proposed for the partitioned…

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…

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,…

Surrogate modeling of costly mathematical models representing physical systems is challenging since it is typically not possible to create a large experimental design. Thus, it is beneficial to constrain the approximation to adhere to the…

Model predictive control is an advanced control approach for multivariable systems with constraints, which is reliant on an accurate dynamic model. Most real dynamic models are however affected by uncertainties, which can lead to…

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…

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…

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…

In the context of uncertainty quantification, computational models are required to be repeatedly evaluated. This task is intractable for costly numerical models. Such a problem turns out to be even more severe for stochastic simulators, the…

We study distributed optimization problems over a network when the communication between the nodes is constrained, and so information that is exchanged between the nodes must be quantized. This imperfect communication poses a fundamental…

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…

Stochastic expansion-based methods of uncertainty quantification, such as polynomial chaos and separated representations, require basis functions orthogonal with respect to the density of random inputs. Many modern engineering problems…

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…

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…

In modern engineering, physical processes are modelled and analysed using advanced computer simulations, such as finite element models. Furthermore, concepts of reliability analysis and robust design are becoming popular, hence, making…

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…

Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for the…

Numerical simulation of stochastic differential equations over long time intervals poses significant computational challenges. In this paper, we propose a novel recursive polynomial chaos evolution method that achieves model reduction…