相关论文: Enhancing Polynomial Chaos Expansion Based Surroga…
The development of efficient surrogates for partial differential equations (PDEs) is a critical step towards scalable modeling of complex, multiscale systems-of-systems. Convolutional neural networks (CNNs) have gained popularity as the…
As non-institutive polynomial chaos expansion (PCE) techniques have gained growing popularity among researchers, we here provide a comprehensive review of major sampling strategies for the least squares based PCE. Traditional sampling…
This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…
Efficient surrogate modelling is a key requirement for uncertainty quantification in data-driven scenarios. In this work, a novel approach of using Sparse Random Features for surrogate modelling in combination with self-supervised…
This paper analyzes the effects of input uncertainties on the outputs of a three dimensional natural convection problem in a differentially heated cubical enclosure. Two different cases are considered for parameter uncertainty propagation…
Surrogate models that combine dimensionality reduction and regression techniques are essential to reduce the need for costly high-fidelity computational fluid dynamics data. New approaches using $\beta$-Variational Autoencoder ($\beta$-VAE)…
In the field of uncertainty quantification, sparse polynomial chaos (PC) expansions are commonly used by researchers for a variety of purposes, such as surrogate modeling. Ideas from compressed sensing may be employed to exploit this…
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,…
The spatiotemporal resolution of Partial Differential Equations (PDEs) plays important roles in the mathematical description of the world's physical phenomena. In general, scientists and engineers solve PDEs numerically by the use of…
This paper presents a method for performing Uncertainty Quantification in high-dimensional uncertain spaces by combining arbitrary polynomial chaos with a recently proposed scheme for sensitivity enhancement (1). Including available…
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…
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…
Compressive sampling has become a widely used approach to construct polynomial chaos surrogates when the number of available simulation samples is limited. Originally, these expensive simulation samples would be obtained at random locations…
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…
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…
This paper presents a surrogate modelling technique based on domain partitioning for Bayesian parameter inference of highly nonlinear engineering models. In order to alleviate the computational burden typically involved in Bayesian…
Black box attacks, where adversaries have limited knowledge of the target model, pose a significant threat to machine learning systems. Adversarial examples generated with a substitute model often suffer from limited transferability to the…
PAC-Bayes learning is a comprehensive setting for (i) studying the generalisation ability of learning algorithms and (ii) deriving new learning algorithms by optimising a generalisation bound. However, optimising generalisation bounds might…
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…
Compressive sampling has been widely used for sparse polynomial chaos (PC) approximation of stochastic functions. The recovery accuracy of compressive sampling highly depends on the incoherence properties of the measurement matrix. In this…