Related papers: Global sensitivity analysis using derivative-based…
This paper explores the application of active learning strategies to adaptively learn Sobol indices for global sensitivity analysis. We demonstrate that active learning for Sobol indices poses unique challenges due to the definition of the…
Global sensitivity analysis (GSA) is used to quantify the influence of uncertain variables in a mathematical model. Prior to performing GSA, the user must specify (or implicitly assume), a probability distribution to model the uncertainty,…
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…
Surrogate modelling techniques have opened up new possibilities to overcome the limitations of computationally intensive numerical models in various areas of engineering and science. However, while fundamental in many engineering…
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…
In the field of surrogate modeling, polynomial chaos expansion (PCE) allows practitioners to construct inexpensive yet accurate surrogates to be used in place of the expensive forward model simulations. For black-box simulations,…
Frequency response functions (FRFs) are important for assessing the behavior of stochastic linear dynamic systems. For large systems, their evaluations are time-consuming even for a single simulation. In such cases, uncertainty…
Poincar{\'e} inequalities are ubiquitous in probability and analysis and have various applications in statistics (concentration of measure, rate of convergence of Markov chains). The Poincar{\'e} constant, for which the inequality is tight,…
In this paper we propose an algorithm for recovering sparse orthogonal polynomials using stochastic collocation. Our approach is motivated by the desire to use generalized polynomial chaos expansions (PCE) to quantify uncertainty in models…
We introduce PoCET: a free and open-scource Polynomial Chaos Expansion Toolbox for Matlab, featuring the automatic generation of polynomial chaos expansion (PCE) for linear and nonlinear dynamic systems with time-invariant stochastic…
Dimensionally decomposed generalized polynomial chaos expansion (DD-GPCE) efficiently performs forward uncertainty quantification (UQ) in complex engineering systems with high-dimensional random inputs of arbitrary distributions. However,…
Sparse principal component analysis with global support (SPCAgs), is the problem of finding the top-$r$ leading principal components such that all these principal components are linear combinations of a common subset of at most $k$…
Phononic crystals have been widely employed in many engineering fields, which is due to their unique feature of frequency band gaps. For example, their capability to filter out the incoming elastic waves, which include seismic waves, will…
Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of…
In this paper we outline a new approach to the analysis of polarimetric synthetic aperture (POLSAR) data. Here we exploit target orthogonality as a multi-dimensional extension of wave orthogonality, familiar on the Poincar\'e sphere. We…
Global sensitivity analysis of complex numerical models can be performed by calculating variance-based importance measures of the input variables, such as the Sobol indices. However, these techniques, requiring a large number of model…
Ordinary differential equations (ODEs) are a conventional way to describe the observed dynamics of physical systems. Scientists typically hypothesize about dynamical behavior, propose a mathematical model, and compare its predictions to…
In uncertainty quantification, variance-based global sensitivity analysis quantitatively determines the effect of each input random variable on the output by partitioning the total output variance into contributions from each input.…
Optimal Bayesian design techniques provide an estimate for the best parameters of an experiment in order to maximize the value of measurements prior to the actual collection of data. In other words, these techniques explore the space of…
Reliability analysis typically relies on deterministic simulators, which yield repeatable outputs for identical inputs. However, many real-world systems display intrinsic randomness, requiring stochastic simulators whose outputs are random…