Related papers: Physics-Informed Polynomial Chaos Expansions
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…
Polynomial chaos expansions (PCE) allow us to propagate uncertainties in the coefficients of differential equations to the statistics of their solutions. Their main advantage is that they replace stochastic equations by systems of…
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…
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…
Polynomial chaos expansions (PCE) are well-suited to quantifying uncertainty in models parameterized by independent random variables. The assumption of independence leads to simple strategies for evaluating PCE coefficients. In contrast,…
In surrogate modeling, polynomial chaos expansion (PCE) is popularly utilized to represent the random model responses, which are computationally expensive and usually obtained by deterministic numerical modeling approaches including finite…
Polynomial chaos expansion (PCE) is a versatile tool widely used in uncertainty quantification and machine learning, but its successful application depends strongly on the accuracy and reliability of the resulting PCE-based response…
This paper introduces a new generalized polynomial chaos expansion (PCE) comprising measure-consistent multivariate orthonormal polynomials in dependent random variables. Unlike existing PCEs, whether classical or generalized, no…
Sparse polynomial chaos expansions (PCE) are a popular surrogate modelling method that takes advantage of the properties of PCE, the sparsity-of-effects principle, and powerful sparse regression solvers to approximate computer models with…
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…
Uncertainty quantification (UQ) has received much attention in the literature in the past decade. In this context, Sparse Polynomial chaos expansions (PCE) have been shown to be among the most promising methods because of their ability to…
Polynomial chaos expansions (PCE) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully…
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…
Polynomial chaos expansions (PCE) are widely used in the framework of uncertainty quantification. However, when dealing with high dimensional complex problems, challenging issues need to be faced. For instance, high-order polynomials may be…
Polynomial chaos expansion (PCE) is a powerful surrogate model-based reliability analysis method. Generally, a PCE model with a higher expansion order is usually required to obtain an accurate surrogate model for some complex non-linear…
Surrogate-modelling techniques including Polynomial Chaos Expansion (PCE) is commonly used for statistical estimation (aka. Uncertainty Quantification) of quantities of interests obtained from expensive computational models. PCE is a…
The surrogate model-based uncertainty quantification method has drawn much attention in many engineering fields. Polynomial chaos expansion (PCE) and deep learning (DL) are powerful methods for building a surrogate model. However, PCE needs…
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…
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,…
Polynomial chaos expansions (PCE) have proven efficiency in a number of fields for propagating parametric uncertainties through computational models of complex systems, namely structural and fluid mechanics, chemical reactions and…