Related papers: SeAr PC: Sensitivity Enhanced Arbitrary Polynomial…
The presence of uncertainties are inevitable in engineering design and analysis, where failure in understanding their effects might lead to the structural or functional failure of the systems. The role of global sensitivity analysis in this…
Growing uncertainty from renewable energy integration and distributed energy resources motivate the need for advanced tools to quantify the effect of uncertainty and assess the risks it poses to secure system operation. Polynomial chaos…
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…
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…
Uncertainty quantification seeks to provide a quantitative means to understand complex systems that are impacted by parametric uncertainty. The polynomial chaos method is a computational approach to solve stochastic partial differential…
We present an enriched formulation of the Least Squares (LSQ) regression method for Uncertainty Quantification (UQ) using generalised polynomial chaos (gPC). More specifically, we enrich the linear system with additional equations for the…
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…
We consider the effect of multiple stochastic parameters on the time-average quantities of chaotic systems. We employ the recently proposed \cite{Kantarakias_Papadakis_2023} sensitivity-enhanced generalized polynomial chaos expansion,…
In the field of computer experiments sensitivity analysis aims at quantifying the relative importance of each input parameter (or combinations thereof) of a computational model with respect to the model output uncertainty. Variance…
A surrogate model approximates a computationally expensive solver. Polynomial Chaos is a method to construct surrogate models by summing combinations of carefully chosen polynomials. The polynomials are chosen to respect the probability…
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…
The large-scale integration of renewable energy sources introduces significant operational uncertainty into power systems. Although Polynomial Chaos Expansion (PCE) provides an efficient tool for uncertainty quantification (UQ) in power…
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…
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…
Many problems in engineering and sciences require the solution of large scale optimization constrained by partial differential equations (PDEs). Though PDE-constrained optimization is itself challenging, most applications pose additional…
Machine learning (ML) surrogate models are increasingly used in engineering analysis and design to replace computationally expensive simulation models, significantly reducing computational cost and accelerating decision-making processes.…
Recently, the use of Polynomial Chaos Expansion (PCE) has been increasing to study the uncertainty in mathematical models for a wide range of applications and several extensions of the original PCE technique have been developed to deal with…
Software engineers often have to estimate the performance of a software system before having full knowledge of the system parameters, such as workload and operational profile. These uncertain parameters inevitably affect the accuracy of…
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…
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…