Related papers: Physics-Informed Polynomial Chaos Expansions
Design-space dimensionality reduction is essential to mitigate the cost of high-fidelity simulation-based optimization, especially when dealing with high-dimensional geometric parameterizations. Traditional linear techniques, such as…
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…
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 present work addresses the issue of accurate stochastic approximations in high-dimensional parametric space using tools from uncertainty quantification (UQ). The basis adaptation method and its accelerated algorithm in polynomial chaos…
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…
Coupled problems with various combinations of multiple physics, scales, and domains can be found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled models is to…
We consider the numerical approximation of different ordinary differential equations (ODEs) and partial differential equations (PDEs) with periodic boundary conditions involving a one-dimensional random parameter, comparing the intrusive…
Polynomial chaos expansions (PCE) have seen widespread use in the context of uncertainty quantification. However, their application to structural reliability problems has been hindered by the limited performance of PCE in the tails of the…
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…
An integrated optimization method based on the constrained multi-objective evolutionary algorithm (MOEA) and non-intrusive polynomial chaos expansion (PCE) is proposed, which solves robust multi-objective optimization problems under…
Embedding physical knowledge into neural network (NN) training has been a hot topic. However, when facing the complex real-world, most of the existing methods still strongly rely on the quantity and quality of observation data. Furthermore,…
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…
Operator learning (OL) has emerged as a powerful tool in scientific machine learning (SciML) for approximating mappings between infinite-dimensional functional spaces. One of its main applications is learning the solution operator of…
This paper proposes an adaptive sparse polynomial chaos expansion(PCE)-based method to quantify the impacts of uncertainties on critical clearing time (CCT) that is an important index in transient stability analysis. The proposed method can…
The paper presents a novel methodology to build surrogate models of complicated functions by an active learning-based sequential decomposition of the input random space and construction of localized polynomial chaos expansions, referred to…
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…
One of the open problems in the field of forward uncertainty quantification (UQ) is the ability to form accurate assessments of uncertainty having only incomplete information about the distribution of random inputs. Another challenge is to…
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…
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…
Foundation models for partial differential equations (PDEs) have emerged as powerful surrogates pre-trained on diverse physical systems, but adapting them to new downstream tasks remains challenging due to limited task-specific data and…