12 citations · 14 across the 7 of their papers we have counts for
8 papers
Uncertainty Quantification of Engineering Structures by Polynomial Chaos Expansion and Multivariate Active Learning
Qitian Lu, Jafar Jafari-Asl, Panagiotis Spyridis +1
In many engineering applications, a single high-fidelity model produces multiple quantities of interest (QoIs) under the same input parameters, e.g. finite element models of comple…
Physics-informed Polynomial Chaos Expansion with Enhanced Constrained Optimization Solver and D-optimal Sampling
Qitian Lu, Himanshu Sharma, Michael D. Shields +1
Physics-informed polynomial chaos expansions (PC) provide an efficient physically constrained surrogate modeling framework by embedding governing equations and other physical c…
Polynomial Chaos Expansion for Operator Learning
Himanshu Sharma, Lukáš Novák, Michael D. Shields
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 m…
On Fractional Moment Estimation from Polynomial Chaos Expansion
Lukáš Novák, Marcos Valdebenito, Matthias Faes
Fractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fracti…
Physics-constrained polynomial chaos expansion for scientific machine learning and uncertainty quantification
Himanshu Sharma, Lukáš Novák, Michael D. Shields
We present a novel physics-constrained polynomial chaos expansion as a surrogate modeling method capable of performing both scientific machine learning (SciML) and uncertainty quan…
Physics-Informed Polynomial Chaos Expansions
Lukáš Novák, Himanshu Sharma, Michael D. Shields
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…
UQpy v4.1: Uncertainty Quantification with Python
Dimitrios Tsapetis, Michael D. Shields, Dimitris G. Giovanis +9
This paper presents the latest improvements introduced in Version 4 of the UQpy, Uncertainty Quantification with Python, library. In the latest version, the code was restructured t…
Active Learning-based Domain Adaptive Localized Polynomial Chaos Expansion
Lukáš Novák, Michael D. Shields, Václav Sadílek +1
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 constru…