Publication result detail

Physics-Informed Polynomial Chaos Expansions: Recent Developments and Comparisons

NOVÁK, L.; LU, Q.; SHARMA, H.; ROY SARKAR, D.; GOSWAMI, S.; SHIELDS, M.

Original Title

Physics-Informed Polynomial Chaos Expansions: Recent Developments and Comparisons

English Title

Physics-Informed Polynomial Chaos Expansions: Recent Developments and Comparisons

Type

Paper in proceedings outside WoS and Scopus

Original Abstract

This work presents recent developments in a constrained polynomial chaos expansion as a physics-informed machine learning technique. Specifically, an optimized numerical solver for straightforward updating of Lagrange multipliers and an improved statistical sampling method are compared to the original algorithm for estimating deterministic coefficients. Both techniques are applied to solve a heat equation with Neumann boundary conditions. A second study presents a preliminary numerical comparison of the constrained polynomial chaos expansion and physics-informed deep operator networks with respect to computational cost and achieved accuracy.

English abstract

This work presents recent developments in a constrained polynomial chaos expansion as a physics-informed machine learning technique. Specifically, an optimized numerical solver for straightforward updating of Lagrange multipliers and an improved statistical sampling method are compared to the original algorithm for estimating deterministic coefficients. Both techniques are applied to solve a heat equation with Neumann boundary conditions. A second study presents a preliminary numerical comparison of the constrained polynomial chaos expansion and physics-informed deep operator networks with respect to computational cost and achieved accuracy.

Keywords

Scientific machine learning, Uncertainty quantification, Physics-informed Polynomial chaos expansion, Physics-informed deep operator networks , Statistical sampling

Key words in English

Scientific machine learning, Uncertainty quantification, Physics-informed Polynomial chaos expansion, Physics-informed deep operator networks , Statistical sampling

Authors

NOVÁK, L.; LU, Q.; SHARMA, H.; ROY SARKAR, D.; GOSWAMI, S.; SHIELDS, M.

RIV year

2026

Released

17.05.2025

Publisher

CIMNE

Book

14th International Conference on Structural Safety and Reliability

Pages from

1

Pages to

9

Pages count

9

URL

https://www.scipedia.com/public/Novak_et_al_2025a

BibTex

@inproceedings{BUT200567,
  author="Lukáš {Novák} and Qitian {Lu} and Himanshu {Sharma} and  {} and Michael {Shields} and  {}",
  title="Physics-Informed Polynomial Chaos Expansions: Recent Developments and Comparisons",
  booktitle="14th International Conference on Structural Safety and Reliability",
  year="2025",
  pages="9",
  publisher="CIMNE",
  doi="10.23967/icossar.2025.076",
  url="https://www.scipedia.com/public/Novak_et_al_2025a"
}