Publication detail

Physics-informed polynomial chaos expansions

NOVÁK, L. SHARMA,H. SHIELDS, M.

Original Title

Physics-informed polynomial chaos expansions

Type

journal article in Web of Science

Language

English

Original Abstract

Developing surrogate models for costly mathematical models representing physical systems is challenging since it is typically not possible to generate large training data sets, i.e. to create a large experimental design. In such cases, it can be beneficial to constrain the surrogate approximation to adhere to the known physics of the model. This paper presents a novel methodology for the construction of physics -informed polynomial chaos expansions (PCE) that combines the conventional experimental design with additional constraints from the physics of the model represented by a set of differential equations and specified boundary conditions. A computationally efficient means of constructing physically constrained PCEs, termed PC 2 , are proposed and compared to the standard sparse PCE. Algorithms are presented for both fullorder and sparse PC 2 expansions and an iterative approach is proposed for addressing nonlinear differential equations. It is shown that the proposed algorithms lead to superior approximation accuracy and do not add significant computational burden over conventional PCE. Although the main purpose of the proposed method lies in combining training data and physical constraints, we show that the PC 2 can also be constructed from differential equations and boundary conditions alone without requiring model evaluations. We further show that the constrained PCEs can be easily applied for uncertainty quantification through analytical post -processing of a reduced PCE by conditioning on the deterministic space-time variables. Several deterministic examples of increasing complexity are provided and the proposed method is demonstrated for uncertainty quantification.

Keywords

Polynomial chaos expansion; Physical constraints; Surrogate modeling; Uncertainty quantification; Physics-informed machine learning

Authors

NOVÁK, L.; SHARMA,H.; SHIELDS, M.

Released

1. 6. 2024

Publisher

ACADEMIC PRESS INC ELSEVIER SCIENCE

Location

SAN DIEGO

ISBN

1090-2716

Periodical

Journal of Computational Physics

Year of study

506

Number

1

State

United States of America

Pages count

18

URL

https://www.sciencedirect.com/science/article/pii/S002199912400175X?via%3Dihub

BibTex

@article{BUT188898,
  author="NOVÁK, L. and SHARMA,H. and SHIELDS, M.",
  title="Physics-informed polynomial chaos expansions",
  journal="Journal of Computational Physics",
  year="2024",
  volume="506",
  number="1",
  pages="18",
  doi="10.1016/j.jcp.2024.112926",
  issn="1090-2716",
  url="https://www.sciencedirect.com/science/article/pii/S002199912400175X?via%3Dihub"
}