Publication detail

Active learning-based domain adaptive localized polynomial chaos expansion

NOVÁK, L. SHIELDS, M. SADÍLEK, V. VOŘECHOVSKÝ, M.

Original Title

Active learning-based domain adaptive localized polynomial chaos expansion

Type

journal article in Web of Science

Language

English

Original Abstract

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 as domain adaptive localized polynomial chaos expansion (DAL-PCE). The approach utilizes sequential decomposition of the input random space into smaller sub-domains approximated by low-order polynomial expansions. This allows the approximation of functions with strong nonlinearities, discontinuities, and/or singularities that often appear in dynamical systems. Decomposition of the input random space and local approximations alleviates the Gibbs phenomenon for these types of problems and confines error to a very small vicinity near the non-linearity. The global behavior of the surrogate model is therefore significantly better than existing methods, as shown in numerical examples, including an engineering dynamical system exhibiting discontinuous response. The whole process is driven by an active learning routine that uses the recently proposed Theta criterion to assess local variance contributions (Novak et al., 2021). The proposed approach balances both exploitation of the surrogate model and exploration of the input random space and thus leads to efficient and accurate approximation of the original mathematical model. The numerical results show the superiority of the DAL-PCE in comparison to (i) a single global polynomial chaos expansion and (ii) the recently proposed stochastic spectral embedding (SSE) method (Marelli et al., 2021) developed as an accurate surrogate model and which is based on a similar domain decomposition process. This method represents a general framework upon which further extensions and refinements can be based and which can be combined with any technique for non-intrusive polynomial chaos expansion construction.

Keywords

Polynomial chaos expansion; Adaptive sampling; Sequential sampling; Local approximations; Active learning; Stochastic spectral embedding

Authors

NOVÁK, L.; SHIELDS, M.; SADÍLEK, V.; VOŘECHOVSKÝ, M.

Released

1. 12. 2023

Publisher

ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD

Location

LONDON

ISBN

0888-3270

Periodical

MECHANICAL SYSTEMS AND SIGNAL PROCESSING

Year of study

204

Number

1

State

United Kingdom of Great Britain and Northern Ireland

Pages count

22

URL

https://www.sciencedirect.com/science/article/abs/pii/S0888327023006362?dgcid=author

BibTex

@article{BUT187200,
  author="NOVÁK, L. and SHIELDS, M. and SADÍLEK, V. and VOŘECHOVSKÝ, M.",
  title="Active learning-based domain adaptive localized polynomial chaos expansion",
  journal="MECHANICAL SYSTEMS AND SIGNAL PROCESSING",
  year="2023",
  volume="204",
  number="1",
  pages="22",
  doi="10.1016/j.ymssp.2023.110728",
  issn="0888-3270",
  url="https://www.sciencedirect.com/science/article/abs/pii/S0888327023006362?dgcid=author"
}