Detail publikace

Active learning-based domain adaptive localized polynomial chaos expansion

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

Originální název

Active learning-based domain adaptive localized polynomial chaos expansion

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

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

Autoři

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

Vydáno

1. 12. 2023

Nakladatel

ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD

Místo

LONDON

ISSN

0888-3270

Periodikum

MECHANICAL SYSTEMS AND SIGNAL PROCESSING

Ročník

204

Číslo

1

Stát

Spojené království Velké Británie a Severního Irska

Strany počet

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"
}