Multi-fidelity reduced-order surrogate modelling
(2024) In Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 480(2283).- Abstract
High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated. Multi-fidelity surrogate modelling aims to leverage less accurate, lower-fidelity models that are computationally inexpensive in order to enhance predictive accuracy when high-fidelity data are scarce. However, low-fidelity models, while often displaying the qualitative solution behaviour, fail to accurately capture fine spatio-temporal and dynamic features of high-fidelity models. To address this shortcoming, we present a data-driven strategy that combines dimensionality reduction with multifidelity neural network... (More)
High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated. Multi-fidelity surrogate modelling aims to leverage less accurate, lower-fidelity models that are computationally inexpensive in order to enhance predictive accuracy when high-fidelity data are scarce. However, low-fidelity models, while often displaying the qualitative solution behaviour, fail to accurately capture fine spatio-temporal and dynamic features of high-fidelity models. To address this shortcoming, we present a data-driven strategy that combines dimensionality reduction with multifidelity neural network surrogates. The key idea is to generate a spatial basis by applying proper orthogonal decomposition (POD) to high-fidelity solution snapshots, and approximate the dynamics of the reduced states—time-parameter-dependent expansion coefficients of the POD basis—using a multi-fidelity long short-term memory network. By mapping low-fidelity reduced states to their high-fidelity counterpart, the proposed reduced-order surrogate model enables the efficient recovery of full solution fields over time and parameter variations in a non-intrusive manner. The generality of this method is demonstrated by a collection of PDE problems where the low-fidelity model can be defined by coarser meshes and/or time stepping, as well as by misspecified physical features.
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- author
- Conti, Paolo ; Guo, Mengwu LU ; Manzoni, Andrea ; Frangi, Attilio ; Brunton, Steven L. and Kutz, J. Nathan
- publishing date
- 2024-02-07
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- LSTM networks, multi-fidelity surrogate modelling, parametrized PDEs, proper orthogonal decomposition, reduced-order modelling
- in
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- volume
- 480
- issue
- 2283
- article number
- 20230655
- publisher
- Royal Society Publishing
- external identifiers
-
- scopus:85185312399
- ISSN
- 1364-5021
- DOI
- 10.1098/rspa.2023.0655
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2024 The Author(s) Published by the Royal Society. All rights reserved.
- id
- a81f72a9-33ed-4be3-b67b-d692892f386b
- date added to LUP
- 2024-03-18 23:02:30
- date last changed
- 2024-04-10 10:43:05
@article{a81f72a9-33ed-4be3-b67b-d692892f386b,
abstract = {{<p>High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated. Multi-fidelity surrogate modelling aims to leverage less accurate, lower-fidelity models that are computationally inexpensive in order to enhance predictive accuracy when high-fidelity data are scarce. However, low-fidelity models, while often displaying the qualitative solution behaviour, fail to accurately capture fine spatio-temporal and dynamic features of high-fidelity models. To address this shortcoming, we present a data-driven strategy that combines dimensionality reduction with multifidelity neural network surrogates. The key idea is to generate a spatial basis by applying proper orthogonal decomposition (POD) to high-fidelity solution snapshots, and approximate the dynamics of the reduced states—time-parameter-dependent expansion coefficients of the POD basis—using a multi-fidelity long short-term memory network. By mapping low-fidelity reduced states to their high-fidelity counterpart, the proposed reduced-order surrogate model enables the efficient recovery of full solution fields over time and parameter variations in a non-intrusive manner. The generality of this method is demonstrated by a collection of PDE problems where the low-fidelity model can be defined by coarser meshes and/or time stepping, as well as by misspecified physical features.</p>}},
author = {{Conti, Paolo and Guo, Mengwu and Manzoni, Andrea and Frangi, Attilio and Brunton, Steven L. and Kutz, J. Nathan}},
issn = {{1364-5021}},
keywords = {{LSTM networks; multi-fidelity surrogate modelling; parametrized PDEs; proper orthogonal decomposition; reduced-order modelling}},
language = {{eng}},
month = {{02}},
number = {{2283}},
publisher = {{Royal Society Publishing}},
series = {{Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}},
title = {{Multi-fidelity reduced-order surrogate modelling}},
url = {{http://dx.doi.org/10.1098/rspa.2023.0655}},
doi = {{10.1098/rspa.2023.0655}},
volume = {{480}},
year = {{2024}},
}