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Multi-fidelity surrogate modeling using long short-term memory networks

Conti, Paolo ; Guo, Mengwu LU ; Manzoni, Andrea and Hesthaven, Jan S. (2023) In Computer Methods in Applied Mechanics and Engineering 404.
Abstract

When evaluating quantities of interest that depend on the solutions to differential equations, we inevitably face the trade-off between accuracy and efficiency. Especially for parametrized, time-dependent problems in engineering computations, it is often the case that acceptable computational budgets limit the availability of high-fidelity, accurate simulation data. Multi-fidelity surrogate modeling has emerged as an effective strategy to overcome this difficulty. Its key idea is to leverage many low-fidelity simulation data, less accurate but much faster to compute, to improve the approximations with limited high-fidelity data. In this work, we introduce a novel data-driven framework of multi-fidelity surrogate modeling for... (More)

When evaluating quantities of interest that depend on the solutions to differential equations, we inevitably face the trade-off between accuracy and efficiency. Especially for parametrized, time-dependent problems in engineering computations, it is often the case that acceptable computational budgets limit the availability of high-fidelity, accurate simulation data. Multi-fidelity surrogate modeling has emerged as an effective strategy to overcome this difficulty. Its key idea is to leverage many low-fidelity simulation data, less accurate but much faster to compute, to improve the approximations with limited high-fidelity data. In this work, we introduce a novel data-driven framework of multi-fidelity surrogate modeling for parametrized, time-dependent problems using long short-term memory (LSTM) networks, to enhance output predictions both for unseen parameter values and forward in time simultaneously — a task known to be particularly challenging for data-driven models. We demonstrate the wide applicability of the proposed approaches in a variety of engineering problems with high- and low-fidelity data generated through fine versus coarse meshes, small versus large time steps, or finite element full order versus deep learning reduced-order models. Numerical results show that the proposed multi-fidelity LSTM networks not only improve single-fidelity regression significantly, but also outperform the multi-fidelity models based on feed-forward neural networks.

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author
; ; and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
LSTM network, Machine learning, Multi-fidelity regression, Parametrized PDE, Time-dependent problem
in
Computer Methods in Applied Mechanics and Engineering
volume
404
article number
115811
publisher
Elsevier
external identifiers
  • scopus:85143728189
ISSN
0045-7825
DOI
10.1016/j.cma.2022.115811
language
English
LU publication?
no
additional info
Publisher Copyright: © 2022 Elsevier B.V.
id
20d08196-ec4a-4fa2-b906-3bdf88bb1d5e
date added to LUP
2024-03-19 12:23:58
date last changed
2024-04-17 14:10:06
@article{20d08196-ec4a-4fa2-b906-3bdf88bb1d5e,
  abstract     = {{<p>When evaluating quantities of interest that depend on the solutions to differential equations, we inevitably face the trade-off between accuracy and efficiency. Especially for parametrized, time-dependent problems in engineering computations, it is often the case that acceptable computational budgets limit the availability of high-fidelity, accurate simulation data. Multi-fidelity surrogate modeling has emerged as an effective strategy to overcome this difficulty. Its key idea is to leverage many low-fidelity simulation data, less accurate but much faster to compute, to improve the approximations with limited high-fidelity data. In this work, we introduce a novel data-driven framework of multi-fidelity surrogate modeling for parametrized, time-dependent problems using long short-term memory (LSTM) networks, to enhance output predictions both for unseen parameter values and forward in time simultaneously — a task known to be particularly challenging for data-driven models. We demonstrate the wide applicability of the proposed approaches in a variety of engineering problems with high- and low-fidelity data generated through fine versus coarse meshes, small versus large time steps, or finite element full order versus deep learning reduced-order models. Numerical results show that the proposed multi-fidelity LSTM networks not only improve single-fidelity regression significantly, but also outperform the multi-fidelity models based on feed-forward neural networks.</p>}},
  author       = {{Conti, Paolo and Guo, Mengwu and Manzoni, Andrea and Hesthaven, Jan S.}},
  issn         = {{0045-7825}},
  keywords     = {{LSTM network; Machine learning; Multi-fidelity regression; Parametrized PDE; Time-dependent problem}},
  language     = {{eng}},
  month        = {{02}},
  publisher    = {{Elsevier}},
  series       = {{Computer Methods in Applied Mechanics and Engineering}},
  title        = {{Multi-fidelity surrogate modeling using long short-term memory networks}},
  url          = {{http://dx.doi.org/10.1016/j.cma.2022.115811}},
  doi          = {{10.1016/j.cma.2022.115811}},
  volume       = {{404}},
  year         = {{2023}},
}