Multi-fidelity surrogate modeling using long short-term memory networks
(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
- Conti, Paolo ; Guo, Mengwu LU ; Manzoni, Andrea and Hesthaven, Jan S.
- publishing date
- 2023-02-01
- 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}},
}