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

Paolo Conti*, Mengwu Guo, Andrea Manzoni, Jan S. Hesthaven

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)
50 Downloads (Pure)


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.
Original languageEnglish
Article number115811
Number of pages22
JournalComputer methods in applied mechanics and engineering
Early online date10 Dec 2022
Publication statusPublished - 1 Feb 2023


  • Machine learning
  • Multi-fidelity regression
  • LSTM network
  • Parametrized PDE
  • Time-dependent problem
  • 22/4 OA procedure

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