mlsanityData to 7 Oct 2026

Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models

arXiv 2201.10215 ↗First posted 25 Jan 2022math.NA cs.LG cs.NAcited by 10

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Abstract (arXiv)

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional ROMs - built, e.g., exclusively through proper orthogonal decomposition (POD) - when applied to nonlinear time-dependent parametrized PDEs. In particular, POD-DL-ROMs can achieve extreme efficiency in the training stage and faster than real-time performances at testing, thanks to a prior dimensionality reduction through POD and a DL-based prediction framework. Nonetheless, they share with conventional ROMs poor performances regarding time extrapolation tasks. This work aims at taking a further step towards the use of DL algorithms for the efficient numerical approximation of parametrized PDEs by introducing the μ t-POD-LSTM-ROM framework. This novel technique extends the POD-DL-ROM framework by adding a two-fold architecture taking advantage of long short-term memory (LSTM) cells, ultimately allowing long-term prediction of complex systems' evolution, with respect to the training window, for unseen input parameter values. Numerical results show that this recurrent architecture enables the extrapolation for time windows up to 15 times larger than the training time domain, and achieves better testing time performances with respect to the already lightning-fast POD-DL-ROMs.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 15 of its 63 references that are in the map. First posted on arXiv 25 Jan 2022.

Builds on

15 of 63 references.

References · 15

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3 more
  1. 2021A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equationscited by 28
  2. 2020Deep learning-based reduced order models in cardiac electrophysiologycited by 22
  3. 2021Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order modelscited by 12

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 3; 2024: 3; 2025: 1; 2026: 1.

10 papers.

  1. 2025Reduced Order Modeling with Shallow Recurrent Decoder Networkscited by 24
  2. 2023Deep Learning-based surrogate models for parametrized PDEs: handling geometric variability through graph neural networkscited by 17
  3. 2024On latent dynamics learning in nonlinear reduced order modelingcited by 14
  4. 2022textitFastSVD-ML-ROM: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applicationscited by 5
  5. 2024PTPI-DL-ROMs: pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEscited by 4
  6. 2023Branched Latent Neural Mapscited by 3
  7. 2024Data-Augmented Predictive Deep Neural Network: Enhancing the extrapolation capabilities of non-intrusive surrogate modelscited by 3
  8. 2022Deep Convolutional Architectures for Extrapolative Forecast in Time-dependent Flow Problemscited by 1
  9. 2023A two stages Deep Learning Architecture for Model Reduction of Parametric Time-Dependent Problemscited by 1
  10. 2026Convolutional Symmetric AutoEncoders: enhancing latent stability via differential geometrycited by 0