• Corpus ID: 246275764

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

@article{Fatone2022LongtimePO,
  title={Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models},
  author={Federico Fatone and Stefania Fresca and Andrea Manzoni},
  journal={ArXiv},
  year={2022},
  volume={abs/2201.10215}
}
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… 

References

SHOWING 1-10 OF 57 REFERENCES
POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition
A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs
TLDR
Numerical results indicate that DL-ROMs whose dimension is equal to the intrinsic dimensionality of the PDE solutions manifold are able to efficiently approximate the solution of parametrized PDEs, especially in cases for which a huge number of POD modes would have been necessary to achieve the same degree of accuracy.
A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equations
TLDR
Within the framework of parameter dependent PDEs, this work develops a constructive approach based on Deep Neural Networks for the efficient approximation of the parameter-to-solution map, based on a nonlinear version of the Kolmogorov n-width over which to base the concept of a minimal latent dimension.
POD-Enhanced Deep Learning-Based Reduced Order Models for the Real-Time Simulation of Cardiac Electrophysiology in the Left Atrium
TLDR
It is shown that performing a prior dimensionality reduction on FOM snapshots through randomized proper orthogonal decomposition (POD) enables to speed up training times and to decrease networks complexity.
Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models
TLDR
The resulting POD-DL-ROMs are shown to provide accurate results in almost real-time for the flow around a cylinder benchmark, the fluid-structure interaction between an elastic beam attached to a fixed, rigid block and a laminar incompressible flow, and the blood flow in a cerebral aneurysm.
Deep Learning with Long Short-Term Memory for Time Series Prediction
TLDR
It is strongly argued that RCLSTM is more competent than LSTM in latency-stringent or power-constrained application scenarios.
Data-driven recovery of hidden physics in reduced order modeling of fluid flows
TLDR
A modular hybrid analysis and modeling approach to account for hidden physics in reduced order modeling of parameterized systems relevant to fluid dynamics provides insights addressing a fundamental limitation of the physics-based models when the governing equations are incomplete to represent underlying physical processes.
Data-driven reduced order modeling for time-dependent problems
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