Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models. (arXiv:2201.10215v1 [math.NA])

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 …

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