Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based ROMs

Abstract

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional ROMs – built, e.g., through proper orthogonal decomposition (POD) – when applied to nonlinear time-dependent parametrized PDEs. Although extremely efficient at testing time, when evaluating the PDE solution for any new testing-parameter instance, DL-ROMs require an expensive training stage. To avoid this latter, a prior dimensionality reduction through POD, and a multi-fidelity pretraining stage, are introduced, yielding the POD-DL-ROM framework, which allows to solve time-dependent PDEs even faster than in real-time. Equipped with LSTM networks, the resulting POD-LSTM-ROMs better grasp the time evolution of the PDE system, ultimately allowing long-term prediction of complex systems’ evolution, with respect to the training window, for unseen input parameter values.

Stefania Fresca

Assistant Professor

My research interests are scientific machine learning, reduced order modeling and AI.