A fast and accurate physicsinformed neural network reduced order model with shallow masked autoencoder
Abstract
Traditional linear subspace reduced order models (LSROMs) are able to accelerate physical simulations, in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov nwidth. However, for physical phenomena not of this type, e.g., any advectiondominated flow phenomena, such as in traffic flow, atmospheric flows, and air flow over vehicles, a lowdimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed a fast and accurate physicsinformed neural network ROM, namely nonlinear manifold ROM (NMROM), which can better approximate highfidelity model solutions with a smaller latent space dimension than the LSROMs. Our method takes advantage of the existing numerical methods that are used to solve the corresponding full order models. The efficiency is achieved by developing a hyperreduction technique in the context of the NMROM. Numerical results show that neural networks can learn a more efficient latent space representation on advectiondominated data from 1D and 2D Burgers' equations. A speedup of up to 2.6 for 1D Burgers' and a speedup of 11.7 for 2D Burgers' equations are achieved with an appropriate treatment of the nonlinear terms through a hyperreduction technique. Finally, a posteriori error bounds for the NMROMs are derived that take account of the hyperreduced operators.
 Publication:

arXiv eprints
 Pub Date:
 September 2020
 arXiv:
 arXiv:2009.11990
 Bibcode:
 2020arXiv200911990K
 Keywords:

 Mathematics  Numerical Analysis;
 Computer Science  Machine Learning;
 Computer Science  Neural and Evolutionary Computing
 EPrint:
 33 pages, 17 figures