Reduced Order Modeling for Parameterized Time-Dependent PDEs using Spatially and Memory Aware Deep Learning
Numerical Analysis
2020-11-24 v1 Numerical Analysis
Abstract
We present a novel reduced order model (ROM) approach for parameterized time-dependent PDEs based on modern learning. The ROM is suitable for multi-query problems and is nonintrusive. It is divided into two distinct stages: A nonlinear dimensionality reduction stage that handles the spatially distributed degrees of freedom based on convolutional autoencoders, and a parameterized time-stepping stage based on memory aware neural networks (NNs), specifically causal convolutional and long short-term memory NNs. Strategies to ensure generalization and stability are discussed. The methodology is tested on the heat equation, advection equation, and the incompressible Navier-Stokes equations, to show the variety of problems the ROM can handle.
Cite
@article{arxiv.2011.11327,
title = {Reduced Order Modeling for Parameterized Time-Dependent PDEs using Spatially and Memory Aware Deep Learning},
author = {Nikolaj T. Mücke and Sander M. Bohté and Cornelis W. Oosterlee},
journal= {arXiv preprint arXiv:2011.11327},
year = {2020}
}