Investigation of Nonlinear Model Order Reduction of the Quasigeostrophic Equations through a Physics-Informed Convolutional Autoencoder

TL;DR

This paper investigates nonlinear model order reduction of quasigeostrophic equations using physics-informed convolutional autoencoders, highlighting the challenges and potential of machine learning approaches for reduced order modeling of complex geophysical systems.

Contribution

It introduces a physics-informed convolutional autoencoder framework for nonlinear ROM, comparing spatial CNN features with spectral features in geophysical modeling.

Findings

PI cost function improves spatial reconstruction

Spectral features outperform CNN spatial features

Machine learning-based ROMs require novel methodologies

Abstract

Reduced order modeling (ROM) is a field of techniques that approximates complex physics-based models of real-world processes by inexpensive surrogates that capture important dynamical characteristics with a smaller number of degrees of freedom. Traditional ROM techniques such as proper orthogonal decomposition (POD) focus on linear projections of the dynamics onto a set of spectral features. In this paper we explore the construction of ROM using autoencoders (AE) that perform nonlinear projections of the system dynamics onto a low dimensional manifold learned from data. The approach uses convolutional neural networks (CNN) to learn spatial features as opposed to spectral, and utilize a physics informed (PI) cost function in order to capture temporal features as well. Our investigation using the quasi-geostrophic equations reveals that while the PI cost function helps with spatial reconstruction, spatial features are less powerful than spectral features, and that construction of ROMs through machine learning-based methods requires significant investigation into novel non-standard methodologies.