Non-intrusive reduced-order modeling using convolutional autoencoders

TL;DR

This paper introduces a non-intrusive reduced-order modeling framework using convolutional autoencoders and Gaussian process regression, demonstrating improved prediction accuracy for nonlinear PDEs like Navier-Stokes over traditional linear methods.

Contribution

The work presents a novel ROM approach combining convolutional autoencoders with GPR, enhancing nonlinear solution manifold approximation for steady-state PDEs.

Findings

Outperforms POD-based ROM in predicting Navier-Stokes solutions

Provides a more accurate nonlinear solution manifold

Demonstrates effectiveness on a lid-driven cavity problem

Abstract

The use of reduced-order models (ROMs) in physics-based modeling and simulation almost always involves the use of linear reduced basis (RB) methods such as the proper orthogonal decomposition (POD). For some nonlinear problems, linear RB methods perform poorly, failing to provide an efficient subspace for the solution space. The use of nonlinear manifolds for ROMs has gained traction in recent years, showing increased performance for certain nonlinear problems over linear methods. Deep learning has been popular to this end through the use of autoencoders for providing a nonlinear trial manifold for the solution space. In this work, we present a non-intrusive ROM framework for steady-state parameterized partial differential equations (PDEs) that uses convolutional autoencoders (CAEs) to provide a nonlinear solution manifold and is augmented by Gaussian process regression (GPR) to approximate the expansion coefficients of the reduced model. When applied to a numerical example involving the steady incompressible Navier-Stokes equations solving a lid-driven cavity problem, it is shown that the proposed ROM offers greater performance in prediction of full-order states when compared to a popular method employing POD and GPR over a number of ROM dimensions.