An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion

TL;DR

This paper introduces an autoencoder-based reduced-order modeling approach for eigenvalue problems, demonstrating its effectiveness in nuclear reactor physics applications and offering a nonlinear alternative to traditional linear methods.

Contribution

It develops and compares autoencoder and hybrid SVD-autoencoder reduced-order models with standard POD-Galerkin methods for eigenvalue problems.

Findings

Autoencoder models capture features more efficiently than POD.

Hybrid SVD-autoencoder improves approximation accuracy.

Models are validated on nuclear reactor physics test cases.

Abstract

Using an autoencoder for dimensionality reduction, this paper presents a novel projection-based reduced-order model for eigenvalue problems. Reduced-order modelling relies on finding suitable basis functions which define a low-dimensional space in which a high-dimensional system is approximated. Proper orthogonal decomposition (POD) and singular value decomposition (SVD) are often used for this purpose and yield an optimal linear subspace. Autoencoders provide a nonlinear alternative to POD/SVD, that may capture, more efficiently, features or patterns in the high-fidelity model results. Reduced-order models based on an autoencoder and a novel hybrid SVD-autoencoder are developed. These methods are compared with the standard POD-Galerkin approach and are applied to two test cases taken from the field of nuclear reactor physics.