Autoencoder

Physics

Linear subspace

Nonlinear system

Singular value decomposition

Subspace topology

Mathematics

Algorithm

Mathematical optimization

Artificial intelligence

Eigenvalues and eigenvectors

Galerkin method

Geometry

Model order reduction

Computer science

Quantum mechanics

Dimensionality reduction

Applied mathematics

Artificial neural network

Projection (relational algebra)

International Journal for Numerical Methods in Engineering

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.

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