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

Abstract

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