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

• Published in: International journal for numerical methods in engineering Vol. 122; no. 15; pp. 3780 - 3811
• Main Authors: Phillips, Toby R. F., Heaney, Claire E., Smith, Paul N., Pain, Christopher C.
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 15.08.2021; Wiley Subscription Services, Inc
• Subjects: autoencoder; Basis functions; Eigenvalues; machine learning; model reduction; neutron diffusion equation; Nuclear reactors; Proper Orthogonal Decomposition; Reactor physics; reduced‐order modeling; Singular value decomposition
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.6681

Using an autoencoder for dimensionality reduction, this article presents a novel projection‐based reduced‐order model for eigenvalue problems. Reduced‐order modeling 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.