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.