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.

中文翻译：

---

应用于中子扩散的特征值问题的基于自编码器的降阶模型

本文使用自动编码器进行降维，提出了一种新颖的基于投影的降阶模型来解决特征值问题。降阶建模依赖于找到合适的基函数，这些基函数定义了一个低维空间，在其中逼近了一个高维系统。适当的正交分解 (POD) 和奇异值分解 (SVD) 通常用于此目的并产生最佳线性子空间。自编码器提供了 POD/SVD 的非线性替代方案，可以更有效地捕获高保真模型结果中的特征或模式。开发了基于自动编码器和新型混合 SVD-自动编码器的降阶模型。这些方法与标准 POD-Galerkin 方法进行了比较，并应用于取自核反应堆物理领域的两个测试案例。