This paper introduces a novel neural network for efficiently solving Structured Inverse Eigenvalue Problems (SIEPs). The main contributions lie in two aspects: firstly, a unified framework is proposed that can handle various SIEPs instances. Particularly, an innovative method for handling nonnegativity constraints is devised using the ReLU function. Secondly, a novel neural network based on multilayer perceptrons, utilizing the Stiefel layer, is designed to efficiently solve SIEP. By incorporating the Stiefel layer through matrix orthogonal decomposition, the orthogonality of similarity transformations is ensured, leading to accurate solutions for SIEPs. Hence, we name this new network Stiefel Multilayer Perceptron (SMLP). Furthermore, SMLP is an unsupervised learning approach with a lightweight structure that is easy to train. Several numerical tests from literature and engineering domains demonstrate the efficiency of SMLP.

翻译：本文提出一种新颖的神经网络，用于高效求解结构化逆特征值问题（SIEPs）。主要贡献体现在两个方面：首先，提出了一个能够处理各类SIEP实例的统一框架。特别地，通过ReLU函数设计了一种处理非负约束的创新方法。其次，基于多层感知器并利用Stiefel层，设计了一种新型神经网络以高效求解SIEP。通过矩阵正交分解引入Stiefel层，确保了相似变换的正交性，从而获得SIEP的精确解。因此，我们将该新网络命名为Stiefel多层感知器（SMLP）。此外，SMLP是一种具有轻量级结构的无监督学习方法，易于训练。来自文献和工程领域的多个数值实验验证了SMLP的高效性。