  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.
