Adversarial neural network methods for topology optimization of eigenvalue problems

Abstract: This research presents a novel method using an adversarial neural network to solve the eigenvalue topology optimization problems. The study focuses on optimizing the first eigenvalues of second-order elliptic and fourth-order biharmonic operators subject to geometry constraints. These models are usually solved with topology optimization algorithms based on sensitivity analysis, in which it is expensive to repeatedly solve the nonlinear constrained eigenvalue problem with traditional numerical methods such as finite elements or finite differences. In contrast, our method leverages automatic differentiation within the deep learning framework. Furthermore, the adversarial neural networks enable different neural networks to train independently, which improves the training efficiency and achieve satisfactory optimization results. Numerical results are presented to verify effectiveness of the algorithms for maximizing and minimizing the first eigenvalues.