  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.
