Neural Networks for Generating Better Local Optima in Topology Optimization

TL;DR

This paper explores how neural network-based material discretizations can improve local optima in acoustic topology optimization, especially when combined with multiple initializations and the Adam optimizer, despite current limitations.

Contribution

It demonstrates the potential of neural network discretizations to find better local optima in challenging acoustic topology optimization problems, highlighting the role of optimizer interplay and initialization strategies.

Findings

Neural network discretizations can improve local optima in acoustic topology optimization.

Multiple initializations significantly increase the chances of finding better solutions.

Current benefits are limited to unconstrained first-order optimization with Adam.

Abstract

Neural networks have recently been employed as material discretizations within adjoint optimization frameworks for inverse problems and topology optimization. While advantageous regularization effects and better optima have been found for some inverse problems, the benefit for topology optimization has been limited -- where the focus of investigations has been the compliance problem. We demonstrate how neural network material discretizations can, under certain conditions, find better local optima in more challenging optimization problems, where we here specifically consider acoustic topology optimization. The chances of identifying a better optimum can significantly be improved by running multiple partial optimizations with different neural network initializations. Furthermore, we show that the neural network material discretization's advantage comes from the interplay with the Adam optimizer and emphasize its current limitations when competing with constrained and higher-order optimization techniques. At the moment, this discretization has only been shown to be beneficial for unconstrained first-order optimization.