Neural Networks for Generating Better Local Optima in Topology Optimization

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.

References in corpus (11)

• Inverse-design of nonlinear mechanical metamaterials via video denoising diffusion models
• A Comprehensive Survey of Deep Transfer Learning for Anomaly Detection in Industrial Time Series: Methods, Applications, and Directions
• On the use of Artificial Neural Networks in Topology Optimisation
• Neural networks meet hyperelasticity: A guide to enforcing physics
• Deep Learning in Deterministic Computational Mechanics
• On the Use of Neural Networks for Full Waveform Inversion
• Quantitative reconstruction of defects in multi-layered bonded composites using fully convolutional network-based ultrasonic inversion
• Deep-pretrained-FWI: combining supervised learning with physics-informed neural network
• Neural Networks for Generating Better Local Optima in Topology Optimization
• Revisiting Non-Convexity in Topology Optimization of Compliance Minimization Problems
• Transfer Learning Enhanced Full Waveform Inversion

Cited by in corpus (6)

• Neural Networks for Generating Better Local Optima in Topology Optimization
• Neural topology optimization: the good, the bad, and the ugly
• A surrogate model for topology optimisation of elastic structures via parametric autoencoders
• A Memory Efficient Adjoint Method to Enable Billion Parameter Optimization on a Single GPU in Dynamic Problems
• Fast approximate solvers for metamaterials design in electromagnetism
• Continuation strategies to mitigate convergence to low-performing local optima in topology optimization of sound transmission loss