# Gradient-free neural topology optimization: Towards effective fracture-resistant designs

arXiv: https://arxiv.org/abs/2403.04937 · HTML: https://mlsanity.com/paper/2403.04937/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 84 references that are in the map.
- First posted on arXiv 7 Mar 2024.

## Builds on (most cited first, 22 of 22)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [Deep Neuroevolution: Genetic Algorithms Are a Competitive Alternative for Training Deep Neural Networks for Reinforcement Learning](https://mlsanity.com/paper/1712.06567/) (2017)
- [Sample-Efficient Optimization in the Latent Space of Deep Generative Models via Weighted Retraining](https://mlsanity.com/paper/2006.09191/) (2020)
- [Diffusion Models Beat GANs on Topology Optimization](https://mlsanity.com/paper/2208.09591/) (2022)
- [TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain](https://mlsanity.com/paper/2003.04685/) (2020)
- [Improving black-box optimization in VAE latent space using decoder uncertainty](https://mlsanity.com/paper/2107.00096/) (2021)
- [Neural reparameterization improves structural optimization](https://mlsanity.com/paper/1909.04240/) (2019)
- [Discovering Evolution Strategies via Meta-Black-Box Optimization](https://mlsanity.com/paper/2211.11260/) (2022)
- [JAX-FEM: A differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data science](https://mlsanity.com/paper/2212.00964/) (2022)
- [evosax: JAX-based Evolution Strategies](https://mlsanity.com/paper/2212.04180/) (2022)
- [Neural networks for topology optimization](https://mlsanity.com/paper/1709.09578/) (2017)
- [On the use of Artificial Neural Networks in Topology Optimisation](https://mlsanity.com/paper/2208.02563/) (2022)
- [Topology Optimization via Machine Learning and Deep Learning: A Review](https://mlsanity.com/paper/2210.10782/) (2022)
- [Length Scale Control in Topology Optimization using Fourier Enhanced Neural Networks](https://mlsanity.com/paper/2109.01861/) (2021)
- [DMF-TONN: Direct Mesh-free Topology Optimization using Neural Networks](https://mlsanity.com/paper/2305.04107/) (2023)
- [A machine learning approach for fighting the curse of dimensionality in global optimization](https://mlsanity.com/paper/2110.14985/) (2021)
- [NSTO: Neural Synthesizing Topology Optimization for Modulated Structure Generation](https://mlsanity.com/paper/2303.11757/) (2023)

## Built on by (most cited first, 2 of 2)

- [Neural Operator-enabled Topology-informed Evolutionary Strategy for PDE-Constrained Optimization](https://mlsanity.com/paper/2607.07682/) (2026)
- [Neural topology optimization of ship structures under propulsion machinery vibrations](https://mlsanity.com/paper/2609.38089/) (2026)

## Abstract (arXiv)

Gradient-free optimizers allow for tackling problems regardless of the smoothness or differentiability of their objective function, but they require many more iterations to converge when compared to gradient-based algorithms. This has made them unviable for topology optimization due to the high computational cost per iteration and the high dimensionality of these problems. We propose a gradient-free neural topology optimization method using a pre-trained neural reparameterization strategy that addresses two key challenges in the literature. First, the method leads to at least one order of magnitude decrease in iteration count to reach minimum compliance when optimizing designs in latent space, as opposed to the conventional gradient-free approach without latent parameterization. This helps to bridge the large performance gap between gradient-free and gradient-based topology optimization for smooth and differentiable problems like compliance optimization, as demonstrated via extensive computational experiments in- and out-of-distribution with the training data. Second, we also show that the proposed method can optimize toughness of a structure undergoing brittle fracture more effectively than a traditional gradient-based optimizer, delivering an objective improvement in the order of 30% for all tested configurations. Although gradient-based topology optimization is more efficient for problems that are differentiable and well-behaved, such as compliance optimization, we believe that this work opens up a new path for problems where gradient-based algorithms have limitations.