# Neural reparameterization improves structural optimization

arXiv: https://arxiv.org/abs/1909.04240 · HTML: https://mlsanity.com/paper/1909.04240/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2019.

## Built on by (most cited first, 30 of 44)

- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [The Low-Rank Simplicity Bias in Deep Networks](https://mlsanity.com/paper/2103.10427/) (2021)
- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [Tutorial on amortized optimization](https://mlsanity.com/paper/2202.00665/) (2022)
- [NTopo: Mesh-free Topology Optimization using Implicit Neural Representations](https://mlsanity.com/paper/2102.10782/) (2021)
- [Physical Design using Differentiable Learned Simulators](https://mlsanity.com/paper/2202.00728/) (2022)
- [Variational Data Assimilation with a Learned Inverse Observation Operator](https://mlsanity.com/paper/2102.11192/) (2021)
- [ICON: Learning Regular Maps Through Inverse Consistency](https://mlsanity.com/paper/2105.04459/) (2021)
- [Fast PDE-constrained optimization via self-supervised operator learning](https://mlsanity.com/paper/2110.13297/) (2021)
- [Topology Optimization via Machine Learning and Deep Learning: A Review](https://mlsanity.com/paper/2210.10782/) (2022)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Deep Diffusion Image Prior for Efficient OOD Adaptation in 3D Inverse Problems](https://mlsanity.com/paper/2407.10641/) (2024)
- [Neural topology optimization: the good, the bad, and the ugly](https://mlsanity.com/paper/2407.13954/) (2024)
- [De-homogenization using Convolutional Neural Networks](https://mlsanity.com/paper/2105.04232/) (2021)
- [NCVX: A General-Purpose Optimization Solver for Constrained Machine and Deep Learning](https://mlsanity.com/paper/2210.00973/) (2022)
- [DMF-TONN: Direct Mesh-free Topology Optimization using Neural Networks](https://mlsanity.com/paper/2305.04107/) (2023)
- [Anatomically Constrained Implicit Face Models](https://mlsanity.com/paper/2312.07538/) (2023)
- [Neural Networks for Generating Better Local Optima in Topology Optimization](https://mlsanity.com/paper/2407.17957/) (2024)
- [Topology Optimization using Neural Networks with Conditioning Field Initialization for Improved Efficiency](https://mlsanity.com/paper/2305.10460/) (2023)
- [DNN-Based Topology Optimisation: Spatial Invariance and Neural Tangent Kernel](https://mlsanity.com/paper/2106.05710/) (2021)
- [Generative Thermal Design Through Boundary Representation and Multi-Agent Cooperative Environment](https://mlsanity.com/paper/2208.07952/) (2022)
- [Gradient-free neural topology optimization: Towards effective fracture-resistant designs](https://mlsanity.com/paper/2403.04937/) (2024)
- [Compliance Minimization via Physics-Informed Gaussian Processes](https://mlsanity.com/paper/2507.09968/) (2025)
- [Multi-material Multi-physics Topology Optimization with Physics-informed Gaussian Process Priors](https://mlsanity.com/paper/2602.17783/) (2026)
- [Multi-scale Topology Optimization using Neural Networks](https://mlsanity.com/paper/2404.08708/) (2024)
- [Pentagonal Photonic Crystal Mirrors: Scalable Lightsails with Enhanced Acceleration via Neural Topology Optimization](https://mlsanity.com/paper/2407.07896/) (2024)
- [Generative Neural Reparameterization for Differentiable PDE-constrained Optimization](https://mlsanity.com/paper/2410.12683/) (2024)
- [Diverse Topology Optimization using Modulated Neural Fields](https://mlsanity.com/paper/2502.13174/) (2025)
- [HGTO: A Unified Graph-Based Physics-Informed Formulation for Structural Topology Optimization](https://mlsanity.com/paper/2609.15001/) (2026)
- [KATOsuper: Surrogate-accelerated neural topology optimization with sensitivity-consistent Fourier neural operators](https://mlsanity.com/paper/2609.27216/) (2026)

## Abstract (arXiv)

Structural optimization is a popular method for designing objects such as bridge trusses, airplane wings, and optical devices. Unfortunately, the quality of solutions depends heavily on how the problem is parameterized. In this paper, we propose using the implicit bias over functions induced by neural networks to improve the parameterization of structural optimization. Rather than directly optimizing densities on a grid, we instead optimize the parameters of a neural network which outputs those densities. This reparameterization leads to different and often better solutions. On a selection of 116 structural optimization tasks, our approach produces the best design 50% more often than the best baseline method.