# Topology Optimization using Neural Networks with Conditioning Field Initialization for Improved Efficiency

arXiv: https://arxiv.org/abs/2305.10460 · HTML: https://mlsanity.com/paper/2305.10460/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 29 references that are in the map.
- First posted on arXiv 17 May 2023.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [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)
- [Neural reparameterization improves structural optimization](https://mlsanity.com/paper/1909.04240/) (2019)
- [NTopo: Mesh-free Topology Optimization using Implicit Neural Representations](https://mlsanity.com/paper/2102.10782/) (2021)
- [Deep learning for determining a near-optimal topological design without any iteration](https://mlsanity.com/paper/1801.05463/) (2018)
- [On the use of Artificial Neural Networks in Topology Optimisation](https://mlsanity.com/paper/2208.02563/) (2022)
- [3D Topology Optimization using Convolutional Neural Networks](https://mlsanity.com/paper/1808.07440/) (2018)
- [Real-Time Topology Optimization in 3D via Deep Transfer Learning](https://mlsanity.com/paper/2102.07657/) (2021)
- [A Parametric Level Set Method for Topology Optimization based on Deep Neural Network (DNN)](https://mlsanity.com/paper/2101.03286/) (2021)
- [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)

## Built on by (most cited first, 3 of 3)

- [NITO: Neural Implicit Fields for Resolution-free Topology Optimization](https://mlsanity.com/paper/2402.05073/) (2024)
- [Multi-scale Topology Optimization using Neural Networks](https://mlsanity.com/paper/2404.08708/) (2024)
- [Heterogeneous Metamaterials Design via Multiscale Neural Implicit Representation](https://mlsanity.com/paper/2511.03012/) (2025)

## Abstract (arXiv)

We propose conditioning field initialization for neural network based topology optimization. In this work, we focus on (1) improving upon existing neural network based topology optimization, (2) demonstrating that by using a prior initial field on the unoptimized domain, the efficiency of neural network based topology optimization can be further improved. Our approach consists of a topology neural network that is trained on a case by case basis to represent the geometry for a single topology optimization problem. It takes in domain coordinates as input to represent the density at each coordinate where the topology is represented by a continuous density field. The displacement is solved through a finite element solver. We employ the strain energy field calculated on the initial design domain as an additional conditioning field input to the neural network throughout the optimization. The addition of the strain energy field input improves the convergence speed compared to standalone neural network based topology optimization.