# A Parametric Level Set Method for Topology Optimization based on Deep Neural Network (DNN)

arXiv: https://arxiv.org/abs/2101.03286 · HTML: https://mlsanity.com/paper/2101.03286/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jan 2021.

## Built on by (most cited first, 11 of 11)

- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Topology Optimization using Neural Networks with Conditioning Field Initialization for Improved Efficiency](https://mlsanity.com/paper/2305.10460/) (2023)
- [NITO: Neural Implicit Fields for Resolution-free Topology Optimization](https://mlsanity.com/paper/2402.05073/) (2024)
- [A surrogate model for topology optimisation of elastic structures via parametric autoencoders](https://mlsanity.com/paper/2507.22539/) (2025)
- [Multi-scale Topology Optimization using Neural Networks](https://mlsanity.com/paper/2404.08708/) (2024)
- [Diverse Topology Optimization using Modulated Neural Fields](https://mlsanity.com/paper/2502.13174/) (2025)
- [GenVoid: Uncertainty-Aware Learning of Subsurface Material Defects with an Experimentally Validated Physics-Informed Generative Model](https://mlsanity.com/paper/2609.23761/) (2026)
- [Machine Learning-Based Multi-Objective Design Exploration Of Flexible Disc Elements](https://mlsanity.com/paper/2304.07245/) (2023)
- [Heterogeneous Metamaterials Design via Multiscale Neural Implicit Representation](https://mlsanity.com/paper/2511.03012/) (2025)
- [How the Classical Baseline Shapes Machine-Learning Speed Claims in Topology Optimization](https://mlsanity.com/paper/2610.16051/) (2026)

## Abstract (arXiv)

This paper proposes a new parametric level set method for topology optimization based on Deep Neural Network (DNN). In this method, the fully connected deep neural network is incorporated into the conventional level set methods to construct an effective approach for structural topology optimization. The implicit function of level set is described by fully connected deep neural networks. A DNN-based level set optimization method is proposed, where the Hamilton-Jacobi partial differential equations (PDEs) are transformed into parametrized ordinary differential equations (ODEs). The zero-level set of implicit function is updated through updating the weights and biases of networks. The parametrized reinitialization is applied periodically to prevent the implicit function from being too steep or too flat in the vicinity of its zero-level set. The proposed method is implemented in the framework of minimum compliance, which is a well-known benchmark for topology optimization. In practice, designers desire to have multiple design options, where they can choose a better conceptual design base on their design experience. One of the major advantages of DNN-based level set method is its ability to generate diverse and competitive designs with different network architectures. Several numerical examples are presented to verify the effectiveness of the proposed DNN-based level set method.