# Diverse Topology Optimization using Modulated Neural Fields

arXiv: https://arxiv.org/abs/2502.13174 · HTML: https://mlsanity.com/paper/2502.13174/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 47 references that are in the map.
- First posted on arXiv 17 Feb 2025.

## Builds on (most cited first, 30 of 31)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Modulated Periodic Activations for Generalizable Local Functional Representations](https://mlsanity.com/paper/2104.03960/) (2021)
- [Mode Regularized Generative Adversarial Networks](https://mlsanity.com/paper/1612.02136/) (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)
- [Neural Redshift: Random Networks are not Random Functions](https://mlsanity.com/paper/2403.02241/) (2024)
- [A Level Set Theory for Neural Implicit Evolution under Explicit Flows](https://mlsanity.com/paper/2204.07159/) (2022)
- [NTopo: Mesh-free Topology Optimization using Implicit Neural Representations](https://mlsanity.com/paper/2102.10782/) (2021)
- [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)
- [Gauss-Newton Natural Gradient Descent for Physics-Informed Computational Fluid Dynamics](https://mlsanity.com/paper/2402.10680/) (2024)
- [Attention Beats Concatenation for Conditioning Neural Fields](https://mlsanity.com/paper/2209.10684/) (2022)
- [An adaptive augmented Lagrangian method for training physics and equality constrained artificial neural networks](https://mlsanity.com/paper/2306.04904/) (2023)
- [Geometry-Informed Neural Networks](https://mlsanity.com/paper/2402.14009/) (2024)
- [A Parametric Level Set Method for Topology Optimization based on Deep Neural Network (DNN)](https://mlsanity.com/paper/2101.03286/) (2021)
- [Neural topology optimization: the good, the bad, and the ugly](https://mlsanity.com/paper/2407.13954/) (2024)
- [Computing multiple solutions of topology optimization problems](https://mlsanity.com/paper/2004.11797/) (2020)
- [Topology Optimization Methods for 3D Structural Problems: A Comparative Study](https://mlsanity.com/paper/2108.03146/) (2021)

## Built on by (most cited first, 1 of 1)

- [How the Classical Baseline Shapes Machine-Learning Speed Claims in Topology Optimization](https://mlsanity.com/paper/2610.16051/) (2026)

## Abstract (arXiv)

Topology optimization (TO) is a family of computational methods that derive near-optimal geometries from formal problem descriptions. Despite their success, established TO methods are limited to generating single solutions, restricting the exploration of alternative designs. To address this limitation, we introduce Topology Optimization using Modulated Neural Fields (TOM) - a data-free method that trains a neural network to generate structurally compliant shapes and explores diverse solutions through an explicit diversity constraint. The network is trained with a solver-in-the-loop, optimizing the material distribution in each iteration. The trained model produces diverse shapes that closely adhere to the design requirements. We validate TOM on 2D and 3D TO problems. Our results show that TOM generates more diverse solutions than any previous method, all while maintaining near-optimality and without relying on a dataset. These findings open new avenues for engineering and design, offering enhanced flexibility and innovation in structural optimization.