# HGTO: A Unified Graph-Based Physics-Informed Formulation for Structural Topology Optimization

arXiv: https://arxiv.org/abs/2609.15001 · HTML: https://mlsanity.com/paper/2609.15001/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 36 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Builds on (most cited first, 14 of 14)

- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications](https://mlsanity.com/paper/1908.10407/) (2019)
- [Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems](https://mlsanity.com/paper/2107.12146/) (2021)
- [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)
- [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)
- [A Finite Element-Inspired Hypergraph Neural Network: Application to Fluid Dynamics Simulations](https://mlsanity.com/paper/2212.14545/) (2022)
- [On the use of graph neural networks and shape-function-based gradient computation in the deep energy method](https://mlsanity.com/paper/2207.07216/) (2022)
- [DMF-TONN: Direct Mesh-free Topology Optimization using Neural Networks](https://mlsanity.com/paper/2305.04107/) (2023)
- [FEM-Informed Hypergraph Neural Networks for Efficient Elastoplasticity](https://mlsanity.com/paper/2602.07364/) (2026)

## 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)

Density-based topology optimization is typically structured as a nested sequence of material updates, structural analyses, and sensitivity assessments. While neural density parameterization and dual-field physics-informed approaches provide data-free alternatives, most existing methods represent density and displacement as coordinate fields and make limited use of the discrete relationships inherent in the finite element mesh. The present study introduces HGTO, a unified graph-based formulation that extends complete neural topology optimization from coordinate space to finite-element graph space. Element densities are parameterized on the element graph derived from the mesh, and the structural state is determined on the corresponding node--element hypergraph. Finite element kinematics, numerical quadrature, constitutive response, and force assembly remain explicitly defined operations within the differentiable computation. The material field and equilibrium state are therefore coupled through a common finite-element incidence structure. Numerical studies show compliance comparable to conventional density-based optimization at substantially lower computational cost than a representative coordinate-based dual-field neural method. The same coupled formulation accommodates high-resolution and irregular meshes, three-dimensional structures, finite deformation, and elastoplastic response.