mlsanityData to 14 Oct 2026

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

arXiv 2609.15001 ↗First posted 14 Sep 2026cs.LGcited by 1

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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.

Key facts. Cited by 1 paper 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

14 of 36 references.

References · 14

  1. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,089
  2. 2019An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applicationscited by 118
  3. 2021Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problemscited by 102
  4. 2022Diffusion Models Beat GANs on Topology Optimizationcited by 79
  5. 2020TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domaincited by 65
  6. 2019Neural reparameterization improves structural optimizationcited by 44
  7. 2021NTopo: Mesh-free Topology Optimization using Implicit Neural Representationscited by 41
  8. 2018Deep learning for determining a near-optimal topological design without any iterationcited by 40
  9. 2017Neural networks for topology optimizationcited by 39
  10. 2022On the use of Artificial Neural Networks in Topology Optimisationcited by 36
  11. 2022A Finite Element-Inspired Hypergraph Neural Network: Application to Fluid Dynamics Simulationscited by 14
  12. 2022On the use of graph neural networks and shape-function-based gradient computation in the deep energy methodcited by 10
2 more
  1. 2023DMF-TONN: Direct Mesh-free Topology Optimization using Neural Networkscited by 6
  2. 2026FEM-Informed Hypergraph Neural Networks for Efficient Elastoplasticitycited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026How the Classical Baseline Shapes Machine-Learning Speed Claims in Topology Optimizationcited by 0