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This research introduces HGTO, a graph-based framework for structural topology optimization that integrates finite element mesh relationships directly into differentiable computation. By parameterizing material densities on the element graph rather than coordinate fields, the method achieves computational efficiency comparable to conventional approaches while handling complex 3D structures and elastoplastic responses. The work represents a significant advancement in machine learning applications for engineering design, specifically addressing the discrete nature of finite element meshes often overlooked by standard neural density methods.
HGTO: A Unified Graph-Based Physics-Informed Formulation for Structural Topology Optimization
arXiv:2609.15001v1 Announce Type: new Abstract: 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.
Abstract: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.
Machine Learning (cs.LG)
arXiv:2609.15001 [cs.LG]
(or arXiv:2609.15001v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.15001 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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