Session: 01-05-02: AI-Driven Modeling and Simulation for Aerospace Structures

Paper Number: 188569

188569 - A Physics-Informed Hyper Graph Neural Network for Topology Optimization 

Physics-informed neural networks (PINNs) have recently emerged as differentiable surrogates for topology optimization, yet many existing formulations suffer from blurred intermediate densities, limited mesh awareness, and poor scalability to multiple load cases. This work introduces a physics-informed hypergraph neural network framework for compliance-based topology optimization that explicitly mirrors finite-element connectivity and stiffness assembly. Nodes and finite elements are represented as dual entities in a node–element hypergraph, enabling bidirectional message passing that embeds local element-level interactions directly into the network architecture.

The proposed method integrates Solid Isotropic Material with Penalization (SIMP) interpolation together with density filtering and Heaviside projection, driving the optimization toward mesh-independent, near-binary designs while preserving full differentiability. Mechanical equilibrium is enforced through an energy-based physics-informed loss derived from the principle of minimum potential energy, evaluated via element-wise numerical integration without explicit global stiffness-matrix assembly. The learned hypergraph surrogate is embedded within a standard optimality-criteria update loop, enabling end-to-end differentiable topology evolution.

Benchmark studies on two-dimensional cantilever beams and L-shaped bracket problems demonstrate that the proposed approach reproduces optimized topologies and compliance values within 2–8% of finite-element reference solutions, while yielding sharper material distributions than baseline PINN-based methods. Additional examples show stable convergence under multiple simultaneous load cases. Computational results indicate a reduction in wall-clock time of approximately 35–55% compared to a conventional finite-element-based topology optimization workflow under the tested GPU–CPU configuration.

The proposed physics-informed hypergraph framework provides a mesh-aware, physically interpretable alternative to conventional solvers, bridging finite-element principles with graph-based learning. The approach offers a scalable foundation for future extensions to nonlinear material behavior, geometric nonlinearity, and large-scale topology optimization problems.

Presenting Author: Leixin Ma Arizona State University

Presenting Author Biography: Leixin Ma joins SEMTE as an assistant professor in 2023. Before joining ASU, she was a postdoctoral fellow in the Department of Mechanical and Aerospace Engineering at UCLA. She received her BSc in Naval Architecture & Ocean Engineering from Shanghai Jiao Tong University in 2015, an S.M. degree, and a Ph.D. in mechanical engineering from MIT in 2017 and 2021, respectively.

Her research interest includes fluid-structure interactions of deformable structures, physics-informed machine learning, and the machine learning-aided design of programmable structures and robots.

Her research approach emphasizes a synergic integration of machine learning into traditionally expensive simulations and experiments for nonlinear mechanics problems. Her career goal is a data-driven and physically consistent approach to modeling and designing programmable smart structures and robots, especially under complex fluid flow conditions. Her work has been featured in the Physics of Fluids Journal.