A Geometric-Enhanced Neural Network Method for Scalable and High-Resolution Topology Optimization

Topology optimization is a powerful methodology for designing lightweight, economical, and efficient structures. However, traditional approaches often face challenges such as numerical instabilities and high computational costs, limiting their practical applicability. Recently, radial basis function (RBF)-based and neural network-based methods have emerged as promising alternatives through the reparameterization of the density field. Despite their potential, these methods typically rely on isotropic basis functions or static feature encodings, which limit their ability to capture fine-scale structural details, particularly in high-aspect-ratio features such as slender bar-like members and in geometrically symmetric structural patterns. To address this research gap, this paper introduces a novel Geometric-enhanced Neural Network (GeNN) for topology optimization based on Anisotropic Radial Basis Functions (ARBFs). By embedding ARBFs into the neural network framework, the proposed method provides a more geometrically informed density representation and inherently suppresses checkerboard patterns without additional filtering techniques. The proposed GeNN framework is thoroughly validated on benchmark problems, including several representative symmetric structural layouts, demonstrating improved computational efficiency compared to traditional methods and other neural-network-based topology optimization methods. In addition, the proposed method demonstrates strong scalability across various optimization problems. Notably, GeNN successfully optimized a 256 m-long bridge involving millions of degrees of freedom within ten minutes on a standard personal computer. This advancement demonstrates the practical potential of the proposed method for large-scale civil engineering applications.