KATO: Neural-Reparameterized Topology Optimization Using Convolutional Kolmogorov-Arnold Network for Stress Minimization

Abstract

Topology optimization (TO) has been a cornerstone of advanced structural design for decades, yet it continues to face challenges in terms of convergence, optimality, and numerical stability, particularly for complex, non-convex problems like stress minimization. This paper introduces a novel approach to stress-based topology optimization through the development of neural-reparameterized topology optimization using the convolutional Kolmogorov-Arnold network (KATO). KATO uses the neural network to reparameterize the optimization problem, offering a unique solution to the challenges posed by stress minimization in TO. It also simplifies the penalization scheme by reducing sensitivity to certain parameters, which reduces the non-convexity of the stress minimization problem, enhancing convergence and stability. Our method demonstrates better performance in stress minimization compared to conventional approaches and a different neural network-based approach, achieving up to 10% lower maximum stress in common benchmark cases. KATO also shows remarkable efficiency, reducing computational time by up to 67% compared to conventional methods for stress minimization problems. We conduct a comprehensive analysis of KATO's performance, computational cost, scalability, and the impact of various neural network architectures. Our results indicate that KATO not only improves stress optimization but also offers insights into the relationship between neural network design and topology optimization performance, paving the way for more efficient and effective structural design processes.