Physics-Informed Kolmogorov-Arnold Networks for multi-material elasticity problems in electronic packaging

Abstract: This paper proposes a Physics-Informed Kolmogorov-Arnold Network (PIKAN) method for analyzing elasticity problems in electronic packaging multi-material structures. The core innovation lies in replacing Multi-Layer Perceptrons (MLPs) with Kolmogorov-Arnold Networks (KANs) within the energy-based Physics-Informed Neural Networks (PINNs) framework. The method constructs admissible displacement fields that automatically satisfy essential boundary conditions and employs various numerical integration schemes to compute loss functions for network optimization. Unlike traditional PINNs that require domain decomposition and penalty terms for multi-material problems, KANs' trainable B-spline activation functions provide inherent piecewise function characteristics that naturally accommodate material property discontinuities. Consequently, this approach requires only a single KAN to achieve accurate approximation across the entire computational domain without subdomain partitioning and interface continuity constraints. Numerical validation demonstrates PIKAN's accuracy and robustness for multi-material elasticity problems. The method maintains high accuracy while significantly reducing computational complexity compared to domain decomposition approaches. Results confirm PIKAN's unique advantages in solving multi-material problems and its significant potential for electronic packaging structure analysis. Source codes are available at https://github.com/yanpeng-gong/PIKAN-MultiMaterial.