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

TL;DR

This paper introduces a physics-informed neural network using Kolmogorov-Arnold networks with B-spline activations to accurately model multi-material elasticity problems in electronic packaging, effectively handling material discontinuities.

Contribution

It presents a novel physics-informed neural network framework that employs Kolmogorov-Arnold networks with B-spline activations for multi-material elasticity analysis, avoiding domain decomposition.

Findings

Achieves high accuracy in multi-material elasticity problems

Handles material discontinuities effectively

Simplifies computational framework

Abstract

This paper proposes a Physics-Informed Kolmogorov-Arnold Network for analyzing elasticity problems in multi-material electronic packaging structures. The method replaces traditional Multi-Layer Perceptrons with Kolmogorov-Arnold Networks within an energy-based Physics-Informed Neural Network framework. By constructing admissible displacement fields satisfying essential boundary conditions and optimizing network parameters through numerical integration, the proposed method effectively handles material property discontinuities. Unlike traditional methods that require domain decomposition and interface constraints for multi-material problems, Kolmogorov-Arnold Networks' trainable B-spline activation functions provide inherent piecewise characteristics. This capability stems from B-splines' local support, which enables effective approximation of discontinuities despite their individual smoothness. Consequently, this approach enables accurate approximation across the entire domain using a single network and simplifying the computational framework. Numerical experiments demonstrate that the proposed method achieves excellent accuracy and robustness in multi-material elasticity problems, validating its practical potential for electronic packaging analysis. Source codes are available at https://github.com/yanpeng-gong/PIKAN-MultiMaterial.