Scientific machine learning: Kolmogorov–Arnold-Informed Neural Network (KINN) for solving PDEs

10/31/2024

Researchers have recently developed an innovative physics-informed deep learning framework called the Kolmogorov–Arnold-Informed Neural Network (KINN), providing a novel AI solution for solving partial differential equations (PDEs) in science and engineering. Compared to traditional multilayer perceptron (MLP) neural networks, this new AI framework achieves significant improvements in efficiency and accuracy. In recent years, Physics-Informed Neural Networks (PINNs) have gained increasing attention for solving PDE problems. However, traditional MLPs often face challenges such as numerous parameters and slow convergence when dealing with complex boundary conditions and multi-scale problems. KINN, based on the Kolmogorov–Arnold Network (KAN), introduces fewer parameters and enhanced interpretability, significantly improving the accuracy and efficiency of solving PDEs.

The study demonstrates KINN's outstanding performance in various complex scenarios, such as stress concentration, singularity issues, nonlinear material simulations, and heterogeneous problems. Experimental results show that KINN not only achieves higher accuracy than traditional PINNs with fewer computational resources but also significantly accelerates the solving process, especially in multi-scale and complex geometry problems.

This groundbreaking AI work opens new doors for solving PDEs, highlighting the enormous potential of physics-informed deep learning in scientific computing. The research team hopes that this method can be widely adopted in material design, structural simulation, and other scientific and engineering applications.

The source code is open and the results are reproducible, providing a valuable resource for the research community.

Authors: Yizheng Wang, Jia Sun, Jinshuai Bai, Cosmin Anitescu, Mohammad Sadegh Eshaghi, Prof. Ph. D. Xiaoying Zhuang, Prof. Dr.-Ing. Timon Rabczuk, Prof. Dr. Yinghua Liu

Institutions: Department of Engineering Mechanics, Tsinghua University; Institute of Structural Mechanics, Bauhaus-Universität Weimar; Institute of Photonics, Leibniz University Hannover

For more details on the research, check out our paper on arXiv: https://arxiv.org/abs/2406.11045

Published by Team CSST

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