The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition

TL;DR

This paper introduces a modified hybrid neural network architecture combining Kolmogorov--Arnold and MLP models with domain decomposition, enhancing efficiency and accuracy in solving high-frequency multiscale problems.

Contribution

It proposes a trainable weighting scheme and domain decomposition to improve physics-informed neural networks' ability to handle multiscale, high-frequency problems.

Findings

Reduces training costs compared to manual tuning

Improves computational efficiency in multiscale problems

Enhances the ability to capture high-frequency components

Abstract

In this work, we propose a modified Hybrid Parallel Kolmogorov--Arnold Network and Multilayer Perceptron Physics-Informed Neural Network to overcome the high-frequency and multiscale challenges inherent in Physics-Informed Neural Networks. This proposed model features a trainable weighting parameter to optimize the convex combination of outputs from the Kolmogorov--Arnold Network and the Multilayer Perceptron, thus maximizing the networks' capabilities to capture different frequency components. Furthermore, we adopt an overlapping domain decomposition technique to decompose complex problems into subproblems, which alleviates the challenge of global optimization. Benchmark results demonstrate that our method reduces training costs and improves computational efficiency compared with manual hyperparameter tuning in solving high-frequency multiscale problems.