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arXiv · 2406.03307

Multi-Patch Isogeometric Convolution Hierarchical Deep-learning Neural Network

Lei Zhang·Chanwook Park·T. J. R. Hughes·Wing Kam Liu
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Abstract

A seamless integration of neural networks with Isogeometric Analysis (IGA) was first introduced in [1] under the name of Hierarchical Deep-learning Neural Network (HiDeNN) and has systematically evolved into Isogeometric Convolution HiDeNN (in short, C-IGA) [2]. C-IGA achieves higher order approximations without increasing the degree of freedom. Due to the Kronecker delta property of C-IGA shape functions, one can refine the mesh in the physical domain like standard finite element method (FEM) while maintaining the exact geometrical mapping of IGA. In this article, C-IGA theory is generalized for multi-CAD-patch systems with a mathematical investigation of the compatibility conditions at patch interfaces and convergence of error estimates. Two compatibility conditions (nodal compatibility and G^0 (i.e., global C^0) compatibility) are presented and validated through numerical examples.

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Lei Zhang, Chanwook Park, T. J. R. Hughes, Wing Kam Liu. 2024-06-05. Multi-Patch Isogeometric Convolution Hierarchical Deep-learning Neural Network. https://arxiv.org/abs/2406.03307

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