  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.
