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Graph-based compactly supported radial basis function neural network
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DOI：10.1016/j.enganabound.2026.106644.png)
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Abstract
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In this paper, a novel graph-based compactly supported radial basis function physics-informed neural network (G-CS-RBN) is proposed for partial differential equations. Compactly supported radial basis functions are employed to replace the linear interpolation to construct an efficient one-hidden-layer neural network. An adaptive support radius is proposed that allows each point to automatically learn its local support according to the loss function. This overcomes the drawback of the traditional numerical compactly supported radial basis functions using fixed empirical support radius, which restricts the accuracy of models. A graph structure is used to store the collocation points and their respective center points to improve the interpretability of the network, storage efficiency, and network learning. Besides, the adaptive center point is also suggested to aid the adaptive support radius, which can further boost the performance of G-CS-RBN. Finally, extensive numerical experiments on 2D and 3D PDEs demonstrate that G-CS-RBN achieves consistently better accuracy and efficiency compared with classical numerical CS-RBF methods and standard PINNs, while showing improved robustness across different PDEs.
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Physics-informed neural networks with domain decomposition for the incompressible Navier-Stokes equations.png)
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