الملخص
Graph Neural Operators (GNOs) provide flexible surrogate models for learning solution operators of partial differential equations (PDEs). However, standard GNOs typically parameterize the integral kernel with a monolithic neural network and evaluate kernel interactions over graph edges, leading to substantial computational and memory overhead at high resolutions or with large neighborhoods. To address these limitations, we propose Functional Tensor Decomposition Graph Neural Operator (FTD-GNO), a memory-efficient GNO framework that decouples the high-dimensional continuous integral kernel into low-dimensional mode-wise functions. By instantiating the kernel with classical tensor decomposition formats, including CP, Tensor-Train, and Tucker decompositions, FTD-GNO enables algebraic reconstruction of the integral operator without explicitly materializing full edge-wise kernel tensors. This factorized formulation reduces the memory footprint of kernel evaluation and aggregation while retaining the continuous operator-learning structure of GNOs. Theoretical complexity analysis shows that FTD-GNO substantially lowers parameter and activation-memory costs associated with high-dimensional kernel construction. Experiments show lower peak memory than the corresponding unfactorized graph-integral baselines, with shorter recorded training times. Fourier-graph experiments further demonstrate that FTD can improve the efficiency of a graph-integral layer within a hybrid operator and has good scalability.
الكلمات المفتاحية
بيانات النشر
- المجلة
- غير متاح
- وصول مفتوح
- وصول مفتوح أخضر
اقتبس هذه المقالة
APA 7
Zhang, X., Wang, B., Gao, J., & Yin, Y. H. A. B. (2026). FTD-GNO: Memory-Efficient Graph Neural Operators through Functional Tensor Decomposition of the Kernel. https://omanscience.com/ar/articles/ftd-gno-memory-efficient-graph-neural-operators-through-functional-tensor-decomposition-of-the-kernel
MLA 9
Zhang, Xiaomin, et al. "FTD-GNO: Memory-Efficient Graph Neural Operators through Functional Tensor Decomposition of the Kernel." https://omanscience.com/ar/articles/ftd-gno-memory-efficient-graph-neural-operators-through-functional-tensor-decomposition-of-the-kernel.
شيكاغو (المؤلف–التاريخ)
Zhang, Xiaomin, Boyue Wang, Junbin Gao, and Yongli Hu anbd Baocai Yin. 2026. "FTD-GNO: Memory-Efficient Graph Neural Operators through Functional Tensor Decomposition of the Kernel." https://omanscience.com/ar/articles/ftd-gno-memory-efficient-graph-neural-operators-through-functional-tensor-decomposition-of-the-kernel.
هارفارد
Zhang, X., Wang, B., Gao, J. and Yin, Y. H. A. B. (2026) 'FTD-GNO: Memory-Efficient Graph Neural Operators through Functional Tensor Decomposition of the Kernel', Available at: https://omanscience.com/ar/articles/ftd-gno-memory-efficient-graph-neural-operators-through-functional-tensor-decomposition-of-the-kernel.
فانكوفر
Zhang X, Wang B, Gao J, Yin YHAB. FTD-GNO: Memory-Efficient Graph Neural Operators through Functional Tensor Decomposition of the Kernel. https://omanscience.com/ar/articles/ftd-gno-memory-efficient-graph-neural-operators-through-functional-tensor-decomposition-of-the-kernel
IEEE
X. Zhang, B. Wang, J. Gao, and Y. H. A. B. Yin, "FTD-GNO: Memory-Efficient Graph Neural Operators through Functional Tensor Decomposition of the Kernel," https://omanscience.com/ar/articles/ftd-gno-memory-efficient-graph-neural-operators-through-functional-tensor-decomposition-of-the-kernel.