Ph-Net: Parallelepiped Microstructure Homogenization Via 3d Convolutional Neural Networks

Hao, Peng; Liu, An; Huang, Jingcheng; Cao, Lingxin; Liu, Ji‐Kai; Lü, Lin

doi:10.2139/ssrn.4179173

Cited by 1 publication

(2 citation statements)

References 34 publications

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“…The downward walk, i.e., petalsto-core walk, allows information to be transferred from simplices back to nodes. These two processes follow that The two-step walk (Zeng et al 2023b) integrates both the upward and downward walks, allowing the information to be transmitted from the flower core and back through the petals. A complete two-step walk process follows that…”

Section: Flower-petals Algebraic Descriptionmentioning

confidence: 99%

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Higher-Order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes

Huang,

Zeng,

et al. 2024

AAAI

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Despite the recent successes of vanilla Graph Neural Networks (GNNs) on various tasks, their foundation on pairwise networks inherently limits their capacity to discern latent higher-order interactions in complex systems. To bridge this capability gap, we propose a novel approach exploiting the rich mathematical theory of simplicial complexes (SCs) - a robust tool for modeling higher-order interactions. Current SC-based GNNs are burdened by high complexity and rigidity, and quantifying higher-order interaction strengths remains challenging. Innovatively, we present a higher-order Flower-Petals (FP) model, incorporating FP Laplacians into SCs. Further, we introduce a Higher-order Graph Convolutional Network (HiGCN) grounded in FP Laplacians, capable of discerning intrinsic features across varying topological scales. By employing learnable graph filters, a parameter group within each FP Laplacian domain, we can identify diverse patterns where the filters' weights serve as a quantifiable measure of higher-order interaction strengths. The theoretical underpinnings of HiGCN's advanced expressiveness are rigorously demonstrated. Additionally, our empirical investigations reveal that the proposed model accomplishes state-of-the-art performance on a range of graph tasks and provides a scalable and flexible solution to explore higher-order interactions in graphs. Codes and datasets are available at https://github.com/Yiminghh/HiGCN.

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Section: Flower-petals Algebraic Descriptionmentioning

confidence: 99%

“…In this paper, we introduce a novel higher-order flowerpetals (FP) representation based on two-step random walk dynamics (Zeng et al 2023b) between the flower core and petals. This representation enables us to incorporate interactions among simplices of various orders into graph learn-ing.…”

Section: Introductionmentioning

confidence: 99%

Higher-Order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes

Huang,

Zeng,

et al. 2024

AAAI

View full text Add to dashboard Cite

show abstract

Ph-Net: Parallelepiped Microstructure Homogenization Via 3d Convolutional Neural Networks

Cited by 1 publication

References 34 publications

Higher-Order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes

Higher-Order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes

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