First-order PDES for Graph Neural Networks: Advection And Burgers Equation Models

arXiv:2404.03081v1 Announce Type: new
Abstract: Graph Neural Networks (GNNs) have established themselves as the preferred methodology in a multitude of domains, ranging from computer vision to computational biology, especially in contexts where data inherently conform to graph structures. While many existing methods have endeavored to model GNNs using various techniques, a prevalent challenge they grapple with is the issue of over-smoothing. This paper presents new Graph Neural Network models that incorporate two first-order Partial Differential Equations (PDEs). These models do …

abstract arxiv biology computational computational biology computer computer vision cs.lg cs.na data domains equation gnns graph graph neural networks math.na methodology networks neural networks type vision