Flow fields are often partitioned into data blocks for massively parallel
computation and analysis based on blockwise relationships. However, most of the
previous techniques only consider the first-order dependencies among blocks,
which is insufficient in describing complex flow patterns. In this work, we
present FlowHON, an approach to construct higher-order networks (HONs) from
flow fields. FlowHON captures the inherent higher-order dependencies in flow
fields as nodes and estimates the transitions among them as edges. We formulate
the HON construction as an optimization problem with three linear
transformations. The first two layers correspond to the node generation and the
third one corresponds to edge estimation. Our formulation allows the node
generation and edge estimation to be solved in a unified framework. With
FlowHON, the rich set of traditional graph algorithms can be applied without
any modification to analyze flow fields, while leveraging the higher-order
information to understand the inherent structure and manage flow data for
efficiency. We demonstrate the effectiveness of FlowHON using a series of
downstream tasks, including estimating the density of particles during tracing,
partitioning flow fields for data management, and understanding flow fields
using the node-link diagram representation of networks.

使用 FlowHON 方法构建高阶网络来分析流场，并通过节点生成和边估计解决对流场的密度估计、数据管理和结构理解等下游任务。

FlowHON: 使用高阶网络表示流场

FlowHON: Representing Flow Fields Using Higher-Order Networks

Text-attributed graphs have recently garnered significant attention due to
their wide range of applications in web domains. Existing methodologies employ
word embedding models for acquiring text representations as node features,
which are subsequently fed into Graph Neural Networks (GNNs) for training.
Recently, the advent of Large Language Models (LLMs) has introduced their
powerful capabilities in information retrieval and text generation, which can
greatly enhance the text attributes of graph data. Furthermore, the acquisition
and labeling of extensive datasets are both costly and time-consuming
endeavors. Consequently, few-shot learning has emerged as a crucial problem in
the context of graph learning tasks. In order to tackle this challenge, we
propose a lightweight paradigm called ENG, which adopts a plug-and-play
approach to empower text-attributed graphs through node generation using LLMs.
Specifically, we utilize LLMs to extract semantic information from the labels
and generate samples that belong to these categories as exemplars.
Subsequently, we employ an edge predictor to capture the structural information
inherent in the raw dataset and integrate the newly generated samples into the
original graph. This approach harnesses LLMs for enhancing class-level
information and seamlessly introduces labeled nodes and edges without modifying
the raw dataset, thereby facilitating the node classification task in few-shot
scenarios. Extensive experiments demonstrate the outstanding performance of our
proposed paradigm, particularly in low-shot scenarios. For instance, in the
1-shot setting of the ogbn-arxiv dataset, ENG achieves a 76% improvement over
the baseline model.

通过采用轻量级范式 ENG 以 Large Language Models 为基础，增强文本属性的图数据，包括通过节点生成使用 LLMs 提取语义信息和生成样本，以及通过边缘预测器将新生成的样本与原始图结合，从而在少样本情况下促进节点分类任务。