FlowHON: Representing Flow Fields Using Higher-Order Networks

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.