FlowHON: Representing Flow Fields Using Higher-Order Networks
Nan Chen Zhihong Li Jun Tao
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.