  This paper presents a novel physics-inspired deep learning approach for point
cloud processing motivated by the natural flow phenomena in fluid mechanics.
Our learning architecture jointly defines data in an Eulerian world space,
using a static background grid, and a Lagrangian material space, using moving
particles. By introducing this Eulerian-Lagrangian representation, we are able
to naturally evolve and accumulate particle features using flow velocities
generated from a generalized, high-dimensional force field. We demonstrate the
efficacy of this system by solving various point cloud classification and
segmentation problems with state-of-the-art performance. The entire geometric
reservoir and data flow mimics the pipeline of the classic PIC/FLIP scheme in
modeling natural flow, bridging the disciplines of geometric machine learning
and physical simulation.
