Rotational and Reflectional Equivariant Convolutional Neural Network for data-limited applications: Multiphase Flow demonstration

TL;DR

This paper introduces an SE(3)-equivariant CNN architecture to accurately predict steady-state multiphase flow fields around particles, leveraging rotational symmetry to improve generalization in data-limited scenarios.

Contribution

It presents a novel SE(3)-equivariant CNN that enforces rotational and translational symmetry for fluid flow prediction around particles, enhancing model robustness and accuracy.

Findings

Accurately predicts flow fields across various Reynolds numbers and particle volume fractions.

Demonstrates improved generalization due to symmetry-aware architecture.

Validates the approach on multiphase flow data with limited training samples.

Abstract

This article deals with approximating steady-state particle-resolved fluid flow around a fixed particle of interest under the influence of randomly distributed stationary particles in a dispersed multiphase setup using Convolutional Neural Network (CNN). The considered problem involves rotational symmetry about the mean velocity (streamwise) direction. Thus, this work enforces this symmetry using $\mathbf{\textbf{SE(3)-equivariant}}$, special Euclidean group of dimension 3, CNN architecture, which is translation and three-dimensional rotation equivariant. This study mainly explores the generalization capabilities and benefits of SE(3)-equivariant network. Accurate synthetic flow fields for Reynolds number and particle volume fraction combinations spanning over a range of [86.22, 172.96] and [0.11, 0.45] respectively are produced with careful application of symmetry-aware data-driven approach.