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

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 $\text{SE(3)-equivariant}$, 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.

arXiv commentMain change: The acronym CNN in title of previous version has been changed to Convolutional Neural Network

References in corpus (17)

• Adam: A Method for Stochastic Optimization
• Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
• Machine Learning for Fluid Mechanics
• Turbulence Modeling in the Age of Data
• Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds
• Machine learning based spatio-temporal super resolution reconstruction of turbulent flows
• Perspectives on Machine Learning-augmented Reynolds-averaged and Large Eddy Simulation Models of Turbulence
• 3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data
• Operator learning for predicting multiscale bubble growth dynamics
• From coarse wall measurements to turbulent velocity fields through deep learning
• Incorporating Symmetry into Deep Dynamics Models for Improved Generalization
• Computing Curvature for Volume of Fluid Methods using Machine Learning
• Towards Particle-Resolved Accuracy in Euler-Lagrange Simulations of Multiphase Flow Using Machine Learning and Pairwise Interaction Extended Point-particle (PIEP) Approximation
• Learning nonlocal constitutive models with neural networks
• Turbulence Enrichment using Physics-informed Generative Adversarial Networks