Transported Memory Networks accelerating Computational Fluid Dynamics

TL;DR

This paper introduces Transported Memory Networks, a novel neural network architecture that enhances PDE solvers for fluid dynamics on unstructured meshes, achieving accuracy and efficiency improvements over existing methods.

Contribution

The paper presents a new neural network architecture compatible with unstructured meshes, addressing limitations of prior CNN-based approaches in industrial fluid simulations.

Findings

Achieves point-wise accuracy comparable to or better than previous methods.

Improves computational efficiency in fluid dynamics simulations.

Compatible with generic discretizations, broadening applicability.

Abstract

In recent years, augmentation of differentiable PDE solvers with neural networks has shown promising results, particularly in fluid simulations. However, most approaches rely on convolutional neural networks and custom solvers operating on Cartesian grids with efficient access to cell data. This particular choice poses challenges for industrial-grade solvers that operate on unstructured meshes, where access is restricted to neighboring cells only. In this work, we address this limitation using a novel architecture, named Transported Memory Networks. The architecture draws inspiration from both traditional turbulence models and recurrent neural networks, and it is fully compatible with generic discretizations. Our results show that it is point-wise and statistically comparable to, or improves upon, previous methods in terms of both accuracy and computational efficiency.