Transported Memory Networks accelerating Computational Fluid Dynamics
This work addresses a bottleneck for industrial applications by enabling neural network augmentation in unstructured mesh solvers, though it is incremental in building on existing differentiable PDE solver approaches.
The paper tackled the challenge of integrating neural networks with industrial-grade computational fluid dynamics solvers that use unstructured meshes, by introducing Transported Memory Networks, which achieved comparable or improved accuracy and computational efficiency over previous methods.
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.