Bridging simulation and deep learning - convolutional neural networks on unstructured grids*

We develop a novel method for efficiently deploying Convolutional Neural Networks (CNNs) on arbitrary unstructured grids. Unstructured grids have been the major workhorse for PDE solvers, while CNNs have been the predominant neural network architecture in deep learning for processing spatial data. Recent works have shown successes in utilizing CNN-based deep neural networks for better modeling of physical systems (e.g., turbulence modeling), and acceleration of solutions to PDEs. However regular CNN framework operates under regular grids and cannot be easily incorporated into PDE solvers that operate on unstructured grids (e.g., FEM, DG, FV). Natively performing CNN-based deep learning in the unstructured grid domain for simulation allows for smooth integration between physical simulations and deep learning based physical models.