Surrogate Modeling of Fluid Dynamics with a Multigrid Inspired Neural Network Architecture
This work addresses improving accuracy in fluid dynamics simulations for researchers and engineers, though it is incremental as it modifies an existing architecture.
The authors tackled surrogate modeling of fluid dynamics by proposing a multigrid-inspired U-Net-MG architecture, which reduced test RMSEs by 20-70% compared to a conventional U-Net across several canonical fluid flow cases.
Algebraic or geometric multigrid methods are commonly used in numerical solvers as they are a multi-resolution method able to handle problems with multiple scales. In this work, we propose a modification to the commonly-used U-Net neural network architecture that is inspired by the principles of multigrid methods, referred to here as U-Net-MG. We then demonstrate that this proposed U-Net-MG architecture can successfully reduce the test prediction errors relative to the conventional U-Net architecture when modeling a set of fluid dynamic problems. In total, we demonstrate an improvement in the prediction of velocity and pressure fields for the canonical fluid dynamics cases of flow past a stationary cylinder, flow past 2 cylinders in out-of-phase motion, and flow past an oscillating airfoil in both the propulsion and energy harvesting modes. In general, while both the U-Net and U-Net-MG models can model the systems well with test RMSEs of less than 1%, the use of the U-Net-MG architecture can further reduce RMSEs by between 20% and 70%.