Surrogate modeling of fluid dynamics with a multigrid inspired neural network architecture

• Published in: Machine learning with applications 2021-12, Vol.6, p.100176, Article 100176
• Main Authors: Le, Quang Tuyen, Ooi, Chinchun
• Format: Article
• Language: English
• Subjects: Computational Fluid Dynamics (CFD); Convolutional Neural Network (CNN); Machine learning; Multigrid; Surrogate modeling
• ISSN: 2666-8270; 2666-8270
• DOI: 10.1016/j.mlwa.2021.100176

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%. •A multigrid-inspired modification to a CNN is proposed.•Canonical fluid dynamics problems such as flow past an oscillating foil are tested.•Model extrapolates well across different geometries and inlet boundary conditions.•Model reduces test RMSE by 20%–70% relative to a baseline U-Net model.•Scientific computing concepts can improve ML model design for engineering problems.