2021/05/09 by Quang Tuyen Le, Le, Quang Tuyen, Chin Chun Ooi +1 · 1 citation
Engineering · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Vibration Analysis #Lattice Boltzmann Simulation Studies #Machine Learning (cs.LG) #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.2105.03854
openalex publication_date 2021/05/09 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Algebraic or geometric multigrid methods are commonly used in numerical\nsolvers as they are a multi-resolution method able to handle problems with\nmultiple scales. In this work, we propose a modification to the commonly-used\nU-Net neural network architecture that is inspired by the principles of\nmultigrid methods, referred to here as U-Net-MG. We then demonstrate that this\nproposed U-Net-MG architecture can successfully reduce the test prediction\nerrors relative to the conventional U-Net architecture when modeling a set of\nfluid dynamic problems. In total, we demonstrate an improvement in the\nprediction of velocity and pressure fields for the canonical fluid dynamics\ncases of flow past a stationary cylinder, flow past 2 cylinders in out-of-phase\nmotion, and flow past an oscillating airfoil in both the propulsion and energy\nharvesting modes. In general, while both the U-Net and U-Net-MG models can\nmodel the systems well with test RMSEs of less than 1%, the use of the U-Net-MG\narchitecture can further reduce RMSEs by between 20% and 70%.\n