Online Learning for the Neural Network Multigrid Solver for the Navier-Stokes Equations and its Application to 3D Simulations

  • Margenberg, Nils (Helmut Schmidt University)
  • Jendersie, Robert (Otto von Guericke University)
  • Lessig, Christian (Otto von Guericke University)
  • Richter, Thomas (Otto von Guericke University)

Please login to view abstract download link

We discuss approaches to connect the finite element method with neural networks. The paradigm is to use classical simulation techniques where their strengths are eminent, such as in the efficient representation of a coarse, large-scale flow field. Neural networks are used where a full resolution of the effects does not seem possible or efficient. The Deep Neural Network Multigrid Solver takes up these ideas by combining a geometric multigrid solver and a deep neural network. We show the efficiency, generalizability and scalability by 2D and 3D simulations. We introduce an online learning approach to retrain the network adaptively based on the uncertainty of the predictions.