AA-PINN: ATTENTION AUGMENTED PHYSICS INFORMED NEURAL NETWORKS

Abhinav Sagar

Abstract:

Physics Informed Neural Networks has been quite successful in modelling the complex nature of fluid flow. Computational Fluid Dynamics using parallel processing
algorithms on GPUs have considerably reduced the time to solve the Navier Stokes
Equations. CFD based approaches uses approximates to make the modelling easy
but it comes at the cost of decrease in accuracy. In this paper, we propose an
attention based network architecture named AA-PINN to model PDEs behind fluid
flow. We use a combination of channel and spatial attention module. We propose a
novel loss function which is more robust in handling the initial as well as boundary
conditions imposed. Using evaluation metrics like RMSE, divergence and thermal
kinetic energy, our network outperforms previous PINNs for modelling Navier
Stokes and Burgers Equation.