Development of a physics-informed machine learning method for aerodynamic and fluids simulation (2021)
An implementation of a non-data driven Physics Informed Neural Network (PINN) for simulation of steady state fluid flow is presented. Through the use of deep convolutional neural networks, the velocity and pressure fields were obtained by using computational fluid dynamics (CFD) simulations as comparison or reference data. The presented approach consists of a PINN implemented with the Deepxde package and trained to solve the Navier-Stokes equation in steady state around a submerged geometry. The algorithm used a dual optimization approach using Adam and L-BFGS and the performance for algorithms trained for different number of epochs was evaluated. The best performing algorithm resulted at 300 epochs of training and compared to the simulation the root mean square error for the x velocity component was (61.14 x 10-5 m/s), for the y velocity (9.44 x 10-5 m/s) and for the pressure (0.016 x 10-5 Pa). Compared to similar approaches these results display an acceptable prediction for the proposed problem. The results of the PINN presented in this paper, showcase the potential that such approaches have for all fields that rely on solving partial differential equations, if implemented correctly such tools could become companions to simulation tools such as CFD soon with gains in speed and lower computational power required.