Optimizing a Physics-Informed Neural Network to solve the Reynolds Equation

This study focuses on the optimization of a Physics-Informed Neural Network (PINN) to address Partial Differential Equation (PDE) problems associated with fluid flow. Specifically, the stationary, one-dimensional classical Reynolds equation is solved using the PINN. Within the conducted studies, a comparison is made between the solutions obtained using the PINN, the numerical Finite Difference Method (FD), and the analytical solution. We study various scenarios with diverse hyper-parameters such as learning rate, epochs, number of training points, etc., for constructing the neural network to identify the optimal setup. The PINN accurately approximated the solution to the Reynolds equation (up to O(10−2 ). This suggests that PINNs can be used to address diverse problems in fluid dynamics. We proposed a PINN configuration that outperformed the PINN presented in the literature. The finite differences method obtains a better approximation than the PINNs, however, the full potential of the PINNs is yet to be determined, as it can include data from the problem, that finite difference method (FD) can not. Further studies are planned to investigate the capabilities of PINNs.