Solutions of the Newtonian Plane Couette Flow with Dynamic Wall Slip Using Machine Learning Methods

This study presents a comparative investigation of Physics-Informed Neural Networks (PINNs) and data-driven Deep Operator Networks (DeepONets) for predicting the evolution of plane Newtonian Couette flow with dynamic wall slip. First, a PINN framework is employed to solve flow for selected physical parameters. Subsequently, we develop a data-driven DeepONet, trained on high-fidelity numerical data, to learn the continuous solution operator across a broad range of slip boundary conditions and upper wall velocities. PINN achieves a relative L2 error of 0.083% for the specific case considered. On the other hand, DeepONet shows a mean relative error of 0.340% on the standard test set and performs well when tested with a deterministic harmonic forcing outside the GRF-based forcing distribution used for training. While PINN gives accuracy for a specific configuration, the trained DeepONet can be reused for different boundary forcings and slip parameters without needing to be retrained. The compatibility of physics-based and data-driven models is highlighted. The results also demonstrate that DeepONet is a very effective surrogate model for quick parametric studies and the real-time prediction of fluid dynamics.