The Development of Physical Informed Neural Networks for Fluid Flow in Infinite Parallel Plates As Compared to CFD and AI Models

Abstract In this study, we developed neural network models from two different perspectives; Artificial Neural Networks (ANNs) and Physics Informed Neural Networks (PINNs) to model fluid flow in infinite parallel plates under laminar flow conditions. The ANNs model compared with the theoretical solution, while the PINNs model evaluated against a Computational Fluid Dynamics (CFD) model. The ANNs model predicts the non-dimensional pressure gradient in fully developed flow between infinite parallel plates. A significant limitation lies in its requirement for extensive data, posing a considerable challenge in practical scenarios. Similar to ANNs model; PINNs model is also mesh-free, applicable to any shape, and does not require a deep understanding of physical phenomena. However, Unlike the ANNs model, the PINNs model does not require extensive data. Despite these advantages interpreting the learned parameters or hidden representations within PINNs is challenging. In contrast, the CFD model, specifically the control volume approach within the SIMPLE algorithm, provides a clear physical interpretation of the numerical solution of fluid flow problems. However, it is affected by grid dependency, highly sensitive to boundary conditions, and it is also mathematically complicated. This comprehensive analysis and comparison provide valuable theoretical and fundamental insights for interdisciplinary researchers in the field, addressing fluid dynamics challenges and offering step by step guideline for implementation of Neural Networks models to solve fluid dynamics problems.