On nonlinear coupled differential equations for corrugated backward facing step (CBFS) with circular obstacle: AI-neural networking

Nonlinear mathematical formulations provide an accurate representation of intricate phenomena, including turbulence, vortices, and chaotic flow behavior. The solution of nonlinear differential equations for narrating flow fields is a challenging task. In this regard, the present article offers a solution remedy by conjecturing finite element method (FEM) outcomes with artificial intelligence-based neural networks. More precisely, a backward-facing step (BFS) is being treated as the study domain. The two corresponding triangular ribs make BFS corrugated, and the inlet has a parabolic pattern. We derive the differential system for the flow field within a BFS rooted with a circular obstacle. The solution is obtained by using the FEM. The artificial neural networks (ANNs) model is created with an input layer containing the viscosity, density, characteristics length, and mean inflow velocity, and it has lift coefficient (LC) to be output in the last layer. We choose 67 (70%) values for training and the remaining data points are taken for validation and testing as a 14 each. ANN has 10 neurons in the hidden layer and is trained with the Levenberg-Marquardt algorithm. Mean square error and regression analysis are performed to validate the model. It is concluded that the ANN design will act as the most accurate forecasting model of hydrodynamic force on circular obstruction in BFS for an extensive range, except normal parameters where classical methodologies were unable to predict.