Approximate Solution of Newell-Whitehead-Segel Equation Using Deep Learning Method

In this paper, the approximation solution of the Newell-Whitehead-Segel equation (NWSE) is found by a deep learning technique. NWSE is a well-known partial differential equation (PDE) in fluid mechanics, and it depicts the dynamic behavior of dual blend fluid around the Rayleigh-Benard convection (RBC) bifurcation point of a binary fluid mixture. Deep-Galerkin Method (DGM) with GRU network is used to define a deep learning technique. The key benefit of the proposed technique is that a deep neural network that is comparable to GRU network is used that satisfies the initial conditions (ICs), boundary conditions (BCs), and differential operator (DO) without constructing a mesh. Adam optimizer is used to optimize the parameters of the DNN. The proposed experiment yielded extremely promising results when compared to recent methods such as: trigonometric cubic B-spline (TCBS), extended cubic uniform B-spline (ECBS), uniform Cubic B-spline (UCBS), and exponential B-spline collocation method (ExBSM).