(untitled) (Contemporary Mathematics, 2025)
This paper focuses on approximate solution of the Jaulent-Miodek nonlinear-coupled partial differential equations. Physics-Informed Neural Network (PINN) architecture is implemented to find an approximate solution against the independent variables. Loss function is defined using PDEs and initial conditions. The PINN is set up to meet both the governing PDEs and the starting conditions. It does this by using automated differentiation to enforce the system’s residuals in the loss function. The results are compared with the exact solution using graphical representations. The model is tested for specific values of ψ. The error is illustrated in table, which shows the model efficiency and accuracy.