A PINN Approach for Solving Singularly Perturbed Parabolic Partial Differential Equations with Two Small Parameters

<title>Abstract</title> <p>This paper presents two Physics Informed Neural Network models named DeepXDE and raw PyTorch for solving singularly perturbed parabolic partial differential equations containing two small parameters. Such equations often arise in the modeling of transport and diffusion processes in fluid dynamics and semiconductor devices, where standard numerical methods fail to capture boundary or interior layers effectively. The proposed schemes utilizes the power of deep learning to approximate the solution of the PDE and its associated initial and boundary conditions.</p>