Stability, robustness, and convergence are problems that deep learning systems often have to deal with when training dynamics aren’t linear and there are hostile changes. Nonlinear partial differential equation (PDE) models are used in this study to look at and improve the stability of deep learning.  Neural dynamics are connected to PDE models, and nonlinear diffusion processes show how weight changes over time and keep things from becoming unstable. Numerical discretization and large-scale computing methods make it possible to run models on systems that are very complicated. Compared to baseline models, the results show big improvements in stability, accuracy of convergence, and resistance to changes.