<p>We construct hybrid solutions (combinations of solitons and degenerate solitons) for the real and complex modified Kortweg-de Vries equations. Specifically, using the Darboux transformation method we derive explicit solutions including one soliton—second order degenerate soliton, two soliton—second order degenerate soliton, and one soliton—third order degenerate soliton. To the best of our knowledge all these solutions are new to the literature. Using these solutions, we investigate the interaction dynamics between higher order degenerate solitons and multisoliton solutions for the aforementioned two equations. Higher order degenerate soliton solutions of real and complex mKdV equations are not studied through deep learning algorithms. We predict second order, third order degenerate solitons, and hybrid solutions for both the equations using physics-informed neural network (PINN) method and examine the outcomes predicted by the PINN approach. By calculating mean squared error values, we establish a correlation between predicted outcomes and the exact analytical degenerate soliton solutions, for these two nonlinear partial differential equations, from which we analyze the effectiveness of the PINN in approximating positon and hybrid solutions. Our results indicate that the deep learning methodology employed through the PINN demonstrates a strong capability for accurately predicting higher-order degenerate solitons and hybrid solutions.</p>