Fins are widely used in many industrial applications, including heat exchangers. They benefit from a relatively economical design cost, are lightweight, and are quite miniature. Thus, this study investigates the influence of a wavy fin structure subjected to convective effects with internal heat generation. The thermal distribution, considered a steady condition in one dimension, is described by a unique implementation of a physics-informed neural network (PINN) as part of machine-learning intelligent strategies for analyzing heat transfer in a convective wavy fin. This novel research explores the use of PINNs to examine the effect of the nonlinearity of temperature equation and boundary conditions by altering the hyperparameters of the architecture. The non-linear ordinary differential equation (ODE) involved with heat transfer is reduced into a dimensionless form utilizing the non-dimensional variables to simplify the problem. Furthermore, Runge-Kutta Fehlberg's fourth-fifth order (RKF-45) approach is implemented to evaluate the simplified equations numerically. To predict the wavy fin's heat transfer properties, an advanced neural network model is created without using a traditional data-driven approach, the ability to solve ODEs explicitly by incorporating a mean squared error-based loss function. The obtained results divulge that an increase in the thermal conductivity variable upsurges the thermal distribution. In contrast, a decrease in temperature profile is caused due to the augmentation in the convective-conductive variable values.