The main objective of this article is to develop novel interpolation operators that interpolate the given real-valued function on the boundary of the compact disk. To achieve this, we introduce a new class of generalized Boolean sum neural network operators \(\mathcal {B}_{n_1, n_2, \varrho }\mathcal{F}\) with one hidden layer, which employs a nonlinear activation function. The interpolation properties are established, and estimates for the error of approximation corresponding to operator \(\mathcal {B}_{n_1, n_2, \varrho }\mathcal{F}\) are computed in terms of mixed modulus of continuity. The advantage of our method is that it does not require training the network; rather, the number of hidden neurons adjusts the weights and bias. Numerical examples are illustrated to show the justifiability of these newly constructed operators. Furthermore, using MATLAB (R2024a), comparative and graphical analysis is carried out to demonstrate the validity and efficiency of the results developed for these operators. The results highlight the potential of these operators as a powerful tool for boundary interpolation problems on compact disks.
