RESUMO
Differential neural networks (DiNNs) encounter a trade-off between the approximation quality and structural complexity. One promising approach to address this trade-off is incorporating dynamic complexity adjustment as an integral part of the learning process. Taking inspiration from the Fourier approximation theory, this study introduces a novel method for adapting the architecture of DiNNs, when they serve as nonparametric identifiers for dynamic systems with uncertain mathematical models. The structural adaptation process is executed through a recursive algorithm based on a modification structure strategy, which dynamically adjusts the number of neurons within the network's structure. By applying a projection operator to the set of neurons, this method identifies the most relevant sequence of sigmoidal functions, intending to minimize the mean square error in approximating the trajectories of uncertain systems. This simultaneous reduction in overall complexity enhances the quality of the approximations. Moreover, the proposed method can implement a coarse-to-fine approach, wherein selecting necessary neurons occurs in multiple steps. These steps are determined by an adaptive structure strategy that alters the topology of the DiNN. The resulting framework's effectiveness is demonstrated by evaluating the proposed identifier's performance in approximating the evolution of real-life data associated with the ocular response during controlled motions or virtual reality engagement. In both experimental cases, there was a noticeable improvement in the accuracy of eye motion approximation by the DiNN, thanks to the variable structure approximation basis determined by the adaptive structure strategy. Overall, this study presents a formal method to automatically determine a feasible DiNN topology.