Modelagem dinâmica de um pêndulo duplo utilizando redes neurais lagrangianas

Abstract

This work aims to study the application of neural networks in the modeling of the double pendulum, a complex and challenging dynamic system. A new class of Hamiltonian Neural Networks (HNN) was proposed to model the double pendulum, but it fails in many physical systems that cannot be expressed as a Hamiltonian system. Therefore, the use of neural networks with Lagrangian formulation (LNN) was proposed. This work seeks to evaluate the effectiveness of this approach, using the double pendulum as a case study and reproducing the work of Cranmer et al. (2020). The results of this research confirm that the LNN approach was effective in obtaining numerical solutions close to the ideal analytical solution. Furthermore, the system also proved to be sensitive to initial conditions, and the analysis of the loss function indicated stability in the results after the training period. The comparison between real and predicted angular velocities and accelerations showed a linear relationship and minimal interference from outliers. The heat map generated from the analysis of the coordinate space showed that the model behaved satisfactorily.