Overview of Design Considerations for Data-Driven Time-Stepping Schemes Applied to Nonlinear Mechanical Systems

Artificial neural networks (NNs) are a type of machine learning (ML) algorithm that mimics the functioning of the human brain to learn and generalize patterns from large amounts of data without the need for explicit knowledge of the system’s physics. Employing NNs to predict time responses in the field of mechanical system dynamics is still in its infancy. The aim of this contribution is to give an overview of design considerations for NN-based time-stepping schemes for nonlinear mechanical systems. To this end, numerous design parameters and choices available when creating a NN are presented, and their effects on the accuracy of predicting the dynamics of nonlinear mechanical systems are discussed. The findings are presented with the support of three test cases: a double pendulum, a duffing oscillator, and a gyroscope. Factors such as initial conditions, external forcing, as well as system parameters were varied to demonstrate the robustness of the proposed approaches. Furthermore, practical design considerations such as noise-sensitivity as well as the ability to extrapolate are examined. Ultimately, we are able to show that NNs are capable of functioning as time-stepping schemes for nonlinear mechanical system dynamics applications.