Comparison of Neural Network Training Approaches That Preserve Physical Properties of Cyber-Physical System

This work introduces methods for validating neu-ral network solutions in the context of governing equations and Hamiltonian structures, crucial for accurately representing physical systems. The first approach focuses on the structural preservation of the Hamiltonian system, emphasizing the re-lationship between coordinates and momentum in the state-space representation. The second method utilizes Monte Carlo techniques, generating distributions of parameters and external, dissipative forces to validate the neural network model. This provides a robust framework for assessing the neural network's compliance with the governing equations of the physical system it aims to model. A case study involving a simple pendulum is presented to test the proposed validation techniques. The results highlight the importance of aligning the neural network training approach with the relevant validation criteria for the application, as different methods exhibit varying performance in terms of mean squared error, Hamiltonian structure preservation, and derivative-based verification. This nuanced approach underscores the necessity of tailoring neural network training strategies to enhance the reliability of predictions in modeling complex dynamical systems.