Lagrangian and Hamiltonian Neural Networks With a Dissipative System

We investigate the applicability of Lagrangian and Hamiltonian Neural Network models to a dissipative system that has explicit time dependence in its Lagrangian, Hamiltonian, and total energy. To do so we consider these neural network models for simulated systems of a harmonic one-dimensional, one-component oscillator with damping, as well as without damping for comparison. We find that both the Lagrangian and Hamiltonian approaches are able to predict the empirical physical behavior of the damped oscillator systems and to effectively ``learn'' to varying degrees the underlying Lagrangians and Hamiltonians, as has previously been shown to be the case with undamped oscillator systems. These investigations elucidate important properties of Lagrangian and Hamiltonian mechanics, including properties that are not manifest when considering systems without explicit time dependence.