🤖 AI Summary
This study addresses the limitation of conventional Lagrangian and Hamiltonian neural networks, which are restricted to non-dissipative systems and struggle to model explicitly time-dependent dissipative dynamics. To overcome this, the proposed approach extends these network architectures to time-varying dissipative systems, with validation conducted through comparative simulations of damped and undamped harmonic oscillators. The resulting model successfully predicts the physical behavior of damped systems while effectively learning the underlying Lagrangian and Hamiltonian functions, thereby revealing novel characteristics of time-dependent dissipative mechanisms. By transcending the theoretical constraints inherent to conservative systems, this work establishes a new paradigm for discovering physical laws governing complex dissipative dynamics.
📝 Abstract
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.