Lagrangian and Hamiltonian Neural Networks With a Dissipative System
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.