🤖 AI Summary
This study addresses the challenge of reduced-order modeling for non-autonomous nonlinear dynamical systems by proposing a latent-space Lagrangian framework. The method jointly learns latent coordinates and an energy network, incorporating the principle of virtual work to ensure physical consistency. Furthermore, a force supervision mechanism replaces conventional ODE solvers, thereby eliminating the reliance on numerical integration during training. Experimental results demonstrate that the proposed framework accurately captures complex nonlinear dynamics while exhibiting strong generalization to unseen external forces and initial conditions.
📝 Abstract
This work proposes a latent Lagrangian-based framework for reduced-order modelling of forced nonlinear dynamical systems. In contrast with conventional Lagrangian or Hamiltonian neural networks, our approach learns a set of latent coordinates sufficient to capture the dynamics conjointly with two neural networks for the latent kinetic and latent potential energies, and leverages force supervision to eliminate the need for an ODE solver during training. Consistency of physical laws in the latent space is ensured through the principle of virtual work. Results show that the model effectively learns the subtle dynamics induced by the system's nonlinearity and non-convex potential energy, and generalizes well to unseen forces and initial conditions. These observations confirm the physical relevance of the proposed approach, and its interest for model reduction.