Equilibrium Propagation for Learning in Lagrangian Dynamical Systems
This work addresses training challenges in Lagrangian dynamical systems, particularly for periodic boundary conditions or fixed states, but appears incremental as it builds on existing Equilibrium Propagation methods.
The authors tackled the problem of training dynamical systems governed by Lagrangian mechanics by extending Equilibrium Propagation to handle dynamical trajectories, enabling efficient parameter updates without explicit backpropagation through time.
We propose a method for training dynamical systems governed by Lagrangian mechanics using Equilibrium Propagation. Our approach extends Equilibrium Propagation - initially developed for energy-based models - to dynamical trajectories by leveraging the principle of action extremization. Training is achieved by gently nudging trajectories toward desired targets and measuring how the variables conjugate to the parameters to be trained respond. This method is particularly suited to systems with periodic boundary conditions or fixed initial and final states, enabling efficient parameter updates without requiring explicit backpropagation through time. In the case of periodic boundary conditions, this approach yields the semiclassical limit of Quantum Equilibrium Propagation. Applications to systems with dissipation are also discussed.