Variational Structure-Preserving Neural Networks for Forced Lagrangian Systems

Structure-preserving machine learning has recently become an active area of research. Popular models in this field, such as Hamiltonian neural networks, would typically require data on the system’s momentum and this can be a limitation of the approach.

Instead, we consider a method for learning the differential equations describing the dynamics of a forced Lagrangian system. The method requires time-series measurements of the system’s position only and can learn external forces, e.g., dissipative frictional forces.