  Identifying the dynamics of physical systems requires a machine learning
model that can assimilate observational data, but also incorporate the laws of
physics. Neural Networks based on physical principles such as the Hamiltonian
or Lagrangian NNs have recently shown promising results in generating
extrapolative predictions and accurately representing the system's dynamics. We
show that by additionally considering the actual energy level as a
regularization term during training and thus using physical information as
inductive bias, the results can be further improved. Especially in the case
where only small amounts of data are available, these improvements can
significantly enhance the predictive capability. We apply the proposed
regularization term to a Hamiltonian Neural Network (HNN) and Constrained
Hamiltonian Neural Network (CHHN) for a single and double pendulum, generate
predictions under unseen initial conditions and report significant gains in
predictive accuracy.
