  Identifying the underlying dynamics of physical systems can be challenging
when only provided with observational data. In this work, we consider systems
that can be modelled as first-order ordinary differential equations. By
assuming a certain pseudo-Hamiltonian formulation, we are able to learn the
analytic terms of internal dynamics even if the model is trained on data where
the system is affected by unknown damping and external disturbances. In cases
where it is difficult to find analytic terms for the disturbances, a hybrid
model that uses a neural network to learn these can still accurately identify
the dynamics of the system as if under ideal conditions. This makes the models
applicable in some situations where other system identification models fail.
Furthermore, we propose to use a fourth-order symmetric integration scheme in
the loss function and avoid actual integration in the training, and demonstrate
on varied examples how this leads to increased performance on noisy data.
