  Physics informed neural networks (PINNs) have proven to be an efficient tool
to represent problems for which measured data are available and for which the
dynamics in the data are expected to follow some physical laws. In this paper,
we suggest a multiobjective perspective on the training of PINNs by treating
the data loss and the residual loss as two individual objective functions in a
truly biobjective optimization approach. As a showcase example, we consider
COVID-19 predictions in Germany and built an extended
susceptibles-infected-recovered (SIR) model with additionally considered
leaky-vaccinated and hospitalized populations (SVIHR model) to model the
transition rates and to predict future infections. SIR-type models are
expressed by systems of ordinary differential equations (ODEs). We investigate
the suitability of the generated PINN for COVID-19 predictions and compare the
resulting predicted curves with those obtained by applying the method of
non-standard finite differences to the system of ODEs and initial data. The
approach is applicable to various systems of ODEs that define dynamical
regimes. Those regimes do not need to be SIR-type models, and the corresponding
underlying data sets do not have to be associated with COVID-19.
