  To tackle heterogeneous time-dependent problems, an algorithm that constructs
problem-adapted basis functions in an embarrassingly parallel and local manner
in time has recently been proposed in [Schleuss, Smetana, ter Maat, SIAM J.
Sci. Comput., 2022+]. Several simulations of the problem are performed for only
few time steps in parallel by starting at different, randomly drawn start time
points. For this purpose, data-dependent probability distributions that are
based on the (time-dependent) data functions of the problem, such as leverage
scores, are employed. In this paper, we suggest as a key new contribution to
perform a deterministic time point selection based on the (discrete) empirical
interpolation method (DEIM) within the proposed algorithm. In numerical
experiments we investigate the performance of a DEIM based time point selection
and compare it to the leverage score sampling approach.
