  The Model Order Reduction (MOR) technique can provide compact numerical
models for fast simulation. Different from the intrusive MOR methods, the
non-intrusive MOR does not require access to the Full Order Models (FOMs),
especially system matrices. Since the non-intrusive MOR methods strongly rely
on the snapshots of the FOMs, constructing good snapshot sets becomes crucial.
In this work, we propose a new active learning approach with two novelties. A
novel idea with our approach is the use of single-time step snapshots from the
system states taken from an estimation of the reduced-state space. These states
are selected using a greedy strategy supported by an error estimator based
Gaussian Process Regression (GPR). Additionally, we introduce a use
case-independent validation strategy based on Probably Approximately Correct
(PAC) learning. In this work, we use Artificial Neural Networks (ANNs) to
identify the Reduced Order Model (ROM), however the method could be similarly
applied to other ROM identification methods. The performance of the whole
workflow is tested by a 2-D thermal conduction and a 3-D vacuum furnace model.
With little required user interaction and a training strategy independent to a
specific use case, the proposed method offers a huge potential for industrial
usage to create so-called executable Digital Twins (DTs).
