  High-performance scientific simulations, important for comprehension of
complex systems, encounter computational challenges especially when exploring
extensive parameter spaces. There has been an increasing interest in developing
deep neural networks (DNNs) as surrogate models capable of accelerating the
simulations. However, existing approaches for training these DNN surrogates
rely on extensive simulation data which are heuristically selected and
generated with expensive computation -- a challenge under-explored in the
literature. In this paper, we investigate the potential of incorporating active
learning into DNN surrogate training. This allows intelligent and objective
selection of training simulations, reducing the need to generate extensive
simulation data as well as the dependency of the performance of DNN surrogates
on pre-defined training simulations. In the problem context of constructing DNN
surrogates for diffusion equations with sources, we examine the efficacy of
diversity- and uncertainty-based strategies for selecting training simulations,
considering two different DNN architecture. The results set the groundwork for
developing the high-performance computing infrastructure for Smart Surrogates
that supports on-the-fly generation of simulation data steered by active
learning strategies to potentially improve the efficiency of scientific
simulations.
