  The field of deep learning has become increasingly important for particle
physics experiments, yielding a multitude of advances, predominantly in event
classification and reconstruction tasks. Many of these applications have been
adopted from other domains. However, data in the field of physics are unique in
the context of machine learning, insofar as their generation process and the
laws and symmetries they abide by are usually well understood. Most commonly
used deep learning architectures fail at utilizing this available information.
In contrast, more traditional likelihood-based methods are capable of
exploiting domain knowledge, but they are often limited by computational
complexity. In this contribution, a hybrid approach is presented that utilizes
generative neural networks to approximate the likelihood, which may then be
used in a traditional maximum-likelihood setting. Domain knowledge, such as
invariances and detector characteristics, can easily be incorporated in this
approach. The hybrid approach is illustrated by the example of event
reconstruction in IceCube.
