  Recent literature has explored various ways to improve soft sensors by
utilizing learning algorithms with transferability. A performance gain is
generally attained when knowledge is transferred among strongly related soft
sensor learning tasks. A particularly relevant case for transferability is when
developing soft sensors of the same type for similar, but physically different
processes or units. Then, the data from each unit presents a soft sensor
learning task, and it is reasonable to expect strongly related tasks. Applying
methods that exploit transferability in this setting leads to what we call
multi-unit soft sensing.
  This paper formulates multi-unit soft sensing as a probabilistic,
hierarchical model, which we implement using a deep neural network. The
learning capabilities of the model are studied empirically on a large-scale
industrial case by developing virtual flow meters (a type of soft sensor) for
80 petroleum wells. We investigate how the model generalizes with the number of
wells/units. Interestingly, we demonstrate that multi-unit models learned from
data from many wells, permit few-shot learning of virtual flow meters for new
wells. Surprisingly, regarding the difficulty of the tasks, few-shot learning
on 1-3 data points often leads to high performance on new wells.
