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.
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