  In energy intensive industrial systems, an evaporative cooling process may
introduce operational flexibility. Such flexibility refers to a systems ability
to deviate from its scheduled energy consumption. Identifying the flexibility,
and therefore, designing control that ensures efficient and reliable operation
presents a great challenge due to the inherently complex dynamics of industrial
systems. Recently, machine learning models have attracted attention for
identifying flexibility, due to their ability to model complex nonlinear
behavior. This research presents machine learning based methods that integrate
system dynamics into the machine learning models (e.g., Neural Networks) for
better adherence to physical constraints. We define and evaluate physics
informed long-short term memory networks (PhyLSTM) and physics informed neural
networks (PhyNN) for the identification of flexibility in the evaporative
cooling process. These physics informed networks approximate the time-dependent
relationship between control input and system response while enforcing the
dynamics of the process in the neural network architecture. Our proposed
PhyLSTM provides less than 2% system response estimation error, converges in
less than half iterations compared to a baseline Neural Network (NN), and
accurately estimates the defined flexibility metrics. We include a detailed
analysis of the impact of training data size on the performance and
optimization of our proposed models.
