Network Thermodynamics, Optimality Principles, and Neural Networks

Our process modeling framework integrates thermodynamic principles with neural network based learning. The process network topology is represented using a graph. The question we want to address is whether there is a natural objective function that is minimized by the network and how we can change this objective function using feedback control. We show that the non-equilibrium entropy production is minimized. We then illustrate how distributed control algorithms steer the system’s equilibrium towards engineered objectives. The basic requirement is that the flow conditions can be expressed in terms of conic sector (passivity) conditions. System specific constitutive equations are learned by the neural ordinary differential equation algorithm using the adjoint method in combination with an adaptive ODE solver using synthetic time-series data. The Neural ODE system was trained in Google Co-Lab using cloud GPU’s.