Accurate Replication of Simulations of Governing Equations of Processes in Industry 4.0 Environments with ANNs for Enhanced Monitoring and Control

Complex governing equations of physical phenomena like the Navier-Stokes' or Maxwell's equations can be numerically solved to yield detailed information on the characteristic variables of a process in the process domain interior, when the values at the boundary are known. This cannot be achieved in real time making it unamenable to achieve true benefits under Industry 4.0 where measured variables are available instantaneously at process boundaries but information in the domain interior is unobtainable for monitoring, control and optimization functions. The Universal Approximation Theorem provides a unique capability to Artificial Neural Networks - the ability to replicate the functionality of arbitrarily complex functions - including those represented by the above governing equations. A trained ANN can in principle replicate this functionality with high accuracy in milliseconds - hence can serve as the method of choice in Industry 4.0 frameworks to acquire characteristic process variables within the domain interior when boundary values are known from sensory inputs. This is however a concept still to be proven. This work intends to demonstrate this principle through numerical experimentation on a physical example that can be easily generalized.