An Introduction to the NMPC-graph as general schema for causal modeling of nonlinear, multivariate, dynamic, and recursive systems with focus on time-series prediction

Abstract

While the disciplines of physics and engineering sciences in many cases have taken advantage from accurate time-series prediction by applying ordinary differential equation systems upon precise basic physical laws such approach hardly could be adopted by other scientific disciplines where precise mathematical basic laws are unknown. A new modeling schema, the NMPC-graph, opens the possibility of interdisciplinary and generic nonlinear, multivariate, dynamic, and recursive causal modeling in domains where basic laws are only known as qualitative relationships among parameters while their precise mathematical nature remains undisclosed at modeling time. The symbolism of NMPC-graph is kept simple and suited for analysts without advanced mathematical skills. This article presents the definition of the NMPC-graph modeling method and its six component types. Further, it shows how to solve the inverse problem of deriving a nonlinear ordinary differential equation system from any NMPC-graph in conjunction with historic calibration data by means of machine learning. This article further discusses how such a derived NMPC-model can be used for hypothesis testing and time-series prediction with the expectation of gaining prediction accuracy in comparison to conventional prediction methods.