  While the disciplines of physics and engineering sciences in many cases have
taken advantage from accurate time-series prediction of system behaviour 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 modelling schema, the
NMPC-graph, opens the possibility of interdisciplinary and generic nonlinear,
multivariate, dynamic, and recursive causal modelling in domains where basic
laws are only known as qualitative relationships among parameters while their
precise mathematical nature remains undisclosed at modelling 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
modelling 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.
