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While the disciplines of physics and engineering sciences in many cases havetaken advantage from accurate time-series prediction of system behaviour byapplying ordinary differential equation systems upon precise basic physicallaws such approach hardly could be adopted by other scientific disciplineswhere precise mathematical basic laws are unknown. A new modelling schema, theNMPC-graph, opens the possibility of interdisciplinary and generic nonlinear,multivariate, dynamic, and recursive causal modelling in domains where basiclaws are only known as qualitative relationships among parameters while theirprecise mathematical nature remains undisclosed at modelling time. Thesymbolism of NMPC-graph is kept simple and suited for analysts without advancedmathematical skills. This article presents the definition of the NMPC-graphmodelling method and its six component types. Further, it shows how to solvethe inverse problem of deriving a nonlinear ordinary differential equationsystem from any NMPC-graph in conjunction with historic calibration data bymeans of machine learning. This article further discusses how such a derivedNMPC-model can be used for hypothesis testing and time-series prediction withthe expectation of gaining prediction accuracy in comparison to conventionalprediction methods.

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