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

TL;DR

The paper introduces the NMPC-graph, a flexible causal modelling schema for nonlinear, multivariate, dynamic systems that can be derived from qualitative relationships and used for accurate time-series prediction without requiring detailed mathematical laws.

Contribution

It presents the definition of the NMPC-graph, its components, and a machine learning approach to derive differential equations from it, enabling interdisciplinary causal modelling.

Findings

NMPC-graph enables causal modelling with qualitative data.

Machine learning can derive differential equations from NMPC-graphs.

Predictions using NMPC-graph show improved accuracy over traditional methods.

Abstract

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.