Christoph Jahnz

Christoph Jahnz

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.

Christoph Jahnz

Intelligence can be understood as an agent's ability to predict its environment's dynamic by a level of precision which allows it to effectively foresee opportunities and threats. Under the assumption that such intelligence relies on a knowledge space any effective reasoning would benefit from a maximum portion of useful and a minimum portion of misleading knowledge fragments. It begs the question of how the quality of such knowledge space can be kept high as the amount of knowledge keeps growing. This article proposes a mathematical model to describe general principles of how quality of a growing knowledge space evolves depending on error rate, error propagation and countermeasures. There is also shown to which extend the quality of a knowledge space collapses as removal of low quality knowledge fragments occurs too slowly for a given knowledge space's growth rate.