The lecture deals with the so-called Taylor Map (TM) approach for solving systems of ordinary differential equations and their inverse problems.  The method for inverse problems applies even if the underlying ordinary differential equation is partially or completely not explicitly known which is the case with many technical applications. This procedure is interpreted in terms of Polynomial Neural Networks (PNNs). The physical knowledge is incorporated into the network since its architecture is designed on directly top of the Taylor Map approach.

This does not only improve the data efficiency but also reduce the effort of the included training procedure.  On this basis we demonstrate the application on a system of catalytic reaction equations to highlight the capabilities of this method in practice. Thus, the PNN approach can also be used as a meta or surrogate model.

Prof Iben received his PhD in numerical mathematics from Otto-von-Guericke University, Magdeburg. Since 1999, he worked as an engineer and Chief Expert for Cavitation and multi-phase flow - Corporate Research at Robert Bosch GmbH.

From 2016-2020, he was the Head of Research and Technology Offices in Russia, and since 2020, the Chief Expert in Applied Mathematics, and Honorarium Professor at Stuttgart University.