Taylor Mapping and Polynomial Neural Networks for solution of forward and inverse ODE problems

CY-MATHS-IN seminar series

January 31st, at 1pm Nicosia time, Eastern European Time EET (UTC+02:00)
The talk will be held online on zoom  https://zoom.us/j/9947402955?pwd=Um8wdTdHeStFMTM3LzNRL3l3Umc5QT09 
It is also advertised on our LinkedIn profile: https://www.linkedin.com/events/profuweiben-sseminar7019269714803634176/

Abstract: 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.

Bio: Master and PhD in numerical mathematics (Moscow State University and Technical University of Dresden), PhD in thermodynamics (Otto-von-Guericke University Magdeburg); since 1999 engineer and Chief Expert for Cavitation and multi-phase flow – Corporate Research at Robert Bosch GmbH, 2016-2020 Head of Research and Technology Offices in Russia, since 2020 Chief Expert Applied Mathematics, Honorarium Professor at Stuttgart University; H-index: 15; i10-index: 20