Conceptual models for most physical systems are based on a continuum; values of the states of a system are assumed to be real numbers.

At the same time science is increasingly becoming data driven and thus based on finite information. Traditional, analytical analysis of dynamical systems is possible only when the mathematical model of the dynamics is available. Frequently, in particular in experimental sciences, in biological, in sociological sciences or in medicine, this is rarely the case. Instead, scientists collect data by experiments. This suggests the need for tools that seamlessly and systematically provide information about continuous structures from finite data and accounts for the rapid rise in use of methods from topological data analysis. In this context sampled dynamics attracts interest of scientists.

Not surprisingly, however, there are significant challenges associated with understanding of the data dynamics.

The aim of the talk is to present recent developments in the Conley index theory for multivalued maps and its applications to the study of dynamical systems known only from data. Moreover, we will tackle Gaussian process surrogate modeling in sampled dynamics.
Meeting ID: 852 4277 3200 Passcode: 103121