Koopman meets polynomial optimization: towards a data-driven analysis of long-term chaotic dynamics
Date and Time: May 27th at 14:15, Seminar Room LFG (12103.00.332)
Speaker: Prof. Dr. Giovanni Fantuzzi, Friedrich-Alexander-Universität Erlangen-Nürnberg
Topic: Estimating long-time averages for chaotic dynamics: A data-driven polynomial optimization approach
Abstract:
When studying dynamical systems that evolve chaotically over time, knowing the average values of key quantities of interest (e.g., energy or power consumption) is often more useful than a detailed simulation. These averages can be predicted without running any simulations using tools from polynomial optimization if we have an explicit model for the dynamics based on polynomial equations. But what if the model isn’t based on polynomial equations or, worse, we don’t know the model at all?
In this talk, I will explain how the situation can be rescued when measurements of the system state are available. The key idea is to combine polynomial optimization with a data-driven technique called “extended dynamic mode decomposition” (EDMD), which approximates the celebrated Koopman operator. I will introduce these tools, show how they work together, and give examples of applications.