Wir freuen uns, bekannt zu geben, dass Dr. Timo Schorlepp, Courant Instructor und Assistant Professor an der New York University, den Dissertationspreis der Fakultät 2024 erhalten hat. In seiner Arbeit hat er sich damit beschäftigt, wie man mithilfe von Instantonen und Fluktuationen seltene Ereignisse in komplexen Systemen vorhersagen kann.
Predicting probabilities and typical shapes of rare but impactful events – such as high waves and strong vortices in fluid flows, or extreme climate events – is an important challenge across
many scientific and engineering disciplines. A principled framework to address these problems in stochastic systems is given by large deviation theory. Here, extreme event probabilities are
approximated by focusing on the most probable path, the „instanton“, that leads to a prescribed outcome. My doctoral thesis focused, among other things, on: (i) robust
instanton calculations via optimal control techniques, and (ii) more precise probability estimates by exactly calculating Gaussian fluctuations around the instanton, using Riccati
equations and Fredholm determinants. These methods will be illustrated through examples of extreme events in fluid turbulence (Burgers and Navier-Stokes equations) and nonlinear
interface growth (Kardar-Parisi-Zhang equation). The broad goal of this work is to provide more robust and precise predictions for rare phenomena in complex systems.
Abstract von Dr. Schorlepp.