Friday, September 29, 2023, 9:00 - 13:00

Hörsaal II, Albertstr. 23b, 79104 Freiburg

The aim of this internal interdisciplinary research workshop between different departments of the university is to present to each other different stochastic system formulations and estimation techniques, to detect similarities and differences, and to spot research synergies between the different research divisions.

**Program **

(abstracts below)

08:30-09:00 (Optional Coffee in Mensa Institutsviertel)

09:00-09:30 Short introductions by all participants

09:30-10:10 Tanja Schilling: How to make noise

10:10-10:50 Alexander Rohrbach: Extracting friction and stiffness changes from Brownian particle trajectories

10:50-11:20 Break

11:20-12:00 Lilli Frison: Learning-based real-time control of unknown nonlinear systems

12:00-12:20 Moritz Diehl: Generic stochastic system models in discrete time

12:30-12:50 Leo Simpson: An Efficient Method for the Joint Estimation of System Parameters and Noise Covariances for Linear Time-Variant Systems

12:50-13:00 Wrap-Up

13:00-14:00 Joint Lunch in Mensa Institutsviertel

*Participants: Mario Brehm, Moritz Diehl, Lilli Frison, Subhro Ghosh, Dirk Lebiedz, Alexander Rohrbach, Tanja Schilling, Leo Simpson*

**Abstracts:**

**How to make noise**

Tanja Schilling (Department of Physics, University of Freiburg)

In physics, we hardly ever describe a system in terms of all of its microscopic degrees of freedom. We usually resort to effective coarse-grained models, which predict the behaviour of "relevant" system properties. One widely used effective equation of motion for coarse-grained variables is the Langevin equation, a stochastic differential equation, in which the effect of the neglected degrees of freedom is encoded in friction terms and stochastic noise.

I will review the steps of derivation and approximation that are required to obtain the Langevin equation from a system's microscopic description. I will discuss the interplay between the potential of mean force and the memory kernel, the range of validity of the second fluctuation dissipation theorem, and the stochastic interpretation of the fluctuating force, i.e. the noise.

**Extracting friction and stiffness changes from Brownian particle trajectories**

Alexander Rohrbach (IMTEK, University of Freiburg)

With a so-called photonic force microscope, we optically trap small particles and move them close to an interaction partner, such as the periphery of the cell or a functionalized surface. By measuring the thermal position fluctuations of the particle in three dimensions with nanometer precision and at 2 MHz, we record a lot of information about the soft interaction of the particle with its local environment. Neglecting the particle mass, we setup mathematical models to recover or extract the underlying forces and the changing friction factors that encode the Brownian motion of the particle.

Accepting a 10-30% error, we simplify the problem by i) assuming quasi-thermal equilibrium, and ii) by linearizing the stochastic differential equations.

In this talk I will introduce and explain our procedures to extract important parameters and the occurring problems with the help of some examples.

**Learning-based real-time control of unknown nonlinear systems**

Lilli Frison (Fraunhofer ISE & IMTEK, University of Freiburg)

I will present two problems in building and heating systems (building heating control and control of coating processes) that due to their unknown system behavior or high uncertainty require learning based system identification. The goal of the talk is to identify control challenges for future research activities.

**Generic stochastic system models in discrete time**

Moritz Diehl (IMTEK and Department of Mathematics, University of Freiburg)

This talk will review standard formulations for stochastic system models in discrete time which are at the core of engineering estimation technologies such as Kalman filtering and learning based time series predictions.

**An Efficient Method for the Joint Estimation of System Parameters and Noise Covariances for Linear Time-Variant Systems**

Leo Simpson (Tool Temp AG, Switzerland & IMTEK, University of Freiburg)

An optimization-based method for the joint estimation of system parameters and noise covariances of linear time-variant systems will be presented.

Given measured data, this method maximizes the likelihood of the parameters. We solve the optimization problem of interest via a novel structure-exploiting solver.

We present the advantages of the proposed approach over commonly used methods in the framework of Moving Horizon Estimation.

Finally, we show the performance of the method through numerical simulations on a realistic example of a thermal system.

Through the presentation, different tutorial examples will be used to illustrate the benefits of this method.

This presentation will be based on a recent submission: https://arxiv.org/abs/2211.12302