Contributed Talks III

Date & Time: Wednesday, September 30, 2026 | 11:00 - 13:00
Place: Campus South, Mathematics Building 20.30 [Englerstraße 02], Room 2.067
Chairs: tba

Speaker: Pascal Jerono (Karlsruhe Institute of Technology) 
Title: Observer design for cell population balance models
Abstract: In control theory, full system state information is a key component for the design of optimal control strategies. In real processes, however, not all system states can typically be measured online due to physical process constraints, insufficient accuracy, or a lack of available sensors. This raises the question of how to design a suitable real-time estimation scheme, called an observer (or software sensor), for reconstructing full system state information from available measurements in processes. In this talk, the observer design problem for the cell mass distribution in a yeast fermentation process is addressed. The cell population dynamics are described by a partial integro-differential equation coupled with a set of nonlinear ordinary differential equations to account for substrate dynamics. Suitable methods for analysis and design of observers for this system class are discussed and considered when the available measurements occur on different time scales and have irregular sampling times. Finally, the observer schemes are validated and integrated into control strategies in lab-scale experiments.

Speaker: Attila Genda (Karlsruhe Institute of Technology) 
Title: Safe basins of coexisting periodic responses in the forced hardening Duffing oscillator
Abstract: The safety of a periodically forced oscillator cannot generally be characterized by a single basin cross-section. When disturbances are expressed relative to a periodic response, the corresponding basin boundary depends on the excitation phase at which the disturbance is applied. This work examines that phase dependence for the coexisting primary-resonant responses of a forced and damped hardening Duffing oscillator. The periodic responses and the saddle separating them are approximated by applying resonance averaging in action-angle coordinates of the underlying nonlinear conservative oscillator. The stable saddle manifold of the averaged system is then mapped back into physical disturbance coordinates. This construction provides both phase-specific safe basins and a phase-independent true safe basin, defined as the set of disturbances that remain within the selected basin of attraction for every excitation phase. In the conservative case, the closed separatrix permits the safe-basin area to be evaluated for both small and non-small actions. For weak damping and small action, a perturbation of the conservative separatrix yields explicit first-order corrections to the relevant manifold passages and to the true-safe-basin boundary. At non-small action, the same construction remains applicable, but its evaluation becomes semi-analytical because the action-angle transformation and the manifold correction involve elliptic functions and trajectory-dependent integrals. Comparisons with direct numerical manifold calculations illustrate the range of validity of the approximations. The results show that damping can either initially enlarge or reduce the true safe basin of the high-amplitude response, depending on the magnitude of the forcing amplitude relative to the frequency detuning. Changes in the active passage of the stable manifold can additionally produce nonsmooth variations in the measured basin size. The analysis therefore relates the robustness of a periodic operating state to the global geometry of its phase-dependent basin boundary.

Speaker: Tom Bdolach (Karlsruhe Institute of Technology) 
Title: Tipping in an adaptive climate network model 
Abstract: With rising global temperatures, Earth’s tipping elements are becoming increasingly more vulnerable to crossing their critical thresholds. The reaching of such tipping points does not only impact other tipping elements through their connections but can also have further effect on the global mean surface temperature (GMT) itself, either increasing or decreasing the probability of further tipping points being reached. Recently, a numerical study analyzing the risk of tipping cascades has been conducted, using a conceptual model describing the dynamics of a tipping element with its interactions with other tipping elements taken into account [N. Wunderling, J. F. Donges, J. Kurths, and R. Winkelmann, Earth Syst. Dyn. 12, 601–619 (2021)]. Here, we extend the model substantially by including adaptation so that the GMT feedback induced by the crossing of a tipping point is incorporated as well. We find that although the adaptive mechanism does not impact the risk for the occurrence of tipping events, large tipping cascades are less probable due to the negative GMT feedback of the ocean circulation systems. Furthermore, several tipping elements can play a different role in cascades in the adaptive model. In particular, the Amazon rainforest could be a trigger in a tipping cascade. Overall, the adaptation mechanism tends to slightly stabilize the network.

Speaker: Christoph Müller (Karlsruhe Institute of Technology) 
Title: Stein based Goodness-of-fit Tests for parametric families of distributions
Abstract: We present a comprehensive framework for goodness-of-fit testing for parametric families of distributions based on Cramér-von-Mises-type statistics and Stein operators. We derive the asymptotic null distribution of the proposed test statistic, which depends on an unknown parameter. To overcome this difficulty, we develop bootstrap procedures and establish their asymptotic validity. We conclude the general part by establishing consistency of the proposed test against fixed alternatives.

The second part of the talk focuses on important special cases in which the general framework simplifies considerably. These connections highlight and unify a variety of existing goodness-of-fit tests proposed in the literature for specific parametric families. Finally, we present Monte Carlo studies for several well-known distributions illustrating the finite-sample performance and power of the proposed procedures.

This talk is based on joint research with Bruno Ebner and Mathias Trabs.