This is a three-part talk where I’ll cover piecewise-linear maps, mechanical systems with impacts, and neurons. Piecewise-linear maps provide a useful tool to explore robust chaos in dynamical systems. One such map is the two-dimensional border-collision normal form which exhibits bifurcation structures that are still not fully understood. In this talk, I will first show how renormalization can be utilized to better understand these. I will also verify Devaney’s definition of chaos, and how robust chaos extends to maps with higher dimensions. In the second part of my talk, I will discuss simple impacting systems that occur in engineering problems. Impacts are onset by grazing bifurcations, and these generate complex dynamics including chaos because the corresponding Poincare map has a highly nonlinear and destabilising square-root term. The main goal of this talk is to determine why leading-order approximations to such maps, such as the Nordmark map, are often only effective in extremely small parameter ranges. This can be caused by a resonance effect, resulting in nearby period-doubling and saddle-node bifurcations. To numerically continue the curves of these bifurcations, we found it necessary to develop a new tool that allows us to use root-finding methods such as Newton's without the method falling off the side of the square root. Finally, in the last part of my talk, I will explore a two-dimensional Chialvo neuron map and how different bifurcation scenarios occur on perturbing the map with electromagnetic flux.

CAR T-cell therapy, based on genetically engineered T cells, has demonstrated significant potential in treating hematological malignancies, including B-cell lymphomas. This treatment has a complex lonoutudinal dynamics due to the interplay of different T-cell phenotypes (effector and memory), the expansion of the drug and the cytotoxic effect on both normal and cancerous B-cells, the exhaustion of the immune cells, the tumor immunosupressive environments, and more. Thus, the outcome of the therapy is not yet well understood leading to a variety of responses ranging from sustained complete responses, different types of partial responses, or no response at all. We developed a mechanistic model for the interaction between CAR T- and tumorous B-cells, accounting for the role of the tumor morphology. Simulations showed that tumor lesions with irregular shapes could contribute to treatment variability by increasing their immunosuppressive capabilities impairing CAR T-cell efficacy. This finding is consistent with our analysis of 18F-FDG PET/CT imaging data from 63 relapsed/refractory diffuse large B-cell lymphoma patients receiving CAR T-cells.

Multi Objective Optimization for Intra Day Scheduling of Residential PV Battery Systems The increasing integration of renewable energy into the electricity grid poses stability challenges due to their inherent volatility. Residential PV-battery systems can help address these issues by dynamically responding to forecast deviations and uncertainties. This thesis builds upon a novel stochastic optimization approach, where the key innovation lies in the asymmetric allocation of uncertainty between the battery system and the power grid, enabled through mixed random variables. The proposed method extends this approach by additionally incorporating an intraday scheduling framework. Based on probabilistic forecasts of the combined production and consumption of the household – which will be referred to as prosumption – the original model provides stochastic schedules for both the grid and battery system over a 24-hour horizon. The intraday approach then consecutively solves optimization problems that update these schedules, all while considering new real time measurements and forecasts. To analyse the interplay of the conflicting objectives of promoting self-sufficiency while ensuring grid stability, various multi objective optimization (MOO) techniques will be implemented. The MOO setting will be combined with sequential decision-making techniques to properly model the consecutive intra-day approach. The effectiveness of this approach will be assessed using sample forecast scenarios.

Combining Bayesian principles with the power of deep learning has long been an attractive direction of research, but its real-world impact has fallen short of the promises. Especially in the context of uncertainty estimation, there seem to be simpler methods that perform at least as well. In this talk, I want to argue that uncertainties are not the only reason to use Bayesian deep learning models, but that they also offer improved model selection and incorporation of prior knowledge. I will showcase these benefits supported by the results of two recent papers and situate them in the context of current research trends in Bayesian deep learning. \[ \] Bio: Vincent Fortuin is a tenure-track research group leader at Helmholtz AI in Munich, leading the group for Efficient Learning and Probabilistic Inference for Science (ELPIS), and a faculty member at the Technical University of Munich. He is also a Branco Weiss Fellow, an ELLIS Scholar, a Fellow of the Konrad Zuse School of Excellence in Reliable AI, and a Senior Researcher at the Munich Center for Machine Learning. His research focuses on reliable and data-efficient AI approaches, leveraging Bayesian deep learning, deep generative modeling, meta-learning, and PAC-Bayesian theory. Before that, he did his PhD in Machine Learning at ETH Zürich and was a Research Fellow at the University of Cambridge. He is a regular reviewer and area chair for all major machine learning conferences, an action editor for TMLR, and a co-organizer of the Symposium on Advances in Approximate Bayesian Inference (AABI) and the ICBINB initiative.