Dynamische Systeme in verschiedenen Maßstäben: Komplexität, Klima und Leben

Discover how simple microscopic rules give rise to large-scale order, phase transitions, and critical phenomena.

How do order and patterns emerge in nature from simple microscopic rules? This course explores the fascinating world of phase transitions and critical phenomena — from magnetism to complex systems — through the lens of statistical physics. Students will be introduced to central concepts such as order parameters, universality, and the maximum entropy principle, while learning powerful tools including the Ising model, mean-field theory, renormalization group methods, and statistical field theory. A mix of theory, calculations, and computational exercises ensures a well-rounded understanding.

This course will be held by Professor Wiesner and Professor Härter, and will be available in the modules 741c, 741e, VMD921. The course will encompass 4 SWS or 6 LP.

Learn the foundations of modern neural networks and their applications to physics through theory and coding practice.

How can modern machine learning help us understand and solve problems in physics? This seminar offers a step-by-step introduction to learning systems with a special focus on neural networks. Students will gain insights into statistical learning concepts such as symbolic regression and Gaussian mixtures, explore the physics-inspired perspective of Boltzmann machines, and study state-of-the-art architectures including convolutional networks, recurrent networks (LSTMs), and transformers. Alongside theory, participants will engage with practical coding exercises and optimization algorithms, building hands-on experience with methods that power today’s breakthroughs in data analysis, prediction, and artificial intelligence.

This course will be held by Dr. Abel, and will be available in the module 711. The course will encompass 2 SWS or 3 LP.

Uncover the universal rules behind oscillations, chaos, and emergent patterns in nonlinear systems.

Why do so many systems in nature and technology behave in complex, unpredictable ways? This course introduces the universal principles of nonlinear dynamics, including multistability, oscillations, chaos, and spatiotemporal pattern formation. Using examples ranging from climate and power grids to living organisms and the brain, students will learn how nonlinear rules give rise to emergent behavior, and how changes in system parameters can transform dynamics. The course provides conceptual insights and practical tools for analyzing nonlinear phenomena across disciplines.

This course will be held by Dr. Omelchenko, and will be available in the modules 541c (Bachelors) and 731c (Masters). In the Master Program, this course will encompass 4 SWS or 6 LP.

Gain powerful tools to model randomness in physical and biological systems using advanced stochastic methods.

How can randomness be systematically described and harnessed to understand complex systems? This course introduces students to advanced methods of stochastic process modeling, with an emphasis on applications in biological physics. Starting from probability theory, the course covers balance equations for Markov processes, the Master and Fokker–Planck equations, and Langevin dynamics. Students will also explore renewal processes and their role in random transport phenomena. Tutorials provide hands-on practice with both analytical derivations and numerical simulations, equipping students with versatile tools for research in physics and beyond.

This course will be held by Dr.Cherstvy and Dr. Großmann, and will be available in the modules 541c (Bachelors) and 731c (Masters). In the Master Program, this course will encompass 4 SWS or 6 LP.

Learn how the Earth’s climate system is represented, simulated, and studied through numerical modeling.

How can we simulate the dynamics of our planet’s climate system? This course introduces the theoretical foundations, practical methods, and applications of numerical modeling in climate science. Students will explore how the coupled Earth system and its components are represented in models, and gain hands-on experience through practical exercises in Earth system simulations. The course highlights both the power and the challenges of modeling climate processes, preparing students to engage with one of the most pressing scientific issues of our time.

This course will be held by Professor Feulner and will be available in the module 741c or 741e. The course will encompass 4 SWS or 6 LP.

Investigate how fractals, diffusion, and self-organized criticality explain complexity in social and climate systems.

How do large-scale patterns arise from simple local interactions? This course explores the physics of emergent phenomena across space and time, from fractals and diffusion to percolation, self-organized criticality, and collective dynamics in social and climate systems. Students will study classic models such as random walks, sandpile models, and forest fire dynamics, and apply concepts like the Hurst exponent and central limit theorem to diverse real-world contexts — from fracture processes and disease spreading to financial markets and opinion dynamics. Through theory, examples, and computational exercises, the course provides deep insight into how complexity emerges across natural and social systems.

This course will be held by Professor Härter and Professor Wiesner and will be available in the module 741c, 741e, 731c and 731z. The course will encompass 4 SWS or 6 LP.