Nonlinear Frontiers

From Dynamical Systems, Information and Complexity to Cutting-Edge Physically Cognitive Artificial Intelligence

Analysing and modelling complex systems often reach technical and theoretical limits under state-of-the-art statistical and computational methods. Their underlying assumptions often encompass structural-functional symmetries and recurrence. However, until very recently the dynamics and predictability of far-from-equilibrium non-ergodic entanglement and coevolution remained elusive.

Our recent advances, ranging from theoretical physics to information theory and cognition, have overcome these issues. This program disseminates our novel theories and applications to empower cutting-edge analysis, modelling and decision support pertaining complex real-world problems.

A set of cutting-edge methodologies is laid out for rigorous analysis and modelling complex dynamic systems, associated predictability and uncertainty, along with the underlying theoretical background and enabling technologies. These enable the robust retrieval and investigation of fundamental dynamic mechanisms and interactions, extending predictability limits and empowering new choices for improving decision support pathways.

The program will guide participants along an excursion through nonlinear frontiers in complex system science, ranging from fundamental physics to artificial intelligence and new cutting-edge developments. We further invite participants to bring their own data, problems and application questions to explore hands-on implementation of the concepts and tools to their fields of interest.

Scholarship support is available to co-sponsor top–tier candidates. For further information, queries and quotes contact:


Module 1: From Dynamical Systems to Information Theory & Complexity

Fundamentals from dynamical systems, information theory, thermodynamics and complexity.

Module 2: Information Physics and Coevolutionary Dynamical Dystems

When invariants of motion are no longer so: mathematical physics of complex coevolutionary systems.

Module 3: Information Retrieval and Model Design in Complex Systems 

From deep machine learning and artificial intelligence to information theoretical evolutionary cognition.

Module 4: Reconciling Artificial Intelligence with Fundamental Physics

New frontiers in mathematical and information physics for realistic cognition, discovery and design.

Module 5: Interdisciplinary Solutions across nature, society & technology

From Earth system dynamics and extremes to socio-environmental modelling and decision support.

Duration: 50 hours + self-practice.

Editions: A) Academic; B) Business.

Chair: Prof. Dr. Rui A. P. Perdigão.

Next Course: Spring Semester 2021

Applications now open for Spring 2021:

Block Course at Karlsruhe Institute of Technology (KIT)

Combining Modern Statistical Methods and Thermodynamic Principles
for Dynamic System Analysis in Environmental Sciences

Analysing complex and dynamic environmental systems often reaches technical and theoretical limits of statistical standard tools. This is the case as most classical statistical approaches fundamentally require assumptions about statistical independence and stationarity, which are especially problematic as soon as we deal with non-linearity and coevolution. Many promising approaches founded in scientific fields ranging from theoretical physics to information theory have been developed. Still, their application to applied climate and environmental sciences remains challenging.

This 4-day block course will introduce a set of modern tools for rigorous analyses of dynamic systems. Starting off with examples from geophysics and fluid mechanics the course will guide you during an excursion through stochastic physics, information theory, phase-state analyses and applications with big data and scaling. We especially invite you to bring own data and application questions to provide hands-on utilisation of the concepts and tools within your field of research.



Day 1 – From fluid mechanics to dynamical systems

The first day ensures a common basis for all participants. With fundamentals from classical fluid dynamics, thermodynamics, stability and scaling laws the foundation is laid.
The day will consist of four teaching units with practical analytical and numerical examples across the earth sciences.

Day 2 – Coevolutionary dynamical systems

The second day will extend the classical fluid dynamics with stochastic physics and information theory. With this, complexity will be rigorously treated in a simple and coherent framework providing the physical background to coevolutionary dynamics and organisation.

The day will consist of two teaching units and two real-world application cases.

Day 3 – Mastering conjugated dimensions

The third day will redefine the state-space system analyses with physical princi- ples and thermodynamic limits as true phase-state analyses towards dynamic system understanding without the requirement for single attractors, finite pha- ses and fixed scales. It also includes conjugated pairs and a new breed of non- paired conjugates.

The day will consist of two teaching units, one unit with real-world applications and one unit transferring the approaches to own analyses of the participants. Evening: Preparation of applications to own data.

Day 4 – Presentations and frontier topics

The fourth day will start with two units presenting first results of applications to own data. Subsequently frontier topics of scaling and big data applications will be tackled.

Evening: Discussion of possible collaboration and emerging aspects.


Lecturer: Rui A. P. Perdigão

[See related courses by Rui Perdigão e.g. on Information Physics]

Schedule: 27 February – 2 March, 2018

Hosted by:

GRACE – Graduate School for Climate and Environment
Engesserstr. 6, 76131 Karlsruhe – T+49-721-608-43676 – F+49-721-608-48475

Karlsruhe Institute of Technology (KIT)