Turbulence, Extreme Wave and Heart Rhythm – Predictions for Irregularities TU Braunschweig develops modeling methodology for dynamic systems
How do you model a turbulent stream? How do you detect irregularities in a heartbeat? And how can you predict a rogue wave? Predicting the behavior for these examples of so-called complex and nonlinear dynamic systems has been difficult until now. Scientists at the TU Braunschweig have developed a method to create models for these and other phenomena in all scientific fields. What is needed is data from measurements. The software uses this data to generate a model that can be used to understand, estimate, predict and even control complex systems. They have presented their research results in the journal “Science Advances“.
Nonlinear dynamics is a field of research that observes nonlinear phenomena in physics, chemistry, biology, and other sciences and analyzes them in mathematical models. Nonlinear systems can be used to reveal complex dynamics. A particular example is Kolmogorov currents, named after the Russian mathematician Andrei Nikolayevich Kolmogorov. Kolmogorov currents exhibit rare events in the form of energy bursts. Such rare events occur in nature, for example, in the form of rogue waves (also called extreme waves) and abrupt squalls. These are singular events of short duration but enormous magnitude. For example, rogue waves can be more than twice as high as surrounding large waves. With a suitable model, it is possible to predict their occurrence and take countermeasures.
Difficulties in modeling many dynamical systems, however, include the stochastic behavior of events and measurement noise. Chaos, a special property of certain dynamical systems, also complicates the modeling process. Often, only data from measurements and observations are available. Researchers must then identify the appropriate equations that describe these data.
Dr. Richard Semaan, head of the Modeling and Control of Flows group at the Institute of Fluid Mechanics (ISM) at TU Braunschweig, together with Dr. Daniel Fernex (as a PhD student at TU Braunschweig) and Prof. Bernd Noack (former professor at ISM), has now proposed a method for data-driven modeling of complex nonlinear dynamics. Their newly developed method, Cluster-based Network Modeling (CNM), describes short- and long-term behavior of dynamics and is fully automatable because it does not rely on application-specific knowledge. The method is also universal because it can theoretically be applied to any application that exhibits dynamical behavior – and thus could be of interest in all scientific fields.
The lack of required prior knowledge is an additional advantage. This is due to the data-driven nature of the method. The code available online can be executed without much customization. In contrast, other existing methods require a lot of expert knowledge to operate and customize.
The method builds on earlier research by Professor Noack and other researchers in the field of clustering and network science. The work itself was part of a DFG-funded project in collaboration with Prof. Wolfgang Schröder (RWTH Aachen University) that investigates active drag reduction methods, i.e., methods that influence the flow by transferring energy into the flow to change its properties. The main area of use is in the field of aerodynamics.
This automatable, universal, data-driven representation of complex nonlinear dynamics complements and extends the science of network connectivity and promises new, rapid ways to understand, estimate, predict, and control complex systems in all scientific fields – including climate science, epidemiology, neurology (brain activity), finance (market turbulence), and aviation (turbulence).
In the Science Advances article, Cluster-based Network Modeling (CNM) is applied to numerous examples ranging from analytical systems to real-world problems using experimental and simulation data. The first two applications are the Lorenz and Rössler attractors, typical candidates for the analysis of dynamic systems. The functionality of CNM is also illustrated in electrocardiogram (ECG) measurements and in the energy conversion in a Kolmogorov current.