The art of portraying the real world in numbers
Mathematicians at Ulm University develop “digital twins”

Ulm University

The so-called “digital twins” are virtual models of objects and processes that build a bridge between the physical and digital worlds. As digital replicas, they aid in the development and improvement of materials and products, as well as manufacturing and testing processes. At Ulm University, mathematicians are developing models for things such as battery materials, the simulation of test procedures and the prediction of wear and ageing processes. For these models, they are utilising methods from the fields of stochastics and numerics as well as a considerable amount of empirical data.

A brand new car is subjected to so much stress on a vehicle test bench that it can only be used as scrap metal afterwards. The test not only costs a lot of money, but also time. “Digital twins can be used to simulate not only individual testing processes, but also the entire test infrastructure, saving both time and money”, relates Professor Karsten Urban. The mathematician heads the Institute of Numerical Mathematics at Ulm University. Urban is a research partner in the joint project “DigiPrüF”, which focuses on developing a digital testing platform for motor vehicles. The intention of the virtual test centre is to enable car manufacturers and suppliers to test their own products in a virtual setting – digitally reproduced in simulation models. This saves resources and helps to optimise testing and production processes, which especially benefits medium-sized companies. “DigiPrüF” is coordinated by the Neu-Ulm software company ATR and supported by the Federal Ministry for Economic Affairs and Climate Action (Bundesministerium für Wirtschaft und Klimaschutz, BMWK) with a total of 5.5 million euros, 460,000 euros of which will go to Ulm University.

The task the Ulm numerical engineers have is to develop a generic model for the testing process. “This is a kind of modular system consisting of various mathematical models for representing various physical processes that are important in vehicle testing”, the simulation expert explains. Because both deterministic and random processes and phenomena have to be captured here, the scientists use methods from the fields of numerics and stochastics as well as mixed forms. Another sub-project addresses the topic of predictive health management. This involves advanced maintenance and control strategies to ensure the reliability of test benches and production, which are implemented using predictive models.

“Whether we’re dealing with landing gear or wings for aeroplanes or catalytic converters for motor vehicles, we always try to replicate the real life cycle in technical simulations, which is why the time factor plays a critical role”, explains the numerical engineer from Ulm, who has been conducting research into the technical simulation of material ageing and wear processes in various projects for many years. Where mathematics becomes important is when it comes to guaranteeing the accuracy, reliability and robustness of the predictions.

Virtual particle models help improve storage materials

In the field of battery research, “digital twins” are being used to find storage materials with optimal properties; the time factor is of secondary concern for the time being. Local scientists from the Institute of Stochastics are developing mathematical structural models that allow conclusions to be drawn about certain chemical-physical properties such as storage capacity, charging speed and durability. “For instance, we are interested in the formation of cracks in active materials, which can have a significant impact on the stability and performance of a battery”, explains Dr Orkun Furat from the Institute of Stochastics at Ulm University. The young mathematician, who won the Südwestmetall Prize last year for his doctorate on “digital twins” in the field of materials research, points to an x-ray microscope image of a battery electrode. The active materials, where the ions are stored during the charging process, are shown as circular areas with cracks running through them. “Using empirical image and measurement data as a basis, we are trying to model the geometry and structure of various storage materials as realistically as possible and derive correlations between the structure and properties of the materials. The models generated in this process are then repeatedly adapted to the empirical conditions until the ‘digital twin’ is calibrated and fits”, explains Professor Volker Schmidt from the Institute of Stochastics. Schmidt, who supervised Furat’s doctorate, has been researching the mathematical modelling of challenges in the field of materials science for many years and cooperates with battery researchers from Ulm and other locations in Germany, including the Federal Ministry of Education and Research (Bundesministerium für Bildung und Forschung, BMBF) Competence Cluster “ProZell”.

The challenge in generating such virtual avatars is determining relevant criteria that make it possible to obtain meaningful information from the empirical data. “We are not conducting research in isolation in an ivory tower; we are working together closely with engineers and scientists”, say Ulm scientists Urban and Schmidt. The project partners determine in advance which material or test parameters are relevant for the construction of the virtual reproductions. The modelling process also reduces complexity, which in turn greatly expedites computing processes. The “digital twin” technology also makes it possible to optimise processes, components or materials and identify ideal properties. “Battery materials, for example, could hypothetically be generated that are more powerful and durable”, adds Dr Orkun Furat. The mathematicians have not only mastered the art of modelling the real world in numbers, they also help to improve the real world.

Research stemming from Ulm on the topic of “digital twins” is largely funded by third parties and has appeared in high-ranking publications. Funding comes from the German Research Foundation, the federal and state governments and industrial partners.

Scientific Computing Centre Ulm

Many of Ulm University’s research projects on “digital twins” are conducted by the UZWR. The Ulm Scientific Computing Centre Ulm (Ulmer Zentrum für Wissenschaftliches Rechnen, UZWR) is an interdisciplinary research centre at the university that works on application-oriented research topics from science and industry using modern mathematical methods. The centre’s staff use numerical and stochastic calculations to simulate and optimise processes, materials and components. There are now a large number of industrial cooperation partners, both local and national, but mathematical modelling is also carried out for the natural sciences. The UZWR specialises in technical simulations, for example for tension, flow and vibration analysis, as well as strength and dynamics testing. Professor Karsten Urban is the centre’s spokesperson and Dr Ulrich Simon is the managing director.

OSARA is a spin-off of UZWR staff. The start-up was founded in collaboration with researchers from the Institute of Trauma Surgery Research and Biomechanics in order to simulate fracture healing processes with the help of “digital twins”.


Text and mediacontact: Andrea Weber-Tuckermann
Translation: Kate Gaugler



“DigiPrüF” project consortium at the vehicle test bench
Members of the “DigiPrüF” project consortium at the vehicle test bench at Aalen University of Applied Sciences (Photo: Aalen University of Applied Sciences)
Prof Karsten Urban
Prof Karsten Urban (Photo: Elvira Eberhardt / Uni Ulm)
Dr. Orkun Furat
Dr Orkun Furat (Photo: Elvira Eberhardt / Uni Ulm)
CT&Visualisierung&Digital twin
Left: Nano-computer tomography of the microstructure of a Li-ion battery cathode. The pale areas show the active materials; Centre: Visualisation of active materials, shown in random colours; Right: Digital twin of a particle; this is statistically similar to the measured particles with respect to shape and size. The virtual particle models can be used as geometry input for numerical simulations of electrochemical properties (Image: Dr Orkun Furat / Uni Ulm)
Prof Volker Schmidt is a project partner in the BMBF Competence Cluster “ProZell”