Volker Mehrmann

Volker Mehrmann

Volker Mehrmann is a Professor of Mathematics at the Technische Universität Berlin, Germany. His research interests are in the areas of numerical mathematics/scientific computing, applied and numerical linear algebra, control theory and the theory and numerical solution of differential algebraic equations. He is a member of the German Academy of Science and Engineering (acatech), a SIAM (Society for Industrial and Applied Mathematics) Fellow and a Past President of the International Association of Applied Mathematics and Mechanics (GAMM). From 2000 to 2004, he served as the Chairman of the Mathematics Committee of the Deutsche Forschungsgemeinschaft (DFG). From 2008 to 2014, he served as the Chairman of MATHEON, a DFG Research Centre developing ‘mathematics for key technologies’ in Berlin. He was also a member of the European Research Council (ERC) advanced grant panel for mathematics and is president-elect of the European Mathematical Society.


We repost here an extract from the interview to Prof. Volker Mehrmann, published in the Mathesia Outlook on Data Science: a report exploring how Data Science and Applied Mathematics will shape our future.


What, in your opinion, have been the biggest successes of applied mathematics so far, and when can we apply these to a business entity or a commercial aspect?

I would say there are so many. There is a very nice book that we wrote while at the MATHEON Research Centre, which I have been the head of for many years. It’s called ‘Mathematics for Key Technologies’, which covers all areas of biomedicine, energy and transportation networks, new materials, finance, energy and markets. In each of these areas, mathematics has been a driving force for making jumps forward.


With respect to data science, do you find it’s enabling applied mathematics to work more efficiently within industry or do you see them as separate entities?

I see data science and applied mathematics as complementary to each other. The way we look at it, is that modelling, simulation and optimization are a key tool for all complex technologies. We now have tons of data and good computers, and together this can be the real breakthrough. I do not believe in pure data-based models; I believe in the combination of first-principle modelling, that is, differential equations and classical modelling tools, together with data. Data simulations are used to improve the models and at the same time models are used to generate data and/ or training data for machine learning. Mixture is the key.


Which is your vision of the future?

The future will be digital twins. Virtual models of every product, perhaps even of humans, will permanently exchange data with real twins in the whole lifetime. Gartner placed it to be future technology number four or five for the upcoming years, and there is a huge amount of money in this area to be earned. This is really a challenge, which is exactly what applied mathematics and data science need.


What are the risks associated with entering into this new world of digital twins?

Well, this depends. In most areas, there are no risks except for something like if we enter into the digital twins of ourselves. There are a lot of ethical and moral issues that we will have to cover; for example, if the digital twin projects that I will get ill very soon, would my health insurance provider like to have this data information? But on the pure engineering or technical side, I would say that it will be a help for everything, because we will be able to carry out predictive maintenance; we will estimate failures before they occur and we will be able to simulate the future society or things along that line. There are a lot of advantages, but this is only in its infancy. We only have a very few examples where digital twins work.


Which application do you think is at the forefront of development, in terms of which industry will benefit from it the most?

My answer would be all the industries that have large machinery with high costs, like the power industry. If you have a turbine in which you can detect when it breaks down before it even does, then you will probably be able to save a couple of millions.

Another example is when you have a public transport system, it is a disaster if something bad happens, and this happens all the time because we do not have a prognosis of something going wrong, and it would be great to have that and to be able to react timely. With human or living systems, I can see that this has a big impact, for example, on bacterial cultures or on the development of chemical pharmaceutical products.


In what application field would you say applied mathematics and data science will truly make a difference in the upcoming four to five years? What do you envision will be the biggest research challenge for applied mathematics in the upcoming years?

The area that will have the largest impact will be that of bio and medical development, not only in the analysis of cells or in the development of pharmaceutical products, but also in technology and machinery that is associated with medicine, such as diagnosis instruments or support instruments for humans in any area, like automatic control and artificial arms among others, which you can control with your brain rather than with an input. In addition, I think individual medicine will be highly reliant on data and applied mathematics. If you want to build an optimal artificial knee or a hip for yourself, at the moment, you take it out of a box of 10. However, principally, you can go and take data from the patient and design the bone structure and force structure in your muscles to design the perfect artificial knee for yourself.
We already have projects, and there is quite a lot of progress that you can make in this direction.

The industry is very much interested in this. We have a big research campus in Berlin that is a public–private partnership (it is called Modal) and has four labs: one is pharmaceutical, one is gas transport, one is railway, one is public transport.
In all of these, we are developing the tools that the industry might need, on the basis of the research that we carry out at universities or in research labs.