Modern mathematical modelling and simulation methods have become a fundamental resource for scientific and technological progress. They make it possible:

  • to avoid expensive, energy-intensive experiments that harm the environment when conducting basic research in science and industry (virtual labour)
  • to obtain new information for spatial areas and timescales that cannot be covered by experiments (super-resolution microscopes/super telescopes)
  • to shorten development cycles and reduce development costs of new products and increase the efficiency and quality of production processes
  • to make more reliable predictions for dangerous or impossible
  • experiments (climate, environment, medicine) and to develop reliable estimation methods in the humanities, economics and social sciences
  • to analyse and utilise the influence of random (stochastic) events
  • to assess risks when using new technologies and in the context of environmental and social policy

Mathematical modelling and simulation is therefore a key methodological area of great relevance for the natural sciences and engineering and for economic, social, life and environmental sciences. As a consequence, many Leibniz Institutes invest in these methods.

Methods from a wide range of mathematical fields are used (statistics, mathematical finance, optimisation/operations research, numerical methods for partial differential equations, mathematical image processing, etc.), to investigate problems on every conceivable temporal and spatial scale (from nanoparticles to immense cosmic structures, from femtoseconds to the age of the universe) with widely differing levels of complexity (from an individual company to the entire global economy, from local environmental events to global climate models).

The common factor in all these methods is that they are based on mathematical principles. This means they are cross-sectional in nature and can generally be used outside of the context in question, to help solve problems in completely different branches of science. There is great potential here for effective utilisation.

One of the key aims of this Leibniz Research Network is therefore to systematically exploit this potential for effective use and synergies. An important question is which is the fastest, most suitable and error-free of the current mathematical research methods to use in each case – to ensure that the available software and hardware resources are used effectively and sustainably.


Dr Torsten Köhler
Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin
T +49 30 20372582