# Mathematical modelling

Mathematics provides the insight and structure to understand complexity in natural, social and virtual systems.

The mathematical modeling process seeks to extract structure from empirical data, identify rules in the form of dynamical systems, analyze and compute solutions to the resulting models, and ultimately make predictions, optimize or control the systems.

Applications range from the fundaments of matter and biochemical processes to the geology and climate of the earth, from finance to social media to medicine. The Mathematical Institute of Utrecht University engages in research in dynamical systems, stochastic processes, and computational science.

Mathematicians investigate solution structures, assess dynamics, stability, and the dependence on parameters. They determine bounds on uncertainty and model error, and they develop efficient and accurate computational methods for solving complex problems.

Exciting current themes in applied mathematics include:

- mathematical treatment of multiple scales (asymptotic analysis, analytical and numerical model reduction, adaptive numerical methods, stochastic parameterization of unresolved dynamics),
- solution methods for ill-posed problems (inverse modelling, Bayesian inference, stochastic sampling),
- extraction of dynamic models from data, and uncertainty quantification.

The Mathematical Institute contributes to the forefront of international research in these themes and more.