Abstract

Mathematical modelling requires the researcher to decide upon an appropriate system description regarding the number of states and processes as well as their spatial and temporal resolution. Complex systems are especially reluctant to such formalization as they typically display behaviour over several length and time scales. For those systems, detailed spatially resolved models are often able to accurately capture the interactions of system constituents. Yet, the microscopic models often give only few insights into dynamics on the actual level of interest, either because the latter is computationally out of reach, or because simulation results present themselves in undesired complexity. On the other hand, more abstract phenomenological models that operate directly on the level of interest are computationally inexpensive and amend themselves to clear analysis, but come to the price of introducing ad-hoc assumptions. Therefore, it is desirable to combine both approaches in ways that minimize computational efford while still minimizing the introduction of phenomenological assumptions.

This talk presents approaches to multiscale modelling with examples from physical chemistry, systems biology, and ecology, where spatially resolved microscale models—such as particle based simulations of single molecules in a supramolecular aggregate, or gap models of individual trees in a forest—are compared to phenomenological models that operate on average states or distributions. Besides mere comparison of model results, the talk presents methodologies to integrate microscale and macroscale simulations into true multiscale simulation frameworks. This is achieved by model renormalization and dimensional reduction techniques. It is shown how such model comparison and integration, in combination with data analysis, can greatly improve our understanding of complex systems.