Project 11

P11: Model reduction via symmetries and conservation laws for systems on multiple time scales

Pro­­ject de­­scrip­­ti­on

Most mathematical models of biological clocks consist of parametric systems of differential or difference equations. As the models often consist of dozens or even hundreds of equations and many more parameters (many of which are usually redundant), it is almost impossible to perform a rigorous mathematical analysis of them. In the literature, one can find many different model reduction techniques. Most of them are, however, of an approximate nature and easily destroy more complex features like oscillations, in particular if these combine modes on different time scales. We will instead focus on exact reduction methods which automatically preserve all qualitative features of the model. Key tools will be symmetries and conservation laws and their extension and adaption to systems with multiple time scales. We will complement traditional analytical approaches with novel data-driven ones exploiting both numerically generated data and data obtained in experiments in other projects of the graduate school. An important aspect of the project is to make all developed methods completely algorithmic and to implement them in software packages, which biologists can apply even if they do not have a deeper understanding of the underlying mathematics.

Figure 1: Machine learning of exact and approximate conservation laws for model reduction (Wetzel et al. 2021)
Figure 2: Automated parameter reduction via approximate scaling symmetries (picture from