Max Tschaikowski from Aalborg University will give a talk in the elite program’s special lecture series. The title of the talk is “Algorithmic reduction of quantitative models” and it will take place virtually as an online meeting at 4:30PM on July 8th 2021.
Differential equations are ubiquitous in quantitative modeling and allow to model, for instance, power grids, epidemic forecasts or protein-interaction networks. Unfortunately, the simulation of many realistic models is computationally prohibitive due to their large size. An approach for the simplification of difficult problems is model reduction where the idea is to formally relate the original model to a smaller model which can be solved more efficiently.
In this talk, I will provide a high-level introduction to simulation-preserving reductions of differential equations. Specifically, we will show that polynomial differential equations can be encoded as graphs which, in turn, can be efficiently reduced by means of partition refinement algorithms in the style of Paige and Tarjan. The reduction of arbitrary differential equations, instead, will be reduced to SAT. The talk will finish with applications to biological models.