Differential equations are one of the standard tools for describing models in the natural sciences. Traditionally, methods to analyze such models come from analysis and numeric computing. One the other hand, the equations themselves are symbolic expressions, and one can use algorithms from symbolic computation to deal with them. Interestingly, there is a number of important questions about the structural properties of systems of differential equations which can be answered this way. In the talk, I will describe two such questions and recent algorithms and software implementations to answer them:

Q1 (identifiability): Assume we have a model described by a system of differential equations with unknown parameters, and the experimental setup allows us to measure only few of the variables. How to compute the set of parameter and/or their combinations whose values can be inferred if we collect enough data?

Q2 (exact reduction): Assume we have a large system of differential equations, and we are really interested in the behavior of only few of the components of the solution. Can we automatically produce a smaller system with produces exactly the same behavior? How can we make such an algorithm to preserve the interpretability of the model after the reduction?

For both these questions, polytechnique students had made some interesting contributions recently, and I will highlight them.