Two Inference Problems in Dynamical Systems from Mathematical and Computational Biology

This talk will discuss two inference problems in dynamical systems, both motivated by applications in mathematical biology. First, we will discuss the classical gene regulatory network inference problem for time-stamped single-cell datasets and recent advances in optimal transport-based methods for this task. Second, if time permits, I will present an algorithm for bifurcation tracing, which aims to identify interfaces in parameter space. Applications to agent-based models and spatially extended reaction-diffusion equations will be demonstrated, both of which simulate Turing patterns commonly observed in animal skin, vegetation patterns, and more.