In this talk, I will present two inference problems arising in dynamical systems in mathematical biology and discuss data-driven numerical methods based on optimal transport. First, we revisit the problem of inferring regulatory networks from time-stamped single-cell transcriptomics data. Optimal transport has been widely used to infer ancestor-descendant relationships across time points; we leverage this structure to infer gene regulatory interactions using Granger causality. Second, time permitting, I will briefly discuss bifurcation tracing in models of pattern formation, including reaction-diffusion systems and agent-based models.