  First-order methods are often analyzed via their continuous-time models,
where their worst-case convergence properties are usually approached via
Lyapunov functions. In this work, we provide a systematic and principled
approach to find and verify Lyapunov functions for classes of ordinary and
stochastic differential equations. More precisely, we extend the performance
estimation framework, originally proposed by Drori and Teboulle [10], to
continuous-time models. We retrieve convergence results comparable to those of
discrete methods using fewer assumptions and convexity inequalities, and
provide new results for stochastic accelerated gradient flows.
