This project explores how to leverage metadata collected a priori and during the execution of a simulation of a differential equation model, with the goal of using these metadata to adapt, improve and predict the simulation. Such metadata, commonly referred to as provenance, include ‘low-level’ performance metrics obtained by monitoring convergence rate, runtime, or memory consumption as well as novel ‘high-level’ measures and derived metrics that help quantify the estimated difficulty of a solution, or the similarity of tasks / components in different simulations. We contribute novel methods and measures to capture these metadata as well as corresponding analysis algorithms to ultimately advance the fundamental problems of deciding when a (possibly expensive) provenance capture is useful to improve the overall performance or to enable more informed design decisions; and of adapting parameter settings to a given problem.