Machine learning of potential energy surfaces offers an attractive way to decrease the cost of classical and path integral ab initio simulations. Often, the construction of a robust training set is a crucial step that determines the quality and utility of the final model. With a suitable active learning protocol, we can construct training sets that yield accurate models suitable for both classical and quantum simulations. Path integral simulations still require larger computational resources due to the multiple replicas and possibly due to the shorter molecular dynamics time steps required in some setups. By learning an effective potential for the centroid, we can avoid that additional cost and perform entirely classical simulations while still answering some quantum questions. Approximate time-dependent quantities can be evaluated within the centroid molecular dynamics framework, with the additional benefit of not having to deal with the adiabatic separation of the centroid from the fluctuation degrees of freedom. Static properties that can be derived from the partition sum are also available in principle, either directly or by extending the original effective potential.