The paper introduces a regularization scheme for neural ODE based on state derivatives of the ODE that favor simpler parameterized vector fields and then allow the control of complexity/ performance of Neural ODE solvers at test time. The reviewers agree that this is an additional step towards the deployment of Neural ODE models and that the specific topic of integration time control has not been much explored for now. The experimental analysis is extensive and explores different merits/ pitfalls of the model. The different issues mentioned in the reviews gave rise to extensive discussions among the reviewers that helped clarify most of the issues. Overall this is considered as a positive and new contribution to the topic. The authors are encouraged to further develop the motivations for the regularization terms that remain largely heuristic in the paper and to clarify the presentation according to the remarks.