We thank all the reviewers for their valuable comments and suggestions. We respond to the main concerns as follows. All the source code will be released to the community soon. Q: The authors should report the actual inference time/latency of their models. We evaluate the proposed method on a Tesla V100 GPU.

I agree with the authors that R1's concerns are not relevant to the acceptance decision and have removed their review from consideration. R2 raised the concern that there are insufficient benchmarks to judge the value of the work; the author rebuttal countered that the baselines identified by R2 do not attack the same use case as the proposed algorithm. I concur with this assessment. R2 also pointed out that the method was evaluated on 1d problems only; the authors rebutted that the method was demonstrated on both 1- and 2d problems, and gave an example of a Bayesian inverse problem that motivates this method even in low dimensions. R4 recommended accept because of the novelty of the proposed multipole graph neural operator.

The paper proposes to introduce pair-copula construction in the autoencoder architecture to create more robust generative model. Specifically, with a conventionally trained autoencoder encoding input data into a low dimensional latent space, the authors propose estimating the encoding vector distribution using vine-copulas. It is claimed that such estimation can be done efficiently based on sequential estimation of the pair copulation decomposition on vine trees. Furthermore, the estimated distribution can be sampled easily and passed to the decoder to create new data, thus serve as a generative model. My biggest issue with the work is the presentation, which needs a lot of improvements.

The paper is very well written and organized and its contributions are quite original as it proposes a novel coarse-ID method for robust model-based reinforcement learning in which both exploration AND exploitation are optimized jointly (which was not the case in previous similar works). The method proposed to solve the robust Reinforcement Learning problem is all the more original as it does not rely on Stochastic Dynamic Programming, but rather on Semidefinite Programming. Concerning clarity, the only element that is not clear for me is related to equation (1) in page 2: do you consider in the system model some uncertainty in the measurements of the states x? For example, it is said in the supplemental material that the velocity of the servo-motor of your second experiment is estimated using a high pass-filter, and is hence not perfectly known. If it is modeled, is it included in the process noise w or how do you deal with it?