From: ~Michael_Chertkov1
comment: We were very pleased to read the reviewer comments.  The reviewer has grasped the essence of the paper perfectly well --- introducing the 4 statistics tests of increasing complexity, reflecting underlying physics of turbulence. And indeed,  as mentioned by the reviewer,  the paper is aimed at bringing DL and other novel ML/AI tools into domain of physics (specifically fluid mechanics) to help accelerating  scientific discovery. 
title: response to reviewer comments

From: ~Michael_Chertkov1
comment: Dear Reviewer,  

thanks a lot for relevant and very useful remarks. We are glad to see you acknowledging  that the material presented in the paper on 1) novel architecture (LAT-NET) and 2) performance metric is of interest.  In fact the latter item (performance metric) is the paper's main focus. 

Wrt your questions "why the authors picked the metrics they did; what kind of target performance is desired under these metrics, i.e. what a "good" correspondence is; and whether the emulation delivers good results under those criteria".   The main point of the paper is in developing methodology which will help using ML for accelerating scientific (in this case turbulence/fluid mechanics) discovery.  The metric is chosen based on the physics input.  Specifically,  the set of tests are of increasing complexity.  We expect any NN scheme to fail at certain level - in reproducing some delicate (but potentially important) statistical properties of turbulence. And this is what we have started to explore in this manuscript.  Information on how the two schemes (discussed in the manuscript) perform in the tests are sketched in the last Section (Conclusions and Path Forward).  We would love to expand this discussion -  which is however difficult given the limited (4 pager) format.    Hope to cover it more comprehensively  in the presentation. 

We also thank the reviewer for attracting our attention to what seems to be a relevant paper indeed.  We will site it in the final version,  where we will also attempt to restructure the intro and supplementary materials following suggestions of the reviewer. 
title: response to reviewer comment

From: ~Ransalu_Senanayake1
comment: Dear authors,
           
You should now be able to see the reviews. We encourage you to engage in the discussion by commenting on the reviews. Please take this as an opportunity to clarify the issues highlighted by the reviewers. 
           
Regards,
Ransalu, Neal, Fabio, and Girish
title: Rebuttal

From: ~Ransalu_Senanayake1
comment: This paper focuses on using deep neural networks to make fast, approximate predictions for the output of fluid dynamics codes.  Turbulent fluid flow is an exceptionally difficult, multi-scale problem in computational physics, and the ability to make fast approximate calculations could have a broad impact on a number of applications in industry (such as aerospace engineering) and academia (such as astrophysics).  The overall method could also apply outside physics-based simulation to more general spatiotemporal problems, so it seems appropriate for this session.

I would expect any paper on emulation of complex physics-based codes to address a number of questions:  what the critical outputs are for the desired application; how well the emulation reproduces the original simulation for those outputs, either for specific inputs or on average over many inputs; whether the emulation includes an estimate of its own model error or inadequacy; and what efficiency gains have been made by emulating the problem.

The paper presents what seems to be a novel model architecture, first using convolutional autoencoders to map the coordinate-space description of snapshots of fluid flow to a latent variable space of reduced dimension, using recurrent neural nets to simulate time evolution within the latent space, and then mapping the time-evolved latent solution back into coordinate space.  This seems a reasonable way to proceed and should realize significant efficiency gains over a full fluid-dynamical simulation.  Additionally, the use of GANs for dimensional reduction results in a generative model that could be used to propagate uncertainties under initial conditions and model inadequacy.

The authors discuss performance metrics on which the code performs well -- for example, reproducing the power spectral density of turbulence in comparison to the original numerical model and to the limiting case of Kolmogorov turbulence -- as well as metrics that prove more challenging, which amount to higher-order moments.  What is less clear to me is why the authors picked the metrics they did; what kind of target performance is desired under these metrics, i.e. what a "good" correspondence is; and whether the emulation delivers good results under those criteria.  It may not be possible to answer these questions in the abstract, outside of the context provided by a specific application in fluid dynamics.  The answers to these questions may all be evident to the authors, but they aren't obvious to a reader specializing in statistics or machine learning rather than fluid mechanics.

Some restructuring of the paper to present a more obvious narrative -- pulling into the introduction, say, some material and literature references scattered throughout section 2 and/or the supplementary material -- and streamlining the narrative may help.  For an analogous contribution that communicates a similar problem well, the authors might look at Ravanbakhsh et al 2016, an ICML paper using 3-D convolutional neural nets for inference in an astrophysics problem.
title: From: NIPS 2018 Workshop Spatiotemporal Paper10 AnonReviewer1

From: NIPS.cc/2018/Workshop/Spatiotemporal/Paper10/AnonReviewer2
evaluation: 	1. What did you learn from reading this paper that you did not know before?
	The paper compares two approaches to simulate turbulence and evaluates them through 4 statistics. One model is based on a GAN, which takes instantaneous snapshots of the turbulence field as input but ignores any dynamics of the system. The second model is based on the LAT-NET architecture, where there are two stages of training: a latent space of turbulent flow is learned through an autoencoder model. Then this latent space is used as input in a separate convolutional network to learn the dynamics of the fluid flow. The results based on the proposed statistics suggests including the temporal dimension in training corrects some of the weaknesses of the GAN model.
	2. What was the most exciting part of the work?
	The author propose four different statistics that could be used to evaluate the effectiveness of models to simulate fluid dynamics. After analysing the various statistics, the authors propose dynamic NN models would have better performance if a loss-function includes a term enforcing large scale physics.
    3. What in your opinion makes this work stand apart from other papers in this area?
	The papers adds more domain expertise of fluid dynamics to further stimulate discussion in the community.
    4. Does the paper fit into the scope of the workshop?
	Yes.
    5. Are you aware of relevant literature that you may want to make the authors aware of?
	No.

From: NIPS.cc/2018/Workshop/Spatiotemporal/Paper10/AnonReviewer2
relevance: 4: high
impact: 3: borderline
novelty: 4: high