GENERATING LIQUID SIMULATIONS WITH DEFORMATION-AWARE NEURAL NETWORKS
We propose a novel approach for deformation-aware neural networks that learn the weighting and synthesis of dense volumetric deformation fields. Our method specifically targets the space-time representation of physical surfaces from liquid simulations. Liquids exhibit highly complex, non-linear behavior under changing simulation conditions such as different initial conditions. Our algorithm captures these complex phenomena in two stages: a first neural network computes a weighting function for a set of pre-computed deformations, while a second network directly generates a deformation field for refining the surface. Key for successful training runs in this setting is a suitable loss function that encodes the effect of the deformations, and a robust calculation of the corresponding gradients. To demonstrate the effectiveness of our approach, we showcase our method with several complex examples of flowing liquids with topology changes. Our representation makes it possible to rapidly generate the desired implicit surfaces. We have implemented a mobile application to demonstrate that real-time interactions with complex liquid effects are possible with our approach.
This is an application paper on dense volumetric synthesis of liquids and smoke. Given densely registered 4D implicit surfaces (volumes over time) for a structured scene, a neural-network based model is used to interpolate simulations for novel scene conditions (e.g. position and size of dropped water ball). The interpolation model composes two components -- given these conditions, it first regresses weights combining a set of precomputed deformation fields, and then a second model regresses dense volumetric deformation corrections -- these are helpful as some events are not easily modeled with a set of basis deformations. 
I found the paper hard to read at first, since the paper is heavy on terminology, only really understood what is going on when I went through the examples in the appendix, which are helpful and then on a second read the content was clear and appears technically correct. I would advise considering defining in more detail early the problem setup (e.g. Fig 13 was helpful), explain some of the variables in context. 
This is primarily an application paper on simulating liquids in controlled scenes using nets and appears novel in that narrow domain. The specific way deformations are composed -- using v_inv to backwards correct basis deformations, following up the mixing of those with a correction model -- is intuitive and is also something I see for the first time. 
The experimental results are sufficient for simulating liquids/smoke, except I would like to also see a comparison to using deformation field network only, without its predecessor. This was done for Fig 6, but would be nice to also see it numerically in ablation in Fig. 4. Another useful experiment would be to vary the number of bases and/or the resolution of the deformation correction network and see the effects. 
More importantly, it would be very helpful is to try this approach for modeling deforming object and body shapes for which there are many datasets (e.g. Shapenet). Right now the implicit surface deformation model is only tested on liquids examples, which limits the impact to that specialist domain -- it's a bit more of a SIGGRAPH type of paper than ICLR. 
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I raised my rating to 7 as the paper itself is solid, main concern as another reviewer points out is it may be a bit too specialist for ICLR. If the AC decides to reject based on this fact I am ok with that as well. 
I think it would be helpful to add more ablation (deformation-only results for all cases) and experiments with different numbers of bases in the final version. If that's added it will strengthen the paper.