Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 7: Good paper, accept
review_content: summary: The paper proposes Aux-SI approach that handles the large-scale seismic inversion problem via dividing it into small blocks of property models, which makes the training feasible. The authors introduce MMI-Unscrambler architecture to handle the multi-modal information for the task. The empirical study shows that the proposed approach outperforms the state-of-the-art algorithms and is scalable to handle large-scale real-world datasets.
main_review: The main novelty of the work is to divide the large-scale seismic inversion problem into local inversion problems, each trained based on its context. The potential challenge of this division is that each block is influenced by all traces, and traces in a single block's context will also account for other blocks. The authors explain how their approach handles these challenges well and provides reasonable empirical studies.

Questions/Comments:
1. What does the M(q.z) in line 177 mean? Does q.z mean the depth information of q?
2. Line 118, in problem definition 1 --> defined in Problem 1
3. Line 195, missing space
4. Line 210, for following reason --> for the following reason
5. Line 217. sum-pooling in standard --> sum-pooling is standard
6. line 220, the data prohibit us --> the data prohibits us
limitations_and_societal_impact: The authors addressed them.
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: This is an interesting paper that proposes to leverage MLP for solving seismic imaging problems, which are well known to be data-intensive and heavy in computation. 
The paper provides an easy-to-follow introduction of the problem of seismic imaging and clearly illustrates how data-driven methods can potentially reform the seismic processing workflow, showing great promise of this specific research direction. 
The proposed method, *MMI-Unscrambler*, consists of three phases. In the first phase, every trace $t\in C(q,w)$ is mapped to embeddings by individual MLP for each different modal information $t[i]$. A concatenation operation is subsequently used to form one single embedding for each trace. In the second phase, the set of embeddings associated with $C(q,w)$ is further mapped by another MLP (shared across different traces) to align these embeddings followed by average pooling. The rationale for this is that each trace has a dramatically different geometric shape and can not be directly aligned.
In the last phase, a MLP maps the aligned embedding of $C(q,w)$ to the final value $P(q,w_p,d)$.

The authors extensively validate their method on three datasets of increasing difficulty. In particular, the last dataset is real, huge, and irregular. In all datasets, MMI-Unscrambler outperforms U-Net and Set-Transformer baselines with noticeable improvements in terms of numerical values, which supports their aforementioned claims.

main_review: **Originality:** I am not a fully active researcher in seismic imaging, but as far as I know, this paper first proposes an MLP-based network for this topic. 

**Quality:** The experimental validation in this paper is comprehensive and convincing. The quality of this paper is high.

**Clarity:** The paper did a very good job in explaining the background of seismic imaging. Figure 1 clearly shows how data-driven methods will reform the overall reconstruction pipeline, helping draw more attention to seismic imaging or waved-based inversion. However, there is some unclarity in the notations that can make the paper not easy to follow.

**Significance:** The paper is significant because it extends the recent popular MLP-base learning to seismic imaging. 
limitations_and_societal_impact: There are some confusions that need the authors' clarification:

1. On what resolution level is the MMI-Unscrambler trained? Is the input of MMI-Unscrumbler a point (voxel) in the $C(q,w)$ and the output a point in $P(q,w_p,d)$? or MMI-Unscrambler takes and outputs a chunk of data, like a slice?

2. Figure 3.(a) is not very clear. What is the meaning of the red circle? The notation $e_i$ is not defined. Maybe $C(q,w)$ is clearer than $C$ since in the text it is always $C(q,w)$. The caption is not informative. Please consider having a self-contain caption. In fact, Figure 7 in the supplement should be used as a replacement for Figure 3(a).

3. In Figure 3.(b), what do different colors mean at the same level (i.e. dark and light red)?

4. Maybe the supplement should be referenced more often in the main paper since it provides necessary information for understanding the technical details.

5. For reproducibility, the author should consider publishing their code. Also, a comparison of sum-pooling and average-pooling will better justify the choice of the latter.

6. The scalability of the network should be discussed. For example, how many MLPs are needed to cover the gulf dataset in the experiment?
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: The paper tackles the scalability issue of seismic inversion in real-world subsurface and property estimation. The authors propose the Aux-SI framework, where Multi-Modal Information Unscrambler (MMI Unscrambler) is designed, which breaks the large problem into local inversion problems and then aggregates the multi-model information. Extensive experiments are conducted, on both synthetic and real massive datasets, to show the effectiveness of the proposed method.
main_review: This paper is well organized and presented. The main strength is the successful application of machine learning on large-scale, real-world problems. As the authors mentioned, deep learning models in such subsurface property estimation has not been applicable on the real industry level. This paper breaks the limit. Thus, I believe this work could be interesting to many NeurIPS audiences.

The problem studied is interesting to me, and using DL in this problem seems quite novel and new. The empirical results are comprehensive and convincing that the proposed method can do a good job in real-world scenarios. Thus, I think this is in general a good application paper that may interest the many practitioners, and may originate more future efforts in combining machine learning with geological prospecting or oil exploration.


Questions:

What is the input dimensionality to the first MLP layer? Is that possible to break the high dimensional input (eg, 5D) into lower dimensions and apply CNN like U-Net?

Could you explain more on why MLP is used instead of CNN and RNN, and the pattern of the time-series data in SI?
limitations_and_societal_impact: NA
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: This study proposes a new method to the problem of seismic inversion, which is an ill-posed inverse problem of major importance for understanding the composition of the earth subsurface that is used in many applications. The proposed method relies on simple MLP blocks, but organized in a clever way in order to be able to use multi-modal, size-varying and sparse input data. Moreover, the separation in different spatial blocks allows the model to be efficient and parallelizable. The results are performed on different data sets, and compared with more standard time-series or spatial methods, such as Unet and Transformer-based methods. The proposed approach seems promising and robust, which is what is needed for being applied in the real world.
main_review: The paper is interesting and worth publishing. Yet, I found that the paper was not sufficiently proofread and it was difficult to follow. I hope the authors can spend time in correcting all the typos, in changing the variable names that are not clear, and adding the missing details. Specifically, please answer the following questions:
1) when you talk about 5D data, do you mean 3D+time (so 4D), and what is the last dimension?
2) Please give more details on your different MLP architectures: for now we don't have any information about their size, their number of layers, their activation functions, etc.
3) what is the size of the bock and of the context that you used for the different data sets, and more importantly how did you chose it? I only saw the size in one of the experiments. 
4) how did you perform the hyperparameter tuning? what parameter were finally selected (size of blocks, learning rate, size of embeddings..)? was the same values used for all the different data sets or not?
5) how many samples did you finally used in practice for your training, even if there was overlap between samples thanks to data augmentation?
6) explain better how you divide your train validation and test samples. Since your data augmentation technique has a large overlap between samples, I just want to check that the separation between the sets is done correctly.
7) please add the 3rd part of your pipeline, the 'downstream tasks', in your figure 3.a. Add also a proper legend so we can understand the figure on its own.
8) CNN models are able to capture long range dependency... that is why there are multiple layers with max poolings, so the dependencies at different scales can be captured. Please explain better why it might not be relevant for this application.
9) Would you say that what actually makes the difference in your method is to separate the problem in small blocks? Could you perform the same division using the other state-of-the-art methods?
10) explain more clearly what is G (I guess it's an MLP, from the figure, but it is never said in the main text). 
11) 'q.z' formulation is not clear, I guess you meant the vertical component of the position q? Same, there is a confusion between the time 't' and the trace 't'. please use another name for the trace so we can understand the text and the figure. Last, in Figure 3b, explain what are the 3 axis of the cube. 
12) would it be possible to interpolate the traces over the surface area in order to have a grid (or otherwise a graph of sensors)? why would that lead to larger errors than your method (if it does)?

typos: please check your paper again as it is not my job to proofread papers before the authors.
- problem deﬁnition 1can
- a separate function blocks
- 2 1 0 − 1 --> 2^⁽10)-1 (I guess??)
- Generally sum-pooling in standard in NLP or embedding based models. --> no verb
- many spaces missing
- many points missing
- check capital letters

limitations_and_societal_impact: This paper is meant to be used to find Oil for Big Oil companies. So it is subject to personal opinion whether this application is positive or negative in terms of societal impact. Yet, it was clear in the paper from the start what is the goal, it was not hidden, and I personally think that since we, authors and reviewers, are all currently relying on Oil and gaz to live our lives, being able to find it easily is a positive impact. I hope that the company that payed for this work also spends efforts in developing other energy or even better, tries to find ways to reduce energy consumption.
Yet, the authors could remind in the societal section a sentence regarding the final application of the work.
review_title: null

Meta-review: This work presents a SOTA Multi-layer perceptron solution for seismic inversion. The reviewers all recognized the improved performance relative to past approaches and the design and work involved in creating a practical block-based multi-modal approach. In particular the care taken to acknowledge and address the issues stemming from cross-block correlations. The authors also seemed to have proposed very doable revisions, which would even further strengthen the paper. Therefore I am happy to recommend that this work be accepted at NeurIPS.
Decision: Accept (Poster)