Venue: ICLR 2023 Conference

Reviews:

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: This paper proposes a new graph deep learning method, PotNet, with several innovations in the field of crystal material modeling. The proposed method models interatomic potentials directly as edge features instead of only using distances and models the complete set of potentials among all atoms with approximations of infinite potential summations instead of only between nearby atoms. With the computations of complete interatomic potentials, the representation learning is performed through message passing neural networks. Evaluation experiments are also performed on the JARVIS and Materials Project benchmarks, showing the proposed method leads to consistent performance improvements with reasonable computational costs.
strength_and_weaknesses: Strength:

The proposed method improves the accuracy of the GNN-based interatomic potentials for crystal property prediction.

Weaknesses:

1. Compared with ALIGNN method, PotNet method consumes about four times as much time when infinite potential summations are considered, but the gain in accuracy is not that obvious.

2. The comparisons in efficiency between the proposed method and direct DFT calculations was not made. Similarly, the advantages and disadvantages of the proposed method compared with the machine learning potentials using the constructed vectors as crystal structure input.
clarity,_quality,_novelty_and_reproducibility: The paper is well-written, and the description is detailed and clear.

There are some minor problems in the paper: the units of the compared physical quantities are not clarified throughout the paper (e.g. Table 1 and Table 2); the importance of the infinite potential summations is not assessed.

The novelty is good. It has two main innovations in the field of crystal material modeling using graph neutral networks. It is the first time that the interatomic potentials are directly as edge features and it is the first time to models the complete set of potentials among all atoms though there are some approximations.

Considering the detailed description was given in the paper, the proposed method is reproducible, but it is still complicated in practice.
summary_of_the_review: This paper proposed a novel graph deep learning method, PotNet, which can improve the performance of the graph neural networks potentials in the field of crystal material modeling with certain computational costs. However, compared with the existing method, the gain of the proposed method in accuracy is not remarkable with the time costs of about 4 times. It is better to illuminate the specific application situations where the proposed method has more pronounced effect or further improve the algorithms to achieve faster implementation.
review_title: null

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: The paper proposes a graph neural network (GNN) for property prediction for crystals. A key issue in modeling crystals is to handle long range interactions. This is handled by using interatomic potentials as edge features in the GNN and approximating the infinite summation over all pairwise interactions using Ewald summation.

strength_and_weaknesses: 
Strengths:
Great example of how incorporation of physical knowledge into a GNN structure leads to a more efficient architecture.

The methods is demonstrated on several examples, and ablation reveals the importance of the infinite summation to handle long range interactions.

Weaknesses:

The description of Ewald summation in the main paper is very concise - it would be nice with a bit more intuition about the methods for readers that are not familiar with this. Also, it is not clear to what extent this is just application of a known result/method, or if this is a novel mathematical result. In case there is something substantially new in the methods, this should be in the main paper in my opinion. I did not carefully check the derivations in the appendix.

I expected to see comparison with other GNN approaches where the cutoff was varied, to be able to more directly understand the importance of the infinite summation. It is not clear from the paper (but from the references) what the cutoff was set to in e.g. the SchNet comparison (5Å i think)

EDIT: (after reading FZse's review) Since the electrostatic (Coulomb) potential is summed infinitely for each (charged) atom, does that not mean that these individual sums in general will diverge, even though the system is electrically neutral? 

clarity,_quality,_novelty_and_reproducibility: The paper is fairly clear, and (at first read to me appeared) technically sound. The main novelty of the paper is the application of Ewald summation within a GNN.

summary_of_the_review: Good paper with a simple but interesting and novel idea. Reasonable empirical evaluation and comparison. The point raised by FZse should be addressed.
review_title: null

final_score: rating: 3: reject, not good enough
review_content: summary_of_the_paper: This paper proposed to incorporate Coulomb potential, London dispersion potential and Pauli repulsion potential in the input features of deep learning models, in order to deal with the long range interactions in PBC systems like crystal materials. It is proved that the proposed model outperforms SOTA in two material datasets: The Materials Project and JARVIS. 
strength_and_weaknesses: Strength: the motivation and idea of the paper is awesome. Traditional neural networks for molecular property prediction usually use local information as atom features, which limits the description for long-range interactions. However, unlike short range interactions which involves complicated electronic structure, the formula of long-range interactions are usually easy. So incorporate fix-formula is a promising solution for long-range interactions.

Weakness: The paper has a fatal mathematical error, which invalidate the computation of Coulomb part. The error occurs in Appendix C.1. In formula (31), it is ... e^{-|Lk+v|t}, but in formula (32), it is miswrote as ... e^{-t|Lk+v|^2}. In appendix C.2, C.3 and C.4, it is e^{-t|Lk+v|^2} everywhere. This error is fatal because if we change e^{-t|Lk+v|^2} back to the correct e^{-t|Lk+v|}, the Poisson summation (39) does not hold, so the summation of Fourier term (40) also does not hold. In fact, if the authors did not make the mistake, the analytic continuation of infinite summation of Coulomb potentials should be diverged, similarly to the fact that Riemann zeta function diverges at s=1.
clarity,_quality,_novelty_and_reproducibility: The paper is written clearly in good quality. The idea of the paper is novel. It is not reproducible due to the wrong math.
summary_of_the_review: This motivation for using closed-form formula to describe long-range interactions in neural network is a great idea. However, a fatal mathematical error (see above) make the computation of Coulomb term completely wrong, which diminish the contribution of this paper.
review_title: null

Meta-review: metareview:_summary,_strengths_and_weaknesses: The reviewers were split about this paper and did not come to a consensus: on one hand they appreciated the importance of the problem addressed and the clarity of the writing, on the other they had doubts about some of the derivations in the paper. After going through the paper and the discussion I have decided to vote to reject for the following reason: the main methodological idea of the paper is to describe a way to formulate the energy of a crystal that takes into account interatomic interactions and potentials in a principled way. However, this leads to infinite sums, so they describe an efficient approximation algorithm to estimate this based on (Ewald, 1921). Unfortunately, the original paper has a number of errors in the derivations, as pointed out by Reviewer FZse. The authors respond that these are typos that do not affect other theoretical proofs or any experimental results, and describe fixes. Reviewer FZse replies that these fixes are not sufficient to resolve the issues. The Reviewer agree and describe more fixes and point out again that this doesn’t affect their experimental results because it is based on the algorithm of Crandall et al., 1998. The Reviewer and authors respond two more times in this way: the reviewer pointing out a derivation issue with the paper/response, and the authors arguing either that (a) they have made a typo in the paper, (b) they misinterpreted the Reviewer’s response, or (c) they actually use the correct formula in another paper, all of which do not change their experimental results. By this point I have lost faith in the author’s ability to write a correct derivation, to clearly communicate any confusion about the derivation, and to write code that avoided all of these issues. The reviewers (particularly FZse) have given extremely detailed feedback and I recommend the authors follow their suggestions closely (if not already done) before submitting to a future ML venue. If the authors are able to fix these things it will make a much stronger submission.
justification_for_why_not_higher_score: See above metareview.
Decision: Reject