Venue: ICLR 2023 Conference

Reviews:

final_score: rating: 5: marginally below the acceptance threshold
review_content: summary_of_the_paper: This paper builds on the PESNet model of NN-based wave functions for small polyatomic molecules [this reviewers recommends avoiding re-using names for model architectures to avoid compromising anonymity). The works proposes two innovations. One is learning a surrogate model of the VMC energies to avoid O(N^4) scaling in the MC integration of the VMC integration. The other is a series of updates based on common approximations and tricks in quantum mechanics 
strength_and_weaknesses: Strengths 

The approach seems fundamentally sound and has good performance. The surrogate model is rather accurate and accelerates inference with little loss of accuracy, whereas the approximations and model updates based on traditional quantum chemistry heuristics are gainful and results in good cost/accuracy tradeoffs.

Weaknesses.

Neither of the innovation of performance improvements are particularly innovative as far as ML is concerned and this seems more fit for a quantum chemistry scientific journal. The use of a surrogate force-field-like potential seems relatively trivial and does not present a large methodological or task-specific innovation. All the quantum chemistry tricks are effective, but again, not that innovative on the ML side. 
clarity,_quality,_novelty_and_reproducibility: What is Eref in Figure 3 ? r12-MR-ACPF would seem to be working great if it wasn't for some systematic bias. 

" is in perfect agreement with the experimental results(Le Royet al., 2006) about the equilibrium structure at 2.074 a0." It is not clear by visual inspection where the minima is, the points seem to move randomly up and down from the true surface

The stoichiometric indices of chemicals should be subscripted

"PlaNet almost perfectly recovers the CCSD(T) results with a maximum disagreement of 0.13 mEh while only requiring ≈ 0.15 ms"  Does this factor in training time ? 

What phase space does the PESNet algorithm explore? 

The Energies reported are for the equilibrium geometry ? (Table 1, 2, 5 )
summary_of_the_review: This paper reports exciting practical improvements to an ML-based model for generatic wave functions and energies of small molecules. The method seems to provide desired improvements in speed while retaining accuracy, but the innovations do not seem to be arising from ML insights and are mostly through use of a surrogate function for energies, which is a common strategy in chemistry and from inclusion of quantum mechanical approximations that are well stablished.
review_title: null

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: This paper aims to simulate the potential energy surfaces of atomic systems by accelerating the variational Monte-Carlo (VMC) approach. It builds on the PESNet by Gao and Gunnemann and contributes two major innovations: 1) it introduces PlaNet which trains a surrogate model to avoid the expensive Monte-Carlo integration; 2) it introduces PESNet++ which improves multiple aspects of the PESNet. It shows 7 orders of magnitude acceleration and reduces the error up to 74%.
strength_and_weaknesses: Strength:
- PlatNet introduces an online learning scheme that learns a PES using the noisy labels from the VMC optimization. This innovation is significant because it enables the use of the very noisy energy data from VMC.
- Multiple innovations are introduced to improve the PESNet++, which results in a new SOTA in VMC for several molecules.

Weakness:
- The motivation of learning a surrogate PlaNet from VMC optimization is unclear. From my understanding, the authors first use VMC to explore the entire PES and use the noisy data generated in the process to train a surrogate PlatNet. Since the entire PES has already been explored with VMC, why do we need a surrogate PatNet to predict the PES again? One argument may be that PatNet can generalize to new configurations that are not simulated by VMC. In that case, the authors probably should compare with a baseline DimeNet++ that is trained on the clean PES data from VMC to demonstrate the advantage of learning from noisy VMC energy.
- The generalization performance of PlaNet is not studied in this paper. In Figure 3, 4, the PESNet++ simulated configurations are extremely dense and PlatNet only interpolates between nearby points. 
The discussion on the results in Table 3 is slightly misleading. It is unfair to compare the training/inference time of the surrogate model to VMC, because the latter requires the former to generate data. 

clarity,_quality,_novelty_and_reproducibility: - The writing of this paper is overall clear and high-quality. However, it combines two slightly independent contributions (PlaNet and PESNet++) into a single paper. The narration could be improved to better clarify the connection between the two contributions.
- The paper introduces multiple innovations for both the PlatNet and PESNet++ to improve the PESNet architecture. The novelty of individual innovations are not very high, but they are combined to solve the important challenge of VMC and achieve the SOTA in several molecules.
- The source code is not provided for review. I presume that the code will be provided possibly upon acceptance, because the paper says code will be open.

summary_of_the_review: In summary, the paper makes two contributions: 1) a PlaNet that learns a PES from the noisy data of VMC; 2) a PESNet++ that improves PESNet and achieves SOTA in several molecules. I think the motivation of 1) needs to be further clarified and additional baseline may be required. Contribution 2) alone makes significant progress in the ab-initio modeling of molecules. The paper may be accepted based on contribution 2) but the paper needs to be significantly revised. I give a score of 5 for now, but I am open to increase my score after satisfying responses from the authors.
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: The paper proposes a method for speeding up the learning of potential energy surfaces by improving PESNet (a neural wavefunction model parameterized by a graph neural network and trained by variational Monte Carlo). In each step, previous methods run Monte Carlo simulations to estimate the energy, and the paper proposes to use these estimated energies to train an energy surrogate GNN (a Dimenet++ model). In addition, several changes to the PESNet neural wave function are presented.
strength_and_weaknesses: The paper is well written and nicely presented.

The idea of using an energy surrogate as part of the VMC is promising.

The proposed improvements to PESNet seem relevant and improve performance.

Weaknesses:
The training of the surrogate energy model is done via samples (targets) which only asymptotically are correct, which is handled by training only on the newest samples. Because of label noise, a heuristic exponential moving average is also used. It could be interesting with some further theoretical insight into the convergence properties of this approach.

I expect that most of the paper might be difficult to follow for the general ML audience.

clarity,_quality,_novelty_and_reproducibility: The paper is clear, technically sound, and of sufficient novelty to be of very high interest to the ML subcommunity interested in physical chemistry.
summary_of_the_review: An interesting and well written paper that takes a small but important step towards solving the Schrodinger equations in a more efficiently and precisely via ML.
review_title: null

final_score: rating: 8: accept, good paper
review_content: summary_of_the_paper: This paper proposed two improvements over the baseline model PESNet. The first one, PlaNet, use the local energy computed in each PESNET training step to train a surrogate model, which takes in the geometry of nucleus and output final energy, namely no dependence on electrons. At inference time, only the surrogate model is used to do prediction. Hence, the orders of magnitude for inference is faster than PESNet. The second one, PES++, includes several improvements to achieve better accuracy than PES with similar cost.
strength_and_weaknesses: Strengths: 1. PESNET++ can produce highly accurate energy results (compared to FermiNet).
                  2. PlaNet can approximate PESNET++ results well, but avoid the QMC inference phase, and thus can produce PES results much more efficiently.

Weakness: The model is still limited, not applicable for real-world PES, for instance, molecular dynamics.

Some questions to the authors: 1. Does PlaNet still have the variational property? 2. The neural Jastrow factor is not considering cusp condition as the traditional ones. Is it by design or just for convenience?
clarity,_quality,_novelty_and_reproducibility: This paper looks good in clarity, quality, novelty and reproducibility.
summary_of_the_review: This paper proposed two improvements over PESNet, which makes the inference of PESNet faster and more accurate. The paper is written in a good manner.
review_title: null

Meta-review: metareview:_summary,_strengths_and_weaknesses: This paper aims to simulate the potential energy surfaces of atomic systems by accelerating the variational Monte-Carlo (VMC) approach.  It introduces PlaNet which trains a surrogate model to avoid the expensive Monte-Carlo integration, and introduces PESNet++ which improves multiple aspects of the PESNet. It shows several orders of magnitude acceleration and reduces the error significantly at the same time.

Overall speaking, this is a nice paper and most reviewers like it. One concern raised during the review process is the technical novelty in terms of machine learning, while the reviewer acknowledged that all the quantum chemistry tricks are effective. The authors had several rounds of discussions and successfully convinced the reviewer about the technical novelty of the paper. Given this, we believe this paper has sufficient value to be accepted. 

justification_for_why_not_higher_score: This paper is heavily quantum chemistry flavor. Its audience will be relatively narrow. We do not think positioning it as a spotlight or oral paper makes too much sense. 
justification_for_why_not_lower_score: Most reviewers like this paper, and most concerns have been addressed by the author rebuttal.
Decision: Accept: poster