Unleashing the power of novel conditional generative approaches for new materials discovery

Thank you for your attentive feedback. We appreciate your thorough review. Here are our responses to your concerns: Regarding the Objectives and Methodology:

The primary objective of this work is to propose models capable of generating stable crystal structures, aligning with the existing research in this field. Hence, formation energy serves as a crucial indicator of structural stability, directly contributing to our aim of generating more stable and synthesizable materials. If our future works we plan to expand the space of thermodynamic properties used. However, it is limited by the number of data in open source database

Addressing Physical Constraints and Symmetry: To incorporate physical constraints, we integrate space groups as conditions within our models(Figure 2a). Moreover, our proposed PBC loss function explicitly accounts for structural symmetry. We acknowledge the relevance of the UniMat work and will cite it accordingly.

Regarding Mathematical Notation and Clarity: We appreciate the feedback regarding mathematical notation and will thoroughly edit it for improved clarity and consistency.

Clarification on "Both Pipelines": We recognize the error in stating "both pipelines" and acknowledge that GNoME utilizes two distinct pipelines. This error will be corrected in the revised variant. We are grateful for your observation.

Explanation of "Conventional Limitations": Our reference to "conventional limitations" refers to the challenges and limitations associated with traditional methods employed in materials science research. These methods often necessitate significantly greater time and computational resources compared to our proposed approaches.

Role of Element Properties: Element properties are incorporated into the model to provide additional features and account for elemental characteristics. The element embeddings, denoted as $𝑒𝑙_{𝑒𝑚𝑏}$, are processed through a dedicated multilayer convolutional network and are treated as conditions rather than part of the input data (x). In addition, the elemental property matrix contains 22 chemical features encoding the chemical element the structure consists of, you can get more information in lines 118-120 of the article. We will also change mathematical notation for that one and other concepts to make it more clear.

Justification for Time Conditioning: Time conditioning is employed specifically in our diffusion and flow-matching models to simulate the temporal aspect of the diffusion process. The use of the time parameter ($t$) is fundamental to the operation of all diffusion models. Also, diffusion models require passing an interpolation $x_t$ (for instance in CFMs $x_t$ is formed as follows $x_t = t * x_1 + (1 - t) * x_0$). Consequently, its inclusion is essential for our approach, which relies on diffusion and flow-matching techniques for material generation.

Results of Modification Experiments: Our experiments with structure modification have yielded less successful results compared to generation tasks. While modification was initially proposed as a potentially superior approach, our empirical findings have shown the opposite trend.

Overall, we are deeply appreciative of your insightful comments and suggestions. We will diligently address all points raised and ensure a comprehensive revision of the manuscript.

Thank you for your valuable feedback. We appreciate your thorough review. Here are our responses to your concerns:

We employed a network architecture not previously used for this task and did not utilize standard invariances/equivalences, but this deviation from standard practices is justified by our contributions. Specifically:

• Our approach involves conditional generation based on crystal composition, space group, number of atoms, and formation energy. The space group, in particular, accounts for all potential crystal symmetries and invariances, addressing concerns about invariance. Details can be seen in section Data.

• It is incorrect to state that we ignored invariances, as we included space groups as one of the conditioning inputs, providing comprehensive information about the crystal’s symmetries and invariances.

• Our model generated eight novel crystal structures with only with 6840 attempts, demonstrating its effectiveness and originality.

As for machine learning issues. Atom Bonds: In crystal structures, each atom interacts with others through attractive and repulsive forces. Thus, explicitly modeling bonds between atoms is not necessary for our approach. PBC Loss: We have described the Periodic Boundary Conditions (PBC) loss in the appendix of the paper. Unit Cell Consideration: The generation process does account for the unit cell, as detailed in Section Data. Atom Types: Our model includes atom types in the generation process, which is also covered in Section Data. Uniform Noise: We provide an explanation for why uniform noise worked better than Gaussian noise in Figure 3 in Appendix section and refer to it in the text. Overfitting in Table 1: Table 1 contains energies metrics on validation data, not train data. Moreover, we also described the algorithm for validation dataset construction in Section 2.2: “The polymorph group formulas were initially divided into distinct training and validation sets, ensuring a relatively balanced distribution of chemical elements across these subset”. That’s enough for lacking the overfitting.

As for chemistry/validation issues. Formation Energy: Formation energy is used to generate structures with specific energy characteristics. This is crucial for creating stable structures, which is our primary objective. DFT Functional: We use the VASP software for DFT calculations, as mentioned in the paper. We have also included the specification of VASP settings for reproducibility in the Appendix section. Structure Comparison: We compared the generated structures against those from AFLOW with the same chemical composition. This comparison validates the results.

As for comparison against methodologies. While the paper does not explicitly compare against other methodologies, our results show a higher percentage of stable structures compared to those reported in GNoME(for example). Valid comparisons require the use of identical datasets, and our models were trained on different data. However, we acknowledge that a more detailed comparison with other methodologies would strengthen our paper.

Overall Results. Table 3 shows the energy above the hull. Most structures have negative formation energies, indicating stability. Even if some structures have positive energies above the hull, they mostly still possess negative formation energies. The structures were chosen from well-researched compositions, which adds to their validity.

Clarity: We acknowledge the reviewer's comments on the manuscript's presentation and the title. We will revise the title to better reflect the scientific content and highlight our contributions. Our novelty lies in the unique architecture and conditional generation methodology, which has not been previously applied in crystalline structure generation. We have described the data for both tasks, provided a detailed model description, and illustrated the model architecture in Figure 2. Sections 4 and 5 cover the model and the methodology for training and building the models, and we encourage a re-examination of these sections.

Presentation of ML Concepts: We agree that Figure 1 might be overly simplistic and will revise or remove it to enhance clarity.

Chemistry Methodology and Claims: There is a significant difference between negative formation energy and negative energy above the hull. Our methodology focuses on generating stable structures with negative energy above the hull, indicating their potential for synthesis. This approach, applied to a single chemical composition, successfully found 8 stable structures with energy above the hull below zero. Extending this methodology to numerous other compositions could uncover many new stable structures, far beyond routine undergraduate-level work.

Thank you for your feedback. We have addressed these issues in our manuscript and believe that our approach and results contribute valuable insights to the field.

Thank you for your detailed feedback on our paper. We appreciate your insights and have addressed your concerns below:

We did compare the AFLOW database with the Materials Project in the critique of the GNOMe paper(Introduction section), noting that the Materials Project has a much smaller dataset (around 100,000 structures) which is insufficient for training large models. Our experiments with smaller datasets were unsuccessful, and we achieved better results only after significantly increasing the dataset size using AFLOW, which contains over 3 million crystal structures.

We apologize for the oversight regarding the partial break of anonymity due to the GitHub link on Page 9. We should have removed the link to maintain anonymity and will ensure this does not happen in future submissions.

We recognize the importance of demonstrating robustness across different datasets and will include more comprehensive comparisons in future work. We will also improve our manuscript to enhance clarity and presentation.

You are correct in noting that our approach involves converting between different polymorphs rather than optimizing the stability of an arbitrary atomic configuration. This method is a practical solution to achieve the stated objective. The difference between converting polymorphs and changing atomic configurations is subtle, as a more optimal atomic configuration essentially results in a more stable polymorph. We do not consider changes in chemical composition, as comparing formation energies is only meaningful among structures with the same chemical formula.

Regarding the generation task, our primary focus was on formation energy due to its importance in crystal stability. We acknowledge that we did not provide detailed discussions on other aspects such as condition controls, validity, and duplicate structures. While many generated structures may be near-duplicates, formation energy remains the key metric for stability in crystal generation, which is why we prioritized it.

Thank you again for your constructive feedback. We will refine our work to address these points in more detail.

Thank you for your valuable feedback on our paper. We appreciate the time you have taken to provide a thorough review. Below, we address each of your concerns:

Firstly, scope. The primary aim of our paper is to create a comprehensive comparison of different generative approaches in the field of machine learning for crystalline structure generation. While we acknowledge that including multiple methods can dilute the focus in a short paper format, we believe that providing a broad overview offers significant value to the community. It allows for a mini-benchmark of different generative approaches, highlighting the strengths and weaknesses of each. This can serve as a foundation for future research to build upon and refine.

Second, approach. We recognize that there are potential design issues with the technical approach. Specifically, the concern about the model's invariance or equivariance under permutation, translation, and rotation is valid. To address this, we have implemented steps to mitigate these issues. For example, we standardize the orientation of all crystal structures and sort atoms according to their chemical elements. Also, crystal structure representation includes space groups, which has sufficient information about symmetries of a structure. In our future work, we will explore the use of equivariant architectures and more robust data representations to further improve the model's reliability.

Third, results. We acknowledge that the explanation of our results and their impact was limited by space constraints. To address this, we will revise the manuscript to better highlight the significance of our findings and provide a more detailed comparison with existing approaches. Specifically, we will include metrics such as the ratio of the number of crystal structures generated by our model to the number of optimal structures, demonstrating that our method is state-of-the-art in this regard.

We agree that Figure 1 is simplistic and may not add substantial value to the paper. We will remove or replace it with a more informative figure. Additionally, we will improve the overall typesetting and presentation to ensure a more professional appearance.

We appreciate your detailed technical questions. To address the concern about the conditioning approach and space group compliance, we agree that a guidance-based conditioning approach could be more suitable. In future work, we will explore methods to enforce space group compliance directly within the generative process. Additionally, we will include a thorough discussion of the limitations of our current approach, acknowledging areas for improvement and potential future directions.

In conclusion, we are committed to addressing the issues raised in your review. We believe that our paper makes a valuable contribution by benchmarking various generative models for crystalline structure generation and providing a distinctive model architecture. We will refine our manuscript to ensure that the results are presented more clearly and the limitations are transparently discussed.

Thank you once again for your constructive feedback.