UniMate: A Unified Model for Mechanical Metamaterial Generation, Property Prediction, and Condition Confirmation

Thank you for the reviewer’s time and constructive comments. We sincerely appreciate the opportunity to address the concerns and clarify our work.

Q1: Similar concepts have been explored in an image-text work (i.e., Janus, which is mentioned by the reviewer).

A1: We appreciate the reviewer for pointing out the paper Janus, a multimodal understanding and generation model. While we acknowledge that our work and Janus may share high-level conceptual similarities, there are significant distinctions between the two:

• Task Focus: Janus is designed for general vision-and-language understanding tasks, whereas our model specifically targets metamaterial design, a domain with unique challenges and goals not addressed in Janus.
• Methodology: Janus integrates image information by projecting it into the input space of a large language model (LLM), combining it with textual data for joint understanding. In contrast, our approach projects all three modalities into a shared embedding space that is not biased toward any single modality. This unified representation is better suited to the nature of metamaterial design problems.

Q2: The reviewer was not sure whether any important baselines are missed in our work.

A2: In our experiments, we have carefully selected representative baselines to provide a fair and comprehensive comparison. To the best of our knowledge, the models we included reflect the current state-of-the-art computer science works in the field of metamaterial design. Still, we are open to including additional baselines should we find any relative suggestions.

Q3: For masked tokens, is the marginal distribution initialized directly as a Gaussian distribution?

A3: We thank the reviewer for the question regarding token initialization. In our implementation, we initialize tokens based on the transport plan, assigning higher probabilities to tokens with higher values in the transport plan. In response to the reviewer's question, we explore several alternative initialization strategies: pure Gaussian noise, a mixture of transport plan-based initialization, and Gaussian noise. The results of these variants are presented below.

We sincerely thank the reviewer for their time and constructive feedback. Please find our detailed responses and corresponding revisions below:

Q1: One point in the work that "it will be simpler...the generation process" is not proven in later experiments.

A1: Thank you for your detailed reviews. To address this issue, i.e., the effectiveness of using a codebook for diffusion starting point initialization, we conduct additional experiments (random noise initialization and mixed initialization), with detailed results reported in reply to Q3 from reviewer 79DH.

Q2: Ablation for partially frozen diffusion is needed.

A2: We appreciate your constructive suggestion. Accordingly, we compare the use of a partially frozen diffusion with a vanilla diffusion setup (i.e., where variables in all dimensions are denoised at each step). The results below verify the effectiveness of partially frozen diffusion. We will include the results in the final version of the manuscript.

Q3: Further ablation studies are needed, such as the size of the code book and different soft-round strategies.

A3: Thanks for the valuable suggestion. According to your suggestion, in addition to the varying codebook sizes experiments conducted in Section 4.4. Below, we provide more results using a soft-round strategy (midpoint interpolation between the initial value and the target rounding token), which shows the effectiveness of codebook rounding.

Q4: It is unclear why Fqua and Fcond are valid metrics for evaluating generation quality; generated topologies are not validated for effectiveness and manufacturability.

A4: Thanks for the detailed reviews. Our evaluation metrics are inspired by and adapted from prior literature that adopted similar concepts. Specifically:

• Fqua evaluates the quality of generated topologies by measuring their symmetry degree and periodicity.
• Fcond evaluates how well the generated topologies satisfy the input conditions by comparing them with ground truth topologies that fully match those conditions.

Please also refer to Reviewer 44SV A1 for more detailed illustrations. We will include these detailed illustrations in our final version.

Furthermore, we have collaborated with a metamaterial lab to physically manufacture the generated topologies and test their properties. We plan to release a demonstration video showcasing this process after the double-blind review period concludes.

Q5: Why the author only compares three baselines in time and memory efficiency analysis?

A5: We appreciate your careful reviews. In the model efficiency analysis section, we present the results for three representative baselines for clarity and brevity. Below, we provide the complete set of results for all baselines, from which we can reach the same conclusion as stated in our manuscript, and we will include these in the appendix of the revised version.

Q6: In parameter sensitivity, why do the authors only use the metric Fqua?

A6: We thank you for the constructive feedback. Accordingly, we include the parameter sensitivity analysis w.r.t. all metrics. In the sensitivity study, since we consider the topology generation task to be relatively hard among the three tasks, and Fqua is a typical indicator of the generation quality, we provide the results related to Fqua. Below, we provide results for the other evaluation metrics as well. These will be added to the appendix in the final version.

Parameter Sensitivity regarding other metrics (Fcond/NRMSE_pp/NRMSE_cc)

Thanks for the reviewer's time and inspiring comments. Here, we summarize the major points from the reviewer and our rebuttal as follows:

Q1: The proposed model is evaluated on a new dataset and custom metrics.

A1: Our work focuses on developing a unified model capable of handling diverse metamaterial design tasks as a whole. This is a relatively underexplored area, and to the best of our knowledge, there has not been a comprehensive effort to address it so far. As a result, no suitable dataset currently exists for this task. Therefore, we propose our own dataset tailored to this problem. Additionally, we introduce custom evaluation metrics to assess the quality of generated structures by referring to previous material works. Specifically, the two metrics—Fqua and Fcond—are inspired by previous works [1–4]. References [1,2] emphasize the importance of symmetry and periodicity in metamaterial design, which directly motivates our Fqua metric that quantifies the degree of symmetry and periodicity in the generated topologies. Similarly, references [3,4] propose comparison techniques for assessing topology similarity and generation coverage. Building on these ideas, our Fcond metric evaluates how well the generated structures match the target conditions by comparing their topological features.

[1]Abu-Mualla, Mohammad, and Jida Huang. "A Dataset Generation Framework for Symmetry-Induced Mechanical Metamaterials." Journal of Mechanical Design 147.4 (2025).

[2]Bitzer, Andreas, et al. "Lattice modes mediate radiative coupling in metamaterial arrays." Optics Express 17.24 (2009): 22108-22113.

[3]Tian Xie, Xiang Fu, Octavian-Eugen Ganea, Regina Barzilay, and Tommi S. Jaakkola. 2022. Crystal Diffusion Variational Autoencoder for Periodic Material Generation. In ICLR.

[4]Nils ER Zimmermann and Anubhav Jain. 2020. Local structure order parameters and site fingerprints for quantification of coordination environment and crystal structure similarity. RSC advances 10, 10 (2020), 6063–6081.

Q2: The baselines are not originally designed for the tasks in our work.

A2: As mentioned in A1, this is a relatively new task, making it difficult to find baselines that are directly aligned with our objective. This challenge is further amplified by the fact that metamaterial design remains largely underexplored within the computer science community. Nevertheless, we conducted extensive experiments by tuning the hyperparameters of existing baseline methods to better assess their potential performance on our task. Here, we focus on the second best model, uniTruss, as an example. uniTruss has two main hyperparameters, learning rate (LR) and latent dimension. As shown in the following, we report the results on four LR and five latent dimensions. Results show that for both property prediction and density confirmation, the best LR is 5e-4 and the best latent dimension under this LR is 32.

(Property Prediction Task) Tuning learning rate, bold denotes the results reported in original manuscript.

(Property Prediction Task) Tuning latent dimension for property prediction

(Density Confirmation Task) Tuning latent dimension for density confirmation

Q3: More experimental details about dataset construction and network design might help readers to reproduce the method.

A3: We appreciate the suggestion to include more details about dataset construction and network design. We will incorporate the following information into the appendix to improve the clarity and completeness of the paper.

• For dataset construction, we use homogenization simulation to calculate the property of topologies. We will add details about how homogenization works. Also, we will add details about density selection, e.g., the range from which the edge radius is selected.
• For network design, we will add more details about each component of our model, including the layer number of the GCN encoder, the MLP encoder, the transformer backbone, the latent dimension of each component, etc. We hope this will help increase the clarity and reproducibility of our work.