- Source of Improvement and Ablation Study:
- Given the presence of various complex architectural choices, it's difficult to determine whether the Helmholtz decomposition is the primary source of the observed performance improvement. Notably, the absence of the multi-head mechanism leads to a performance drop (0.1261 -> 0.1344) for the 64x64 Navier-Stokes, which is somewhat comparable to the performance decrease resulting from the ablation of the Helmholtz decomposition (0.1261 -> 0.1412). These results raise questions about the model's overall performance gain compared to the baseline models when the multi-head trick is absent. Additionally, the ablation studies need to be explained more comprehensively with sufficient details, as the current presentation makes it difficult to understand the methodology and outcomes.
- The paper claims that Vortex (Deng et al., 2023) cannot be tested on other datasets, which seems unusual, as they are the same type of task and data that are disconnected from the choice of dynamics modeling itself. It should be further clarified why Vortex cannot be applied to other datasets.
- Interpretability Claim:
- The paper's claim about interpretability is not well-explained. If the interpretability claim is based on the model's prediction of an explicit term of velocity, it needs further comparison and a more comprehensive explanation. Does the Helmholtz decomposition significantly improve interpretability compared to baseline models, such as Vortex (Deng et al., 2023)?
- In Figure 4, it appears that the model predicts incoherent velocity fields around the circle boundary, even with non-zero velocity outside the boundary, while baseline models do not exhibit such artifacts. This weakens the interpretability claim.
- Multiscale modeling:
- The aggregation operation after "Integration" needs further clarification. Please provide more details in the main paper, and if you refer to other architectures, acknowledge their structure properly.
- Regarding some missing experimental results with cited baselines, it's crucial to include and report all baseline results to ensure transparency, even if the outcomes are considered inferior.
- Minor issues:
- Ensure proper citation format for baseline models (Authors, Year).
- Make sure that symbols are well-defined with clear reference to their definitions. For example, in Equation (4), the undefined operator $\mathbb{I}_{\vec r\in\mathbb{S}}$ needs clarification. If it's an indicator function, use standard notation with a proper explanation. "Embed(•)" should be indicated more explicitly.
- Multiscale modeling:- The aggregation operation after "Integration" needs further clarification. Please provide more details in the main paper, and if you refer to other architectures, acknowledge their structure properly.