Response to Reviewer CHTQ

Thank you for your positive review and insightful questions. We are grateful for your recognition of our work's novelty and contributions. We address your comments below:

Weakness 1: Need more parameter sensitivity analysis.

We appreciate this valuable feedback. For example, the orthogonality loss weight $\lambda_o$ is critical for balancing disentanglement and prediction accuracy. Our preliminary analysis shows:

As shown above, $\lambda_o$=0.5 and $\lambda_o$=1.0 provide the optimal balance for ID and OOD settings respectively. Too small a value ($\lambda_o$<0.3) results in insufficient separation of static and dynamic components, while too large a value ($\lambda_o$>1.0) overly constrains the model's expressiveness. The model maintains strong performance across a reasonable range of values.

Weakness 2: Limited discussion of baseline methods.

Thank for the friendly reminder. We will provide a more comprehensive discussion of baseline methods in the revised version.

Question 1: Implementation details of variational inference?

Our CMCD module implements variational inference by treating coupling factors $\eta_i(t)$ as confounding variables, parameterized via $q(\eta_i(t)|h_i(t))$ with $\zeta_i(t) = \text{Softmax}(W_\eta h_i(t))$. We employ Gumbel-Softmax sampling for differentiability: $\eta_{i,k}(t) = \frac{\exp((\zeta_{i,k}(t)+g_k)/\tau)}{\sum_j \exp((\zeta_{i,j}(t)+g_j)/\tau)}$. The KL divergence term $\text{KL}(q(\eta_i(t)|h_i(t))\|p(\eta_i(t)))$ regularizes against a context-agnostic prior, reducing spurious correlations. This approximates the interventional likelihood $\log p(y_i(T)|\text{do}(h_i(t_0)),\mathcal{G})$, enabling our model to learn universal physical dynamics rather than domain-specific patterns. All components are jointly optimized, allowing the coupling inference to leverage both static and dynamic information for robust generalization.

Question 2: Reason for superior performance in longer predictions?

GREAT's superior long-term prediction performance stems from several key mechanisms working in concert: First, our effective disentanglement prevents error accumulation by maintaining consistent static components while allowing dynamic components to evolve naturally. Second, the CMCD module enables coupling-aware evolution that explicitly models inter-node influences, capturing complex interdependencies crucial for extended horizons. Third, the DHPA component captures self-exciting temporal patterns at multiple scales, effectively modeling both short-term fluctuations and long-term trends. Finally, empirical stability analysis shows our error growth rate is significantly lower in Figure 6. These advantages make GREAT particularly suitable for applications requiring extended forecasting horizons in complex physical systems.

Response to Reviewer XMqH

Thank you for your thorough review and encouraging feedback. We are grateful for your positive assessment about novelty and importance of our work. We address your questions below:

Weakness: Limited exploration of approach limitations.

We fully agree that a more thorough discussion of limitations would significantly strengthen the paper. In the revised version, we will add a dedicated limitations section that provides comprehensive analysis. One potential limitation is training stability: Similar to many deep learning approaches utilizing variational inference, our method requires careful tuning to balance multiple loss components (prediction loss, orthogonality loss, and KL divergence term). We will provide detailed discussion of these potential training challenges along with practical strategies for mitigating them through hyperparameter selection and optimization techniques.

Comment: Need clearer baseline implementation details.

We sincerely thank you for this suggestion. We will enhance the baseline description and implementation details in the revised version.

Question 1: Robustness when static/dynamic distinction is ambiguous?

This is an excellent question. Our decoupling mechanism employs several strategies to maintain robustness:

1. Orthogonality regularization ($L_o$): The loss function in Eq.8 enforces strict orthogonality between the static and dynamic subspaces, helping to separate features even when they appear entangled. Our experiments show that without this regularization, performance drops by 12.3% on average in OOD settings.
2. Learnable subspaces: Rather than using predetermined feature splits, our approach learns the separation through end-to-end training. The embedding layers $S_{static}$ and $S_{dynamic}$ adaptively determine the optimal projection for each domain, allowing the model to discover natural separations even in ambiguous cases.
3. We employ a synergy decoder (Eq.12) that allows information to flow from both static and dynamic components. This ensures that even if some features are misclassified during training, critical information is not lost during reconstruction.
4. We introduce a DHPA that dynamically adjusts the importance of different feature patterns at multiple scales. This helps the model better handle ambiguous cases by learning to focus on the most relevant patterns for dynamic separation at each level of abstraction. Our experiments show this further improves robustness in Figure 5.

Question 2: Stability across different training configurations?

We have conducted extensive experiments to verify GREAT's stability across different training configurations. The final reported results from all tables are the result of 5 random seeds. Here, we also tested various learning rates and training epochs on the SPRING dataset. The results demonstrate that GREAT maintains stable performance across a range of configurations:

Response to Reviewer qXoi

Thank you for your constructive comments and positive assessment of our work. We address your concerns below and hope our responses will help update your score:

Weakness 1: Limited background on coupling dynamics.

We sincerely appreciate this valuable suggestion. Due to space limitations, we provided only essential background information. We will expand the background section in the revised version to include more examples and fundamental principles of coupled dynamical systems.

Weakness 2 & Comment 2: Small datasets and need molecular system testing.

We greatly appreciate these insightful suggestions. We respectfully would like to clarify several points regarding the systems in our experiments:

1. While appearing simple, our systems exhibit strong interaction patterns: the CHARGED system demonstrates complex electromagnetic interactions with high coupling strengths, and the PENDULUM system captures chaotic behaviors with highly entangled dynamics.

2. Following standard settings in previous works [1,2], these systems were deliberately chosen as they present the core challenges (static-dynamic entanglement and coupling bias) that our method addresses. These challenges are fundamental across coupled systems regardless of complexity level and have been widely recognized in the field.

3. Our OOD experiments already demonstrate generalization across varying interaction strengths by testing with different coupling parameters (e.g., interaction strength γ∈[0.05,0.15] for SPRING and γ∈[0.5,1.5] for CHARGED in OOD settings).

4. We appreciate your suggestion about molecular systems and have conducted preliminary experiments on MD17:

We report RMSE values (Å) on MD17 dataset with irregular temporal sampling where only 60% of timesteps were randomly sampled and follow other stanard setting in our manuscript. GREAT also performs well on molecular systems because these systems naturally exhibit the same challenges our method addresses: varying interaction patterns. Our approach effectively captures both local and global dynamics, achieving the best performance on 7 molecules. We acknowledge the value of testing on diverse systems and will include more comprehensive results including QM9 in the revised version.

Comment 1: Need visualization of orthogonality loss.

Thank you for this valuable suggestion. The orthogonality loss trajectory during training on SPRING:

As shown, the orthogonality loss steadily decreases during training, indicating effective disentanglement of static and dynamic components. We have also demonstrated its effectiveness through ablation studies in Sec. 4.4 and Figure 5. We will include more detailed visualizations in the revised version.

Concern 1 (Experimental Designs Or Analyses): OOD setting.

Our OOD split based on system parameters follows established practices in prior work [1] and directly tests the primary challenge in coupled dynamical systems: generalization across varying initialization conditions. This design has strong physical meaning as parameter changes, fundamentally alter system dynamics.

[1]: Pgode: Towards high-quality system dynamics modeling. In ICML, 2024. [2]: Physics-informed regularization for domain-agnostic dynamical system modeling. In NeurIPS, 2024.

Response to Reviewer LVHe

Thank you for your thorough review and constructive feedback. We address your concerns below and hope these clarifications will help you re-evaluate and update the score:

Weakness 1: Systems too simple with low dimensionality (≤5).

Thank you for this observation. We would like to offer several considerations that guided our experimental design:

1. These systems exhibit complex nonlinear dynamics and chaotic behaviors. We calculated the Maximum Lyapunov Exponent (MLE) for each system, where positive values indicate chaotic dynamics:

   SPRING	CHARGED	PENDULUM
   0.651	0.875	18.932

   As shown, all systems exhibit positive MLEs, with PENDULUM showing strong chaos (MLE≫0). The SPRING system captures elastic interactions with long-range dependencies, the CHARGED system models electromagnetic forces with phase transitions, and the PENDULUM system demonstrates extreme sensitivity to initial conditions—each representing distinct coupling mechanisms common in real-world applications.

2. Our research addresses two challenges in GraphODE generalization: static-dynamic entanglement and coupling pattern bias. These challenges are intrinsic to coupled systems regardless of dimensionality.

3. Following established practice [1,2], these systems serve as standard benchmarks enabling fair comparison with prior work.

4. We conducted additional experiments on a higher-dimensional SPRING system (10 particles) and the MD17 molecular dynamics (please refer to response to Reviewer qXoi), where GREAT consistently outperformed baselines:

   RMSE	LatentODE	LG-ODE	PGODE	GREAT
   ID	7.65	6.27	4.92	4.29
   OOD	8.37	6.81	5.39	5.01

[1]: Neural Relational Inference for Interacting Systems. In ICML, 2018. [2]: Physics-informed regularization for domain-agnostic dynamical system modeling. In NeurIPS, 2024.

Weakness 2: Unclear motivation for Dynamic Hawkes Process Augmentation.

DHPA addresses a fundamental challenge: coupled systems exhibit complex temporal dependencies that basic representations cannot capture. While our disentanglement separates static and dynamic features, the dynamic component needs enhancement to model multi-scale patterns. Following a "divide and conquer" strategy, DHPA strengthens the dynamic representation with weighted historical information: $\hat{o}\_i(t) = o_i(t) + \delta\sum_{\tau=1}^s w_{\tau,t}\cdot o_i(t-\tau)$. This approach is universal across systems because its adaptive weights $w_{\tau,t}$ automatically adjust to each system's temporal characteristics, with its effectiveness confirmed by our ablation studies (Fig.5).

Weakness 3: Insufficient validation of claimed advantages.

We provided ablation studies in Figure 5 and Section 4.4 demonstrating each component's contribution. Additional evidence validates our key contributions:

Challenge 1: Static-Dynamic Disentanglement: The orthogonality loss decreases during training, showing successful separation:

Feature separation testing: Mutual information (MI) analysis between static and dynamic representations with permutation tests: https://anonymous.4open.science/r/Response_to_Reviewer_LVHe-F29E/table-MI.md. MI was estimated using the Kraskov estimator across 1000 time points, with permutation tests (10,000 shuffles). Decreasing p-values confirm statistically significant separation. The steady MI decrease demonstrates our model eliminates information leakage between representation spaces.

Temporal consistency: Cosine similarity between representations at t=0 and later points confirms static representations maintain higher consistency: https://anonymous.4open.science/r/Response_to_Reviewer_LVHe-F29E/table-time-consistency.md

Challenge 2: Coupling Pattern Capture: Our experiments and ablation studies demonstrate GREAT's superior performance in OOD scenarios. Our theoretical analysis in Section 3.3 provides rigorous justification by formulating the problem through a causal lens - modeling coupling factors as confounding variables and deriving an interventional likelihood $p(y_i(T)|do(h_i(t_0)), \mathcal{G})$ rather than observational likelihood. Theorem 3.1 proves this formulation captures intrinsic physical dynamics invariant, going beyond empirical validation to provide theoretical guarantees.

We will include more detailed analyses in the revised version.

Other Comment: Excessive icons in Figure 3.

We agree and will simplify Figure 3 while maintaining the figure's informational content.