Eulerian Neural Network Informed by Chemical Transport for Air Quality Forecasting

Dear reviewer,

We thank you for the positive feedback on our manuscript, particularly for highlighting the clarity of our problem setting and methodology, as well as the physical grounding of our model components.

We address the your concerns as follows:

To W1: About Clarity and Reproducibility

1. Clarity and Style

We apologize for any lack of clarity in the method description. The modular approach we adopted in describing CTENet is intentional, as it aligns with prior works in NeurIPS(such as [1,2]). These works also decompose complex systems into well-defined modules, which aids in presenting the model in a more structured manner. We will strive to improve the clarity of the model description, ensuring that the individual components and their relationships are more explicitly defined.

2. Reproducibility

We provide implementation details in Section 5 and Appendix D, including data, model settings, and training procedures. The source code is publicly available (link in Abstract), and we’re happy to share the processed dataset upon request to support reproducibility.

[1] Zhang, Y., Liu, Q., & Chen, H. (2024). Suitable is the Best: Task-Oriented Knowledge Fusion in Vulnerability Detection. In Proceedings of the 38th Conference on Neural Information Processing Systems (NeurIPS 2024).

[2] Wang, L., Zhao, M., & Xu, J. (2024). Neural Krylov Iteration for Accelerating Linear System Solving. In Proceedings of the 38th Conference on Neural Information Processing Systems (NeurIPS 2024).

To Q1: About Eulerian Definition

Thank you for your question.

As stated in Section 1 Introduction of the paper, Eulerian model[3] refers to the fact that our model operates on a fixed, gridded spatial domain. In contrast to prior air quality forecasting approaches—many of which, whether physics-guided or not, rely on discrete station-level modeling—CTENet models the continuous spatial evolution of pollutant concentrations over a structured and uniform Eulerian grid. This gridded representation is crucial for capturing fine-grained spatial correlations and for enforcing physically consistent processes—such as advection and diffusion—that are inherently defined in continuous space.

[3] Johnson JB. An introduction to atmospheric pollutant dispersion modelling. Environmental Sciences Proceedings. 2022 Jul 14;19(1):18.

To Q2: About Missing Term

We apologize for the confusion.

Equation 6 presents the continuous form of the Advection–Diffusion–Reaction (ADR) equation. As in references [44, 45, 11, 17] cited in our paper, the equation does not include the additional term $X \cdot \mathrm{div}(\vec{W})$.

This is because atmospheric wind speeds on Earth are typically below 30 m/s, which is significantly lower than the speed of sound in air (~343 m/s). Under such conditions, the flow can be reasonably approximated as incompressible, so that $\mathrm{div}(\vec{W})=0$ . This assumption is widely adopted in air quality modeling and greatly simplifies the advection operator.

To W2 & W4.1: About Fairness in Data Usage

Thank you for the question about fairness in Data Usage!

As described in Section 5 (Experiments), all baseline models are provided with the same set of meteorological data as CTENet, including the full 354-channel input. For station-based baselines that cannot directly process gridded inputs, we extract the corresponding meteorological features from the grid cell that contains each station's location (see Section 5: Baselines). This design ensures a fair and controlled comparison across all methods. Therefore, the performance gain of CTENet is attributable to its architectural design rather than differences in input data.

To W4.2 & Q3: About Novelty and RBF

We sincerely apologize if our presentation led to any misunderstanding of the central Novelty of our work. Here is my detailed explanation:

1. Previous air quality forecasting network often operate on sparse station data and neglect spatial continuity, despite pollution being inherently continuous. CTENet is, to the best of our knowledge, the first to introduce continuous pollutant modeling into air quality prediction via deep learning, using chemical transport priors within a PINN-style architecture.

2. Regarding RBF interpolation, our aim is not optimal interpolation accuracy but a fast, parameter-free method that ensures stable and efficient training. While more accurate methods exist, they are computationally costly and beyond the scope of this work. RBF provides a continuous spatial estimate from discrete stations, enabling convolutional processing in our architecture. As shown in Appendix F, we compare RBF with alternatives and include an ablation without interpolation, validating the robustness of our choice.

To Q4: About Evaluation Metrics

Thank you for the helpful comment. We believe there may be a misunderstanding between MAE and RMSE (likely referred to as MSE in your note). These metrics capture different aspects of error—MAE measures average error magnitude, while RMSE penalizes larger deviations more heavily. As shown in the toy example below:

Baseline 2 has lower MAE but higher RMSE, due to the outlier at x₄. Thus, discrepancies between MAE and RMSE are expected and informative. We hope this clears up any confusion.

To W3&Q5: On Interpretability and Physical Decomposition

We sincerely apologize for the confusion this may have caused.

1. On Interpretability

While deep learning models are often criticized as black boxes, CTENet is specifically designed to move beyond black-box behavior by embedding domain knowledge from chemical transport modeling (CTM) into the learning architecture. In particular, the model learns:

• How meteorological variables interact with air pollutant dynamics — including temperature, wind, and solar radiation effects — enabling the network to capture nonlinear, spatial-temporal dependencies that are difficult to model explicitly using traditional CTMs.
• How to dynamically integrate multiple predictive sources — including physical components such as diffusion, advection, and chemical reactions, as well as purely data-driven residual models. This fusion is learned through a neural attention-based weighting mechanism that adapts over space and time.

2. On Signal Decomposition

As shown in Figure 2, our model dynamically fuses four predictive components—diffusion, advection, chemical reaction, and a data-driven correction—each reflecting a distinct physical or empirical process. These components are treated as separate input channels, but their integration is handled implicitly through learned non-linear mappings. As a result, the final prediction is not a simple additive combination and cannot be directly decomposed as in traditional PDE solvers. This design allows the model to flexibly capture complex, context-dependent interactions that are challenging to encode explicitly.

To W5: About statistical Significance

We thank you for your helpful suggestion regarding the statistical robustness of our results. In response:

1. Statistical Significance Analysis:

As documented in Appendix J, we conducted statistical significance analysis to assess the reliability of the performance differences.

2. Standard Deviations:

Due to time constraints, we conducted five independent runs (with different random seeds) for the best-performing CTENet variant and the two strongest baselines. The mean and standard deviation of the results are reported below:

Moreover, two-sided t-tests confirm that CTENet's improvements over both baselines are statistically significant across nearly all metrics (p < 0.005), reinforcing the robustness of the observed performance gains.

To Q6: About Wind Prediction

Thank you for the insightful question !

We confirm that our model does include a lightweight wind forecasting component to predict future wind fields. As described in the paper, the Wind Predictor module is implemented using a Spatiotemporal Sequence Predictor, which takes historical wind fields as input and predicts wind fields at the next time step. These predicted wind components are then passed into the Eulerian ADR Decoder to simulate wind-driven advection.

We believe our wind predictor is sufficiently accurate for the intended use case, for the following reasons:

1. Ablation studies(Section 5.2) demonstrate the importance of advection: removing the advection module (which depends on wind prediction) leads to significant performance degradation. Specifically, the RMSE increases by 10.6% and 21.8% on the two datasets, respectively, when advection is ablated.

2. A case study (Section 5.4) visually demonstrates the role of wind-driven advection in pollutant transport, further validating the model’s ability to learn physically meaningful wind patterns that align with observed pollutant dispersion behavior.

In Summary

We are grateful for your thoughtful comments and suggestions. We have conducted additional experiments in response to your feedback and are in the process of further revising the manuscript accordingly. We fully respect your judgment and would greatly appreciate any further guidance you may have.

Dear reviewer,

We sincerely thank you for your time and constructive comments. We are glad that our work's practical potential for improving air quality forecasting has been recognized.

Below, we provide detailed responses to the concerns raised and clarify the novelty and significance of our contributions within the ML context.

To W1:

Thank you for your thoughtful comment. CTENet was not originally designed with the goal of producing uncertainty-aware predictions; instead, our focus was on achieving accurate and timely point forecasts. We acknowledge that the ability to quantify predictive uncertainty is crucial in health-critical applications, where decision robustness is essential.

Importantly, the architecture of CTENet is flexible enough to accommodate uncertainty estimation methods. Techniques such as Monte Carlo Dropout, deep ensembles, or Bayesian neural networks can be integrated with minimal structural modification. We believe that coupling these approaches with CTENet’s physics-informed design can enable reliable prediction intervals or probabilistic outputs, thereby enhancing its applicability to high-risk scenarios.

To W2:

Thank you for your detailed and professional comment regarding scalability. As you correctly pointed out, and as analyzed in Appendix G, CTENet employs a grid-based architecture that incurs higher computational complexity compared to graph-based models. We fully acknowledge this trade-off between physical fidelity and computational efficiency.

• We believe that in large-scale operational settings—such as enterprise-level or national-scale deployments—the modest increase in computational cost is acceptable given the substantial performance gains CTENet offers over existing methods. For example, on the USA dataset, CTENet achieves an average RMSE reduction of 45.8% compared to strong graph-based baselines.

• Despite the increased theoretical complexity, CTENet remains highly practical for real-world deployment. On a single RTX 4090 GPU, the complete training process can be completed within 3 to 6 hours, depending on the data volume and forecast horizon. More importantly, during inference, generating a 72-hour forecast over the China dataset takes less than 0.15 seconds, which is fast enough to meet the requirements of most real-time applications.

That said, we agree that scalability is a meaningful consideration, and we are actively exploring architectural optimizations such as mixed-precision computation and model pruning to further reduce CTENet’s computational footprint in future work.

To Q1:

Thank you for the thoughtful question.

We acknowledge that observational noise—especially in low-cost sensor data—is a critical challenge in air quality modeling. CTENet does not explicitly model uncertainty or input-level noise. However, it benefits from several indirect mechanisms that enhance robustness.

1.First, the incorporation of a chemically inspired transport-reaction model serves as a strong structural constraint. By encouraging the model to follow physically plausible pollutant dynamics, it helps suppress overfitting to spurious or noisy fluctuations in the observations—particularly those that violate mass conservation or chemical balance.

2.Second, standard training practices such as early stopping, dropout, and gradient clipping are used to reduce the model's sensitivity to label noise.

That said, CTENet currently does not include dedicated noise modeling components such as uncertainty-aware loss functions or observation-level confidence weighting. We see this as a meaningful direction for future work—for example, by incorporating heteroscedastic noise models, robust PDE solvers, or sensor-aware weighting schemes.

We appreciate you raising this important point.

To Q2:

Thank you for the insightful question. While social vulnerability data is not directly relevant to the physical processes modeled by CTENet—such as pollutant transport and chemical transformation—the framework is modular and can be extended to incorporate additional data sources in downstream applications.

For example, once pollutant concentrations are forecasted, social vulnerability indices (e.g., age distribution, income level, access to healthcare) can be integrated in post-processing or risk assessment layers to support health impact forecasting, environmental justice analyses, or targeted early warning systems. In such contexts, CTENet's outputs could serve as physically grounded inputs to broader decision-support frameworks where social vulnerability plays a critical role.

Therefore, although CTENet does not require social data for concentration prediction, it can be readily combined with such datasets in multi-task or multi-stage systems aimed at population-level risk mitigation.

To Q3: Thank you for your detailed and professional comment. CTENet is inherently resolution-adaptive and supports deployment across multiple grid scales, from regional to national levels. Since the model operates on both discrete station observations and continuous meteorological fields, its effective resolution is typically aligned with that of the meteorological input to ensure optimal performance.

When the input data is provided on a coarser or finer grid, the overall model architecture remains unchanged. However, certain hyperparameters—particularly those related to the numerical implementation of the PDE constraints—are adjusted to match the spatial resolution. For instance, spatial step sizes used in the calculation of gradients and Laplacians are resolution-dependent, and must be set accordingly to preserve the stability and accuracy of the PDE-based loss terms.

Dear reviewer,

We sincerely thank the you for your thoughtful evaluation and constructive feedback. We appreciate the acknowledgment of our physics-driven spatial continuity modeling. We now address your raised concerns in detail:

To W1:

Thank you for your comments regarding the originality of our work. We apologize for any confusion caused by our previous explanation. While it is true that CTENet incorporates established techniques such as RBF interpolation, modular predictors, and physics-informed neural networks (PINNs), we would like to clarify that these components are not the main novelty of our work. As highlighted in the Introduction, the primary contributions of CTENet are as follows:

1. Eulerian spatial modeling:

Prior works on air quality prediction typically treat the problem as a set of discrete monitoring stations, overlooking the spatial continuity of pollutant fields. To the best of our knowledge, CTENet is the first PINN-based framework to model air quality prediction directly in continuous space. Furthermore, although some of the prior works [1,2] incorporate physical constraints, but they are still based on discrete station-level modeling. As a result, advection and diffusion are modeled via edge-weighted graph operators, which do not reflect the continuous nature of atmospheric transport. In contrast, CTENet models pollution dynamics over a spatially continuous domain, enabling more realistic and physically consistent forecasting.

In this process, the use of RBF interpolation serves purely as a preprocessing step to convert sparse station data into a gridded format compatible with subsequent convolutional operations. We also provide comparisons with alternative interpolation methods—as well as a non-interpolated setting—in Appendix F. The results support the effectiveness and robustness of our choice.

2. Incorporation of chemical reactions:

Unlike prior PINN-based approaches that focus solely on advection and diffusion, CTENet explicitly incorporates a chemical transport module—an element absent from existing physics-informed air quality models. This design allows CTENet to account for a range of additional environmental factors that significantly influence pollutant evolution, including solar radiation, atmospheric stability, terrain elevation, and even soil moisture. These drivers enable the modeling of essential processes such as photochemical reactions and gas-to-particle conversion, which are known to cause nonlinear transformations among pollutants. As a result, CTENet can capture dynamic equilibrium shifts between gaseous and particulate species, enabling more realistic and chemically consistent multi-pollutant forecasting.

To the best of our knowledge, CTENet is the first to implement a physics-informed neural network based on the Eulerian framework for air quality prediction. We will revise the paper to more clearly highlight these contributions—both in terms of methodology and their implications for real-world data-driven environmental modeling.

[1] Kethmi Hirushini Hettige, Jiahao Ji, Shili Xiang, Cheng Long, Gao Cong, and Jingyuan Wang.Airphynet: Harnessing physics-guided neural networks for air quality prediction. arXiv preprint arXiv:2402.03784, 2024.381

[2] Jindong Tian, Yuxuan Liang, Ronghui Xu, Peng Chen, Chenjuan Guo, Aoying Zhou, Lujia Pan,Zhongwen Rao, and Bin Yang. Air quality prediction with physics-guided dual neural odes in open systems. In The Thirteenth International Conference on Learning Representations, 2025.

To W2:

We apologize for any confusion caused by our explanation. We would like to clarify that the observed performance improvements are not solely due to architectural adjustments. As mentioned earlier, the main novelty of our work lies in several key aspects that distinguish it from prior approaches:

1. From the perspective of spatial continuity, we employ Eulerian spatial modeling to more accurately capture the evolution of pollutants in space. This approach allows for a more robust representation of pollutant dispersion and transformation across regions using NN, which goes beyond what has been addressed in earlier works.

   • Although AirFormer captures spatial correlation by encoding relative positions of neighboring stations, it does not model spatial continuity in any physically meaningful sense. In fact, AirFormer's design reinforces the importance of spatial structure in air quality prediction, yet it remains fundamentally a discrete, station-based model. It lacks any mechanism to simulate continuous spatial transport processes such as advection and diffusion, which are central to our Eulerian PDE-based framework. This distinction is also reflected in empirical performance. As shown in our experiments (§5.1), CTENet consistently outperforms AirFormer across multiple datasets and metrics, highlighting the effectiveness of physically grounded, continuous-domain modeling over discrete attention-based approaches.

2. We account for the intricate chemical transformations of pollutants, distinguishing our model from previous works that focused primarily on physical processes. This inclusion of chemical processes enhances the predictive capability of CTENet, making it more suitable for real-world applications.

We will revise the manuscript to better highlight these distinctions and to clarify how CTENet advances the state of the art both in terms of formulation and real-world applicability.

To W3:

Thank you for your detailed and professional comment regarding scalability. As you correctly pointed out, and as analyzed in Appendix G, CTENet employs a grid-based architecture that incurs higher computational complexity compared to graph-based models. We fully acknowledge this trade-off between physical fidelity and computational efficiency.

• We believe that in large-scale operational settings—such as enterprise-level or national-scale deployments—the modest increase in computational cost is acceptable given the substantial performance gains CTENet offers over existing methods. For example, on the USA dataset, CTENet achieves an average RMSE reduction of 45.8% compared to strong graph-based baselines.

• Despite the increased theoretical complexity, CTENet remains highly practical for real-world deployment. On a single RTX 4090 GPU, the complete training process can be completed within 3 to 6 hours, depending on the data volume and forecast horizon. More importantly, during inference, generating a 72-hour forecast over the China dataset takes less than 0.15 seconds, which is fast enough to meet the requirements of most real-time applications.

That said, we agree that scalability is a meaningful consideration, and we are actively exploring architectural optimizations such as mixed-precision computation and model pruning to further reduce CTENet’s computational footprint in future work.

Thank you for the detailed rebuttal. I appreciate the authors' thoughtful clarifications. I agree with many of the points raised and commend the overall quality of the response. That said, I still have some concerns regarding the core novelty of the work.

In the rebuttal, the authors emphasize two main aspects as key contributions:

The paper is the first to model air quality as a continuous spatial process.

The paper explicitly incorporates chemical priors.

While these claims are understandable, I would like to keep my confidence in them.

Regarding the first point, I acknowledge that air quality data is usually collected as discrete observations over a broad spatial domain. However, the underlying diffusion process is inherently continuous, a perspective that many prior works—especially those leveraging ODE-based or PINN-style approaches—have already adopted. To the best of my understanding, these previous studies have treated the problem as one of continuous spatial modeling, often with architectural designs tailored to this goal[1][2][3]. Given this context, I find it somewhat difficult to fully agree with the claim that this work is the first to treat air quality as a continuous modeling problem.

[1] AIR QUALITY PREDICTION WITH PHYSICS-GUIDED DUAL NEURAL ODES IN OPEN SYSTEMS

[2] AirPhyNet: Harnessing physics-guided neural networks for air quality prediction

[3] Airformer: Predicting nationwide air quality in china with transformers

As for the incorporation of chemical priors, I appreciate the inclusion of chemically relevant features during data representation. However, from the current description, it appears that the model does not directly enforce chemical reaction mechanisms or explicitly utilize reaction equations as constraints. In this light, I see the contribution more as an enhancement of input richness rather than a structural innovation. While this is certainly valuable, I remain slightly hesitant to consider it a defining novelty.

Overall, while I acknowledge the merits of the work and the authors' efforts to clarify their contributions, I still find the central innovation to be somewhat unclear. I would welcome further discussion from the authors.

Thank you again for your thoughtful response. I now better appreciate the contribution of incorporating chemical priors into your framework and have accordingly revised my assessment of the paper’s originality. That said, I still have some remaining questions regarding the following two claims:

• This work is the first to introduce vector fields and model air quality as a continuous process;

• This work requires a fundamental redesign of Physics-Informed Neural Networks (PINNs).

From my understanding, previous studies [1,2] have already explored the use of field-based representations in air quality modeling, and [3,4] have explicitly incorporated chemical transport mechanisms within a continuous spatial formulation. I would be very interested to better understand how your approach fundamentally differs from these prior works. In particular, since [3,4] appear to address similar challenges in continuous domains, it would be helpful if you could further clarify why your method constitutes a fundamental redesign of the PINN framework, whereas theirs does not.

[1] Spatio-Temporal Field Neural Networks for Air Quality Inference

[2] AirRadar: Inferring Nationwide Air Quality in China with Deep Neural Networks

[3] Orders‑of‑magnitude speedup in atmospheric chemistry modeling through NN emulation

[4] FastCTM: Atmospheric chemical transport modelling with a principle-informed neural network for air quality simulations

I encourage the authors to include a more in-depth comparison and discussion of these related works in the revised manuscript. Additionally, the current version only compares the proposed method against AirPhyNet, without benchmarking against other task-specific or state-of-the-art baselines. This makes it somewhat difficult to fully evaluate the effectiveness and broader contribution of your method. Including more comprehensive comparisons with a diverse set of baselines might help further clarify the strengths of your approach.

Thank you for your response.

Regarding the baseline issue, I do not require additional experiments—I only intended to point out what I consider to be a potential issue in the current version of the paper. It would be unfair to request new experimental results at the discussion stage. At this point, clarifying the novelty and contribution of your work is sufficient.

I appreciate your hard efforts. My current evaluation remains borderline, but I will lower my confidence. In addtition, I will consider all AC’s and other reviewers’ opinions during the AC-reviewer discussion phase.

Dear reviewer,

We sincerely thank you for your thoughtful and constructive feedback. We appreciate the recognition of CTENet's strengths in embedding real atmospheric dynamics, achieving strong empirical performance, and enhancing physical realism. Below, we address your specific questions and concerns.

To W1, Q1, and L1:

Thank you for your thoughtful comment. CTENet was not originally designed with the goal of producing uncertainty-aware predictions; instead, our focus was on achieving accurate and timely point forecasts. We acknowledge that the ability to quantify predictive uncertainty is crucial in health-critical applications, where decision robustness is essential.

Importantly, the architecture of CTENet is flexible enough to accommodate uncertainty estimation methods. As you suggested in Limitation 1, techniques such as Monte Carlo Dropout, deep ensembles, or Bayesian neural networks can be integrated with minimal structural modification. We believe that coupling these approaches with CTENet’s physics-informed design can enable reliable prediction intervals or probabilistic outputs, thereby enhancing its applicability to high-risk scenarios.

We once again appreciate this valuable suggestion, and we plan to actively explore this direction in future work to further improve CTENet’s reliability in real-world decision-making contexts.

To W2:

Thank you for your insightful and technically informed comment. Indeed, as you correctly noted, the interactions between nitrogen oxides and particulate matter during extreme pollution episodes are governed by complex chemical processes. We are pleased to see your attention to this important aspect.

As you pointed out, our current model does not explicitly encode the detailed reaction equations typically used in atmospheric chemistry. This is a deliberate design choice: rather than reconstructing the full reaction pathways under specific environmental conditions (e.g., photochemical reactions influenced by solar radiation, temperature, and humidity), our modeling objective is to capture the eventual atmospheric chemical equilibrium that results from a given initial pollution state. In this formulation, the final pollutant concentrations can be treated as a nonlinear function of the initial state.

This is precisely where the strength of our method lies. By incorporating ideas from chemical transport modeling (CTM) and integrating them with a data-driven framework, CTENet is capable of learning an effective end-to-end mapping from initial to equilibrium pollutant states, without requiring the explicit simulation of each reaction mechanism. This enables the model to bypass the need for precise specification of all environmental factors, while still capturing key dependencies. We will clarify and emphasize this modeling philosophy more explicitly in the revised version.

To Q2: Thank you for the insightful question. In coastal and mountainous regions, the evolution of pollutant concentrations often deviates from standard assumptions due to spatial heterogeneity, making classical Neumann boundary conditions potentially inadequate. CTENet addresses this challenge not by relying solely on boundary condition assumptions, but by explicitly incorporating heterogeneous terrain information into the modeling process.

Specifically, the meteorological data used by CTENet includes several key variables that capture complex topographic and coastal features:

• Orography (Channel 249): directly encodes surface elevation, allowing the model to learn the impact of terrain height on pollutant dispersion.
• MSLP (Eta model reduction) (Channel 246): represents sea-level-reduced pressure, effectively correcting for elevation-induced pressure differences.
• Surface pressure (Channel 248): captures actual pressure at the surface, which varies significantly with altitude and terrain type.

To capture coastal influences:

• Land-sea mask (Channel 338): a binary mask (1 for land, 0 for sea) identifying coastal boundaries.
• Land-sea coverage (nearest neighbor) (Channel 354): provides a more refined classification using nearest-neighbor interpolation to distinguish land and sea grid points.

By integrating these features into its deep learning architecture, CTENet is able to model pollutant dynamics more faithfully across spatially heterogeneous domains, including complex coastal and mountainous areas, without relying on potentially fragile boundary condition approximations. A more detailed discussion of how CTENet leverages these variables to handle topographic and coastal complexity will be provided in the full paper.

To Q3: To deploy CTENet in real-time air quality monitoring systems, the following steps are needed:

1. Data Preparation: Collect and preprocess multi-source air quality and meteorological data, as described in the paper.
2. Model Training: Train CTENet on historical data to learn spatiotemporal correlations. On an RTX 4090 GPU, the full training process can be completed within 3 to 6 hours, depending on the data volume and forecast horizon.
3. System Integration: Integrate the trained model into the real-time data processing pipeline.
4. Real-time Inference: Feed incoming meteorological forecasts and sensor readings into CTENet to generate predictions. For example, generating a 72-hour PM$_{2.5}$ forecast over the China takes less than 0.15 seconds on an RTX 4090 GPU. Therefore, we believe that even on a CPU-based system, the model can still produce forecasts within a few minutes, which is acceptable for most real-time applications.
5. Model Update: Periodically fine-tune the model using recent observations to adapt to seasonal or structural changes in emission patterns and meteorological drivers.

To L2: We sincerely thank you for recognizing the effectiveness of our forecasting system. All of our experiments are conducted using real-world air quality and meteorological data collected from ground-based sensors across the continental United States and China, ensuring practical relevance.

We appreciate the suggestion to validate CTENet within real-world decision-making contexts, such as assessing forecasts against hospitalization risk thresholds. While this represents an important and meaningful direction, we consider such analyses to be downstream tasks that extend beyond the scope of the present work. Nevertheless, the system can be adapted to support such integration. Prior studies have quantitatively linked air pollution to adverse health outcomes. For instance, Bell et al. demonstrated significant associations between specific PM$_{2.5}$ components (e.g., sulfate, elemental carbon) and increased hospitalization rates for cardiovascular and respiratory diseases [1]. Building on these literature, future work could extend CTENet by coupling its forecasts with health impact models, enabling validation under operational scenarios such as early warning issuance or risk-based alert systems, such as forecasting the likelihood of hospitalization threshold exceedances or issuing early warnings for at-risk communities.

[1]Bell, M. L., Ebisu, K., Peng, R. D., Samet, J. M., & Dominici, F. (2009). "Hospital admissions and chemical composition of fine particle air pollution." JAMA, 300(11), 1127–1135.