Title: Eulerian Neural Network Informed by Chemical Transport for Air Quality Forecasting
Venue: NeurIPS 2025
Accepted: yes
Keywords: air quality prediction

chemical transport modeling

Eulerian neural network
Abstract: Air pollution remains one of the most critical environmental challenges globally, posing severe threats to public health, ecological sustainability, and climate governance. While existing physics-based and data-driven models have made progress in air quality forecasting, they often struggle to jointly capture the complex spatiotemporal dynamics and ensure spatial continuity of pollutant distributions. In this study, we introduce CTENet, a novel chemical transport deep learning model that embeds the Advection-Diffusion-Reaction equation into a Physics-Informed Neural Network (PINN) framework using an Eulerian representation to model the spatiotemporal evolution of pollutants. Extensive experiments on two real-world datasets demonstrate that CTENet consistently outperforms state-of-the-art (SOTA) baselines, achieving a remarkable RMSE improvement of 45.8% on the USA dataset and 21.0% on the China dataset.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper considers the problem of forecasting future pollutant concetrations from past observations, where data is not in a grid. The paper proposes a transport equation that predicts the dynamics through advection, diffusion, reaction and source terms; and suggests off-the-shelf neural networks to model them. The method achieves dramatic performance improvements of 30%-50%.\n\nSTRENGTHS AND WEAKNESSES:\nThe clarity of the paper is generally weak. The method description, math and writing is not sufficiently clear on describing the model. The method is described mostly in terms of what neural networks are used in what parts of the pipeline, which makes the paper read like a technical report or an applied use-case of ML. I don’t think I could reproduce this method for it’s vagueness. I also have hard time aligning fig2 to the method description. \n\nThe method has little ML novelty, and I’m not sure what is novel in general. The forecasting problem is appropriately modelled through the transport equations and through off-the-shelf neural networks. This seems to be very useful for this particular problem, but I’m not sure what ML significance or impact this has. I don’t think there is enough ML contributions for a ML conference.\n\nThe method is a black box, and there is not enough insight given to what the model learns, how and why. We only see one short time-series of the predictions, and no decomposition of the signal to the different equation terms.\n\nI’m a bit confused why the method performs so well. I suspect that the performance largely depends on using meteorological data to drive the forecasts. This is a good idea, but I’m not sure if the competing methods have access to this, which makes comparisons somewhat unfair. I’m also not sure if simply using extra data source is particularly interesting as the main contribution: obviously using more data is helpful, but is this scientifically interesting?  I might have misunderstood something, and I’d be happy to hear author’s comments about this. The paper also claims novelty of support sparse data through RBF interpolation. I’m not sure if the spatial continuity really is an open problem; and the solution of RBF interpolation seems overly simplistic. \n\nThe results lack statistical significance testing or standard deviations. \n\nDespite the good results, I’m suggesting rejection. The ML significance and contributions are too thin, the presentation and experiments are insufficient.\n\nQUESTIONS:\n- What does “eulerian” mean?\n- eq 6 is missing the X div(w) component: why?\n- Do the competing methods also use the meteorological data? What data does each method use?\n- In table 1 the VAR and GTS results on USA 24h are 6.32/14.41 and 5.57/14.65. This does not seem to make sense: how can you have lower MAE but higher MSE?\n- It’s a bit unclear what is being learnt: can you clarify?\n- It seems that wind is the driving force behind the good results. Do you predict the wind, and if so, how accurate is that?\n\nLIMITATIONS:\nNo issues", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-13"}

comments: SUMMARY:
The paper introduces a deep learning model that learns continuous time dynamics from irregularly sampled data for chemical transport. The method embeds  Advection-Diffusion-Reaction (ADR) equation into a Physics-Informed Neural Network (PINN) framework to simulate the spatiotemporal evolution of pollutants over continuous space and time.

STRENGTHS AND WEAKNESSES:
Strengths:
- This method has potential to improve real-world application of air quality forecasting. 
- The proposed method shows high prediction accuracy which outperforms  baselines with an average RMSE improvement of 45.8% in the USA dataset and 21.0% in the China dataset
- The method integrates Chemical Transport Modeling Principles which allows for direct simulation of pollutant transport and transformation grounded in physical and chemical principles, enhancing interpretability.
- The method includes a modular and replaceable components for various forecasting modules.
- The method handles data sampled with irregular grid.

Weaknesses:
- The paper states limitation that the current formulation lacks uncertainty quantification.
- Computational complexity seems higher than graph-based methods.

QUESTIONS:
- How does the method handle noise?
- Can the method be applied with other data sources such as social vulnerability?
- How does the approach vary for varying data grid resolutions?

LIMITATIONS:
Yes.
TITLE: Official Review
CLARITY: 4
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-06-29

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper combines Eulerian representation with Physics-Informed Neural Networks (PINNs) to propose CTENet, an air quality forecasting model. It converts sparse station data into spatial fields via Radial Basis Function (RBF) interpolation and embeds the Advection-Diffusion-Reaction (ADR) equation to simulate pollutant dynamics. While CTENet shows improved accuracy over baselines, its core methodology primarily integrates existing components—RBF interpolation, modular predictors, and ADR physics constraints—without introducing fundamentally novel mechanisms. The approach reframes established concepts for air quality tasks, but its architectural innovations appear incremental rather than transformative.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. Experimental Reproducibility\nExtensive validation on real-world datasets demonstrates 45.8% and 21.0% RMSE reduction against 9 SOTA baselines. Ablation studies robustly justify design choices, and open-sourced code ensures reproducibility. Statistical significance testing (99.5% confidence) further strengthens reliability of this model.\n\n2. Physics-Driven Spatial Continuity\nRadial Basis Function (RBF) interpolation effectively converts sparse station data into continuous fields, resolving structural mismatches in graph-based methods and outperforming nearest-neighbor alternatives. The Neumann boundary conditions enhance stability and physical plausibility in predictions.\n\nWeakness:\n\n1. Limited Originality: CTENet combines established techniques—RBF interpolation, modular predictors, and physics-informed neural networks (PINNs)—within an Advection-Diffusion-Reaction (ADR) framework. However, this hybrid design are similar to prior works. Thus, it has incremental contributions.\n\n2. Novelty: The claimed advances in are not supported by methodological innovation. The observed performance gains largely arise from architectural adjustments—such as the dynamic weighting of reaction terms (Eq. 12)—rather than from a new algorithmic framework. Moreover, spatial continuity has already been effectively addressed in prior work, including AirFormer (§2.1), which diminishes the claimed novelty.\n\n3. Limited scalability: As confirmed by computational complexity analysis in Appendix G, CTENet incurs significantly higher computational demands than graph-based methods. The theoretical overhead grows drastically due to its grid-based architecture, with empirical tests (Table 3) showing 21.7× higher computations for China and 26.8× for the USA dataset compared to graph models. Consequently, its complexity impedes real-time forecasting feasibility, and no mitigation strategies are proposed for this bottleneck.\n\nQUESTIONS:\nplease see in Weakness\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

comments: SUMMARY:
The paper introduces CTENet (Chemical Transport Eulerian Network), a physics-informed deep learning model that integrates the Advection-Diffusion-Reaction (ADR) equation into a neural network framework. CTENet uses an Eulerian representation to model pollutant spatiotemporal dynamics, addressing limitations of discrete station-based or graph-based methods by capturing spatial continuity and complex chemical transformations.

STRENGTHS AND WEAKNESSES:
Strengths:

1. CTENet embeds real atmospheric processes (like wind-driven advection) into its neural network, making predictions more physically realistic.

2. It outperforms existing models by up to 45.8% on real-world datasets (USA/China), proving its effectiveness.

Weaknesses:

1.  The model gives single-point predictions without confidence intervals, limiting its use in high-risk scenarios.

2. It assumes basic chemical reactions, potentially missing complex pollutant interactions in extreme pollution events.

QUESTIONS:
Question 1 : How can CTENet be extended to provide probabilistic forecasts (e.g., prediction intervals) for health-risk alerts?

Quesiton 2: How does CTENet handle coastal/mountainous regions where Neumann boundary conditions may fail?

Question 3: What steps are needed to deploy CTENet in real-time air quality monitoring systems?

LIMITATIONS:
There are two improved suggestions: 
1. Integrate Monte Carlo dropout or Bayesian neural networks to output uncertainty estimates alongside predictions.
2. Validate with real-world decision-making scenarios (e.g., hospitalization risk thresholds).
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-03