Title: FuncGenFoil: Airfoil Generation and Editing Model in Function Space
Venue: NeurIPS 2025
Accepted: yes
Keywords: Generative Model

AI for Engineering

Generative Model in Function Space

Flow Model
Abstract: Aircraft manufacturing is the jewel in the crown of industry, in which generating high-fidelity airfoil geometries with controllable and editable representations remains a fundamental challenge. Existing deep learning methods, which typically rely on predefined parametric representations (e.g., Bézier curves) or discrete point sets, face an inherent trade-off between expressive power and resolution adaptability.
To tackle this challenge, we introduce FuncGenFoil, a novel function-space generative model that directly reconstructs airfoil geometries as function curves. Our method inherits the advantages of arbitrary-resolution sampling and smoothness from parametric functions, as well as the strong expressiveness of discrete point-based representations.
Empirical evaluations demonstrate that FuncGenFoil improves upon state-of-the-art methods in airfoil generation, achieving a relative 74.4% reduction in label error and a 23.2% increase in diversity on the AF-200K dataset. Our results highlight the advantages of function-space modeling for aerodynamic shape optimization, offering a powerful and flexible framework for high-fidelity airfoil design.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes a generative model for 2D airfoil generation and editing by combining Gaussian Processes and Fourier Neural Operators through a flow-matching training strategy. It combines advantages from both parametric representations, as well as point-based representations of airfoils. Experiments show that the model surpasses baselines in terms of diversity, smoothness and label error in the conditional airfoil generation task. Further, the model allows for constrained editing of the airfoil.\n\nSTRENGTHS AND WEAKNESSES:\n# Strengths\n\nThe paper is clearly written and well structured. Experiments seem to answer the asked research question and show the advantages of the model. Especially the aerodynamic simulation of generated airfoils highlights that the model is able to generate useful geometries. Ablation studies further underline certain design choices and make them transparent.\n\n# Weaknesses\n\nFor the conditional airfoil generation task, only one baseline is provided for the smaller UIUC and Super datasets. I see that the best performing baseline on AF-200K was used for the other datasets as well, but given that the other datasets are way smaller in terms of the number of samples available, it would be interesting to see how at least one more baseline model copes with the limited data regime (that is usually the big constraint in this domain).\n\nThe model seems to have issues learning angles as the label error on the PARSEC parameters $p_{10}$ and $p_{11}$ are quite large relative to baselines. Could you elaborate on that?\n\nThe experiment on airfoil editing shows that the model is able to incorporate user constraints. It seems like the editing scales and perturbations during editing are rather small. It would be interesting to see how robust the model is when asked for larger edits.\n\nQUESTIONS:\n- Is there a reason that only PK-DiT is provided as baseline for the UIUC and Super datasets?\n- Could you provide some visualizations of generated airfoils by the model, maybe also for the baselines?\n- As written above, could you elaborate on the model performance on the error of the PARSEC angle parameters, in particular give an explanation why the model struggles?\n- How does the model handle large edits? Is it robust?\n\nLIMITATIONS:\nLimitations are provided, but only in the appendix. Please move them to the main text.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-06-22"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\n# Review of Submission #9911\n\n## Summary\n\nThe paper introduces FuncGenFoil, a generative model to generate airfoil designs/geometries. \nIt is a Flow Matching model with a Fourier Neural Operator (FNO) backbone and is trained on large, open-source datasets (AF-200K, UIUC, Super).\nFuncGenFoil allows both conditional generation and \"freestyle editing\" of geometries. The paper shows that FuncGenFoil outperforms previous deep-learning-based approaches (GANs, Diffusion models) in the conditional generation task. Ablation studies justifying architecture and training/generation choices are provided.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n\n- Good introduction and related work section, introducing the problem setting (airfoil design for the aviation industry) and previous works on this topic,\nboth \"classical\" computational design (e.g., NURBS, Bézier curves) and deep learning (VAE, GANs, Diffusion) approaches. Good mathematical notation is kept throughout the paper.\n\n- Clear training description: Flow matching based on [1], Gaussian Processes as noise distribution, conditioning on geometric parameters (PARSEC) with an explanatory Figure.\n\n- Clear generation/editing description: Inference with ODE solver and finetuning the model for editing is well explained and shown in the Figure.\n\n- Well-written experimental section, detailing the used metrics, training, and tasks/comparisons.\n\n- Extensive comparison with other DL approaches (VAE, GANs, Diffusion) for conditional generation.\n\n## Weaknesses\n\n- The limitation of classical methods is not really explained; it is just said that picking certain function families limits the design space. But how strong of a limitation is this in practice? Furthermore, neural networks are not random functions [2]. So there is also a clear bias in the shapes/geometries neural networks will learn, depending on the architecture, activation functions, etc, which is well explored in the neural implicit shape and geometry processing literature. We are simply using a different class of function family, but to me it is not clear what underlying problem the authors are trying to solve with this. It looks like just applying a different function class to the problem. I would ask for clarification from the authors on this point.\n\n- This point follows from W1: while the authors provide extensive comparisons to previous DL methods, they provide none to other \"classical\" computational design methods. These should serve as a baseline for the data-driven approaches. \n\n- No comparison methods for the airfoil editing task. Also, the edited airfoils from \"Freestyle Airfoil editing\" are not being tested for their aerodynamic performance. Instead, a new model is trained on a different dataset to test this. It is not clear to me why, please clarify.\n\n- No clear overview of the computational cost of dataset generation, training, finetuning (for editing), and inference is provided. Recent review articles of DL methods for numerical problems (PDEs, simulation, shape/topology optimization) have raised the issue that the full computational costs of DL methods/surrogates are often not provided and compared to SoTA numerical methods (see e.g.[3]). The paper gives the training time, but this should be more thorough. \n\n- I find Figure 4 a bit hard to read/process; the color choices (light green, light blue, light gray) seem suboptimal. Just a minor point.\n\n[1] LIPMAN, Yaron, et al. Flow matching guide and code. arXiv preprint arXiv:2412.06264, 2024.\n[2] TENEY, Damien, et al. Neural redshift: Random networks are not random functions. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024. S. 4786-4796.\n[3] WOLDSETH, Rebekka V., et al. On the use of artificial neural networks in topology optimisation. Structural and Multidisciplinary Optimization, 2022, 65. Jg., Nr. 10, S. 294.\n\nQUESTIONS:\n- How does the full cost of FuncAirGen compare to a classical method using e.g. NURBS? What is the advantage of FuncAirGen? Are there failure cases of classical methods that it can fix? Are there failure cases of FuncAirGen?\n\n- The paper makes the point that FuncAirGen enables superresolution with smooth, arbitrary resolution shapes. Is this smoothness not a direct consequence of the FNO backbone, which approximates the data with a finite Fourier representation of the signal (geometric curve)? Is the size of the FNO sum a limit/upper bound of FuncGenFoil similar to parametric-model-based methods?\n\n- Why use a FNO backbone instead of typical INRs like SIREN? The paper mentions it is possible in principle, but does not elaborate on this choice further. FNOs are not commonly used in neural geometry processing literature.\n\nLIMITATIONS:\nSee Weaknesses/Questions", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-06-23"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents a novel generative model for generating airfoil geometries (2D contours) based on flow matching. The proposed model includes an optional conditioning variable and supports customized editing on the airfoil geometry. The paper evaluates the proposed model on two tasks: conditional generation and freestyle editing, and compares its performance with multiple baselines on several established datasets.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. I think the paper tackles a valuable research problem through the lens of modern AI tools. Exploring airfoil geometry designs may have a significant impact, especially if the proposed AI method can discover novel geometries with high-performance aerodynamics.\n2. The technical method proposes a generative model in a function space, rather than the standard Bezier-curve shape space used in airfoil design. This is a novel and timely exploration of diffusion and flow models in this specific problem domain.\n3. I appreciate that the experiments also include aerodynamic simulations of the shapes generated by the proposed generative model. This makes the proposed method more useful in practice.\n\nWeaknesses:\n1. The paper does not present a hardware prototype to confirm the physical fidelity of the results. For example, whether the airfoil geometry proposed by the generative model is more useful than existing designs remains unclear. This is probably beyond the scope of this work, though.\n\nQUESTIONS:\nOverall, the paper appears to be in good shape, and I do not have major concerns with it at this time. I am not an expert in airfoil design, though.\n\nThat said, I still have a few questions:\n1. I didn’t find any discussions on the paper’s limitations in the main paper. Please discuss.\n2. Following up on the weakness I mentioned above, is there a way to validate the performance of these explored airfoil designs in the real world?\n3. I’d also like to ask about the potential of this method for 3D airfoil design.\n\nLIMITATIONS:\nThe paper seems to lack discussions on its limitations. I suggest the authors add a paragraph about it.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-27"}

comments: SUMMARY:
This paper focus on an important task to generate airfoil that satisify the requirement for several key parameters.
Instead of generating hyperparameters to define the airfoil shape or its discrete boundary points, this paper proposes representing the airfoil as a closed-form function.
Then, with the With the usage of operator flow matching and sampling from guassian distribution, it generates the function for the target airfoil step by step.

STRENGTHS AND WEAKNESSES:
Strength:
1. The experimental results achieve state-of-the-art performance on AFBench, with a significant boost in accuracy. As shown in Table 1, the error is reduced by orders of magnitude.

2. The writing of this paper is clear and easy to follow. The idea of representing the airfoil as a closed-form function is well-motivated. Due to this, the method can produce the arifoil with any resolutions.


Weakness:
1. A more thorough efficiency study of the proposed method should be provided to better demonstrate its advantages. In particular, a comparison with discrete point-based generation methods would be valuable. 
Intuitively, the proposed approach should offer efficiency gains over these methods, and it would strengthen the paper to provide evidence supporting this.

QUESTIONS:
N/A.

LIMITATIONS:
N/A.
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 2
DATE: 2025-07-03

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper presents FuncGenFoil, a novel generative model for airfoil design that operates in function space rather than traditional discrete or parametric representations. By leveraging Fourier Neural Operators (FNO) and Flow Matching, FuncGenFoil enables:\n\n- Resolution-free generation of smooth and continuous airfoil shapes.\n\n- Flexible conditional generation, guided by geometric parameters.\n\n- Freestyle editing capabilities via a MAP-based fine-tuning procedure.\n\nThe method demonstrates significant improvements in label error, diversity, and smoothness over existing state-of-the-art baselines (e.g., CVAE, CGAN, PK-DIT), across multiple datasets (AF-200K, UIUC, Supercritical Airfoil). The model also generalizes well to different sampling resolutions and shows physically plausible aerodynamic performance through CFD simulation.\n\nSTRENGTHS AND WEAKNESSES:\n### Strength\n1. **Novelty and Technical Innovation**: Modeling airfoils as continuous functions in function space, rather than point clouds or fixed parametric families, is a substantial conceptual advancement. Avoids limitations in discrete point set expressiveness and parametric function rigidity. Uses Flow Matching with Neural Operators to support infinite-dimensional generative modeling. Supports conditional generation and geometric editing through a unified framework.\n\n2. **Thorough Experiments**: Strong improvements in label accuracy (e.g., 74.4% reduction on AF-200K), diversity, and smoothness. Extensive ablation studies (kernel choice, ODE solvers, Fourier modes). Evaluation includes classical metrics and physics-based simulation.\n\n### Weaknesses\n1. **Complexity and Accessibility**: The method requires a sophisticated combination of operator learning, Gaussian processes, and differential solvers, which may hinder reproducibility.\n\n2. **Generality of Shape Types**: Although the method is proposed in a general form, the experiments are restricted to airfoils and wings, which are relatively smooth and regular.\n\n3. **Runtime Efficiency**: While performance is strong, training involves millions of iterations and inference requires solving ODEs, which may be costly in time or resources.\n\nQUESTIONS:\n1. **Generality Beyond Airfoils**: Have you considered applying FuncGenFoil to more general or irregular geometries (e.g., full aircraft surfaces or automotive shapes)?\n\n2. **Editing Scope and Flexibility**: How does the method handle conflicting or dense constraints (e.g., multiple overlapping or incompatible edits)?\n\n\n3. **Scalability and Efficiency**: What are the training/inference times compared to point-based models like PK-DIT or diffusion models? It is suggested to include a table comparing computational costs, memory usage, and runtime to help readers assess deployment feasibility.\n\n4. **Design Parameter Interpretability**: Can the latent space or generated airfoils be interpreted in terms of classical aerodynamic design principles?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}