Computational Fluid Dynamics (CFD) is essential in contemporary engineering design, yet it remains expensive to compute and can take thousands of CPU/GPU hours or more for a single high-fidelity simulation. Recent developments in machine learning for scientific modeling have led to powerful surrogate frameworks that can approximate flow fields and physical quantities by using a fraction of the computational cost. However, most of these methods require largescale homogeneous datasets or simple geometries, exhibiting severe generalization gaps when applied to complex and data-scarce configurations. To address this, we propose the Factorized Geometry Convolutional Neural Operator (FG-ConvNO) for robust geometry-aware propeller pressure prediction under limited training data. We introduce geometryaware encoding, efficient interpolation-based decoding, and auxiliary global quantity supervision. In addition, we incorporate DISCO blocks that use discrete continuous convolutions to make the model discretization agnostic. In our experiments, FG-ConvNO achieves the highest accuracy for both surface pressure and global thrust prediction on a procedurally generated propeller CFD dataset. Geometry-aware encoding and architectural simplification improve stability, while random vertex subsampling enhances robustness. Overall, adding geometric priors to grid-based convolutional operators reduces overfitting on complex propeller geometries and improves generalization in low-data regimes.
Figures & tables
Figure 1: Visualization of procedurally generated propeller geometries. Each sample is colored by time-averaged pressure obtained from simulations, illustrating flow variations across different blade designs.
Figure 2: The Factorized Geometry Convolutional Neural Operator (FG-ConvNO) for propeller pressure prediction. Each propeller geometry is first represented as a centroid-based surface point cloud, where each centroid corresponds to a local patch on the propeller surface. FG-ConvNO then projects vertex features onto multiple latent grids, performs hierarchical convolutional aggregation across the grids, and decodes the resulting latent fields back to the vertex domain for pressure prediction. Compared with FIGConv, FG-ConvNO incorporates geometry-aware conditioning (using boundary conditions, SDFs, and normals), interpolation-based feature decoding, an explicit global prediction head to infer quantities such as thrust and torque, and hierarchical DISCO blocks for discretization convergence, which preserves consistent local support across different grid resolutions.
Figure 3: Comparison of aerodynamic and propulsive forces. (a) Aircraft wings generate lift perpendicular to the inflow. (b) Propellers produce thrust opposite to the inflow. This illustrates how global quantities such as thrust and drag integrate local pressure distributions.
Model
Surface ↓
Global ↓
GraphSAGE
42.47%
8.32×10−3
Transolver++
27.96%
2.41×10−3
GINO
29.16%
3.15×10−3
FG-ConvNO (surface only)
23.68%
1.76×10−3
FG-ConvNO (surface + global)
24.07%
3.43×10−4
Table 1: Performance comparison with existing architectures on the propeller dataset. Both FG-ConvNO variants achieve lower surface error than the graph-based baseline (GraphSAGE) and the recent operator models (GINO and Transolver++), while explicit global supervision substantially improves the accuracy of global quantity prediction.
Figure 4: Ablation on dataset size and random vertex subsampling for training (tsub) . Increasing training samples reduces both surface and global losses, confirming the importance of data scale. Random subsampling consistently improves global prediction and provides stronger gains on surface accuracy when training data are limited.
Figure 5: Quantitative and qualitative ablation of U-Net hierarchy. (a) Comparison of surface and global losses and GPU memory usage across six configurations of nlevels and block counts ( nup,ndown ). (b) Example predictions and error maps for representative models (1,1) , (1,2) , and (3,2) .
Configuration
Surface ↓
Global ↓
PointConv (w/ Grid SDF)
45.07%
7.67×10−3
Interp (w/o Grid SDF)
26.85%
9.72×10−4
Proposed
24.07%
3.43×10−4
Table 2: Ablation on decoder formulation and grid SDF conditioning. Interpolation enhances smoothness and stability, while SDF features improve geometric consistency.
We introduce a dataset of approximately 10,000 Reynolds-Averaged Navier-Stokes (RANS) simulations of steady, incompressible, two-dimensional subsonic flow around downforce-generating NACA 4-digit airfoils, targeting aerodynamic regimes relevant to automotive and motorsport applications (openly available on https://huggingface.co/datasets/ratiolabs/downforce-airfoils). Using this resource, we study geometry-conditioned neural surrogates for fast flow prediction, comparing neural fields with neural ODEs, MLPs with graph-based models, and several spectral geometry-conditioning methods. We further propose Airfoil2Vec, an airfoil-specific spectral geometry encoder that combines the joint contour spectrum with separate spectral representations of camber and thickness, for predicting continuous pressure and velocity fields. We evaluate generalization through angle-of-attack interpolation, interpolation and extrapolation to unseen NACA 4-digit geometries, and generalization to unseen non-NACA airfoils. The resulting surrogate accurately captures aerodynamic quantities and qualitative flow features while providing orders-of-magnitude speedups over conventional computational fluid dynamics.
Haitz Sáez de Ocáriz Borde, Flavio Savarino, Andrei Cristian Popescu +3
Deep learning surrogates for CFD flow-field prediction often rely on large, complex models, which can be slow and fragile when data are noisy or incomplete. We introduce FlowForge, a staged local rollout engine that predicts future flow fields by compiling a locality-preserving update schedule and executing it with a shared lightweight local predictor. Rather than producing the next frame in a single global pass, FlowForge rewrites spatial sites stage by stage so that each update conditions only on bounded local context exposed by earlier stages. This compile-execute design aligns inference with short-range physical dependence, keeps latency predictable, and limits error amplification from global mixing. Across PDEBench, CFDBench, and BubbleML, FlowForge matches or improves upon strong baselines in pointwise accuracy, delivers consistently better robustness to noise and missing observations, and maintains stable multi-step rollout behavior while reducing per-step latency.
Xiaowen Zhang, Ziming Zhou, Fengnian Zhao +1
Shanghai Jiao Tong University · University of Michigan
Accurate aerodynamic prediction is critical for designing fuel-efficient and safe transportation systems such as aircraft and automobiles, yet traditional computational fluid dynamics (CFD) simulations remain computationally expensive and expertise-intensive, severely limiting their use in iterative design and real-time analysis. Existing deep learning surrogates suffer from two major limitations: (i) they are evaluated on datasets with narrow flow-condition ranges, leaving their performance under complex flow conditions undemonstrated; (ii) they treat global flow conditions as a single vector injected uniformly across all surface points, ignoring that different geometric regions experience distinct local flow phenomena, which degrades prediction accuracy under complex flow conditions. To address these limitations, we propose the Flow State Attention Network (FSAN). FSAN separately encodes point cloud and flow conditions, then partitions the geometry into multiple flow states via learnable soft assignments, and uses flow features to update these state representations, which in turn influence point cloud features through state changes. This enables fine-grained, state-specific interaction between geometry and flow information. Extensive experiments on two well-recognized aerodynamic benchmarks demonstrate that FSAN achieves the highest accuracy among the methods compared in this work at a higher computational cost. On Emmi-Wing, FSAN reduces the Relative L2 (REL-L2) error by over 20% compared to the strongest baseline (Transolver), and on DrivAerNet++, it achieves a 10% reduction compared to the strongest baseline (AdaField). These results establish FSAN as a promising neural surrogate on public benchmarks with diverse flow conditions and geometries.
Wenxuan Jin, Jianguo Yao, Haibing Guan +1
Shanghai Key Laboratory of Scalable Computing and Systems · School of Computer Science, Shanghai Jiao Tong University