Organizations: Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, 518055, China · Shenzhen Key Laboratory of Complex Aerospace Flows, Southern University of Science and Technology,Shenzhen 518055, China · Ningbo Key Laboratory of Advanced Manufacturing Simulation, Eastern Institute of Technology, Ningbo, 315200, China · Shenzhen Tenfong Science and Technology Co., Ltd., Shenzhen, 518000, China
Rapid aerodynamic evaluation is crucial for modern vehicle design, yet existing neural operators struggle to capture intricate spatial correlations. We propose the rotary-enhanced transformer operator (RETO), a novel neural solver featuring a dual-stage spatial awareness mechanism: sinusoidal-cosine encodings for global referencing and rotary positional encodings (RoPE) for relative displacements. RoPE encodes spatial relations via unitary rotations, enforcing translation invariance and enhancing local gradient resolution. RETO is validated on ShapeNet and the high-fidelity DrivAerML benchmark. On ShapeNet, RETO achieves a relative L2 error of 0.063, outperforming RegDGCNN at 0.125 and representing a 16% improvement over the Transolver baseline, which yields an error of 0.075. These performance gains are further amplified on the DrivAerML dataset, where RETO achieves relative L2 errors of 0.089 for surface pressure and 0.097 for velocity. In comparison, Transolver results in errors of 0.116 and 0.121 for the same metrics, indicating that RETO achieves precision enhancements of 23% and 19%, respectively. For comprehensive comparison, the surface pressure and velocity errors for AB-UBT are 0.102 and 0.124, while RegDGCNN yields 0.235 and 0.312, respectively. Information-theoretical analysis shows that the entropy peak of RETO at 0.35 is significantly lower than that of Transolver at 0.75 under 104 resolution, indicating a focused attentional mechanism capable of preserving localized gradients against global diffusion.
High-fidelity computational fluid dynamics (CFD) is crucial to vehicle aerodynamic analysis, but its cost still constrains early-stage design exploration. Machine-learning-based surface-field prediction offers a faster alternative if the model can efficiently capture both global flow context and local geometric detail. This work proposes a machine-learning-based method, named the geometry-aware triplane field network (GTF-Net), for vehicle aerodynamic pressure and wall shear stress prediction. GTF-Net constructs triplane features directly from sampled surface points through a shared multilayer perceptron (MLP) and smooth bilinear rasterization. The planes are then processed by a dual-stream backbone that combines adaptive Fourier neural operator (AFNO) spectral mixing with convolutional neural network (CNN) refinement, so long-range aerodynamic coupling and local geometry-induced variations are modeled in the same representation. At query stage, sampled triplane features are combined with vehicle-aligned directional coordinates, normal-projection features, and a voxel-based curvature proxy. GTF-Net is compared with Transolver, geometry-informed neural operator (GINO), and TripNet, a triplane-based surrogate model. GTF-Net improves the relative L2 error from the strongest baseline value of 0.157 to 0.145 for pressure prediction and from 0.237 to 0.226 for wall shear stress prediction. Ablation results show that AFNO mixing, local CNN refinement, and query-side geometric encoding each contribute to accuracy, supporting the proposed mechanism of combining structured triplane representation with explicit aerodynamic geometry cues.
Deploying Scientific Machine Learning surrogates in industrial CFD workflows requires adapting pretrained models to new vehicle families without large datasets; yet whether geometric representations learned by a geometry encoder transfer to topologically distinct shapes remains unvalidated. We address this through leave-one-family-out experiments on a 61.47M-parameter Transformer surrogate (AB-UPT) pretrained on four vehicle families (411 external aerodynamics cases) and adapted to the held-out fifth with only 20 samples. Three strategies are compared: Full Fine-Tuning (FFT), Lightweight Fine-Tuning (LFT), and Low-Rank Adaptation (LoRA). The central finding is that pretrained geometry encoders learn transferable representations, but the adaptation mechanism determines whether they can be exploited. FFT destabilizes as 61.47M unconstrained parameters overfit to 20 samples (R^2=0.40); LFT fails because the frozen encoder cannot represent unseen shapes (R^2<0). LoRA resolves both: rank-constrained adapters injected into all layers regularize the loss landscape while preserving pretrained features, achieving R^2=0.85+/-0.02 across all five families with 50% lower force RMSE than FFT and 28% lower pointwise field errors. LoRA also outperforms from-scratch training using 3x more target-family data, eliminating the need for large per-family datasets. These results recast LoRA from a memory-saving convenience into a convergence enabler for geometry transfer: a shared backbone paired with lightweight per-family adapters trainable in hours from minimal data.
Accurate prediction of unsteady separated flows is challenging because the aerodynamic loads depend on nonlinear separation and vortex-shedding dynamics. Although high-fidelity CFD resolves these mechanisms, its cost limits repeated use in design and control. Standard field-level surrogate training, however, does not distinguish the flow regions that contribute most strongly to the aerodynamic loads. We introduce VATO (Vortex-Force-Aware Transformer Operator), which couples the Vortex Force Map (VFM) method to a geometry-aware neural operator through two complementary mechanisms. VATO-S adds training-only supervision of the local VFM force-contribution field, with no increase in model size or inference cost. VATO-A uses VFM contribution and sensitivity fields to prioritise force-relevant source locations for residual cross attention. The methods are evaluated on unsteady CFD data for double-edged-plate aerofoils over 54 trajectories from nine geometries. Over lead times of 1-20~ms, VATO-S reduces velocity, pressure, and vorticity errors by 10.4%, 1.0%, and 15.6%, respectively, while VATO-A achieves reductions of 15.8%, 7.5%, and 31.2%. VATO-S gives the lowest VFM-derived drag error, whereas VATO-A gives the lowest pressure-derived lift and drag errors. Over lead times extending 50% beyond the training range, VATO-A retains a 26.9% reduction in vorticity error and larger improvements in all four force readouts, despite reduced gains in velocity and pressure. These results show that force-aware operator learning can improve both flow-field prediction and aerodynamic functional accuracy in unsteady separated flows.