VATO: A Vortex-Force-Aware Transformer Operator for Unsteady Separated Aerofoil Flows

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.

A Residual Learning Approach for Unsteady Aerodynamic Load Prediction

This paper investigates the feasibility of using residual learning to improve unsteady aerodynamic load prediction for aeroelastic applications. The machine learning technique selected for the study is the long short-term memory (LSTM) neural network, which is used for its suitability for sequential data with aerodynamic memory effects. The approach is investigated for the NLR 7301 airfoil benchmark using high-fidelity CFD lift data for prescribed pitch and plunge motions in the transonic flow regime in the presence of shock motion. An analytical unsteady aerodynamic model based on the Wagner function is used as a physics-based baseline, and the neural network is trained to learn the difference between the CFD lift coefficient and the Wagner prediction. The residual model is compared with a direct neural-network model trained to predict the CFD lift coefficient. The comparison includes feature and normalization studies, external benchmark cases, and leave-one-out and leave-family-out generalization tests across a range of sinusoidal and non-sinusoidal motions. The residual model performs best when its inputs align with the Wagner formulation variables, generally giving lower error and more consistent performance across training runs, though the direct model remains more accurate for some high-frequency cases. The residual model also generalizes better in the leave-one-out and leave-family-out tests, with a smaller increase in error than the direct model when entire motion families are withheld from training. Overall, the results indicate that residual learning shows promise as a modular approach for augmenting classical low-order aerodynamic theories, especially when the physics baseline removes a structured part of the aerodynamic response and leaves a lower-variance correction for the neural network to learn.

Robostreet Flow: A Lightweight, Ultra-Low-Drag Electric Tractor and Four-Truck Hybrid Convoy Architecture for Minimum-Cost Point-to-Point Freight

Line-haul trucking costs are dominated by three comparably sized components: energy, driver labor, and equipment. Most efficiency technologies address only one component at a time. This paper presents Robostreet Flow, a freight architecture that jointly optimizes the vehicle, convoy formation, and operating model to minimize cost per ton-mile on high-volume point-to-point corridors. The Flow platform is a battery-electric 6x4 tractor with a teardrop single-seat cab and a drag coefficient of 0.35, approximately 40% below that of conventional Class 8 tractors. A carbon-composite monocoque and structurally integrated batteries reduce net vehicle weight by 50%. A 513 kWh tractor battery and a 340 kWh powered trailer battery provide a 500-mile single-charge range. Four Flow trucks operate as a coordinated convoy with a safety driver only in the lead vehicle, while three followers operate in SAE Level 4 automated mode. Computational fluid dynamics simulations show that close following at an 8 m gap reduces follower drag coefficients by 42-48% and follower peak frontal pressure by approximately a factor of four relative to the exposed lead vehicle. A longitudinal energy model calibrated to these results predicts fleet-average consumption of 1.27 kWh/mi in convoy, compared with 1.60 kWh/mi for an isolated vehicle, for a 20.5% energy saving. Electricity cost is approximately 17% of the equivalent diesel fuel cost. Amortizing one driver across four trucks and accounting for the additional payload enabled by lightweighting reduce operating cost from 9.4 to 4.1 cents per ton-mile, a 56% reduction relative to a diesel baseline. Sensitivity analysis, a hub-to-hub operating concept, and regulatory implications are also presented.

Spatio-Temporal Prediction of Unsteady Airfoil Aerodynamics Using Augmented Graph Neural Ordinary Differential Equations with Exogenous Controls

Unsteady aerodynamic phenomena, such as gusts, turbulence, and fluid-structure interactions affect an aircraft during flight. For design, optimisation and certification, it is indispensable to quantify such unsteady aerodynamic effects. Industry-standard computational fluid dynamics methods, such as solving the unsteady Reynolds-averaged Navier-Stokes equations or the linearized frequency domain method, are either computationally expensive or restricted by assumptions like linearity. Once trained, machine learning methods are capable of computing non-linear relationships very fast, making them suitable as surrogate models. By autoregressively applying graph neural networks (GNNs), operating on a discretised spatial domain, spatio-temporal predictions can be made. However, autoregressive GNNs suffer from error accumulation leading to unstable rollouts over time. Here we show that combining GNNs with augmented Neural Ordinary Differential Equations yields temporally stable predictions of the surface forces on a pitching airfoil. We found that our approach, called GNODE, based on Graph Neural Ordinary Differential Equations, provides temporally more stable, spatially smoother, and overall more accurate results than an autoregressive GNN baseline. Tests are conducted on a dataset consisting of a simulations of a pitching airfoil, including transonic shocks, transient behaviour and dynamic non-linearities. Augmenting GNODEs with additional latent dimensions improves the expressivity and accuracy by capturing underlying history effects. The developed method demonstrates an approach that is suitable to model non-linear spatio-temporal systems with exogenous inputs.

IG-GAN: A Generative Adversarial Network for Aerodynamic Data Generation Based on Intrinsic Geometry

Existing generative models learn data distributions in flat Euclidean space. However, most data in our real world are manifolds embedded in high dimensional Euclidean space. Therefore, we propose an intrinsic-geometry-based generative adversarial network (IG-GAN) for data generation in the field of aerodynamics. The generator of the IG-GAN represents aerodynamic data as a piecewise smooth manifold constructed by Bézier surfaces, and the generator tries to learn the coefficients of each Bézier surface to further combine multiple Bézier surfaces into a smooth manifold automatically. The discriminator in the IG-GAN is a radial-basis-function based discriminator (RBF-D). Experimental results show that IG-GAN achieves lower predicted Mean Squared Errors (MSEs) than those of three baselines. Specifically, on the Burgers' equation dataset, IG-GAN reduces the predicted MSE of velocity u by 97.41% compared with state of the art SSL-Transformer. Additionally, on the ONERA M6 aircraft dataset, IG-GAN reduces the overall MSE of nine aerodynamic coefficients by 82.95% compared with SSL-Transformer.

A Bayesian latent Gaussian process framework for aerodynamic uncertainty quantification

Predicting the aerodynamic performance (e.g. lift, drag, and moment coefficients) of an aircraft is challenging -- computational models are biased and direct simulations are prohibitive. A pragmatic way to overcome this limitation is by calibrating low-fidelity computational predictions with experimental measurements. This, however, requires calibrating against \emph{sparse} measurements contaminated with \emph{uncertainty} in both the control inputs and the measured aerodynamic response. We develop a methodology to address this problem based on Gaussian process surrogates and the classical Kennedy-O'Hagan calibration. A surrogate model learned on abundant-but-cheap low-fidelity data is calibrated with a sparse set of measurement data. Crucialy, we develop a Bayesian latent Gaussian process based approach that marginalizes the calibrated surrogate model over the input uncertainty, while also matching the marginal mean and variance of the measured output uncertainty. Once calibrated, our surrogate model predicts the uncertainty in aerodynamic coefficients with very high accuracy, including at extrapolative input settings. We validate our calibrated surrogate model predictions against measurement data with \emph{true} uncertainty intervals to demonstrate that the model places $94.2-95.8\%$ of its predictive samples inside the released $95\%$ truth intervals, with endpoint cumulative probabilities very close to the nominal 0.025 and 0.975 levels.

Kolmogorov Arnold networks (KAN) for aerodynamic prediction: a comparison with MLPs and GNNs

Kolmogorov Arnold networks (KAN) have recently been introduced as a (deep) neural network architecture whose trainable parameters adapt the activation functions, instead of the coefficients of the affine transformations at the core of traditional architectures such as deep multilayer perceptrons (MLPs). This architecture builds on the Kolmogorov-Arnold theorem, which endows it with universal approximation properties. While the advent of KANs has been received with excitement, there is a current debate about the possible KAN supremacy over deep multilayer perceptrons (MLPs) for classic fields such as symbolic regression, generic-purpose machine learning, natural language processing or computer vision. Here we assess the performance of KANs --and its nuanced comparison against MLPs and graph neural networks (GNNs)-- in the realm of fluid dynamics surrogate modelling. To that aim, we consider the task of predicting the surface pressure distribution over subsonic and transonic airfoils, a canonical task in aerodynamics. Our results show that KAN models show good performance in predicting the whole pressure coefficients and is able to interpolate across Mach numbers and angles of attack, however its performance is comparable --marginally inferior-- to a suitably trained MLP, where best performance is achieved by a GNN at the expense or requiring lengthier training. While the optimal KAN model have typically much lower complexity than MLP and GNN --hence resulting in faster training--, we find that KANs suffer from training instabilities, and their performance is highly dependent on a proper hyperparameter optimisation.

A Geometry-Aware Triplane Field Network for Vehicle Aerodynamic Prediction

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.