Automotive Aerodynamics

Neural operators offer an efficient data-driven approach to rapid prediction of complex automotive aerodynamic flows. However, spectral bias and other factors limit accurate reconstruction of fine-scale flow variations near complex geometries. Existing studies improve the representation and fitting of fine-scale information mainly through information extraction and training objectives. Further study is needed to determine how extracted local details can be used continually in subsequent operator computations and contribute effectively to the overall flow-field representation. We propose CIS-Transolver, a cross-layer incremental-state neural operator that extends fine-scale modeling from local information extraction to its use across layers. The method extracts fine-scale information through local multiscale analysis and encodes it as geometric moment states that are propagated and updated across layers. By combining information from previous layers with feedback to the value representations in Physics-Attention, the method allows local details to contribute continually to subsequent modeling of global physical correlations. We systematically evaluate CIS-Transolver on three public automotive aerodynamics benchmarks, ShapeNet-Car, AhmedML, and DrivAerNet++, covering surface pressure fields and volumetric pressure and velocity fields. CIS-Transolver achieves the lowest mean relative L2 error among the evaluated methods for all five prediction metrics across the three benchmarks. The relative error reductions average 8.72% across the five metrics compared with the best baseline for each metric, reaching 16.38% for ShapeNet-Car pressure prediction and 15.60% for AhmedML velocity prediction. These results provide a new approach to fine-scale flow prediction for complex geometries.

Pickup trucks account for 14% of new light-duty vehicles produced in the United States, yet are among the least aerodynamic. Their open cargo bed adds a flow absent from existing automotive aerodynamics datasets such as DrivAerML and SHIFT-SUV: the shear layer leaving the cab roof passes over a recirculating bed flow before separating again at the tailgate. The resulting drag lowers fuel efficiency, raises emissions and limits the range of electric trucks. Scale-resolved Computational Fluid Dynamics (CFD) is too costly for broad design exploration; neural surrogates can predict flow features at a fraction of that cost, provided they are trained on large-scale, high-fidelity, domain-specific data. We introduce SHIFT-Truck, the first such dataset for pickup trucks. It comprises 1,000 Spalart-Allmaras delayed detached-eddy simulations (SA-DDES) of a reference pickup geometry morphed across 17 shape parameters. Each case is run on a mesh of about 100 million cells at a Reynolds number of $1.4 \times 10^7$ and released with time-averaged surface pressure, wall shear stress, volumetric pressure and velocity. The setup is verified by grid refinement and repeated runs, and checked against wind-tunnel measurements. We define geometry-grouped splits and benchmark four neural surrogates, DoMINO, GeoTransolver, AB-UPT and SMART, on surface and volume tracks. SHIFT-Truck also introduces controlled distribution shifts in the operating point, the input surface discretization and the vehicle archetype. Models with strong in-distribution performance can degrade substantially under these shifts: operating-condition changes expose failures to infer speed dependence, while tessellation and cross-vehicle shifts reveal markedly different robustness across architectures. SHIFT-Truck is thus a benchmark not only for surrogate accuracy but also for generalization across physical and numerical distributions.

Accurate and rapid prediction of the aerodynamic drag coefficient ($C_D$) is essential for vehicle design, particularly during early-stage design, where many candidate geometries must be evaluated. Although computational fluid dynamics (CFD) provides reliable aerodynamic estimates, its high computational cost limits large-scale design exploration. This paper proposes the hierarchical graph-pooling Transolver (HGPTrans), which combines hierarchical graph pooling with Transolver-based attention to directly predict $C_D$ from vehicle surface meshes. Motivated by the fact that vehicle aerodynamics depends on both local geometric features and long-range interactions among spatially distant surface regions, HGPTrans integrates three complementary components. Graph isomorphism convolutions encode discriminative local geometry, Transolver-style slice attention captures global interactions with linear computational complexity, and information-redundancy-aware hierarchical pooling progressively removes redundant nodes while preserving informative geometric structures. The model is trained and evaluated on the large-scale DrivAerNet and DrivAerNet++ datasets, where it achieves the lowest mean absolute error and mean squared error among the evaluated baselines. Its generalization capability is further assessed through transfer learning on a real-vehicle dataset containing both sedans and sport utility vehicles (SUVs), achieving relative $L_1$ errors of 1.56% (sedans) and 2.12% (SUVs) with an inference time of approximately $0.293$ s per vehicle. This corresponds to an acceleration of several orders of magnitude relative to high-fidelity CFD while keeping the predicted drag coefficients within a few percent of the CFD reference. Ablation studies confirm each component's contribution and reveal the effects of depth and pooling ratio.

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.

Engineering shape optimization faces challenges in both expert-dependent problem setup and surrogate-model reliability. In practical aerodynamic design, optimization settings such as editable regions, deformation ranges, and design-preservation constraints are typically specified manually by experienced engineers, while surrogate-based optimization may become unreliable for heterogeneous geometry databases and out-of-distribution designs. To address these challenges, we propose a knowledge-constrained shape-optimization framework that translates knowledge-based constraints and user intent into quantifiable parameters of DFFD-based deformation operators, enabling engineering-aware and controllable constrained optimization. We further develop a Mixture-of-Experts Neural Operator (MoE-NO) to improve drag prediction and trend consistency over heterogeneous aerodynamic datasets. Based on the MoE-NO encoder and Mahalanobis distance, an uncertainty-estimation strategy is introduced to detect out-of-distribution geometries and selectively trigger physics-solver feedback for local sample enrichment. Experiments on in-house MPV, SUV, and Sedan datasets show that MoE-NO achieves a test-set MAPE of $1.16\%$ and a trend-prediction accuracy of $94.34\%$, outperforming the best baseline results of $1.52\%$ and $90.34\%$, respectively. Vehicle shape-optimization experiments further yield CFD-validated drag coefficient reductions of approximately $4\%$ to $10\%$.

Numerical simulations in industrial applications often require performing numerous high-precision computations parameterized by specific experimental conditions. For instance, in vehicle body design, aerodynamic simulations are essential for evaluating the aerodynamic characteristics of various proposed body geometries. However, computational resource constraints often become a bottleneck. Therefore, achieving the desired accuracy while minimizing computational cost is crucial. To address this challenge, model reduction methods have been developed to decrease the degrees of freedom by constraining the possible states of a physical system to a lower-dimensional subspace. In particular, reduction techniques that project the system onto a nonlinear subspace using neural networks have been actively studied. Our previous research developed a reduced-order model that integrates neural-network-based model reduction with a time-evolution method, implemented as a distributed parallel training framework to process high-resolution flow field data efficiently. In this study, we extend this reduction approach by incorporating a variational autoencoder to assess its robustness in high-Reynolds-number flows around multiple vehicle bodies with varying geometries. Specifically, we evaluate the reconstruction accuracy of vortex generation across different spatial and temporal scales using a compact latent representation, with a particular focus on the flow behavior near the rear end of the vehicle body.

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.

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 $L_2$ 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 $L_2$ 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 $10^4$ resolution, indicating a focused attentional mechanism capable of preserving localized gradients against global diffusion.

Computational Fluid Dynamics (CFD) is central to race-car aerodynamic development, yet its cost -- tens of thousands of core-hours per high-fidelity evaluation -- severely limits the design space exploration feasible within realistic budgets. AI-based surrogate models promise to alleviate this bottleneck, but progress has been constrained by the limited complexity of public datasets, which are dominated by smoothed passenger-car shapes that fail to exercise surrogates on the thin, complex, highly loaded components governing motorsport performance. This work presents three primary contributions. First, we introduce a high-fidelity RANS dataset built on a parametric LMP2-class CAD model and spanning six operating conditions (map points) covering straight-line and cornering regimes, generated and validated by aerodynamics experts at Dallara to preserve features relevant to industrial motorsport. Second, we present the Gauge-Invariant Spectral Transformer (GIST), a graph-based neural operator whose spectral embeddings encode mesh connectivity to enhance predictions on tightly packed, complex geometries. GIST guarantees discretization invariance and scales linearly with mesh size, achieving state-of-the-art accuracy on both public benchmarks and the proposed race-car dataset. Third, we demonstrate that GIST achieves a level of predictive accuracy suitable for early-stage aerodynamic design, providing a first validation of the concept of interactive design-space exploration -- where engineers query a surrogate in place of the CFD solver -- within industrial motorsport workflows.

High-fidelity vehicle drag evaluation is constrained less by solver runtime than by workflow friction: geometry cleanup, meshing retries, queue contention, and reproducibility failures across teams. We present a contract-centric blueprint for self-evolving coding agents that discover executable surrogate pipelines for predicting drag coefficient $C_d$ under industrial constraints. The method formulates surrogate discovery as constrained optimization over programs, not static model instances, and combines Famou-Agent-style evaluator feedback with population-based island evolution, structured mutations (data, model, loss, and split policies), and multi-objective selection balancing ranking quality, stability, and cost. A hard evaluation contract enforces leakage prevention, deterministic replay, multi-seed robustness, and resource budgets before any candidate is admitted. Across eight anonymized evolutionary operators, the best system reaches a Combined Score of 0.9335 with sign-accuracy 0.9180, while trajectory and ablation analyses show that adaptive sampling and island migration are primary drivers of convergence quality. The deployment model is explicitly ``screen-and-escalate'': surrogates provide high-throughput ranking for design exploration, but low-confidence or out-of-distribution cases are automatically escalated to high-fidelity CFD. The resulting contribution is an auditable, reusable workflow for accelerating aerodynamic design iteration while preserving decision-grade reliability, governance traceability, and safety boundaries.

Benchmarking has been the cornerstone of progress in computer vision, natural language processing, and the broader deep learning domain, driving algorithmic innovation through standardized datasets and reproducible evaluation protocols. The growing availability of large-scale Computational Fluid Dynamics (CFD) datasets has opened new opportunities for applying machine learning to aerodynamic and engineering design. Yet, despite this progress, there exists no standardized benchmark for large-scale numerical simulations in engineering design. In this work, we introduce CarBench, the first comprehensive benchmark dedicated to large-scale 3D car aerodynamics, performing a large-scale evaluation of state-of-the-art models on DrivAerNet++, the largest public dataset for automotive aerodynamics, containing over 8,000 high-fidelity car simulations. We assess eleven architectures spanning neural operator methods (e.g., Fourier Neural Operator), geometric deep learning (PointNet, RegDGCNN, PointMAE, PointTransformer), transformer-based neural solvers (Transolver, Transolver++, AB-UPT), and implicit field networks (TripNet). Beyond standard interpolation tasks, we perform cross-category experiments in which transformer-based solvers trained on a single car archetype are evaluated on unseen categories. Our analysis covers predictive accuracy, physical consistency, computational efficiency, and statistical uncertainty. To accelerate progress in data-driven engineering, we open-source the benchmark framework, including training pipelines, uncertainty estimation routines based on bootstrap resampling, and pretrained model weights, establishing the first reproducible foundation for large-scale learning from high-fidelity CFD simulations, available at https://github.com/Mohamedelrefaie/CarBench.