A Blueprint for Self-Evolving Coding Agents in Vehicle Aerodynamic Drag Prediction

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.

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.

Self-evolving agents improve through repeated cycles of modification and evaluation. However, existing methods receive feedback on modifications only after costly evaluations, and aggregate scores may obscure distinctions between failures that require different repairs. We introduce predictive self-evolution through an editable Improvement Dynamics Model (IDM). Before evaluation, the IDM predicts task-level outcomes of a proposed modification and guides an optional revision. After evaluation, past modifications and their observed outcomes are used to improve the IDM, allowing predictive knowledge to accumulate across generations. The system can thus improve how it solves tasks, proposes modifications, and predicts their effects. Building on HyperAgents, we evaluate this approach across multilingual coding, paper review, robotics reward design, and Olympiad-level mathematical grading. Our approach outperforms HyperAgents across all four domains, with up to 46% higher average performance over generations. Gains also persist under matched token budgets that include both agent evolution and task evaluation, and extend to held-out tasks. Forecast accuracy improves as the IDM evolves, and the learned predictive knowledge transfers to improve evolution in a new domain.