AhmedML dataset

Dataset summary

Geometry

Parametric Ahmed car body variants.

Cases

500 CFD simulations.

Solver

OpenFOAM v2212 finite-volume simulations.

Fidelity

Transient hybrid RANS-LES, approximately 80 convective time units per case.

Mesh scale

Approximately 20 million cells per case.

License

CC BY-SA 4.0, as stated by the dataset source.

Published source splits

AhmedML publishes the eight train, validation, and test manifests below. The evaluator binds these exact public run_N case IDs and the immutable source revision. Check the submission guide for current availability.

Evaluate and submit

Follow the AhmedML participant quickstart for pinned Linux setup, data and prepared-support downloads, complete-split evaluation with resume, reports and validated packaging. Predict both surface and volume fields in native cell order. The evaluator derives forces and all seven profile series per case. Submit only the generated result directory, following the submission instructions.

Cp stations

AhmedML does not publish a canonical set of one-dimensional pressure traces. FluidsBench therefore defines the following symmetry-plane benchmark traces, informed by the body regions described in the AhmedML paper. The target lines move with each body: their coordinates use that case's length, height, width, slant dimensions, and actual surface bounds. The evaluator then samples a frozen nearest-native-polygon mapping. The dataset frame itself remains fixed at rear plane x=0, symmetry plane y=0, and ground z=0. Use the exact ID in station_id.

Wake velocity stations

Wake targets are also geometry-relative. For each case, L, H, and W come from that body's published parameters, and the evaluator freezes the native volume-cell mapping before any submission is scored. Each trace contains exactly 128 samples.

Metric definitions

Relative L2 error

For each evaluation/test geometry, map predictions to every entity in the release-bound public field support and return predictions and targets to dimensional physical space, \(q^\ast = T_q^{-1}(q)\). Calculate both paired relative-L2 values from the accumulated sufficient statistics: area-weighted L2 is primary on the boundary, while unweighted cell L2 (each cell counts equally) is primary in the flow volume. Report the complete-case percentages first, then take the arithmetic mean of the geometry-level values.

Relative L1 error

When reported as a supplementary metric, relative L1 uses the same complete dimensional support and the primary weighting for that domain. Calculate a percentage for each geometry, then take the arithmetic mean of the geometry-level percentages.

Dimensional evaluation

Relative L1 and L2 metrics are not computed on normalized, standardized, or non-dimensional training targets. If a model predicts normalized values, the submission/evaluator must undo that transform before scoring. C_d, C_l, and Cp-cut comparisons remain coefficient-based by definition.

Surface pressure relative L1/L2

Relative L1 and L2 error for dimensional surface pressure p_surface_pred against the evaluator surface pressure values. Cp is used only for the Cp-cut comparisons and plots.

Surface wall-shear relative L1/L2

Relative L1 and L2 error for the wall-shear vector \(\tau_w = (\tau_{w,x}, \tau_{w,y}, \tau_{w,z})\) on the Ahmed body surface.

Volume velocity relative L1/L2

Relative L1 and L2 error for the velocity vector \(u = (u_x, u_y, u_z)\) on every field-bearing cell in the release-bound volume_<case-id>.vtu file.

Volume pressure relative L1/L2

Relative L1 and L2 error for pressure on every field-bearing cell in the same public volume file.

AB-UPT convention

The secondary unweighted polygon relative L2 (each polygon counts equally) is the AB-UPT-compatible value: targets may be normalized for training, but evaluation uses unnormalized predictions and targets. FluidsBench additionally uses the area-weighted boundary value as its primary surface metric.

Coefficient of determination

For scalar values \(y_i\), \(R^2 = 1 - \sum_i(\hat{y}_i - y_i)^2 / \sum_i(y_i - \bar{y})^2\). Higher is better; 1.0 is perfect.

C_d and C_l R²

R² computed over all evaluated cases using predicted drag coefficient cd_pred and lift coefficient cl_pred.

Force R²

Mean of C_d R² and C_l R².

Cp cut R²

One global R² over all selected surface pressure coefficient samples from the held-out test cases. The evaluator flattens cp_pred and ground-truth cp across case_id, cut_id, station_id, and cut sample locations before computing R². The plotted trace is chosen with the leaderboard station selector.

Cp cut comparisons

Per-case and per-cut R² values can be reported as profile comparisons, but the leaderboard ranking should use the global held-out score so that cases with low Cp variance do not dominate through unstable per-case averages.

Velocity profile R²

One global R² over evaluator-derived scalar Ux/Uinf samples, flattened across the four frozen stations, held-out cases, and 128 sample locations. The other velocity components are part of native volume-field scoring, not this profile metric.

Default overall score

The leaderboard can be ranked by any individual metric. Its default ranking is a bounded 0-100 weighted score:

Relative L1 fields are reported as sortable supplementary metrics, but they are not included in this default score unless a future benchmark rule assigns them weights.

S_error(q) = 100 * max(0, 1 - E_q / cap_q)
S_R2(q)    = 100 * min(1, max(0, R2_q))
S_overall  = sum(weight_q * S_q)

Links

• AhmedML dataset page
• AhmedML paper
• FluidsBench leaderboard