Surrogate modelling and NSGA-II optimization

Paper · Master's thesis, Ch. 5

This paper covers the data-driven core of the front-wing thesis: fitting a surrogate to a limited set of CFD runs and extracting the optimal designs from it.

Training the surrogate

A Gaussian Process surrogate was trained on 70×2 Latin Hypercube designs — about 2.7 samples per dimension over the 26-dimensional design space, which is sparse by any standard and is precisely why the active-learning stage matters.

The kernel is squared-exponential with Automatic Relevance Determination, so a separate length-scale is fitted per design variable. As a by-product, the fitted length-scales provide a data-driven sensitivity ranking of the 26 variables.

Active learning

The surrogate was then refined iteratively. At each step the q-Expected Hypervolume Improvement acquisition function selects a batch of designs that would most enlarge the dominated region of the C_D–C_L plane; those designs are evaluated with the true CFD and the surrogate re-fitted.

Active-learning convergence across batches/assets/img/papers/active-learning-convergence.png

Fig. 1 — Surrogate accuracy across successive active-learning batches.

Parity plots and forward-prediction checks track accuracy batch by batch until the surrogate is trustworthy enough to be frozen.

Parity plot of surrogate prediction against CFD/assets/img/papers/surrogate-parity.png

Fig. 2 — Predicted vs CFD coefficients for the validation points.

Multi-objective optimization

With the surrogates frozen, NSGA-II is run directly over the surrogate means to produce a Pareto front of downforce-versus-drag optima. Selected points on the front were then re-evaluated with full CFD to quantify the surrogate offset — the discrepancy between predicted and actual performance at the optimum.

Pareto front with the selected and validated points marked/assets/img/papers/nsga2-pareto.png

Fig. 3 — Pareto front from NSGA-II with validated front points.

Track-specific selection

Every point on the front is an optimal compromise, so the algorithm does not select for you. The final choice was made per circuit, weighting the two modes by the fraction of each 2025 F1 lap spent with DRS open — which turns an abstract trade-off curve into concrete, track-specific geometries.

Optimal geometry selected for each track/assets/img/papers/optimal-per-track.png

Fig. 4 — Optimal geometries for each track.

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