Mappings and surrogate models¶

A Mapping is a surrogate model of your CFD results. It learns how each performance, such as drag or balance, depends on the parameters, such as ride heights and yaw, from the Attitudes you've simulated. It then predicts the performance anywhere in between, without running more CFD.

What a Mapping is¶

A Mapping fits one kriging model per performance to a fixed set of simulated Attitudes.

Inputs and outputs. The inputs are the parameters you choose: Map parameters or Run parameters that vary across the Runs. The outputs are the performances: columns of a Results table view. Each performance gets its own model.

Kriging. Kriging (Gaussian-process regression) treats the response as a smooth random surface. It predicts at a new point from a weighted combination of the nearby simulated points, with the weights set by how strongly the response is correlated over distance in each parameter. Bramble scales each parameter to the same range and fits those correlation lengths to your data, so a parameter that barely affects the result has little influence.

Interpolating or smoothed. By default the model passes exactly through every simulated point. That's right when the results are clean, but scatter, for example from convergence noise, makes the surface wiggle to hit every point. Apply Smoothing lets the model fit a noise level too, so it follows the trend instead of every point.

Multi-component. A multi-component Mapping models each zone's force components separately and adds them up, so totals such as lift, balance and L/D are built from their parts.

Fixed when created. A Mapping only knows the Runs it was created from. It doesn't update when new Runs finish.

Why the design of experiments matters¶

A surrogate is only as good as the points it's trained on. Points bunched in one corner leave the rest of the space unknown, however many you run.

A space-filling design such as Optimised Latin Hypercube spreads the Attitudes evenly across every parameter's range with far fewer points than a full grid. That makes it the usual choice for an aero map. A Full Factorial grid covers the space too, but the number of Attitudes grows quickly with each parameter. See generate a sweep.

Set the ranges to cover everywhere you'll want predictions. A Mapping can't see beyond the data.

How far to trust a prediction¶

Kriging gives a variance with every prediction, as well as the value. It shows how uncertain the model is at that point:

At a simulated point, the variance is close to zero (unless the Mapping is smoothed).
Between points, it rises. The bigger the gap, the higher it goes.
Outside the simulated range, it grows quickly. Predictions there are extrapolations.

Plot it with Show normalised uncertainties on the contour plot. Pareto and Cloud plots search 25% beyond the simulated range, and the Pareto plot marks those points Outside of original range.

Trust predictions most where the variance is low: inside the range and close to simulated points. Treat an optimum that sits in a high-variance area, or on the edge of the bounds, as a lead to check with CFD rather than an answer.

When to add more points¶

Add Attitudes when:

the variance is high in a region you care about
an optimum or a Pareto point you want to use is far from any simulated point
a CFD check of a prediction disagrees with the Mapping
the surface wiggles between points (try Apply Smoothing first if the results are noisy)

To refine a Mapping, add the predictions you want to check to a Map, run them, then create a new Mapping that includes the new Runs. See create a mapping.