Training snapshots in the plane of the two leading global POD coefficients, coloured by the chart that owns them. The lines are the closed-loop forecasts, drawn up to the instant each one leaves the range of the attractor, which a cross marks.
Predictability time of every model in the sweep. Click a cell to load it.
Representation error of K charts divided by that of a single global basis of the same size. Below 1, quantization represents the test window better at equal cost.
The field u(x, t) of the full-order model, of the selected reduced model, and of the one-chart model at the same number of modes, from the same initial condition and on the same colour scale.
Relative error of the closed-loop forecast against the reference solution, and the representation error, which is the floor the geometry sets.
Fraction of the training attractor each chart owns, and the fraction of the forecast spent in it.
Which chart holds the state at each instant: the closed-loop forecast, and the full-order model over the same window. Where the two agree, the reduced model is in the chart the physics is in.