Charts partition the attractor; each carries its own basis and its own projected equations.
Local basis size. The reduced state has this many degrees of freedom at any instant.
Predictability time
-
Lyapunov times, error threshold 0.5
Representation error
-
test window projected onto the charts
Reduced state size
-
of 128 grid points
Charts visited
-
by the closed-loop forecast
One chart, same modes
-
Lyapunov times

Attractor and charts

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 over the sweep

Predictability time of every model in the sweep. Click a cell to load it.

Rows: charts. Columns: modes per chart.

Representation error against one chart

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.

Each cell prints its ratio. A single chart is 1 by construction.

Space-time forecast

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.

Error history

Relative error of the closed-loop forecast against the reference solution, and the representation error, which is the floor the geometry sets.

Chart occupancy

Fraction of the training attractor each chart owns, and the fraction of the forecast spent in it.

training attractor forecast
Read the numbers as a table

Chart sequence

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.