gemseo.problems.dataset.burgers module

Burgers dataset.

This Dataset contains solutions to the Burgers' equation with periodic boundary conditions on the interval \([0, 2\pi]\) for different time steps:

\[u_t + u u_x = \nu u_{xx},\]

An analytical expression can be obtained for the solution, using the Cole-Hopf transform:

\[u(t, x) = - 2 \nu \frac{\phi'}{\phi},\]

where \(\phi\) is solution to the heat equation \(\phi_t = \nu \phi_{xx}\).

This Dataset is based on a full-factorial design of experiments. Each sample corresponds to a given time step \(t\), while each feature corresponds to a given spatial point \(x\).

More information about Burgers' equation

create_burgers_dataset(n_samples=30, n_x=501, fluid_viscosity=0.1, categorize=True)

Burgers dataset parametrization.

Parameters:

• n_samples (int) --

  The number of samples.

  By default it is set to 30.

• n_x (int) --

  The number of spatial points.

  By default it is set to 501.

• fluid_viscosity (float) --

  The fluid viscosity.

  By default it is set to 0.1.

• categorize (bool) --

  Whether to distinguish between the different groups of variables.

  By default it is set to True.

Returns:

The Burgers dataset.

Return type:

IODataset