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

class gemseo.problems.dataset.burgers.BurgersDataset(name='Burgers', by_group=True, n_samples=30, n_x=501, fluid_viscosity=0.1, categorize=True)[source]

Bases: gemseo.core.dataset.Dataset

Burgers dataset parametrization.

Constructor.

Parameters

  • name (str) – name of the dataset.

  • by_group (bool) – if True, store the data by group. Otherwise, store them by variables. Default: True.

  • n_samples (int) – number of samples. Default: 30.

  • n_x (int) – number of spatial points. Default: 501.

  • fluid_viscosity (float) – fluid viscosity. Default: 0.1.

  • categorize (bool) – distinguish between the different groups of variables. Default: True.

Parma bool opt_naming

use an optimization naming. Default: True.