Source code for gemseo.problems.dataset.burgers

# Copyright 2021 IRT Saint Exupéry,
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License version 3 as published by the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# Lesser General Public License for more details.
# You should have received a copy of the GNU Lesser General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
# Contributors:
#    INITIAL AUTHORS - initial API and implementation and/or initial
#                           documentation
#        :author: Syver Doving Agdestein
Burgers dataset

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

.. math::

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

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

.. math::

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

where :math:`\phi` is solution to the heat equation
:math:`\phi_t = \nu \phi_{xx}`.

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

`More information about Burgers' equation
from __future__ import annotations

from numpy import exp
from numpy import hstack
from numpy import linspace
from numpy import pi
from numpy import square

from gemseo.core.dataset import Dataset
from gemseo.core.discipline import MDODiscipline

[docs]class BurgersDiscipline(MDODiscipline): def __init__(self): super().__init__() self.input_grammar.initialize_from_data_names(["x", "z"]) self.output_grammar.initialize_from_data_names(["f", "g"])
[docs]class BurgersDataset(Dataset): """Burgers dataset parametrization.""" def __init__( self, name: str = "Burgers", by_group: bool = True, n_samples: int = 30, n_x: int = 501, fluid_viscosity: float = 0.1, categorize: bool = True, ) -> None: """ Args: name: The name of the dataset. by_group: Whether to store the data by group. Otherwise, store them by variables. n_samples: The number of samples. n_x: The number of spatial points. fluid_viscosity: The fluid viscosity. categorize: Whether to distinguish between the different groups of variables. """ super().__init__(name, by_group) time = linspace(0, 2, n_samples)[:, None] space = linspace(0, 2 * pi, n_x)[None, :] visc = fluid_viscosity alpha = space - 4 * time alpha_2 = square(alpha) beta = 4 * visc * (time + 1) gamma = space - 4 * time - 2 * pi gamma_2 = square(gamma) phi = exp(-alpha_2 / beta) + exp(-gamma_2 / beta) phi_deriv = -2 * alpha / beta * exp(-alpha_2 / beta) phi_deriv -= 2 * gamma / beta * exp(-gamma_2 / beta) u_t = -2 * visc / phi * phi_deriv if categorize: groups = {"t": Dataset.INPUT_GROUP, "u_t": Dataset.OUTPUT_GROUP} else: groups = None data = hstack([time, u_t]) self.set_from_array(data, ["t", "u_t"], {"t": 1, "u_t": n_x}, groups=groups) self.set_metadata("x", [[node] for node in space[0]]) self.set_metadata("nu", visc)