Scalable diagonal discipline

Let us consider the SobieskiAerodynamics discipline. We want to build its ScalableDiscipline counterpart, using a ScalableDiagonalModel

For that, we can use a 20-length DiagonalDOE and test different sizes of variables or different settings for the scalable diagonal discipline.

from __future__ import absolute_import, division, unicode_literals

from future import standard_library

Import

from gemseo.api import (
    configure_logger,
    create_discipline,
    create_scalable,
    create_scenario,
)
from gemseo.problems.sobieski.core import SobieskiProblem

configure_logger()

standard_library.install_aliases()

Learning dataset

The first step is to build an AbstractFullCache dataset from a DiagonalDOE.

Instantiate the discipline

For that, we instantiate the SobieskiAerodynamics discipline and set it up to cache all evaluations.

discipline = create_discipline("SobieskiAerodynamics")
discipline.set_cache_policy(discipline.MEMORY_FULL_CACHE)

Get the input space

We also define the input space on which to sample the discipline.

input_space = SobieskiProblem().read_design_space()
input_space.filter(discipline.get_input_data_names())

Out:

<gemseo.algos.design_space.DesignSpace object at 0x7fc29db32ac0>

Build the DOE scenario

Lastly, we sample the discipline by means of a DOEScenario relying on both discipline and input space. In order to build a diagonal scalable discipline, a DiagonalDOE must be used.

scenario = create_scenario(
    [discipline], "DisciplinaryOpt", "y_2", input_space, scenario_type="DOE"
)
scenario.execute({"algo": "DiagonalDOE", "n_samples": 20})

Out:

{'eval_jac': False, 'algo': 'DiagonalDOE', 'n_samples': 20}

Scalable diagonal discipline

Build the scalable discipline

The second step is to build a ScalableDiscipline, using a ScalableDiagonalModel and the cache of the discipline.

scalable = create_scalable("ScalableDiagonalModel", discipline.cache)

Visualize the input-output dependencies

We can easily access the underlying ScalableDiagonalModel and plot the corresponding input-output dependency matrix where the level of gray and the number (in [0,100]) represent the degree of dependency between inputs and outputs. Input are on the left while outputs are at the top. More precisely, for a given output component located at the top of the graph, these degrees are contributions to the output component and they add up to 1. In other words, a degree expresses this contribution in percentage and for a given column, the elements add up to 100.

scalable.scalable_model.plot_dependency(save=False, show=True)

Visualize the 1D interpolations

For every output, we can also visualize a spline interpolation of the output samples over the diagonal of the input space.

scalable.scalable_model.plot_1d_interpolations(save=False, show=True)

• 
• 
• 
• 
• 
• 
• 

Out:

[]

Increased problem dimension

We can repeat the construction of the scalable discipline for different sizes of variables and visualize the input-output dependency matrices.

Twice as many inputs

For example, we can increase the size of each input by a factor of 2.

sizes = {
    name: discipline.cache.varsizes[name] * 2
    for name in discipline.get_input_data_names()
}
scalable = create_scalable("ScalableDiagonalModel", discipline.cache, sizes)
scalable.scalable_model.plot_dependency(save=False, show=True)

Twice as many outputs

Or we can increase the size of each output by a factor of 2.

sizes = {
    name: discipline.cache.varsizes[name] * 2
    for name in discipline.get_output_data_names()
}
scalable = create_scalable("ScalableDiagonalModel", discipline.cache, sizes)
scalable.scalable_model.plot_dependency(save=False, show=True)

Twice as many variables

Or we can increase the size of each input and each output by a factor of 2.

names = list(discipline.get_input_data_names())
names += list(discipline.get_output_data_names())
sizes = {name: discipline.cache.varsizes[name] * 2 for name in names}
scalable = create_scalable("ScalableDiagonalModel", discipline.cache, sizes)
scalable.scalable_model.plot_dependency(save=False, show=True)

Binary IO dependencies

By default, any output component depends on any input component with a random level. We can also consider sparser input-output dependency by means of binary input-output dependency matrices. For that, we have to set the value of the fill factor which represents the part of connection between inputs and outputs. Then, a connection is represented by a black square while an absence of connection is presented by a white one. When the fill factor is equal to 1, any input is connected to any output. Conversely, when the fill factor is equal to 0, there is not a single connection between inputs and outputs.

Fill factor = 0.2

Here, there is a 20% connection rate

scalable = create_scalable(
    "ScalableDiagonalModel", discipline.cache, sizes, fill_factor=0.2
)
scalable.scalable_model.plot_dependency(save=False, show=True)

Fill factor = 0.5

Here, there is a 50% connection rate

scalable = create_scalable(
    "ScalableDiagonalModel", discipline.cache, sizes, fill_factor=0.5
)
scalable.scalable_model.plot_dependency(save=False, show=True)

Fill factor = 0.8

Here, there is a 80% connection rate

scalable = create_scalable(
    "ScalableDiagonalModel", discipline.cache, sizes, fill_factor=0.8
)
scalable.scalable_model.plot_dependency(save=False, show=True)

Heterogeneous dependencies

We could also imagine a more complex situation where an output would depend inputs with a particular fill factor. For example, let us consider a 20% connection rate for "y_2".

scalable = create_scalable(
    "ScalableDiagonalModel", discipline.cache, sizes, fill_factor={"y_2": 0.2}
)
scalable.scalable_model.plot_dependency(save=False, show=True)

Group dependencies

We could also imagine another particular situation where an output would depend only on certain inputs. For example, let us suppose that "y_2" depends only on "x_shared".

scalable = create_scalable(
    "ScalableDiagonalModel", discipline.cache, sizes, group_dep={"y_2": ["x_shared"]}
)
scalable.scalable_model.plot_dependency(save=False, show=True)