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 division, unicode_literals

from matplotlib import pyplot as plt

Import

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

configure_logger()

Out:

<RootLogger root (INFO)>

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 0x7fcaa46148e0>

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:

    INFO - 14:42:51:
    INFO - 14:42:51: *** Start DOE Scenario execution ***
    INFO - 14:42:51: DOEScenario
    INFO - 14:42:51:    Disciplines: SobieskiAerodynamics
    INFO - 14:42:51:    MDOFormulation: DisciplinaryOpt
    INFO - 14:42:51:    Algorithm: DiagonalDOE
    INFO - 14:42:51: Optimization problem:
    INFO - 14:42:51:    Minimize: y_2(x_shared, x_2, y_32, y_12)
    INFO - 14:42:51:    With respect to: x_shared, x_2, y_32, y_12
    INFO - 14:42:51: DOE sampling:   0%|          | 0/20 [00:00<?, ?it]
    INFO - 14:42:51: DOE sampling: 100%|██████████| 20/20 [00:00<00:00, 437.83 it/sec, obj=[7.72500000e+04 1.27392070e+04 6.06395673e+00]]
    INFO - 14:42:51: Optimization result:
    INFO - 14:42:51: Objective value = 25508.372961119574
    INFO - 14:42:51: The result is feasible.
    INFO - 14:42:51: Status: None
    INFO - 14:42:51: Optimizer message: None
    INFO - 14:42:51: Number of calls to the objective function by the optimizer: 20
    INFO - 14:42:51: Design space:
    INFO - 14:42:51: +----------+-------------+-------+-------------+-------+
    INFO - 14:42:51: | name     | lower_bound | value | upper_bound | type  |
    INFO - 14:42:51: +----------+-------------+-------+-------------+-------+
    INFO - 14:42:51: | x_shared |     0.01    |  0.01 |     0.09    | float |
    INFO - 14:42:51: | x_shared |    30000    | 30000 |    60000    | float |
    INFO - 14:42:51: | x_shared |     1.4     |  1.4  |     1.8     | float |
    INFO - 14:42:51: | x_shared |     2.5     |  2.5  |     8.5     | float |
    INFO - 14:42:51: | x_shared |      40     |   40  |      70     | float |
    INFO - 14:42:51: | x_shared |     500     |  500  |     1500    | float |
    INFO - 14:42:51: | x_2      |     0.75    |  0.75 |     1.25    | float |
    INFO - 14:42:51: | y_32     |    0.235    | 0.235 |    0.795    | float |
    INFO - 14:42:51: | y_12     |    24850    | 24850 |    77250    | float |
    INFO - 14:42:51: | y_12     |     0.45    |  0.45 |     1.5     | float |
    INFO - 14:42:51: +----------+-------------+-------+-------------+-------+
    INFO - 14:42:51: *** DOE Scenario run terminated ***

{'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, converted to a Dataset.

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

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=False)

Out:

'None'

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=False)

• 
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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", dataset, sizes)
scalable.scalable_model.plot_dependency(save=False, show=False)

Out:

'None'

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", dataset, sizes)
scalable.scalable_model.plot_dependency(save=False, show=False)

Out:

'None'

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", dataset, sizes)
scalable.scalable_model.plot_dependency(save=False, show=False)

Out:

'None'

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

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

Out:

'None'

Fill factor = 0.5

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

Out:

'None'

Fill factor = 0.8

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

Out:

'None'

Heterogeneous dependencies

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

Out:

'None'

Group dependencies

scalable = create_scalable(
    "ScalableDiagonalModel", dataset, sizes, group_dep={"y_2": ["x_shared"]}
)
scalable.scalable_model.plot_dependency(save=False, show=False)
# Workaround for HTML rendering, instead of ``show=True``
plt.show()