Create a discipline from analytical expressions

from __future__ import annotations

from numpy import array

from gemseo import create_discipline

Import

Introduction

A simple Discipline can be created using analytic formulas, e.g. \(y_1=2x^2\) and \(y_2=5+3x^2z^3\), thanks to the AnalyticDiscipline class which is a quick alternative to model a simple analytic MDO problem.

Create the dictionary of analytic outputs

First of all, we have to define the output expressions in a dictionary where keys are output names and values are formula with string format:

expressions = {"y_1": "2*x**2", "y_2": "5+3*x**2+z**3"}

Create the discipline

Then, we create and instantiate the corresponding AnalyticDiscipline, which is a particular Discipline. For that, we use the API function create_discipline() with:

• discipline_name="AnalyticDiscipline",

• name="analytic",

• expressions=expr_dict.

In practice, we write:

disc = create_discipline("AnalyticDiscipline", expressions=expressions)

Note

GEMSEO takes care of the grammars and Discipline._run() method generation from the expressions argument. In the background, GEMSEO considers that x is a mono-dimensional float input parameter and y_1 and y_2 are mono-dimensional float output parameters.

Execute the discipline

Lastly, we can execute this discipline any other:

input_data = {"x": array([2.0]), "z": array([3.0])}
disc.execute(input_data)

{'x': array([2.]), 'z': array([3.]), 'y_1': array([8.]), 'y_2': array([44.])}

About the analytic jacobian

The discipline will provide analytic derivatives (Jacobian) automatically using the sympy library.

This can be checked easily using Discipline.check_jacobian():

disc.check_jacobian(
    input_data,
    derr_approx=disc.ApproximationMode.FINITE_DIFFERENCES,
    step=1e-5,
    threshold=1e-3,
)

    INFO - 16:23:08: Jacobian: dp y_1/dp x succeeded.
    INFO - 16:23:08: Jacobian: dp y_1/dp z succeeded.
    INFO - 16:23:08: Jacobian: dp y_2/dp x succeeded.
    INFO - 16:23:08: Jacobian: dp y_2/dp z succeeded.
    INFO - 16:23:08: Linearization of Discipline: AnalyticDiscipline is correct.

True