Modeling Multiple OutputsΒΆ

This tutorial is a short demonstration of how to construct a MetaModel of a component with multiple outputs. This tutorial builds off of the single-output tutorial, with modifications for multiple outputs in a component.

We created a new component called Trig(). This component has one input and two outputs, both of which will be mimicked by the MetaModel.

from openmdao.main.api import Assembly, Component, SequentialWorkflow, set_as_top
from math import sin, cos

from openmdao.lib.datatypes.api import Float
from openmdao.lib.drivers.api import DOEdriver
from openmdao.lib.doegenerators.api import FullFactorial, Uniform
from openmdao.lib.components.api import MetaModel
from openmdao.lib.casehandlers.api import DBCaseRecorder
from openmdao.lib.surrogatemodels.api import LogisticRegression, KrigingSurrogate

class Trig(Component):

    x = Float(0,iotype="in",units="rad")

    f_x_sin = Float(0.0,iotype="out")
    f_x_cos = Float(0.0,iotype="out")

    def execute(self):
        self.f_x_sin = .5*sin(self.x)
        self.f_x_cos = .5*cos(self.x)

This next section differs from the the previous example in that there are two surrogate models, one specified for each of the outputs. Note that each of the outputs had been assigned a specific surrogate model, a logistic regression for sin, and a Kriging Surrogate for cos. In this case, no default was set at all.

The parameter x still needs to be added only once in this case, since the same input is being evaluated for both outputs.

class Simulation(Assembly):

    def configure(self):

        self.trig_meta_model.surrogate = {"f_x_sin":LogisticRegression(),
        self.trig_meta_model.model = Trig()
        self.trig_meta_model.recorder = DBCaseRecorder()

        #Training the MetaModel
        self.DOE_Trainer.DOEgenerator = FullFactorial()
        self.DOE_Trainer.DOEgenerator.num_levels = 20
        self.DOE_Trainer.case_outputs = ["trig_meta_model.f_x_sin","trig_meta_model.f_x_cos"]
        self.DOE_Trainer.recorders = [DBCaseRecorder()]

        #MetaModel Validation
        self.DOE_Validate.DOEgenerator = Uniform()
        self.DOE_Validate.DOEgenerator.num_samples = 20
        self.DOE_Validate.case_outputs = ["trig_calc.f_x_sin","trig_calc.f_x_cos","trig_meta_model.f_x_sin","trig_meta_model.f_x_cos"]
        self.DOE_Validate.recorders = [DBCaseRecorder()]

        #Iteration Hierarchy
        self.driver.workflow = SequentialWorkflow()

The iteration hierarchy is structurally the same as it would be with one output. Even though there’re multiple surrogate models for multiple outputs, they are still contained within only one MetaModel component. So once again there is the MetaModel component separately added to each workflow and the trig_calc component being added to the validation stage so that comparative values may be generated.

In printing the information we have now included all four of the outputs. For the Kriging Surrogate model, the answer returned as a normal distribution (Kriging Surrogate predicts both a mean and a standard deviation for a given input). When comparing the data, we just look at the mean here. This is why there is a .mu appended to the cos case under predicted_cos. An alternative would be to append .sigma which would return the standard deviation.

if __name__ == "__main__":

    sim = set_as_top(Simulation())

    #This is how you can access any of the data
    train_data = sim.DOE_Trainer.recorders[0].get_iterator()
    validate_data = sim.DOE_Validate.recorders[0].get_iterator()
    train_inputs = [case['trig_meta_model.x'] for case in train_data]
    train_actual_sin = [case['trig_meta_model.f_x_sin'] for case in train_data]
    train_actual_cos = [case['trig_meta_model.f_x_cos'].mu for case in train_data]
    inputs = [case['trig_calc.x'] for case in validate_data]
    actual_sin = [case['trig_calc.f_x_sin'] for case in validate_data]
    actual_cos = [case['trig_calc.f_x_cos'] for case in validate_data]
    predicted_sin = [case['trig_meta_model.f_x_sin'] for case in validate_data]
    predicted_cos = [case['trig_meta_model.f_x_cos'].mu for case in validate_data]

    for a,b,c,d in zip(actual_sin,predicted_sin,actual_cos,predicted_cos):
        print "%1.3f, %1.3f, %1.3f, %1.3f"%(a,b,c,d)

To view this example, and try running and modifying the code for yourself, you can download it here:

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