# Using a MetaModel Component¶

This tutorial is a demonstration of how to construct a MetaModel of a component using a Kriging surrogate. Generally, MetaModel capabilities are used to construct a low computational cost replacement for an expensive component. A more detailed description of this class can be found under the source documentation for MetaModel.

For this example, a component was written for the sine function. This component has only one input and output, which will be mimicked by the MetaModel. Had there been additional variables, access to those would also be available through the MetaModel.

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

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 CSVCaseRecorder
from openmdao.lib.surrogatemodels.api import KrigingSurrogate

class Sin(Component):

f_x = Float(0.0,iotype="out")

def execute(self):
self.f_x = .5*sin(self.x)


To create a MetaModel, we first define an assembly to work in. After we have created an assembly, the MetaModel component needs to be instantiated. In this example, the MetaModel was instantiated as sin_meta_model, making it easy to identify.

Once the MetaModel component is in place, the first step is to tell the MetaModel which component it should create an approximation for. This is done by placing the component in the slot called model. For this case we are looking at the Sin component created earlier, so this is what’s placed in the model slot. The MetaModel will now have the same inputs and outputs as our sine component (an input named x and an output named f_x copied directly from the names in the Sine component).

The next step is to fill the default_surrogate slot. In this case we set it to KrigingSurrogate, meaning that all outputs would be modeled with Kriging surrogate models, unless otherwise specified. Specific surrogate models can be specified for specific output variables. We cover that in the next tutorial.

class Simulation(Assembly):
def configure(self):

#Components
self.sin_meta_model.default_surrogate = KrigingSurrogate()
self.sin_meta_model.model = Sin()


Once the model and default_surrogate slots of the MetaModel have been filled, the MetaModel is ready for training.

#Training the MetaModel
self.DOE_Trainer.DOEgenerator = FullFactorial()
self.DOE_Trainer.DOEgenerator.num_levels = 25
self.DOE_Trainer.case_outputs = ["sin_meta_model.f_x"]
self.DOE_Trainer.recorders = [CSVCaseRecorder()]


In this case, we’re going to train with a DOEdriver, called DOE_Trainer. We specify a FullFactorial DOEgenerator, which creates a set of evenly spaced points across an interval. We (somewhat arbitrarily) selected 25 points for our training set, specified by num_levels under the DOEgenerator. The proper training set, is of course, highly problem dependent. The training interval is based on the low and high values specified in the add_parameter call.

When the train_next event is set, MetaModel passes the inputs to the model (i.e., Sin) to be run. By adding the train_next event to the DOE_Trainer driver, the driver will set the train_next event in the MetaModel driver for each iteration. The outputs generated by each training run are stored for use in training a surrogate model. MetaModel stores the training data internally for its own uses, but you can also specify an extra CaseRecorder to store the training cases for your own analysis if you want. Here this storage occurs via the use of CSVCaseRecorder, but you could use any CaseRecorder here.

After you train a MetaModel, you want to do something with it. Here, we just run a simple validation with another DOEDriver called DOE_Validate. This time, the Uniform DOEGenerator was used. This provides a random sampling of points from within the range of input variables. Twenty validation points are being used in this particular case.

Here, we add a new instance of the sine component called sin_calc, so we can calculate an actual and a predicted value simultaneously.

#MetaModel Validation
self.DOE_Validate.DOEgenerator = Uniform()
self.DOE_Validate.DOEgenerator.num_samples = 20
self.DOE_Validate.case_outputs = ["sin_calc.f_x","sin_meta_model.f_x"]
self.DOE_Validate.recorders = [CSVCaseRecorder()]

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


Notice that the train_next event is not added to the DOE_Validate driver like it was for for the training driver. MetaModel automatically runs in predict mode when this event is not set. On any prediction run, Metamodel will check for new training data and if present, automatically train surrogate models for each of the outputs with that data. Since training data is required to run, the training mode must always be run prior to the running of predict mode.

Now, the outputs of the MetaModel will be the predicted values as determined by the surrogate model.

The last thing we do is specify the workflows which control the execution order of this example. Remember that the top driver in any assembly must be called driver. The type of workflow being executed is a sequential workflow, meaning that is a simple sequence of components.

The following figure visually shows the iteration hierarchy for this MetaModel. Note that sin_meta_model appears in two workflows. This is necessary since in the training workflow the MetaModel is trained, and within the prediction workflow, that data is used to run the MetaModel again in order to produce predictions. Thus it must be added to each workflow separately.

View of the Iteration Hierarchy

Finally, the first two lines of the following code are required to actually run the MetaModel. The remaining code is for accessing and printing the data. Using the data recorded by the implementation of DBCaseRecorder(), we can access and print the run data.

if __name__ == "__main__":

sim = set_as_top(Simulation())
sim.run()

#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['sin_meta_model.x'] for case in train_data]
#Note: Kriging outputs NormalDistribution (not float), so you need to grab
#    the mean (.mu) or the std-deviation (.sigma) from the returned object
train_actual = [case['sin_meta_model.f_x'].mu for case in train_data]
inputs = [case['sin_calc.x'] for case in validate_data]
actual = [case['sin_calc.f_x'] for case in validate_data]
predicted = [case['sin_meta_model.f_x'].mu for case in validate_data]

for a,p in zip(actual,predicted):
print "%1.3f, %1.3f"%(a,p)


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

MetaModel

#### Next topic

Modeling Multiple Outputs