The quick-start uses the same model shown on the OMLT README, but it provides a little more detail. The example imports a neural network trained in TensorFlow, formulates a Pyomo model, and seeks the neural network input that produces the desired output.

We begin by importing the necessary packages. These include tensorflow to import the neural network and pyomo to build the optimization problem. We also import the necessary objects from omlt to formulate the neural network in Pyomo.

import tensorflow
import pyomo.environ as pyo
from omlt import OmltBlock, OffsetScaling
from omlt.neuralnet import FullSpaceNNFormulation, NetworkDefinition
from omlt.io import load_keras_sequential

We first load a simple neural network from the tests directory that contains 1 input, 1 output, and 3 hidden nodes with sigmoid activation functions.

#load a Keras model
nn = tensorflow.keras.models.load_model('tests/models/keras_linear_131_sigmoid', compile=False)

We next create a Pyomo model and attach an OmltBlock which will be used to formulate the neural network. An OmltBlock is a custom Pyomo block that we use to build machine learning model formulations. We also create Pyomo model variables to represent the input and output of the neural network.

#create a Pyomo model with an OMLT block
model = pyo.ConcreteModel()
model.nn = OmltBlock()

#the neural net contains one input and one output
model.input = pyo.Var()
model.output = pyo.Var()

OMLT supports the use of scaling and input bound information. This information informs how the Pyomo model applies scaling and unscaling to the neural network inputs and outputs. It also informs variable bounds on the inputs.

#apply simple offset scaling for the input and output
scale_x = (1, 0.5)       #(mean,stdev) of the input
scale_y = (-0.25, 0.125) #(mean,stdev) of the output
scaler = OffsetScaling(offset_inputs=[scale_x[0]],

#provide bounds on the input variable (e.g. from training)
scaled_input_bounds = {0:(0,5)}

We now create a NetworkDefinition using the load_keras_sequential function where we provide the scaler object and input bounds. Once we have a NetworkDefinition, we can pass it to various formulation objects which decide how to build the neural network within the OmltBlock. Here, we use the FullSpaceNNFormulation, but others are also possible (see formulations).

#load the keras model into a network definition
net = load_keras_sequential(nn,scaler,scaled_input_bounds)

#multiple formulations of a neural network are possible
#this uses the default NeuralNetworkFormulation object
formulation = FullSpaceNNFormulation(net)

#build the formulation on the OMLT block

We can query the input and output pyomo variables that the build_formulation method produces (as well as scaled input and output varialbes). We lastly create pyomo constraints that connect our input and output variables defined earlier to the neural network input and output variables on the OmltBlock.:

#query inputs and outputs, as well as scaled inputs and outputs

#connect pyomo model input and output to the neural network
def connect_input(mdl):
    return mdl.input == mdl.nn.inputs[0]

def connect_output(mdl):
    return mdl.output == mdl.nn.outputs[0]

Lastly, we formulate an objective function and use Ipopt to solve the optimization problem.:

#solve an inverse problem to find that input that most closely matches the output value of 0.5
model.obj = pyo.Objective(expr=(model.output - 0.5)**2)
status = pyo.SolverFactory('ipopt').solve(model, tee=False)