OMLT: Optimization and Machine Learning Toolkit

@misc{ceccon2022omlt,
     title={OMLT: Optimization & Machine Learning Toolkit},
     author={Ceccon, F. and Jalving, J. and Haddad, J. and Thebelt, A. and Tsay, C. and Laird, C. D. and Misener, R.},
     year={2022},
     eprint={2202.02414},
     archivePrefix={arXiv},
     primaryClass={stat.ML}
}

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

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

#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()

#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]],
                    factor_inputs=[scale_x[1]],
                    offset_outputs=[scale_y[0]],
                    factor_outputs=[scale_y[1]])

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

#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
model.nn.build_formulation(formulation)

#query inputs and outputs, as well as scaled inputs and outputs
model.nn.inputs
model.nn.outputs
model.nn.scaled_inputs
model.nn.scaled_outputs

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

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

#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)
print(pyo.value(model.input))
print(pyo.value(model.output))