Using the predict() methods of fitted models with gekko

Many model-fitting Python packages have a predict() method, which outputs a prediction of the fitted model given observations of the predictor(s).

Question: How would I use these predict() methods to predict a single value when the observation is a variable in a gekko model?

Below is a very simple reproducible example:

Note: The actual model that I am fitting is a cubic spline using statsmodels.gam.smooth_basis.BSplines and statsmodels.gam.generalized_additive_model.GLMGam. However, I am hoping that this simple example with sklearn.linear_model.LinearRegression will translate to more complex model classes from other packages.

from sklearn.linear_model import LinearRegression
import numpy as np
import matplotlib.pyplot as plt
from gekko import GEKKO

# create example data
x = np.arange(100)[:, np.newaxis]
y = np.arange(100) * 2 + 10

plt.plot(x, y)  # plot x vs y data
# plt.show()

model = LinearRegression()  # instantiate linear model
model.fit(x, y)  # fit model

x_predict = np.arange(100, 200)[:, np.newaxis]  # create array of predictor observations
y_predict = model.predict(x_predict)  # use model to make prediction

plt.plot(x_predict, y_predict)  # plot prediction
# plt.show()

m = GEKKO()  # instantiate gekko model

x2 = m.FV()  # instantiate free variable
x2.STATUS = 1  # make variable available for solver

y2 = 50  # true value

# place x2 variable in numpy array to adhere to `predict()`'s argument requirements
x2_arr = np.array(x2).reshape(1, -1)

# minimize squared error between the true value and the model's prediction
m.Minimize((y2 - model.predict(x2_arr)) ** 2)

m.options.IMODE = 3
m.solve(disp=True)

print(f"x2 = {x2.value[0]:3f}")

I get the following sequential errors:

TypeError: float() argument must be a string or a real number, not 'GK_FV'

ValueError: setting an array element with a sequence.

My first thought is that I would have to create a wrapper class around the gekko.gk_parameter.GK_FV class to modify the float() method, but that's where my knowledge and skills end.

source https://stackoverflow.com/questions/76408801/using-the-predict-methods-of-fitted-models-with-gekko