import numpy as np
from sklearn.neural_network import MLPRegressor
from gekko import GEKKO, ML

# Create training data for the unknown physics f_true(x) = -0.2*x^2
X = np.linspace(0, 2, 21).reshape(-1, 1)
y = -0.2 * X.ravel()**2
mlp = MLPRegressor(hidden_layer_sizes=(5,), activation='tanh', max_iter=5000).fit(X, y)

# Set up GEKKO model and import the trained MLP
m = GEKKO(remote=False)
m.time = np.linspace(0, 5, 101)  # simulate 5 seconds
x = m.Var(value=1.0)
# Create scaling for GEKKO's ML interface (custom scaler with min/max values)
data = np.concatenate([X, y.reshape(-1, 1)], axis=1)
# Assume the scaler is defined with known min/max (details omitted for brevity)
scaler = ML.CustomMinMaxGekkoScaler(data, features=[0], label=[1])
mma = scaler.minMaxValues()
ml_model = ML.Gekko_NN_SKlearn(mlp, mma, m)
f = ml_model.predict([x])

# Define the hybrid ODE: dx/dt = -0.5*x + f(x)
m.Equation(x.dt() == -0.5 * x + f)
m.options.IMODE = 4  # dynamic simulation mode
m.solve(disp=False)
print("Hybrid model final x:", x.value[-1])