Error with the prediction of variance derivatives in GPX

[MaelTremouille]

There is an issue with the computation of the predicted variance derivatives in GPX. Actually, the values differ significantly between the computation with KRG and GPX.
Here are some commands to show how different they are:

import numpy as np
from smt.sampling_methods import LHS
from smt.surrogate_models import GPX, KRG


def target_fun(x):
    return np.cos(5 * x)


def pb(x):
    # sin + linear trend
    y = (
        np.atleast_2d(np.sin(x[:, 0])).T
        + np.atleast_2d(2 * x[:, 0] + 5 * x[:, 1]).T
        + 10
    )  # + linear trend
    return y


xlimits = np.array([[-5, 10], [-5, 10]])
sampling = LHS(xlimits=xlimits, random_state=42)
xt = sampling(12)
yt = pb(xt)
trends = ["constant", "linear"]
kernels = [
    "pow_exp",
    "squar_exp",
    "abs_exp",
    "matern32",
    "matern52",
    "squar_sin_exp",
]

sm_gpx = GPX(
    theta0=[0.01],
    print_global=False,
    poly="constant",
    corr="abs_exp",
    seed=42,
)
sm_krg = KRG(
    theta0=[0.01],
    print_global=False,
    poly="constant",
    corr="abs_exp",
    random_state=42,
)
# train
sm_gpx.set_training_values(xt, yt)
sm_gpx.train()
sm_krg.set_training_values(xt, yt)
sm_krg.train()

# Predicted
e = 5e-6
xa = -1.3
xb = 2.5
x_valid = np.array([[xa, xb], [xa + e, xb], [xa - e, xb], [xa, xb + e], [xa, xb - e]])
y_predicted_gpx = sm_gpx.predict_variances(x_valid)
y_predicted_krg = sm_krg.predict_variances(x_valid)
x = np.atleast_2d(x_valid[0])

# diff
diff_g_gpx = (y_predicted_gpx[1, 0] - y_predicted_gpx[2, 0]) / (2 * e)
diff_d_gpx = (y_predicted_gpx[3, 0] - y_predicted_gpx[4, 0]) / (2 * e)
diff_g_krg = (y_predicted_krg[1, 0] - y_predicted_krg[2, 0]) / (2 * e)
diff_d_krg = (y_predicted_krg[3, 0] - y_predicted_krg[4, 0]) / (2 * e)

deriv_gpx = np.array(
    [
        sm_gpx.predict_variance_derivatives(x, 0)[0],
        sm_gpx.predict_variance_derivatives(x, 1)[0],
    ]
).T

deriv_krg = np.array(
    [
        sm_krg.predict_variance_derivatives(x, 0)[0],
        sm_krg.predict_variance_derivatives(x, 1)[0],
    ]
).T
print("deriv_gpx", deriv_gpx)
print("[diff_g_gpx,diff_d_gpx]", [diff_g_gpx, diff_d_gpx])
print("deriv_krg", deriv_krg)
print("[diff_g_krg,diff_d_krg]", [diff_g_gpx, diff_d_gpx])

[relf]

Good catch, thanks! This issue is fixed with egobox 0.21.1.