class InterceptorSurrogateQoI(QuantityOfInterest):
"""
Class that creates a surrogate model for the dymos supersonic intercpetor problem
for analysis
"""
def __init__(self, systemsize, input_dict, data_type=np.float):
QuantityOfInterest.__init__(self, systemsize, data_type=data_type)
# Load the eigenmodes
fname = input_dict['surrogate info full path']
surrogate_info = np.load(fname)
surrogate_samples = surrogate_info['input_samples']
fval_arr = surrogate_info['fvals']
# Create the surrogate
self.surrogate_type = input_dict['surrogate_type']
if self.surrogate_type == 'quadratic':
self.surrogate = QP()
elif self.surrogate_type == 'kriging':
theta0 = input_dict['kriging_theta']
self.surrogate = KRG(theta0=[theta0],
corr=input_dict['correlation function'])
else:
raise NotImplementedError
self.surrogate.set_training_values(surrogate_samples.T, fval_arr)
self.surrogate.train()
def eval_QoI(self, mu, xi):
rv = mu + xi
return self.surrogate.predict_values(np.expand_dims(rv, axis=0))
def eval_QoIGradient(self, mu, xi):
rv = np.expand_dims(mu + xi, axis=0)
dfdrv = np.zeros(self.systemsize, dtype=self.data_type)
for i in range(self.systemsize):
dfdrv[i] = self.surrogate.predict_derivatives(rv, i)[0, 0]
return dfdrv
def eval_QoIGradient_fd(self, mu, xi):
# This function uses numdifftools to compute the gradients. Only use for
# debugging.
def func(xi):
return self.eval_QoI(mu, xi)
G = nd.Gradient(func)(xi)
return G
def test_krg(self):
import numpy as np
import matplotlib.pyplot as plt
from smt.surrogate_models import KRG
xt = np.array([0.0, 1.0, 2.0, 3.0, 4.0])
yt = np.array([0.0, 1.0, 1.5, 0.9, 1.0])
sm = KRG(theta0=[1e-2])
sm.set_training_values(xt, yt)
sm.train()
num = 100
x = np.linspace(0.0, 4.0, num)
y = sm.predict_values(x)
# estimated variance
s2 = sm.predict_variances(x)
# derivative according to the first variable
dydx = sm.predict_derivatives(xt, 0)
fig, axs = plt.subplots(2)
axs[0].plot(xt, yt, "o")
axs[0].plot(x, y)
axs[0].set_xlabel("x")
axs[0].set_ylabel("y")
axs[0].legend(["Training data", "Prediction"])
# add a plot with variance
axs[1].plot(xt, yt, "o")
axs[1].plot(x, y)
axs[1].fill_between(
np.ravel(x),
np.ravel(y - 3 * np.sqrt(s2)),
np.ravel(y + 3 * np.sqrt(s2)),
color="lightgrey",
)
axs[1].set_xlabel("x")
axs[1].set_ylabel("y")
axs[1].legend(
["Training data", "Prediction", "Confidence Interval 99%"])
plt.show()
