def test_mfk(self):
self.problems = ["exp", "tanh", "cos"]
for fname in self.problems:
prob = TensorProduct(ndim=self.ndim, func=fname)
sampling = FullFactorial(xlimits=prob.xlimits, clip=True)
np.random.seed(0)
xt = sampling(self.nt)
yt = prob(xt)
for i in range(self.ndim):
yt = np.concatenate((yt, prob(xt, kx=i)), axis=1)
y_lf = 2 * prob(xt) + 2
x_lf = deepcopy(xt)
np.random.seed(1)
xe = sampling(self.ne)
ye = prob(xe)
sm = MFK(theta0=[1e-2] * self.ndim)
if sm.options.is_declared("xlimits"):
sm.options["xlimits"] = prob.xlimits
sm.options["print_global"] = False
sm.set_training_values(xt, yt[:, 0])
sm.set_training_values(x_lf, y_lf[:, 0], name=0)
with Silence():
sm.train()
t_error = compute_rms_error(sm)
e_error = compute_rms_error(sm, xe, ye)
self.assert_error(t_error, 0.0, 1)
self.assert_error(e_error, 0.0, 1)
def cokriging(i):
# Xt_e = np.array([[1.57894737, 17.8947368],
# [8.42105263, 17.8947368],
# [1.57894737, 2.10526316],
# [8.42105263, 2.10526316],
# ])
Xt_e = np.array([
[50.0891841, 11.000994],
[49.9108168, 38.999006],
[84.200043, 41.5655806],
[16.0943345, 7.97111717],
[15.7955774, 41.584603],
[83.9713379, 7.94023456],
])
Xt_c = arr_xy_low
yt_e = arr_stress_high_train[i]
yt_c = np.array(low_predict_data_by_force()[0][i])
sm = MFK(theta0=np.array(Xt_e.shape[1] * [1.0]), print_global=False)
sm.set_training_values(Xt_c, yt_c, name=0)
sm.set_training_values(Xt_e, yt_e)
sm.train()
Xp = arr_xy_high
y = sm.predict_values(Xp)
# MSE = sm.predict_variances(Xp)
# der = sm.predict_derivatives(Xp, kx=0)
return y.flatten()
def test_mfk_derivs(self):
prob = Sphere(ndim=self.ndim)
sampling = LHS(xlimits=prob.xlimits)
nt = 500
np.random.seed(0)
xt = sampling(nt)
yt = prob(xt)
dyt = {}
for kx in range(prob.xlimits.shape[0]):
dyt[kx] = prob(xt, kx=kx)
y_lf = 2 * prob(xt) + 2
x_lf = deepcopy(xt)
np.random.seed(1)
xe = sampling(self.ne)
ye = prob(xe)
dye = {}
for kx in range(prob.xlimits.shape[0]):
dye[kx] = prob(xe, kx=kx)
sm = MFK(theta0=[1e-2] * self.ndim)
if sm.options.is_declared("xlimits"):
sm.options["xlimits"] = prob.xlimits
sm.options["print_global"] = False
sm.set_training_values(xt, yt)
sm.set_training_values(x_lf, y_lf, name=0)
with Silence():
sm.train()
t_error = compute_rms_error(sm)
e_error = compute_rms_error(sm, xe, ye)
e_error0 = compute_rms_error(sm, xe, dye[0], 0)
e_error1 = compute_rms_error(sm, xe, dye[1], 1)
if print_output:
print("%8s %6s %18.9e %18.9e %18.9e %18.9e" %
(pname[:6], sname, t_error, e_error, e_error0, e_error1))
self.assert_error(e_error0, 0.0, 1e-1)
self.assert_error(e_error1, 0.0, 1e-1)
def setUp(self):
ndim = 2
nt = 5000
ne = 100
problems = OrderedDict()
problems["sphere"] = Sphere(ndim=ndim)
sms = OrderedDict()
if compiled_available:
sms["RBF"] = RBF()
sms["RMTC"] = RMTC()
sms["RMTB"] = RMTB()
sms["MFK"] = MFK(theta0=[1e-2] * ndim)
self.nt = nt
self.ne = ne
self.problems = problems
self.sms = sms
def setUp(self):
ndim = 3
nt = 100
ne = 100
ncomp = 1
problems = OrderedDict()
problems["exp"] = TensorProduct(ndim=ndim, func="exp")
problems["tanh"] = TensorProduct(ndim=ndim, func="tanh")
problems["cos"] = TensorProduct(ndim=ndim, func="cos")
sms = OrderedDict()
sms["LS"] = LS()
sms["QP"] = QP()
sms["KRG"] = KRG(theta0=[1e-2] * ndim)
sms["MFK"] = MFK(theta0=[1e-2] * ndim)
sms["KPLS"] = KPLS(theta0=[1e-2] * ncomp, n_comp=ncomp)
sms["KPLSK"] = KPLSK(theta0=[1] * ncomp, n_comp=ncomp)
sms["GEKPLS"] = GEKPLS(theta0=[1e-2] * ncomp,
n_comp=ncomp,
delta_x=1e-1)
sms["GENN"] = genn()
if compiled_available:
sms["IDW"] = IDW()
sms["RBF"] = RBF()
sms["RMTC"] = RMTC()
sms["RMTB"] = RMTB()
t_errors = {}
t_errors["LS"] = 1.0
t_errors["QP"] = 1.0
t_errors["KRG"] = 1e0
t_errors["MFK"] = 1e0
t_errors["KPLS"] = 1e0
t_errors["KPLSK"] = 1e0
t_errors["GEKPLS"] = 1e0
t_errors["GENN"] = 1e0
if compiled_available:
t_errors["IDW"] = 1e0
t_errors["RBF"] = 1e-2
t_errors["RMTC"] = 1e-1
t_errors["RMTB"] = 1e-1
e_errors = {}
e_errors["LS"] = 1.5
e_errors["QP"] = 1.5
e_errors["KRG"] = 1e-2
e_errors["MFK"] = 1e-2
e_errors["KPLS"] = 1e-2
e_errors["KPLSK"] = 1e-2
e_errors["GEKPLS"] = 1e-2
e_errors["GENN"] = 1e-2
if compiled_available:
e_errors["IDW"] = 1e0
e_errors["RBF"] = 1e0
e_errors["RMTC"] = 2e-1
e_errors["RMTB"] = 2e-1
self.nt = nt
self.ne = ne
self.ndim = ndim
self.problems = problems
self.sms = sms
self.t_errors = t_errors
self.e_errors = e_errors
def run_mfk_example(self):
import numpy as np
import matplotlib.pyplot as plt
from smt.applications import MFK
# Define the
def LF_function(x):
import numpy as np
return (0.5 * ((x * 6 - 2)**2) * np.sin(
(x * 6 - 2) * 2) + (x - 0.5) * 10.0 - 5)
def HF_function(x):
import numpy as np
return ((x * 6 - 2)**2) * np.sin((x * 6 - 2) * 2)
# Problem set up
ndim = 1
Xt_e = np.linspace(0, 1, 4, endpoint=True).reshape(-1, ndim)
Xt_c = np.linspace(0, 1, 11, endpoint=True).reshape(-1, ndim)
nt_exp = Xt_e.shape[0]
nt_cheap = Xt_c.shape[0]
# Evaluate the HF and LF functions
yt_e = HF_function(Xt_e)
yt_c = LF_function(Xt_c)
sm = MFK(theta0=np.array(Xt_e.shape[1] * [1.0]))
# low-fidelity dataset names being integers from 0 to level-1
sm.set_training_values(Xt_c, yt_c, name=0)
# high-fidelity dataset without name
sm.set_training_values(Xt_e, yt_e)
# train the model
sm.train()
x = np.linspace(0, 1, 101, endpoint=True).reshape(-1, 1)
# query the outputs
y = sm.predict_values(x)
MSE = sm.predict_variances(x)
der = sm.predict_derivatives(x, kx=0)
plt.figure()
plt.plot(x, HF_function(x), label="reference")
plt.plot(x, y, linestyle="-.", label="mean_gp")
plt.scatter(Xt_e, yt_e, marker="o", color="k", label="HF doe")
plt.scatter(Xt_c, yt_c, marker="*", color="g", label="LF doe")
plt.legend(loc=0)
plt.ylim(-10, 17)
plt.xlim(-0.1, 1.1)
plt.xlabel(r"$x$")
plt.ylabel(r"$y$")
plt.show()
return (6 * x - 2)**2 * np.sin(12 * x - 4) # Problem set up ndim = 1 Xt_e = np.linspace(0, 1, 4).reshape(-1, ndim) Xt_c = np.linspace(0, 1, 11).reshape(-1, ndim) nt_exp = Xt_e.shape[0] nt_cheap = Xt_c.shape[0] # Evaluate the HF and LF functions yt_e = HF_function(Xt_e) yt_c = LF_function(Xt_c) sm = MFK(theta0=np.array(Xt_e.shape[1] * [1.0]), print_global=False) print(Xt_e.shape[1] * [1.0]) # low-fidelity dataset names being integers from 0 to level-1 sm.set_training_values(Xt_c, yt_c, name=0) print(Xt_c) # high-fidelity dataset without name sm.set_training_values(Xt_e, yt_e) print(Xt_e) # train the model sm.train() x = np.linspace(0, 1, 101, endpoint=True).reshape(-1, 1)