def f(x):
return x * np.sin(4 * np.pi * x)
X = lb + (ub - lb) * lhs(D, N)
y = f(X) + noise * np.random.randn(N, 1)
# Generate test data
N_star = 400
X_star = lb + (ub - lb) * np.linspace(0, 1, N_star)[:, None]
y_star = f(X_star)
# Normalize Input Data
if ModelInfo["Normalize_input_data"] == 1:
X_m = np.mean(X, axis=0)
X_s = np.std(X, axis=0)
X = Normalize(X, X_m, X_s)
X_star = Normalize(X_star, X_m, X_s)
# Normalize Output Data
if ModelInfo["Normalize_output_data"] == 1:
y_m = np.mean(y, axis=0)
y_s = np.std(y, axis=0)
y = Normalize(y, y_m, y_s)
y_star = Normalize(y_star, y_m, y_s)
ModelInfo.update({"X": X})
ModelInfo.update({"y": y})
# Training
def f(x):
return (x < -0.5) + 1.0 + 1.5 * (x > 0.5)
X = lb + (ub - lb) * lhs(X_dim, N)
Y = f(X) + noise * np.random.randn(N, Y_dim)
# Generate test data
N_star = 400
X_star = lb + (ub - lb) * np.linspace(0, 1, N_star)[:, None]
Y_star = f(X_star)
# Normalize Input Data
if Normalize_input_data == 1:
X_m = np.mean(X, axis=0)
X_s = np.std(X, axis=0)
X = Normalize(X, X_m, X_s)
X_star = Normalize(X_star, X_m, X_s)
# Normalize Output Data
if Normalize_output_data == 1:
Y_m = np.mean(Y, axis=0)
Y_s = np.std(Y, axis=0)
Y = Normalize(Y, Y_m, Y_s)
Y_star = Normalize(Y_star, Y_m, Y_s)
# Model creation
model = ConditionalVariationalAutoencoders(X,
Y,
layers_encoder_0,
layers_encoder_1,
layers_decoder,
layers_decoder = np.array([Z_dim,50,100,Y_dim])
# generate synthetic data
def f(z):
return z/10 + z/np.linalg.norm(z,2,axis = 1, keepdims = True)
Z = np.random.randn(N,2)
Y = f(Z)
Normalize_data = 1
# Normalize Output Data
if Normalize_data == 1:
Y_m = np.mean(Y, axis = 0)
Y_s = np.std(Y, axis = 0)
Y = Normalize(Y, Y_m, Y_s)
# Model creation
model = VariationalAutoencoders(Y, layers_encoder, layers_decoder,
max_iter = 5000, N_batch = 200, monitor_likelihood = 10,
lrate = 1e-3)
model.train()
mean_star, var_star = model.generate_samples(1000)
plt.figure(figsize=(10,5))
plt.rcParams.update({'font.size': 14})
plt.subplot(1, 2, 1)
plt.scatter(Y[:,0], Y[:,1], color='blue')
# Generate traning data
def f(x):
return x*np.sin(4*np.pi*x)
X = lb + (ub-lb)*lhs(D, N)
y = f(X) + noise*np.random.randn(N,1)
# Generate test data
N_star = 400
X_star = lb + (ub-lb)*np.linspace(0,1,N_star)[:,None]
y_star = f(X_star)
# Normalize Input Data
if Normalize_input_data == 1:
X_m = np.mean(X, axis = 0)
X_s = np.std(X, axis = 0)
X = Normalize(X, X_m, X_s)
X_star = Normalize(X_star, X_m, X_s)
# Normalize Output Data
if Normalize_output_data == 1:
y_m = np.mean(y, axis = 0)
y_s = np.std(y, axis = 0)
y = Normalize(y, y_m, y_s)
y_star = Normalize(y_star, y_m, y_s)
# Model creation
M = 8
pgp = PGP(X, y, M, max_iter = 6000, N_batch = 1,
monitor_likelihood = 10, lrate = 1e-3)
y = data["Y_H"]
data_star = scipy.io.loadmat('SSTData/XStarMap.mat')
XStarMap = data_star["XStar"]
data_star = scipy.io.loadmat('SSTData/XStarBuoy.mat')
XStarBuoy = data_star["XStar"]
Normalize_input_data = 1
Normalize_output_data = 1
# Normalize Input Data
if Normalize_input_data == 1:
X_m = np.mean(X, axis=0)
X_s = np.std(X, axis=0)
X = Normalize(X, X_m, X_s)
XStarMap = Normalize(XStarMap, X_m, X_s)
XStarBuoy = Normalize(XStarBuoy, X_m, X_s)
# Normalize Output Data
if Normalize_output_data == 1:
y_m = np.mean(y, axis=0)
y_s = np.std(y, axis=0)
y = Normalize(y, y_m, y_s)
# Model creation
M = 2000
pgp = PGP(X,
y,
M,
max_iter=2000,