"""
@author: Maziar Raissi
"""
import numpy as np
import tensorflow as tf
from FBSNNs import FBSNN
import matplotlib.pyplot as plt
from plotting import newfig, savefig
class BlackScholesBarenblatt(FBSNN):
def __init__(self, Xi, T,
M, N, D,
layers):
super().__init__(Xi, T,
M, N, D,
layers)
def phi_tf(self, t, X, Y, Z): # M x 1, M x D, M x 1, M x D
return 0.05*(Y - tf.reduce_sum(X*Z, 1, keepdims = True)) # M x 1
def g_tf(self, X): # M x D
return tf.reduce_sum(X**2, 1, keepdims = True) # M x 1
def mu_tf(self, t, X, Y, Z): # M x 1, M x D, M x 1, M x D
return super().mu_tf(t, X, Y, Z) # M x D
def sigma_tf(self, t, X, Y): # M x 1, M x D, M x 1
return 0.4*tf.matrix_diag(X) # M x D x D
###########################################################################
if __name__ == "__main__":
M = 100 # number of trajectories (batch size)
N = 50 # number of time snapshots
D = 100 # number of dimensions
layers = [D+1] + 4*[256] + [1]
Xi = np.array([1.0,0.5]*int(D/2))[None,:]
T = 1.0
# Training
model = BlackScholesBarenblatt(Xi, T,
M, N, D,
layers)
model.train(N_Iter = 2*10**4, learning_rate=1e-3)
model.train(N_Iter = 3*10**4, learning_rate=1e-4)
model.train(N_Iter = 3*10**4, learning_rate=1e-5)
model.train(N_Iter = 2*10**4, learning_rate=1e-6)
##### PLOT RESULTS
t_test, W_test = model.fetch_minibatch()
X_pred, Y_pred = model.predict(Xi, t_test, W_test)
def u_exact(t, X): # (N+1) x 1, (N+1) x D
r = 0.05
sigma_max = 0.4
return np.exp((r + sigma_max**2)*(T - t))*np.sum(X**2, 1, keepdims = True) # (N+1) x 1
Y_test = np.reshape(u_exact(np.reshape(t_test[0:M,:,:],[-1,1]), np.reshape(X_pred[0:M,:,:],[-1,D])),[M,-1,1])
samples = 5
plt.figure()
plt.plot(t_test[0:1,:,0].T,Y_pred[0:1,:,0].T,'b',label='Learned $u(t,X_t)$')
plt.plot(t_test[0:1,:,0].T,Y_test[0:1,:,0].T,'r--',label='Exact $u(t,X_t)$')
plt.plot(t_test[0:1,-1,0],Y_test[0:1,-1,0],'ko',label='$Y_T = u(T,X_T)$')
plt.plot(t_test[1:samples,:,0].T,Y_pred[1:samples,:,0].T,'b')
plt.plot(t_test[1:samples,:,0].T,Y_test[1:samples,:,0].T,'r--')
plt.plot(t_test[1:samples,-1,0],Y_test[1:samples,-1,0],'ko')
plt.plot([0],Y_test[0,0,0],'ks',label='$Y_0 = u(0,X_0)$')
plt.xlabel('$t$')
plt.ylabel('$Y_t = u(t,X_t)$')
plt.title('100-dimensional Black-Scholes-Barenblatt')
plt.legend()
# savefig('./figures/BSB_Apr18_50', crop = False)
errors = np.sqrt((Y_test-Y_pred)**2/Y_test**2)
mean_errors = np.mean(errors,0)
std_errors = np.std(errors,0)
plt.figure()
plt.plot(t_test[0,:,0],mean_errors,'b',label='mean')
plt.plot(t_test[0,:,0],mean_errors+2*std_errors,'r--',label='mean + two standard deviations')
plt.xlabel('$t$')
plt.ylabel('relative error')
plt.title('100-dimensional Black-Scholes-Barenblatt')
plt.legend()
# savefig('./figures/BSB_Apr18_50_errors', crop = False)
