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Styblinski Tang Function Approximation.py
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Styblinski Tang Function Approximation.py
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import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation
from Neural_Network import Multi_Layer_Neural_Network
from Functions import Styblinski_Tang_Function, Styblinski_Tang_Function_Limits
# Sets resolution of the function to be approximated
num_grid_points_each_axis = 20
# Sets number iteration the batch training is performed
num_training_iterations = 1000
# Points along each axis
axis = np.linspace(Styblinski_Tang_Function_Limits[0], Styblinski_Tang_Function_Limits[1], num_grid_points_each_axis)
def target_function(matrix) :
return Styblinski_Tang_Function(matrix[0:1, :], matrix[1:, :])
def f1(x) :
return x**4
def f1_derivative(x) :
return 4 * x**3
def f2(x) :
return np.copy(x)
def f2_derivative(x) :
return np.ones_like(x)
a0 = [[], []]
t = [[]]
for x in axis :
for y in axis :
a0[0].append(x)
a0[1].append(y)
t[0].append(Styblinski_Tang_Function(x,y))
a0 = np.array(a0)
t = np.array(t)
nn = Multi_Layer_Neural_Network.generate_network_structure(
[2, np.ceil(0.25 * (num_grid_points_each_axis**2 - 1)), 1],
[f1, f2],
[f1_derivative, f2_derivative]
)
nn.set_learning_rate(0.1)
nn.set_learning_rate_decay_factor(0.7)
nn.set_learning_rate_growth_factor(1.05)
nn.set_momentum_coefficient(0.7)
nn.set_critical_error_growth_ratio(0.04)
nn.init_network(train_model=True)
plt.style.use('dark_background')
fig = plt.figure(constrained_layout=True)
gs = fig.add_gridspec(2,2)
ax1 = fig.add_subplot(gs[0, 1])
ax2 = fig.add_subplot(gs[1, 1])
ax3 = fig.add_subplot(gs[:, 0])
nn.network_graph_init(ax3)
ax3.set_title('Iteration # 0', {'fontsize':15})
c = []
d = []
for x in axis :
c_buf = []
d_buf = []
for y in axis :
c_buf.append(nn.predict(np.array([[x],[y]]))[0,0])
d_buf.append(target_function(np.array([[x],[y]]))[0,0])
c.append(c_buf)
d.append(d_buf)
X, Y = np.meshgrid( axis, axis, indexing='ij' )
lvl = np.linspace(np.min(d), np.max(d), 20)
cont1 = ax1.contourf(X, Y, np.array(d), cmap='magma', levels=lvl)
ax1.set_xlabel('x')
ax1.set_ylabel('y')
cont2 = ax2.contourf(X, Y, np.array(c), cmap='magma', levels=lvl)
ax2.set_xlabel('x')
ax2.set_ylabel('y')
random_points = Styblinski_Tang_Function_Limits[0] + (Styblinski_Tang_Function_Limits[1] - Styblinski_Tang_Function_Limits[0]) * np.random.rand(2, 40)
np.savetxt('Styblinski Tang Function Approximation Test Points.csv', random_points.transpose(), delimiter=',')
def update(i) :
global cont2
nn.train_model(a0, t)
ax3.set_title( 'Iteration # ' + str(i+1) + '\nMSE = ' + str(round(np.mean(np.square(target_function(random_points) - nn.predict(random_points))), 2)),
{'fontsize':15})
c = []
for x in axis :
c_buf = []
for y in axis :
c_buf.append(nn.predict(np.array([[x],[y]]))[0,0])
c.append(c_buf)
for objs in cont2.collections :
objs.remove()
cont2 = ax2.contourf(X, Y, np.array(c), cmap='magma', levels=lvl)
return nn.network_graph_update().append(cont2)
anim = FuncAnimation(fig, update, frames=num_training_iterations, repeat=False)
plt.show()
anim.save('Styblinski Tang Training Model.mp4', writer='ffmpeg', fps=30)