· Use TensorFlow to fit curves

  • Y = x* x-2x +3 + 0.1(random value from -1 to 1) curve given x range (0,3)
  • Problem analysis In the last blog, we successfully fitted a straight line using the simplest y=wx+b model. Now we are further fitting the curve. The simple y=wx+ B model can no longer meet our needs, and more neurons are needed to solve the problem.
  • Generate the data
import numpy as np 
import matplotlib.pyplot as plt
import tensorflow as tf

def get_data(x,w,b,d) :
    c,r = x.shape
    y = (w * x * x + b*x + d)+ (0.1* (2*np.random.rand(c,r)-1))
    return(y)
xs = np.arange(0.3.0.01).reshape(-1.1)
ys = get_data(xs,1, -2.3)
plt.title("curve")
plt.plot(xs,ys)
plt.show()
Copy the code

The generated data images are as follows:

  • Building a network structure
x = tf.placeholder(tf.float32,[None.1])
y_ = tf.placeholder(tf.float32,[None.1])

w1 = tf.get_variable("w1",initializer=tf.random_normal([1.16]))
w2 = tf.get_variable("w2",initializer=tf.random_normal([16.1]))
b1 = tf.get_variable("b1",initializer=tf.zeros([1.16]))
b2 = tf.get_variable("b2",initializer=tf.zeros([1.1]))
l1 = tf.matmul(x,w1)+b1
l1 = tf.nn.elu(l1)
y = tf.matmul(l1,w2)+b2
Copy the code
  • Defining learning functions
loss = tf.reduce_mean(tf.square(y-y_))
opt = tf.train.GradientDescentOptimizer(0.02).minimize(loss)
Copy the code
  • Training network parameters
with tf.Session() as sess:
    srun = sess.run
    init = tf.global_variables_initializer()
    srun(init)
    
    for e in range(4001):
        loss_val,_ = srun([loss,opt],{x:xs,y_:ys})
        if(e%200= =0) :print("%d steps loss is %f"%(e,loss_val))

    ys_pre = srun(y,{x:xs})
Copy the code
  • Show forecast results
plt.title("curve")
plt.plot(xs,ys)
plt.plot(xs,ys_pre)
plt.legend("ys"."ys_pre")
plt.show()
Copy the code
  • Run result log:
0 steps loss is 49.556065
200 steps loss is 0.352589
400 steps loss is 0.108551
600 steps loss is 0.042510
800 steps loss is 0.030316
1000 steps loss is 0.024551
1200 steps loss is 0.020459
1400 steps loss is 0.017488
1600 steps loss is 0.015306
1800 steps loss is 0.013710
2000 steps loss is 0.012510
2200 steps loss is 0.011569
2400 steps loss is 0.010802
2600 steps loss is 0.010148
2800 steps loss is 0.009566
3000 steps loss is 0.009039
3200 steps loss is 0.008552
3400 steps loss is 0.008097
3600 steps loss is 0.007674
3800 steps loss is 0.007285
4000 steps loss is 0.006934
Copy the code

Running result diagram

  • The complete code
import os
os.environ["KMP_DUPLICATE_LIB_OK"] ="TRUE"
import numpy as np 
import matplotlib.pyplot as plt
import tensorflow as tf

def get_data(x,w,b,d) :
    c,r = x.shape
    y = (w * x * x + b*x + d)+ (0.1* (2*np.random.rand(c,r)-1))
    return(y)

xs = np.arange(0.3.0.01).reshape(-1.1)
ys = get_data(xs,1, -2.3)
"""plt.title("curve")
plt.plot(xs,ys)
plt.show()"""

x = tf.placeholder(tf.float32,[None.1])
y_ = tf.placeholder(tf.float32,[None.1])

w1 = tf.get_variable("w1",initializer=tf.random_normal([1.16]))
w2 = tf.get_variable("w2",initializer=tf.random_normal([16.1]))
b1 = tf.get_variable("b1",initializer=tf.zeros([1.16]))
b2 = tf.get_variable("b2",initializer=tf.zeros([1.1]))
l1 = tf.matmul(x,w1)+b1
l1 = tf.nn.elu(l1)
y = tf.matmul(l1,w2)+b2

loss = tf.reduce_mean(tf.square(y-y_))
opt = tf.train.GradientDescentOptimizer(0.02).minimize(loss)

with tf.Session() as sess:
    srun = sess.run
    init = tf.global_variables_initializer()
    srun(init)
    
    for e in range(4001):
        loss_val,_ = srun([loss,opt],{x:xs,y_:ys})
        if(e%200= =0) :print("%d steps loss is %f"%(e,loss_val))

    ys_pre = srun(y,{x:xs})

plt.title("curve")
plt.plot(xs,ys)
plt.plot(xs,ys_pre)
plt.legend("ys"."ys_pre")
plt.show()
Copy the code