参考：

https://morvanzhou.github.io/tutorials/machine-learning/keras/2-1-regressor/#%E5%8F%AF%E8%A7%86%E5%8C%96%E7%BB%93%E6%9E%9C

https://blog.csdn.net/cymy001/article/details/78647933

#!/usr/bin/env python3

import numpy as np
np.random.seed(0)
from keras.models import Sequential
from keras.layers import Dense, Activation
from keras.optimizers import SGD
import matplotlib.pyplot as plt

X = np.linspace(-1, 1, 1000)
np.random.shuffle(X)
Y = np.square(X)+ np.random.normal(0, 0.05, (1000, ))

#80% training 20% testing
X_train, Y_train = X[:800], Y[:800]    
X_test, Y_test = X[800:], Y[800:]
# fig= plt.figure(figsize=(4,3))
# plt.subplot(1,2,1)    
# plt.scatter(X_train, Y_train)
# plt.subplot(1,2,2)
# plt.scatter(X_test, Y_test)


# plt.plot(X_test,Y_pred,'r')
# plt.show()

model = Sequential()
model.add(Dense(input_dim = 1, units=10))
model.add(Activation('tanh'))
model.add(Dense(units=1))
model.add(Activation('tanh'))

#定义优化算法(修改学习率)
# defsgd=SGD(lr=0.3)
model.compile(loss='mse', optimizer='sgd')

print("training........")
for step in range(10001):
    cost = model.train_on_batch(X_train, Y_train)
    if step % 2000 == 0:
        print("train cost:", cost)
print("Testing.........")
# cost = model.evaluate(X_test, Y_test, batch_size=40)
# print("test cost:", cost)

W, b = model.layers[0].get_weights()
print('Weights=', W, '\nbiases=', b)


# plotting the prediction
plt.scatter(X_test, Y_test, c='b')
X_test = np.sort(X_test)  #这里需要排序，之前打乱了X_test, 不然plt.plot会变成一坨
Y_pred = model.predict(X_test)
plt.scatter(X_test, Y_pred, c='r')
plt.plot(X_test, Y_pred,'r')
plt.show()

model = Sequential()
model.add(Dense(input_dim = 1, units=10))
model.add(Activation('tanh'))
model.add(Dense(units=1))
model.add(Activation('tanh'))

这里如果只有一层只能进行线性拟合， 如：

model.add(Dense(units=1, input_dim=1))
model.add(Activation('tanh'))

结果：

Figure_1.png

这里如果有两层并用relu作为激活函数

model.add(Dense(input_dim = 1, units=10))
model.add(Activation('relu'))
model.add(Dense(units=1, input_dim=1))
model.add(Activation('relu'))

Figure_1.png

增加units和全连接层数

model.add(Dense(input_dim = 1, units=10))
model.add(Activation('relu'))
model.add(Dense(units=50))
model.add(Activation('relu'))
model.add(Dense(units=1, input_dim=1))
model.add(Activation('relu'))

Figure_2.png

换成tanh激活函数

model.add(Dense(input_dim = 1, units=10))
model.add(Activation('tanh'))
model.add(Dense(units=50))
model.add(Activation('tanh'))
model.add(Dense(units=1, input_dim=1))
model.add(Activation('tanh'))

Figure_3.png