Created
July 3, 2017 17:39
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Neural network for small datasets with derivative info supplied.
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| import tensorflow as tf | |
| import numpy as np | |
| import matplotlib.pyplot as plt | |
| #Wether or not to include derivative information | |
| derinfo=False | |
| learning_rate = 0.001 | |
| training_epochs = 15000 | |
| display_step = 100 | |
| np.random.seed(3) | |
| xmin=-10.0 | |
| xmax=10.0 | |
| X=np.random.random((5,1))*(xmax-xmin)+xmin | |
| x_test=np.linspace(xmin,xmax,101).reshape(-1,1) | |
| def f(x): | |
| return np.sin(x) | |
| def dfdx(x): | |
| return np.cos(x) | |
| if derinfo: | |
| Y=np.zeros((len(X),2)) | |
| y_test=np.zeros((len(x_test),2)) | |
| Y[:,1]=dfdx(X[:,0]) | |
| y_test[:,1]=dfdx(x_test[:,0]) | |
| else: | |
| Y=np.zeros((len(X),1)) | |
| y_test=np.zeros((len(x_test),1)) | |
| Y[:,0]=f(X[:,0]) | |
| y_test[:,0]=f(x_test[:,0]) | |
| x_train=X | |
| y_train=Y | |
| batch_size = len(X) | |
| # tf Graph input | |
| x = tf.placeholder("float", [None, 1],name='x') | |
| if derinfo: | |
| y = tf.placeholder("float", [None, 2]) | |
| else: | |
| y = tf.placeholder("float", [None, 1]) | |
| n_1=200 | |
| W_0=tf.Variable(0.01*tf.random_normal([1,n_1])) | |
| W_2=tf.Variable(0.01*tf.random_normal([n_1,1])) | |
| b_0=tf.Variable(0.01*tf.random_normal([n_1])) | |
| b_2=tf.Variable(0.01*tf.random_normal([1])) | |
| act=tf.nn.sigmoid | |
| def neuralnet(x): | |
| h1=act(tf.matmul(x,W_0)+b_0) | |
| pred=tf.matmul(h1,W_2)+b_2 | |
| return pred | |
| pred=neuralnet(x) | |
| pred2=tf.gradients(pred,x)[0] | |
| if derinfo: | |
| pred=tf.concat([pred,pred2],1) | |
| cost=tf.reduce_mean((pred-y)**2)+1e-6*(tf.reduce_mean(W_0**2)+tf.reduce_mean(W_2**2)) | |
| optimizer = tf.train.AdamOptimizer(learning_rate=learning_rate).minimize(cost) | |
| # Initializing the variables | |
| init = tf.global_variables_initializer() | |
| # Launch the graph | |
| with tf.Session() as sess: | |
| sess.run(init) | |
| # Training cycle | |
| for epoch in range(training_epochs): | |
| avg_cost = 0. | |
| total_batch = int(len(x_train)/batch_size) | |
| # Loop over all batches | |
| for i in range(total_batch): | |
| batch_x=x_train[i*batch_size:(i+1)*batch_size] | |
| batch_y=y_train[i*batch_size:(i+1)*batch_size] | |
| # Run optimization op (backprop) and cost op (to get loss value) | |
| _, c = sess.run([optimizer, cost], feed_dict={x: batch_x, y: batch_y}) | |
| # Compute average loss | |
| avg_cost += c / total_batch | |
| # Display logs per epoch step | |
| if epoch % display_step == 0: | |
| print("Epoch:", '%04d' % (epoch+1), "cost=", "{:.9f}".format(avg_cost)) | |
| print("Optimization Finished!") | |
| y_t=sess.run(pred,feed_dict={x:x_test}) | |
| plt.plot(x_test[:,0],y_t[:,0]) | |
| plt.plot(x_test[:,0],y_test[:,0]) | |
| plt.legend(["prediction","true function"]) | |
| plt.plot(x_train[:,0],y_train[:,0],'.') | |
| plt.show() |
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