TF2 0 ANN Regression
================ by Jawad Haider
# Install TensorFlow
# !pip install -q tensorflow-gpu==2.0.0-beta1
try:
%tensorflow_version 2.x # Colab only.
except Exception:
pass
import tensorflow as tf
print(tf.__version__)
2.0.0-beta1
# Other imports
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
# Make the dataset
N = 1000
X = np.random.random((N, 2)) * 6 - 3 # uniformly distributed between (-3, +3)
Y = np.cos(2*X[:,0]) + np.cos(3*X[:,1])
This implements the function:
\[ y = \cos(2x_1) + cos(3x_2) \]
# Plot it
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(X[:,0], X[:,1], Y)
# plt.show()
<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x7f2e953549e8>
# Build the model
model = tf.keras.models.Sequential([
tf.keras.layers.Dense(128, input_shape=(2,), activation='relu'),
tf.keras.layers.Dense(1)
])
# Compile and fit
opt = tf.keras.optimizers.Adam(0.01)
model.compile(optimizer=opt, loss='mse')
r = model.fit(X, Y, epochs=100)
Train on 1000 samples
Epoch 1/100
1000/1000 [==============================] - 0s 493us/sample - loss: 0.9276
Epoch 2/100
1000/1000 [==============================] - 0s 58us/sample - loss: 0.9060
Epoch 3/100
1000/1000 [==============================] - 0s 68us/sample - loss: 0.8808
Epoch 4/100
1000/1000 [==============================] - 0s 54us/sample - loss: 0.8457
Epoch 5/100
1000/1000 [==============================] - 0s 57us/sample - loss: 0.8115
Epoch 6/100
1000/1000 [==============================] - 0s 59us/sample - loss: 0.7682
Epoch 7/100
1000/1000 [==============================] - 0s 59us/sample - loss: 0.6904
Epoch 8/100
1000/1000 [==============================] - 0s 58us/sample - loss: 0.6319
Epoch 9/100
1000/1000 [==============================] - 0s 51us/sample - loss: 0.5543
Epoch 10/100
1000/1000 [==============================] - 0s 58us/sample - loss: 0.5207
Epoch 11/100
1000/1000 [==============================] - 0s 54us/sample - loss: 0.4973
Epoch 12/100
1000/1000 [==============================] - 0s 52us/sample - loss: 0.4889
Epoch 13/100
1000/1000 [==============================] - 0s 58us/sample - loss: 0.4715
Epoch 14/100
1000/1000 [==============================] - 0s 55us/sample - loss: 0.4714
Epoch 15/100
1000/1000 [==============================] - 0s 53us/sample - loss: 0.4387
Epoch 16/100
1000/1000 [==============================] - 0s 58us/sample - loss: 0.4519
Epoch 17/100
1000/1000 [==============================] - 0s 53us/sample - loss: 0.4498
Epoch 18/100
1000/1000 [==============================] - 0s 53us/sample - loss: 0.4180
Epoch 19/100
1000/1000 [==============================] - 0s 53us/sample - loss: 0.4163
Epoch 20/100
1000/1000 [==============================] - 0s 54us/sample - loss: 0.4128
Epoch 21/100
1000/1000 [==============================] - 0s 67us/sample - loss: 0.4110
Epoch 22/100
1000/1000 [==============================] - 0s 62us/sample - loss: 0.3984
Epoch 23/100
1000/1000 [==============================] - 0s 58us/sample - loss: 0.3825
Epoch 24/100
1000/1000 [==============================] - 0s 52us/sample - loss: 0.3734
Epoch 25/100
1000/1000 [==============================] - 0s 54us/sample - loss: 0.4398
Epoch 26/100
1000/1000 [==============================] - 0s 57us/sample - loss: 0.3796
Epoch 27/100
1000/1000 [==============================] - 0s 53us/sample - loss: 0.3603
Epoch 28/100
1000/1000 [==============================] - 0s 54us/sample - loss: 0.3120
Epoch 29/100
1000/1000 [==============================] - 0s 58us/sample - loss: 0.2797
Epoch 30/100
1000/1000 [==============================] - 0s 53us/sample - loss: 0.2815
Epoch 31/100
1000/1000 [==============================] - 0s 54us/sample - loss: 0.2600
Epoch 32/100
1000/1000 [==============================] - 0s 54us/sample - loss: 0.2221
Epoch 33/100
1000/1000 [==============================] - 0s 52us/sample - loss: 0.2036
Epoch 34/100
1000/1000 [==============================] - 0s 59us/sample - loss: 0.1905
Epoch 35/100
1000/1000 [==============================] - 0s 54us/sample - loss: 0.1502
Epoch 36/100
1000/1000 [==============================] - 0s 51us/sample - loss: 0.1368
Epoch 37/100
1000/1000 [==============================] - 0s 51us/sample - loss: 0.1300
Epoch 38/100
1000/1000 [==============================] - 0s 52us/sample - loss: 0.1043
Epoch 39/100
1000/1000 [==============================] - 0s 66us/sample - loss: 0.1022
Epoch 40/100
1000/1000 [==============================] - 0s 49us/sample - loss: 0.0823
Epoch 41/100
1000/1000 [==============================] - 0s 49us/sample - loss: 0.0787
Epoch 42/100
1000/1000 [==============================] - 0s 51us/sample - loss: 0.0593
Epoch 43/100
1000/1000 [==============================] - 0s 53us/sample - loss: 0.0528
Epoch 44/100
1000/1000 [==============================] - 0s 48us/sample - loss: 0.0616
Epoch 45/100
1000/1000 [==============================] - 0s 50us/sample - loss: 0.0351
Epoch 46/100
1000/1000 [==============================] - 0s 50us/sample - loss: 0.0273
Epoch 47/100
1000/1000 [==============================] - 0s 49us/sample - loss: 0.0288
Epoch 48/100
1000/1000 [==============================] - 0s 51us/sample - loss: 0.0281
Epoch 49/100
1000/1000 [==============================] - 0s 49us/sample - loss: 0.0362
Epoch 50/100
1000/1000 [==============================] - 0s 48us/sample - loss: 0.0585
Epoch 51/100
1000/1000 [==============================] - 0s 52us/sample - loss: 0.0842
Epoch 52/100
1000/1000 [==============================] - 0s 54us/sample - loss: 0.0780
Epoch 53/100
1000/1000 [==============================] - 0s 53us/sample - loss: 0.0700
Epoch 54/100
1000/1000 [==============================] - 0s 49us/sample - loss: 0.0232
Epoch 55/100
1000/1000 [==============================] - 0s 50us/sample - loss: 0.0149
Epoch 56/100
1000/1000 [==============================] - 0s 49us/sample - loss: 0.0159
Epoch 57/100
1000/1000 [==============================] - 0s 49us/sample - loss: 0.0140
Epoch 58/100
1000/1000 [==============================] - 0s 52us/sample - loss: 0.0108
Epoch 59/100
1000/1000 [==============================] - 0s 66us/sample - loss: 0.0088
Epoch 60/100
1000/1000 [==============================] - 0s 52us/sample - loss: 0.0077
Epoch 61/100
1000/1000 [==============================] - 0s 50us/sample - loss: 0.0132
Epoch 62/100
1000/1000 [==============================] - 0s 50us/sample - loss: 0.0108
Epoch 63/100
1000/1000 [==============================] - 0s 50us/sample - loss: 0.0105
Epoch 64/100
1000/1000 [==============================] - 0s 53us/sample - loss: 0.0077
Epoch 65/100
1000/1000 [==============================] - 0s 51us/sample - loss: 0.0084
Epoch 66/100
1000/1000 [==============================] - 0s 50us/sample - loss: 0.0101
Epoch 67/100
1000/1000 [==============================] - 0s 49us/sample - loss: 0.0093
Epoch 68/100
1000/1000 [==============================] - 0s 49us/sample - loss: 0.0082
Epoch 69/100
1000/1000 [==============================] - 0s 49us/sample - loss: 0.0076
Epoch 70/100
1000/1000 [==============================] - 0s 58us/sample - loss: 0.0145
Epoch 71/100
1000/1000 [==============================] - 0s 47us/sample - loss: 0.0127
Epoch 72/100
1000/1000 [==============================] - 0s 50us/sample - loss: 0.0101
Epoch 73/100
1000/1000 [==============================] - 0s 49us/sample - loss: 0.0058
Epoch 74/100
1000/1000 [==============================] - 0s 50us/sample - loss: 0.0051
Epoch 75/100
1000/1000 [==============================] - 0s 53us/sample - loss: 0.0053
Epoch 76/100
1000/1000 [==============================] - 0s 52us/sample - loss: 0.0073
Epoch 77/100
1000/1000 [==============================] - 0s 50us/sample - loss: 0.0065
Epoch 78/100
1000/1000 [==============================] - 0s 53us/sample - loss: 0.0066
Epoch 79/100
1000/1000 [==============================] - 0s 60us/sample - loss: 0.0202
Epoch 80/100
1000/1000 [==============================] - 0s 49us/sample - loss: 0.0130
Epoch 81/100
1000/1000 [==============================] - 0s 50us/sample - loss: 0.0093
Epoch 82/100
1000/1000 [==============================] - 0s 49us/sample - loss: 0.0149
Epoch 83/100
1000/1000 [==============================] - 0s 50us/sample - loss: 0.0147
Epoch 84/100
1000/1000 [==============================] - 0s 46us/sample - loss: 0.0085
Epoch 85/100
1000/1000 [==============================] - 0s 49us/sample - loss: 0.0048
Epoch 86/100
1000/1000 [==============================] - 0s 51us/sample - loss: 0.0041
Epoch 87/100
1000/1000 [==============================] - 0s 48us/sample - loss: 0.0041
Epoch 88/100
1000/1000 [==============================] - 0s 50us/sample - loss: 0.0106
Epoch 89/100
1000/1000 [==============================] - 0s 50us/sample - loss: 0.0112
Epoch 90/100
1000/1000 [==============================] - 0s 47us/sample - loss: 0.0051
Epoch 91/100
1000/1000 [==============================] - 0s 48us/sample - loss: 0.0121
Epoch 92/100
1000/1000 [==============================] - 0s 52us/sample - loss: 0.0384
Epoch 93/100
1000/1000 [==============================] - 0s 51us/sample - loss: 0.0463
Epoch 94/100
1000/1000 [==============================] - 0s 49us/sample - loss: 0.0190
Epoch 95/100
1000/1000 [==============================] - 0s 49us/sample - loss: 0.0340
Epoch 96/100
1000/1000 [==============================] - 0s 52us/sample - loss: 0.0133
Epoch 97/100
1000/1000 [==============================] - 0s 49us/sample - loss: 0.0062
Epoch 98/100
1000/1000 [==============================] - 0s 67us/sample - loss: 0.0043
Epoch 99/100
1000/1000 [==============================] - 0s 67us/sample - loss: 0.0050
Epoch 100/100
1000/1000 [==============================] - 0s 51us/sample - loss: 0.0045
# Plot the prediction surface
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(X[:,0], X[:,1], Y)
# surface plot
line = np.linspace(-3, 3, 50)
xx, yy = np.meshgrid(line, line)
Xgrid = np.vstack((xx.flatten(), yy.flatten())).T
Yhat = model.predict(Xgrid).flatten()
ax.plot_trisurf(Xgrid[:,0], Xgrid[:,1], Yhat, linewidth=0.2, antialiased=True)
plt.show()
# Can it extrapolate?
# Plot the prediction surface
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(X[:,0], X[:,1], Y)
# surface plot
line = np.linspace(-5, 5, 50)
xx, yy = np.meshgrid(line, line)
Xgrid = np.vstack((xx.flatten(), yy.flatten())).T
Yhat = model.predict(Xgrid).flatten()
ax.plot_trisurf(Xgrid[:,0], Xgrid[:,1], Yhat, linewidth=0.2, antialiased=True)
plt.show()
