In [13]:
import numpy as np
import matplotlib.pyplot as plt
from tensorflow import keras
layers = keras.layers
print(keras.__version__)
Generation of data¶
We start by creating a signal trace: t = 0-100, f = sin(pi * t)
In [2]:
N = 10000
t = np.linspace(0, 100, N) # time steps
f = np.sin(np.pi * t) # signal
Split into semi-redundant sub-sequences of length = window_size + 1 and perform shuffle
In [3]:
window_size = 20
n = N - window_size - 1 # number of possible splits
data = np.stack([f[i: i + window_size + 1] for i in range(n)])
Finally, split the data into features
In [4]:
X, y = np.split(data, [-1], axis=1)
X = X[..., np.newaxis]
print('Example:')
print('X =', X[0, :, 0])
print('y =', y[0, :])
Define and train RNN¶
In [5]:
z0 = layers.Input(shape=[None, 1])
z = layers.LSTM(16)(z0)
z = layers.Dense(1)(z)
model = keras.models.Model(inputs=z0, outputs=z)
print(model.summary())
model.compile(loss='mse', optimizer='adam')
In [6]:
results = model.fit(X, y,
epochs=60,
batch_size=32,
verbose=2,
validation_split=0.1,
callbacks=[
keras.callbacks.ReduceLROnPlateau(factor=0.67, patience=3, verbose=1, min_lr=1E-5),
keras.callbacks.EarlyStopping(patience=4, verbose=1)])
In [7]:
plt.figure(1, (12, 4))
plt.subplot(1, 2, 1)
plt.plot(results.history['loss'])
plt.plot(results.history['val_loss'])
plt.ylabel('loss')
plt.yscale("log")
plt.xlabel('epoch')
plt.legend(['train', 'val'], loc='upper right')
plt.tight_layout()
Evaluate the model¶
Investigate the forecasting capabilities of the model.
In [8]:
def predict_next_k(model, window, k=10):
"""Predict next k steps for the given model and starting sequence """
x = window[np.newaxis, :, np.newaxis] # initial input
y = np.zeros(k)
for i in range(k):
y[i] = model.predict(x, verbose=0)
# create the new input including the last prediction
x = np.roll(x, -1, axis=1) # shift all inputs 1 step to the left
x[:, -1] = y[i] # add latest prediction to end
return y
In [9]:
def plot_prediction(i0=0, k=500):
""" Predict and plot the next k steps for an input starting at i0 """
y0 = f[i0: i0 + window_size] # starting window (input)
y1 = predict_next_k(model, y0, k) # predict next k steps
t0 = t[i0: i0 + window_size]
t1 = t[i0 + window_size: i0 + window_size + k]
plt.figure(figsize=(12, 4))
plt.plot(t, f, label='data')
plt.plot(t0, y0, color='C1', lw=3, label='prediction')
plt.plot(t1, y1, color='C1', ls='--')
plt.xlim(0, 10)
plt.legend()
plt.xlabel('$t$')
plt.ylabel('$f(t)$')
In [10]:
plot_prediction(12)
In [11]:
plot_prediction(85)
In [12]:
plot_prediction(115)
