# Training with Online Algorithms#

import brainpy as bp
import brainpy.math as bm
import matplotlib.pyplot as plt

bm.enable_x64()


Online training algorithms, such as FORCE learning, have played vital roles in brain modeling. BrainPy provides brainpy.train.OnlineTrainer for model training with online algorithms.

## Train a reservoir model#

Here, we are going to use brainpy.train.OnlineTrainer to train a next generation reservoir computing model (NGRC) to predict chaotic dynamics.

We first get the training dataset.

def get_subset(data, start, end):
res = {'x': data['x'][start: end],
'y': data['y'][start: end],
'z': data['z'][start: end]}
res = bm.hstack([res['x'], res['y'], res['z']])
# Training data must have batch size, here the batch is 1
return res.reshape((1, ) + res.shape)

dt = 0.01
t_warmup, t_train, t_test = 5., 100., 50.  # ms
num_warmup, num_train, num_test = int(t_warmup/dt), int(t_train/dt), int(t_test/dt)

lorenz_series = bp.datasets.lorenz_series(t_warmup + t_train + t_test, dt=dt,
inits={'x': 17.67715816276679,
'y': 12.931379185960404,
'z': 43.91404334248268})

X_warmup = get_subset(lorenz_series, 0, num_warmup - 5)
X_train = get_subset(lorenz_series, num_warmup - 5, num_warmup + num_train - 5)
X_test = get_subset(lorenz_series,
num_warmup + num_train - 5,
num_warmup + num_train + num_test - 5)

# out target data is the activity ahead of 5 time steps
Y_train = get_subset(lorenz_series, num_warmup, num_warmup + num_train)
Y_test = get_subset(lorenz_series,
num_warmup + num_train,
num_warmup + num_train + num_test)


Then, we try to build a NGRC model to predict the chaotic dynamics ahead of five time steps.

class NGRC(bp.dyn.DynamicalSystem):
def __init__(self, num_in):
super(NGRC, self).__init__()
self.r = bp.layers.NVAR(num_in, delay=2, order=2, constant=True, mode=bp.modes.batching)
self.o = bp.layers.Dense(self.r.num_out, num_in, b_initializer=None, mode=bp.modes.training)

def update(self, sha, x):
return self.o(sha, self.r(sha, x))

model = NGRC(3)
model.reset_state(1)


Here, we use ridge regression as the training algorithm to train the chaotic model.

trainer = bp.train.OnlineTrainer(model, fit_method=bp.algorithms.RLS(), dt=dt)

# first warmup the reservoir

_ = trainer.predict(X_warmup)

# then fit the reservoir model

_ = trainer.fit([X_train, Y_train])

def plot_lorenz(ground_truth, predictions):
fig = plt.figure(figsize=(15, 10))
ax = fig.add_subplot(121, projection='3d')
ax.set_title("Generated attractor")
ax.set_xlabel("$x$")
ax.set_ylabel("$y$")
ax.set_zlabel("$z$")
ax.grid(False)
ax.plot(predictions[:, 0], predictions[:, 1], predictions[:, 2])

ax2 = fig.add_subplot(122, projection='3d')
ax2.set_title("Real attractor")
ax2.grid(False)
ax2.plot(ground_truth[:, 0], ground_truth[:, 1], ground_truth[:, 2])
plt.show()

# finally, predict the model with the test data

outputs = trainer.predict(X_test)
print('Prediction NMS: ', bp.losses.mean_squared_error(outputs, Y_test))
plot_lorenz(bm.as_numpy(Y_test).squeeze(), bm.as_numpy(outputs).squeeze())

Prediction NMS:  0.0008260664931486222 