Using Pybrain library for neural network function fitting __ function

Pybrain is a well-known Python neural network library, today I used it to do an experiment, referring to this blog, thanks to the original author, gave a specific implementation, the code can be directly copied to run.
Our main problems are as follows:

First we give a function to construct the dataset that is required to generate this problem .

Def generate_data (): "" "
    generate original data of U and Y" ""
    u = Np.random.uniform ( -1,1,200)
    y=[]
    Former_y_value = 0 for
    i in Np.arange (0,200):
        y.append (former_y_value)
        next_y_value = (29/40) * Np.sin (
   (* U[i] + 8 * former_y_value)/(3 + 4 * (u[i] * * * 2) + 4 * (Former_y_value * * 2))) +
                       (2/10) * U[i] + (2/10 ) * Former_y_value
        former_y_value = next_y_value return
    u,y

The function of this question is drawn in this way:

Our example is to use the first 100 points of training, the last 100 points as a prediction. The basic steps of constructing the Pybrain neural network: Constructing the neural network structure Data set training neural networks result visualization verification and analysis constructing neural net

The process of building a neural network is very clear, set several levels, several nodes, are simple and clear, see it once.

Import NumPy as NP
import Matplotlib.pyplot as plt from

pybrain.structure import * from
pybrain.datasets impo RT Superviseddataset from
pybrain.supervised.trainers import backproptrainer

# Createa neural network
FNN = Feedforwardnetwork ()

# Create three layers, input layer:2 input unit; hidden layer:10 units; output layer:1 output
Inlayer = Linearlayer (2, name= ' Inlayer ')
HiddenLayer0 = Sigmoidlayer (name= ' HiddenLayer0 ') outlayer
= Linearlayer (1, name= ' Outlayer ')

# Add three layers to the neural network
(fnn.addinputmodule)
Fnn.addmodule (HIDDENLAYER0)
fnn.addoutputmodule (outlayer)

# link three layers
= Fullconnection (INLAYER,HIDDENLAYER0)
hidden0_to_out = Fullconnection (HiddenLayer0, Outlayer)

# Add the Links to Neural network
fnn.addconnection (in_to_hidden0)
fnn.addconnection (hidden0_to_out)

# Make Neural network come into effect
fnn.sortmodules ()

Building Data sets

We choose 2 input 1 output, 80% for training, 20% for forecasting

# definite the dataset as two input, one output
DS = Superviseddataset (2,1)

# Add data element to the dataset
  
   for I in Np.arange (199):
    ds.addsample ([u[i],y[i]],[y[i+1]])

# You can get your input/output this way
X = ds[' Input ']
Y = ds[' target ']

# split the dataset into train dataset and test DataSet
Datatrain, datatest = Ds.spli Twithproportion (0.8)
xtrain, ytrain = datatrain[' input '],datatrain[' target ']
xtest, ytest = datatest[' Input '], datatest[' target '
  

Training Neural Networks

Let's give him a 1000-time iteration.

# Train The NN
# we use BP algorithm
# verbose = True means print th total error
trainer = Backproptrainer ( FNN, Datatrain, verbose=true,learningrate=0.01) # Set the Epoch Times to make the
NN fit
Trainer.trainuntilconvergence (maxepochs=1000)

Visualization of results

We're using Matlibplot to draw the predictions and the actual values.

Predict_resutl=[] for
i in Np.arange (Len (xtest)):
    predict_resutl.append (Fnn.activate (xtest[i)) [0])
Print (PREDICT_RESUTL)

plt.figure ()
Plt.plot (Np.arange (0,len (xtest)), Predict_resutl, ' ro--', label= ' Predict number ')
Plt.plot (Np.arange (0,len (xtest)), Ytest, ' ko-', label= ' true number ')
plt.legend ()
Plt.xlabel ("x")
Plt.ylabel ("y")

plt.show ()

Let's make a prediction with this topic and draw the following figure
Analysis

For mod in fnn.modules:
  print ("Module:", mod.name)
  if Mod.paramdim > 0:
    print ("--parameters:", Mod.params) for
  Conn in fnn.connections[mod]:
    print ("-connection to", Conn.outmod.name)
    if Conn.paramdim > 0:
       print ("-parameters", conn.params)
  if Hasattr (FNN, "Recurrentconns"):
    print ("Recurrent Connections ") for
    Conn in Fnn.recurrentconns:
       print ("-", Conn.inmod.name," to ", Conn.outmod.name)
       if Conn.paramdim > 0:
          print ("-parameters", Conn.params)

It can print out the specific information of the neural network, the result is as follows:

Module:hiddenlayer0
-connection to Outlayer
-parameters [ -0.48485978  1.94439991-1.1686299  - 1.01764515-1.04221    -0.78088745
  0.27321985-1.76426041  2.0747614   1.98425053]
module:inlayer
-connection to HiddenLayer0
-parameters [1.48125364-0.97942827  4.7258546   2.08059918- 1.96960441-0.03098871
  0.52430318  1.64983933  0.43738152  1.95122015  0.81952423- 0.24019787
 -0.86026329  0.63505556  0.53870484  0.94078527  1.42263437  1.87720358
 -1.12582038  0.70344489]
Module:outlayer

The complete code

Finally, I post the complete code, and note that you have to install Pybrain first.

Import NumPy as NP import Matplotlib.pyplot as PLT from pybrain.structure Import * from pybrain.datasets Import supervise Ddataset from pybrain.supervised.trainers import Backproptrainer def generate_data (): "" "Generate original data of U and Y "" "U = Np.random.uniform ( -1,1,200) y=[] Former_y_value = 0 for I in Np.arange (0,200): Y.appe nd (former_y_value) next_y_value = (29/40) * Np.sin ((u[i) + 8 * former_y_value)/(3 + 4 * (u[i ] * * * 2) + 4 * (Former_y_value * * 2))) \ + (2/10) * U[i] + (2/10) * Former_y_value forme  R_y_value = Next_y_value return U,y # Obtain the original data U,y = Generate_data () # Createa neural network FNN = Feedforwardnetwork () # Create three layers, input layer:2 input unit; Hidden layer:10 units; Output layer:1 Output Inlayer = Linearlayer (2, name= ' Inlayer ') HiddenLayer0 = Sigmoidlayer (name= ' HiddenLayer0 ') Outla Yer = Linearlayer (1, name= ' Outlayer ') # Add three Layers to the neural network Fnn.addinputmodule (inlayer) fnn.addmodule (HIDDENLAYER0) Fnn.addoutputmodule (outlayer) # Li NK three Layers In_to_hidden0 = fullconnection (INLAYER,HIDDENLAYER0) hidden0_to_out = Fullconnection (HiddenLayer0, Outlayer) # Add the links to neural network fnn.addconnection (in_to_hidden0) fnn.addconnection (hidden0_to_out) # make NE Ural network come into effect fnn.sortmodules () # Definite the dataset as two input, one output DS = Superviseddataset (2  , 1) # Add data element to the dataset for I-Np.arange (199): Ds.addsample ([u[i],y[i]],[y[i+1]]) # you can get your Input/output this way X = ds[' input '] Y = ds[' target '] # split the dataset into train dataset and test dataset Datatrain , datatest = ds.splitwithproportion (0.8) Xtrain, Ytrain = datatrain[' input '],datatrain[' target '] xtest, ytest = datatest[ ' Input '], datatest[' target '] # train The NN # we use BP algorithm # verbose = True means print th total error trainer = B Ackproptrainer (FNN, Datatrain, verbose=true,learningrate=0.01) # Set the Epoch Times to make the NN fit Trainer.trainuntilconvergence (maxepochs=1000) # p Rediction = Fnn.activate (xtest[1]) # print ("The prediction number is:", prediction, "The real number is:", ytest[1]) pred

Ict_resutl=[] for I in Np.arange (Len (xtest)): Predict_resutl.append (Fnn.activate (xtest[i)) [0]) print (PREDICT_RESUTL) Plt.figure () Plt.plot (Np.arange (0,len (xtest)), Predict_resutl, ' ro--', label= ' predict number ') Plt.plot (0, Len (xtest)), Ytest, ' ko-', label= ' true number ') Plt.legend () Plt.xlabel ("X") Plt.ylabel ("Y") plt.show () for mod in FNN.M Odules:print ("Module:", mod.name) if Mod.paramdim > 0:print ("--parameters:", Mod.params) for Conn in FNN. Connections[mod]: Print ("-connection to", conn.outmod.name) if Conn.paramdim > 0:print ("-Parameters" , conn.params) if Hasattr (FNN, "Recurrentconns"): Print ("recurrent connections") for Conn in Fnn.recurrentconns : Print ("-", Conn.inmoD.name, "to", Conn.outmod.name) if Conn.paramdim > 0:print ("-Parameters", Conn.params) 

Article reference:
[1] using Pybrain Library for neural network fitting