Learn elliptical orbits with Chainer

Learn elliptical orbits with Feedforward Neural Network using chainer. The test is done in an open loop.

I will solve this problem while explaining how to use chainer.

Problems and approaches

[problem] Learn the elliptical orbits of x = 0.8cos (θ) and y = 0.8sin (θ).

[approach] x(θn)＝(0.8cos(θn),0.8sin(θn)), (0<=θn<=2π) Design an FNN that predicts x (θn + 1) from x (θn). Then, use this FNN to learn using training data, and test and confirm the results using test data.

Data creation and variable setting

Training data and test data

Specify any point on the ellipse.

[Training data] xtrain (θn) = (0.8cos (θn), 0.8sin (θn)), θn = 2πn / 20 (0 <= n <= 20, n is a natural number) will do. Write as follows.

a=np.linspace(0,20,sample_no).reshape(sample_no,1) 
xtrain=np.zeros(input_no*sample_no).reshape(sample_no,input_no).astype(np.float32)
xtrain[:,0]=[0.8*np.cos(2.0*np.pi*i/20) for i in a]
xtrain[:,1]=[0.8*np.sin(2.0*np.pi*i/20) for i in a]

[test data] xtest (θn) = (0.8cos (θn), 0.8sin (θn)), θn = 2πn / 27 (0 <= n <= 27, n is a natural number) will do. Similarly, write as follows.

a=np.linspace(0,27,sample_no).reshape(sample_no,1) 
xtest=np.zeros(input_no*sample_no).reshape(sample_no,input_no).astype(np.float32)
xtest[:,0]=[0.8*np.cos(2.0*np.pi*i/27) for i in a]
xtest[:,1]=[0.8*np.sin(2.0*np.pi*i/27) for i in a]

variable

Set as follows. Number of teacher data: sample_no Number of learning: epoch Number of layers: Input layer: input_no = 2 (fixed) Middle layer: hidden_no Output layer: output_no = 2 (fixed) Batch size: bs

Construction of learning model by chainer

Preparing a connection (Link)


class FNN(Chain):
	def __init__(self): #Prepare a connection
		super(FNN,self).__init__(
			l1=L.Linear(input_no,hidden_no),
			l2=L.Linear(hidden_no,output_no),

In addition, it should be noted l1=L.Linear(input_no,hidden_no), l2=L.Linear(hidden_no,output_no), Is self.add_link("l1",F.Linear(input_no,hidden_no)), self.add_link("l2",F.Linear(hidden_no,output_no)), Is the same as writing.

forward calculation

The registered Link is called as a function. The argument seems to be a variable class in principle.

Chainer.variable (data): Create a variable for chainer with a numerical value called data. The activation function is called from chainer.functions (F). (This time it is tanh.)

#class FNN
	def fwd(self,x):
		h1=F.tanh(self.l1(x))
		h2=F.tanh(self.l2(h1))
		return h2
	
	def get_predata(self,x):
		return self.fwd(Variable(x.astype(np.float32).reshape(sample_no,input_no))).data

Loss function

Called from chainer.functions. This time, we will use the mean square error.

#class FNN
	def __call__(self,x,y): #Loss function
		return F.mean_squared_error(self.fwd(x),y)

optimisation

Create an optimizer and set it with the FNN model. There are various types such as SGD, Adam, and RMS Drop.

model=FNN()
optimizer=optimizers.SGD()
optimizer.setup(model)

Training

Train the next data set (Xtrain_n + 1) as the correct answer for the current data set (Xtrain_n). Gradient initialization, backpropagation, and update 　　optimizer.zero_grads() 　　loss.backward() 　　optimizer.update() Repeat.

for i in range(epoch):
	for j in range(sample_no): #Put one ahead
		if (j+1<sample_no):
			ytrain[j]=np.array(xtrain[j+1])
		else:
			ytrain[j]=np.array(xtrain[0])

	model.zerograds()
	loss=model(xtrain,ytrain)
	loss.backward()
	optimizer.update()

test

Since it is done in an open loop, it reads the test data every time and predicts the next point. Since the test data is calculated by FeedForward and output to you, just write as follows.

yout=model.get_predata(xtest)

test results

The teacher data (target ellipse) is drawn in blue and the test results are drawn in red.

100 learning times: still out of sync

5000 lessons: It's getting closer to an ellipse

Number of learning 5000000 times: Almost correct answer

Full code

`ellipse.py`


#-*- coding:utf-8 -*-
import numpy as np
import chainer
from chainer import cuda,Function,gradient_check,Variable,optimizers,serializers,utils
from chainer import Link,Chain,ChainList
import chainer.functions as F
import chainer.links as L
from sklearn import datasets
import matplotlib.pyplot as plt

#Number of teacher data
sample_no=100 

#Number of learning
epoch=500000

#Number of layers
input_no=2
hidden_no=2
output_no=2

#Teacher data creation
a=np.linspace(0,20,sample_no).reshape(sample_no,1) 
xtrain=np.zeros(input_no*sample_no).reshape(sample_no,input_no).astype(np.float32)
xtrain[:,0]=[0.8*np.cos(2.0*np.pi*i/20) for i in a]
xtrain[:,1]=[0.8*np.sin(2.0*np.pi*i/20) for i in a]

#Model building
class FNN(Chain):
	def __init__(self): #Prepare a connection
		super(FNN,self).__init__(
			l1=L.Linear(input_no,hidden_no),
			l2=L.Linear(hidden_no,output_no),
		)
	def __call__(self,x,y): #Loss function
		return F.mean_squared_error(self.fwd(x),y)

	def fwd(self,x):
		h1=F.tanh(self.l1(x))
		h2=F.tanh(self.l2(h1))
		return h2
	
	def get_predata(self,x):
		return self.fwd(Variable(x.astype(np.float32).reshape(sample_no,input_no))).data

#Optimization method
model=FNN()
optimizer=optimizers.SGD()
optimizer.setup(model)

#Stores the correct answer value for training
ytrain=np.zeros(input_no*sample_no).reshape(sample_no,input_no).astype(np.float32)

#Batch size
bs=25

#Training
for i in range(epoch):
	for j in range(sample_no): #Put one ahead
		if (j+1<sample_no):
			ytrain[j]=np.array(xtrain[j+1])
		else:
			ytrain[j]=np.array(xtrain[0])

	model.zerograds()
	loss=model(xtrain,ytrain)
	loss.backward()
	optimizer.update()

#test(openloop)
a=np.linspace(0,27,sample_no).reshape(sample_no,1) 
xtest=np.zeros(input_no*sample_no).reshape(sample_no,input_no).astype(np.float32)
xtest[:,0]=[0.8*np.cos(2.0*np.pi*i/27) for i in a]
xtest[:,1]=[0.8*np.sin(2.0*np.pi*i/27) for i in a]
yout=model.get_predata(xtest)
print yout

#drawing
plt.plot(yout[:,0],yout[:,1],"r",label="training data")    #Draw learning results in red
plt.plot(xtrain[:,0],xtrain[:,1],"b",label="teaching data") #Draw teacher data in blue
plt.show()