Straight line fit under condition

Keras
,
1 
# data
myinput = np.array([ [ 1,0 ],[ 1,1 ],[ 1,2 ],[ 1,3 ],[ 1,4 ],[ 1,5 ] ])
myotput = np.array([ [ 0 ],[ 1 ],[ 2 ],[ 3 ],[ 4 ],[ 5 ] ])
# model
model = Sequential()
model.add(Dense(32, input_dim=2, activation='tanh'))
model.add(Dense(1, activation='tanh'))
model.compile(loss='mean_squared_error',
              optimizer='adam',
              metrics=['accuracy'])
# train
model.fit(x=myinput, y=myotput, epochs=10000, verbose=0)
# check
print(model.predict(myinput))

A straight line fit under condition “1” seems not feasible. Thanks!

3

To illustrate the question think of a spinning wheel of a certain size i.e. diameter or radius which is kept fixed at first (condition).

A relation between its velocity at the outer diamter, angular velocity and radius exists: velocity = omega (angular velocity) * radius.

If the angular velocity i.e. omega changes, then the outer velocity changes.

outer velocity (output) omega (input 2) fixed radius (input 1)
1 1 1
2 2 1
3 3 1
4 4 1
… … 1

The ultimate goal is to retrieve velocities for different angular velocities and diameters, if the physical relation is not given. Let us keep the wheel diameter (condition) fixed for now.

4

It might be possible for a deep learning network to learn this function. You will need to generate thousands of training samples, which fully explore the function space.

6

Question 1: does

# 32 inner nodes, 2 input nodes
model.add(Dense(32, input_dim=2, activation='tanh'))
# 1 output node
model.add(Dense(1, activation='tanh')

classify as a deep learning network, if not, how to modify it?

Question 2: like that:

myinput=[];myotput=[]
myinput[0] = np.array([ [ 1,0 ],[ 1,1 ],[ 1,2 ],[ 1,3 ],[ 1,4 ],[ 1,5 ] ])
myotput[0] = np.array([ [ 0 ],[ 1 ],[ 2 ],[ 3 ],[ 4 ],[ 5 ] ])
myinput[1] = np.array([ [ 1,0.5 ],[ 1,1.0 ],[ 1,1.5 ],[ 1,2.0 ],[ 1,2.5 ],[ 1,3.0 ] ])
myotput[1] = np.array([ [ 0.5],[ 1.0 ],[ 1.5 ],[ 2.0 ],[ 2.5 ],[ 3.0 ] ])
...

Question 3: let us assume only a single data set exists, is it possible to train a network to reproduce just that?

8

#1 Yes, that is a deep learning network. It can learn to approximate a very simple function.
#2 This technology requires hundreds of unique training samples as a minimum.

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