[ARCHIVED] Learning High School Physics with Tensorflow

2018-05-28 318 words 2 minutes

Contents

## Introduction Learning to convert from Angular displacement to linear displacement was nothing fancy in highschool, but TEACHING a machine learning model how to do the translation is on a whole new level . Just kidding, it's also nothing fancy.

Task

What we want to do is learn the mapping between the angular rotation (complete circle) of a circular object given its diameter to the distance covered on a linear path

So we want to find the length of the underlying line that the circle covers while completing a full rotation.

What we already know

From highschool, we already know the formula to calculate this function.

$y = 2 \times \Pi \times r$

which yields to

$y = 6.283185 \times r$

So we want our Neural network to learn the parameter a = 6.283185

Dataset

Since we already have the mapping from input to output, then we can generate the dataset ourselves.

import numpy as np 
import math 
dataset_size = 200

def generate_dataset():
  
  radii = np.random.uniform(-20, 20, size=dataset_size)
  np.random.shuffle(radii)
  distance_covered_by_one_lap =  2.0 * math.pi * radii

  return radii , distance_covered_by_one_lap

We are going to consider the distance covered by 1 full rotation of circles with different radii

Since the function is linear, then the curve will be a straight line.

Model

We are going to use a very simple neural network. Actually it’s not going to be a network, just 1 neuron.

Code

X = tf.placeholder(dtype=tf.float32,shape=(dataset_size,),name = 'Input_X')
Y = tf.placeholder(dtype=tf.float32,shape=(dataset_size,),name = 'Y')

def step(X, weight):
    h = tf.multiply(X,weight)
    a = tf.nn.relu(h)
    return a

yhat = step(X,w)

cost = tf.reduce_sum(tf.pow(tf.subtract(yhat,Y), 2))/(dataset_size)
train = tf.train.GradientDescentOptimizer(learning_rate=lr).minimize(cost)


init = tf.global_variables_initializer()

with tf.Session() as sess :
  sess.run(init)
  print(w.eval())
  for i in range(100):
    sess.run(train,feed_dict = {
        X : radii,
        Y : distance
    })
  print(w.eval())

While training, after just a few iterations, we will see that the network converged and the scalar w we are training is about 6.2831855 which is the desired value