Can someone explain a few things about the code below?

1.The tools, libraries, and APIs utilized

2.Search methods used and how they contributed toward the program goal

3.Inclusion of any deep learning models

4.Aspects of the program that utilize expert system concepts

5.How the program represent knowledge

6.How symbolic planning is used in the program

CODE BELOW:

import numpy as np

# Define a simple function for the neural network to learn

def function(x):

return x**2 + 2*x + 1

# Define the neural network architecture

input_size = 1

hidden_size = 16

output_size = 1

# Initialize the weights and biases

W1 = np.random.randn(input_size, hidden_size)

b1 = np.random.randn(hidden_size)

W2 = np.random.randn(hidden_size, output_size)

b2 = np.random.randn(output_size)

# Define the sigmoid activation function

def sigmoid(x):

return 1 / (1 + np.exp(-x))

# Define the derivative of the sigmoid function

def sigmoid_derivative(x):

return x * (1 - x)

# Define the neural network forward pass

def forward(x):

z1 = np.dot(x, W1) + b1

a1 = sigmoid(z1)

z2 = np.dot(a1, W2) + b2

a2 = sigmoid(z2)

return a2

# Define the neural network backward pass

def backward(x, y, a2):

dz2 = a2 - y

dw2 = np.dot(a1.T, dz2)

db2 = np.sum(dz2, axis=0)

da1 = np.dot(dz2, W2.T)

dz1 = da1 * sigmoid_derivative(a1)

dw1 = np.dot(x.T, dz1)

db1 = np.sum(dz1, axis=0)

return dw1, db1, dw2, db2

# Define the A* search algorithm

def a_star(start, goal):

# Define the heuristic function

def heuristic(x):

return abs(x - goal)

# Create a priority queue and add the starting point

queue = [(start, 0)]

# Keep track of the path taken

path = {}

path[start] = None

# Keep track of the cost of each point

cost = {}

cost[start] = 0

while queue:

# Get the point with the lowest f value

current = min(queue, key=lambda x: x[1])[0]

# Check if we have reached the goal

if current == goal:

return path, cost[goal]

# Remove the current point from the queue

queue.remove((current, cost[current] + heuristic(current)))

# Generate the neighbors of the current point

for neighbor in [current - 1, current + 1]:

if neighbor in path:

continue

# Calculate the cost of reaching the neighbor

new_cost = cost[current] + 1

# Add the neighbor to the queue

queue.append((neighbor, new_cost + heuristic(neighbor)))

# Update the path and cost

path[neighbor] = current

cost[neighbor] = new_cost

#Train the neural network

num_epochs = 10000

learning_rate = 0.1

#for epoch in range(num_epochs):

# Generate a random input

x = np.random.randn(1)

# Calculate the output of the neural network

a2 = forward(x)

# Calculate the error

error = function(x) - a2

# Calculate the gradients

dw1, db1, dw2, db2 = backward(x, function(x), a2)

# Update the weights and biases

W1 -= learning_rate * dw1

b1 -= learning_rate * db1

W2 -= learning_rate * dw2

b2 -= learning_rate * db2

#Test the neural network

x = 3

a2 = forward(x)

print("Input:", x)

print("Expected output:", function(x))

print("Predicted output:", a2[0])

#Test the A* search algorithm

start = 0

goal = 10

path, cost = a_star(start, goal)

print("Path from", start, "to", goal, ":", path)

print("Cost:", cost)