solution1.py

#Solution to Q1:

def construct_func_nn(x_grid,y_grid,width,f2):
    def func_nn(x):
        y = 0
        for i in range(len(x_grid)):
            x0 = x_grid[i]
            y0 = y_grid[i]
            y += f2((x-x0)/width)*y0
        return y
    return func_nn


#Solution to Q2:

def construct_hat2d(r,f2):
    func1 = lambda x,y: f2(x)
    func2 = lambda x,y: f2(y)
    func3 = lambda x,y: f2(x) + f2(y)
    func4 = lambda x,y: r(f2(x) + f2(y) - 1 )
    funcs = [func1, func2, func3, func4]
    return funcs

#Solution to Q3:

import tensorflow as tf
from tensorflow import keras
from tensorflow.keras import layers
def construct_nn():
    layer1 = layers.Dense(10, activation="relu", name="layer1")
    layer2 = layers.Dense(10, activation="relu", name="layer2")
    layer3 = layers.Dense(1, name="layer3")
    model = keras.Sequential([layer1, layer2, layer3])
    model.build((None,2))
    return model

def construct_Vnn(func_nn):
    inputs = keras.Input(shape=(1,))
    S = inputs
    for i in range(10):
        t = tf.ones(tf.shape(inputs)) * i
        S_and_t = tf.concat([S,t],axis = -1)
        S = S + func_nn(S_and_t)
    outputs = S
    model = keras.Model(inputs=inputs, outputs=outputs)
    return model