## Introduction to Pytorch

### Shuaiqiang Liu

### Outline

* A toy example: approximating  $y=\cos(x)$
 1. Polynomial approximation
 2. Neural networks

* Basics of Pytorch
 1. Introduction to Tensor
 2. Tensor Operations

* Common Modules in Pytorch
 1. torch.nn (Neural networks components)
 2. torch.optim (Optimation algorithms)

* Building a neural network
* Training with Pytorch
* Save and load the model

## What is  Pytorch?
pytorch tutorial
https://pytorch.org/tutorials/

```python
import torch
print(torch.__version__)
```

    1.10.1

### A toy example: $y=\cos(x)$
The aim is to approximate the function $y=\cos(x)$, $\frac{1}{2} \pi  \leq x \leq \frac{3}{2} \pi$.

```python
import numpy as np
import matplotlib.pyplot as plt
import warnings
warnings.filterwarnings('ignore')

x = np.linspace(-0.5*np.pi, 1.5*np.pi, 2000)
y = np.cos(x)

# plot the function
plt.figure(1)
plt.scatter(x,y,label='y=cos(x)')
plt.xlabel('$x$')
plt.ylabel('$y$')
plt.title('$y=\cos(x)$')
plt.grid()
```

***1. A polynnomial approximation, that is, finding the coefficients in a third polynomial,***
$$\hat y=a+b*x+c*x^2+d*x^3.$$
Define a polynomial function as follows,
$$\hat y =f(x;a,b,c,d)$$
Given the data set, that is, input-output pairs $(x_i,y_i), i=1,\ldots,n$, the loss function is
$$L = \sum_i(\hat{y}_i-y_i)^2 = \sum_i(f(x_i;a,b,c,d)-y_i)^2.$$

In order to minimize the loss function,  the gradient descent algorithm is used as follows
\begin{equation}
\begin{cases}
a \leftarrow  a - \eta \frac{\displaystyle \partial L}{\displaystyle \partial a}, \\[1.5ex]
b \leftarrow  b - \eta \frac{\displaystyle \partial L}{\displaystyle  \partial b},\\[1.5ex]
c \leftarrow  c - \eta \frac{\displaystyle \partial L}{\displaystyle \partial c}, \\[1.5ex]
d \leftarrow  d - \eta \frac{\displaystyle \partial L}{\displaystyle  \partial d},\\[1.5ex]
\end{cases}
\end{equation}

the gradient of the loss w.r.t the coefficients is computed by Pytorch automatically.

```python
%%time

import torch
import math

dtype  = torch.float
device = torch.device("cpu")
torch.manual_seed(0)

x = torch.from_numpy(x)
y = torch.from_numpy(y)

# Create random Tensors for coefficients.
a = torch.randn((), device=device, dtype=dtype, requires_grad=True)
b = torch.randn((), device=device, dtype=dtype, requires_grad=True)
c = torch.randn((), device=device, dtype=dtype, requires_grad=True)
d = torch.randn((), device=device, dtype=dtype, requires_grad=True)

learning_rate = 3e-7
loss_values = []

for t in range(25000):

    # Forward pass: compute yhat using operations on Tensors.
    yhat = a + b * x + c * x ** 2 + d * x ** 3

    # Now loss is a Tensor of shape (1,)
    loss = (yhat - y).pow(2).sum()

    # print out the loss item, equals MSE times N
    loss_values.append(loss.item())
    if t % 1000 == 99:
        print('Iteration', t,  'Loss=', loss.item())

    # Use autograd to compute the backward pass.
    loss.backward()

    # Manually update coefficients using gradient descent.
    with torch.no_grad():
        a -= learning_rate * a.grad
        b -= learning_rate * b.grad
        c -= learning_rate * c.grad
        d -= learning_rate * d.grad

        # Manually assign zeros to the gradients after updating weights
        a.grad = None
        b.grad = None
        c.grad = None
        d.grad = None

print(f'Result: y = {a.item()} + {b.item()} x + {c.item()} x^2 + {d.item()} x^3 ')
```

    Iteration 99 Loss= 6556.619941564821
    Iteration 1099 Loss= 446.92491406852776
    Iteration 2099 Loss= 241.21402109470145
    Iteration 3099 Loss= 133.49242447391555
    Iteration 4099 Loss= 75.89898519738732
    Iteration 5099 Loss= 44.9582016365039
    Iteration 6099 Loss= 28.299989811121772
    Iteration 7099 Loss= 19.32277402302733
    Iteration 8099 Loss= 14.482675437593517
    Iteration 9099 Loss= 11.872631256475533
    Iteration 10099 Loss= 10.465070419085736
    Iteration 11099 Loss= 9.705943319988961
    Iteration 12099 Loss= 9.296506718220758
    Iteration 13099 Loss= 9.07570319580605
    Iteration 14099 Loss= 8.95660668827864
    Iteration 15099 Loss= 8.892372101573153
    Iteration 16099 Loss= 8.857728584579863
    Iteration 17099 Loss= 8.839043986456021
    Iteration 18099 Loss= 8.828964248375843
    Iteration 19099 Loss= 8.823533906163705
    Iteration 20099 Loss= 8.820603495319524
    Iteration 21099 Loss= 8.81902164341793
    Iteration 22099 Loss= 8.818171423570888
    Iteration 23099 Loss= 8.817709289304672
    Iteration 24099 Loss= 8.817461342018822
    Result: y = 0.984532356262207 + -0.16577181220054626 x + -0.4400693476200104 x^2 + 0.09337902814149857 x^3
    Wall time: 7.36 s

```python
plt.plot(np.array(np.log(loss_values)), 'r')
plt.xlabel('iterations')
plt.ylabel('log(MSE)')
plt.title('Loss history')
```

#### Testing the polynomial with the learned coefficients

```python
# test data---no overlapping data points except two ending points
xtest = torch.linspace(-0.5*math.pi, 1.5*math.pi, 1111, device=device, dtype=dtype)

ytrue = torch.cos(xtest)
yhat  = a + b * xtest + c * xtest ** 2 + d * xtest ** 3

plt.scatter(xtest.detach(),ytrue.detach(),label='y=cos(x)')
plt.scatter(xtest.detach(),yhat.detach(),label='y=polynomial(x)')
plt.legend()
plt.xlabel('$x$')
plt.ylabel('$y$')
plt.grid()
```

## How to create a Tensor in Pytorch?

1. create a tensor from an existing array

```python
import torch
data        = [[0.0, 1.0], [2.0, 3.0]]
tensor_data = torch.tensor(data)
print(tensor_data)
```

    tensor([[0., 1.],
            [2., 3.]])

```python
print(data)
```

    [[0.0, 1.0], [2.0, 3.0]]

```python
tensor_data[0][0] = 9.0
print(tensor_data)
print(data)
```

    tensor([[9., 1.],
            [2., 3.]])
    [[0.0, 1.0], [2.0, 3.0]]

**Note: The array and Tensor do not share the same memory.**

2. from numpy

```python
import numpy as np
np_array    = np.array(data)
tensor_data = torch.from_numpy(np_array)
print(tensor_data)
```

    tensor([[0., 1.],
            [2., 3.]], dtype=torch.float64)

```python
tensor_data[0][0]=9.0
print(tensor_data)
print(np_array)
```

    tensor([[9., 1.],
            [2., 3.]], dtype=torch.float64)
    [[9. 1.]
     [2. 3.]]

```python
np_array[0][0]=10.0
print(tensor_data)
print(np_array)
```

    tensor([[10.,  1.],
            [ 2.,  3.]], dtype=torch.float64)
    [[10.  1.]
     [ 2.  3.]]

**Note: Convertion between Numpy and Torch, the torch Tensor and numpy array share the same memory, and changing one will change the other.**

3. from an existing tensor

```python
x_ones = torch.ones_like(tensor_data)
print(f"Ones Tensor: \n {x_ones} \n")

x_rand = torch.rand_like(tensor_data, dtype=torch.float32)
print(f"Random Tensor: \n {x_rand}, dtype={x_rand.dtype} \n")
```

    Ones Tensor:
     tensor([[1., 1.],
            [1., 1.]], dtype=torch.float64)

    Random Tensor:
     tensor([[0.4556, 0.6323],
            [0.3489, 0.4017]]), dtype=torch.float32

4. given a specific size

Suppose we want to create a tensor $x$ of shape (m,n) with Pyrorch

```python
shape = (3,2)
rand_tensor = torch.rand(shape)
print(f"Random Tensor: \n {rand_tensor} \n")

ones_tensor = torch.ones(shape)
print(f"Ones Tensor: \n {ones_tensor} \n")

zeros_tensor = torch.zeros(shape)
print(f"Zeros Tensor: \n {zeros_tensor}")
```

    Random Tensor:
     tensor([[0.0223, 0.1689],
            [0.2939, 0.5185],
            [0.6977, 0.8000]])

    Ones Tensor:
     tensor([[1., 1.],
            [1., 1.],
            [1., 1.]])

    Zeros Tensor:
     tensor([[0., 0.],
            [0., 0.],
            [0., 0.]])

### Each Tensor has the following attributes,
1. torch.dtype,
2. torch.device,
3. torch.layout (physical memory).

```python
x1 = torch.randn((2,3), device=torch.device('cpu'))
print(f"x1: \n dtype={x1.dtype}, device={x1.device}, layout={x1.layout}")
```

    x1:
     dtype=torch.float32, device=cpu, layout=torch.strided

```python
if torch.cuda.is_available():
    x2 = torch.randn((2,3), device=torch.device('cuda'))
    print(f"x2: \n dtype={x2.dtype}, device={x2.device}, layout={x2.layout}")
```

    x2:
     dtype=torch.float32, device=cuda:0, layout=torch.strided

####  PyTorch supports multiple types of tensors, including:
1. FloatTensor: 32-bit float
2. DoubleTensor: 64-bit float
3. HalfTensor: 16-bit float
4. IntTensor: 32-bit int
5. LongTensor: 64-bit int

### Tensor Operations
Refer to https://pytorch.org/docs/stable/tensors.html for the list of supported operations

**Manipulate a Tensor**

```python
a = torch.randn(1, 2, 3, 4)
print(a.size())

# Swaps 2nd and 3rd dimension
b = a.transpose(1, 2)
print(b.size())

c = torch.transpose(a, 1, 2)
print(c.size())
```

    torch.Size([1, 2, 3, 4])
    torch.Size([1, 3, 2, 4])
    torch.Size([1, 3, 2, 4])

**Math operations**

```python
m,n =3,3
x = torch.zeros((m,n)) +2
y = torch.zeros((m,n)) +1

z_add    = x+y
z_minus  = x-y
z_times  = x*y
z_divide = x/y

print('addition: \n',z_add)
print('division: \n',z_divide)
```

    addition:
     tensor([[3., 3., 3.],
            [3., 3., 3.],
            [3., 3., 3.]])
    division:
     tensor([[2., 2., 2.],
            [2., 2., 2.],
            [2., 2., 2.]])

```python
torch.cat((x, y), 0)
```

    tensor([[2., 2., 2.],
            [2., 2., 2.],
            [2., 2., 2.],
            [1., 1., 1.],
            [1., 1., 1.],
            [1., 1., 1.]])

 **multiplication of Tensors**

```python
## matrix multiplication
z   = torch.matmul(x,y)
zmm = torch.mm(x,y)

## elementwise multiplication
zz   = x*y
zzem = torch.mul(x,y)

print(f'torch.matmul:\n{z} \n torch.mm:\n{zmm}')
print(f'x*y:\n{zz} \n torch.mul:\n{zzem}')
```

    torch.matmul:
    tensor([[6., 6., 6.],
            [6., 6., 6.],
            [6., 6., 6.]])
     torch.mm:
    tensor([[6., 6., 6.],
            [6., 6., 6.],
            [6., 6., 6.]])
    x*y:
    tensor([[2., 2., 2.],
            [2., 2., 2.],
            [2., 2., 2.]])
     torch.mul:
    tensor([[2., 2., 2.],
            [2., 2., 2.],
            [2., 2., 2.]])

**Broadcasting in element-wise multiplication**

```python
x = torch.ones(2, 1)
y = torch.randn(1, 2)
print(x)
print(y)
```

    tensor([[1.],
            [1.]])
    tensor([[ 1.1317, -0.6455]])

```python
z1 = x*y
```

```python
print(z1)
```

    tensor([[ 1.1317, -0.6455],
            [ 1.1317, -0.6455]])

```python
z2 = y*x
```

```python
print(z2)
```

    tensor([[ 1.1317, -0.6455],
            [ 1.1317, -0.6455]])

### Dynamic computational graph

### Computional Graph of $y=\cos(wx+b)$

```python
import torch
x=torch.tensor(0.5,requires_grad=False)
w=torch.tensor(1.0,requires_grad=True)
b=torch.tensor(0.5*torch.pi-0.5,requires_grad=True)

wx  = w*x
z   = wx +b
y   = torch.cos(z)

print(f'w={w},x={x},wx={wx},z={z},y={y}')
```

    w=1.0,x=0.5,wx=0.5,z=1.5707963705062866,y=-4.371138828673793e-08

```python
import base64
from IPython import display
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display.Image(base64.b64decode(encoded_string),width=600,height=600)
```

The analytical partial derivatives are $$\frac{\partial y}{\partial w} = -x \sin(wx+b) $$
$$\frac{\partial y}{\partial b} =  -\sin(wx+b).$$
Here we want to find their value when $x=0.5$ and $wx+b = \frac{1}{2} \pi$.

```python
y.backward()
```

```python
print('gradient of leaf Tensors :', '\n dy/dw=',w.grad, '\n dy/db=',b.grad)
```

    gradient of leaf Tensors :
     dy/dw= tensor(-0.5000)
     dy/db= tensor(-1.)

### a step-by-step backpropagation using .grad_fn and .next_functions

```python
encoded_string = 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display.Image(base64.b64decode(encoded_string),width=600,height=600)
```

```python
# initial again
x=torch.tensor(0.5,requires_grad=False)
w=torch.tensor(1.0,requires_grad=True)
b=torch.tensor(0.5*torch.pi-0.5,requires_grad=True)
wx  = w*x
z   = wx+b
y   = torch.cos(z)
```

```python
# fetch the backward function
CosBack = y.grad_fn
dy = torch.tensor(1.)  # dy=1.0
dz = CosBack(dy)
print('CosBack function:',CosBack, '\n dz=',dz)
```

    CosBack function: <CosBackward0 object at 0x000001646FAD4D30>
     dz= tensor(-1., grad_fn=<MulBackward0>)

```python
# next_functions of back_cos
AddBack = CosBack.next_functions[0][0]
dwx, db  = AddBack(dz)
print('AddBack function:',AddBack)
print('dwx=',dwx,'\n db=',db)
```

    AddBack function: <AddBackward0 object at 0x000001646FAD4940>
    dwx= tensor(-1., grad_fn=<MulBackward0>)
     db= tensor(-1., grad_fn=<MulBackward0>)

```python
MulBack= CosBack.next_functions[0][0].next_functions[0][0]
dw = MulBack(dwx)
print(' dw=',dw)
```

     dw= (tensor(-0.5000, grad_fn=<MulBackward0>), None)

### 2. A neural network is also a function approxiamtor.

Next we use fully connected neural networks to approximate the function
$y=\cos(x)$.

Define an ANN function as follows,
$$\hat y =f(x;\mathbf{W},\mathbf{b}),$$
where $\mathbf{W},\mathbf{b}$ are weights and biases respectively.
Given the data set, that is, input-output pairs $(x_i,y_i), i=1,\ldots,n$, the loss function is
$$L = \sum_i(\hat{y}_i-y_i)^2 = \sum_i(f(x_i;\mathbf{W},\mathbf{b})-y_i)^2.$$

In order to minimize the loss,  the gradient descent algorithm is used as follows
\begin{equation}
\begin{cases}
\mathbf{W} \leftarrow  \mathbf{W} - \eta \frac{\displaystyle \partial L}{\displaystyle \mathbf{W}}, \\[1.5ex]
\mathbf{b} \leftarrow  \mathbf{b} - \eta \frac{\displaystyle \partial L}{\displaystyle  \mathbf{b}},\\[1.5ex]
\end{cases}
\end{equation}

## Artifical Neural Networks (ANNs) within Pytorch

### Version A: ANNs using Pytorch's low level functions

```python
import torch
from torch import nn
import math
import matplotlib.pyplot as plt
```

```python

def softplus(x): return torch.log(1.0+torch.exp(-x))
def sigmoid(x): return 1.0/(1.0+torch.exp(-x))

class NeuralNetworkLow(nn.Module):

    def __init__(self,in_features=1,out_features=1,NofUnits=2, activation_fun=sigmoid):

        super(NeuralNetworkLow, self).__init__()

        ## input layer
        self.w1 = torch.rand(in_features, NofUnits, requires_grad=True) # create a tensor
        self.w1 = nn.Parameter(self.w1) # register this tensor as an nn.Parameter for Optimizer

        self.b1 = nn.Parameter(torch.zeros(NofUnits, requires_grad=True))

        ##  hidden layer
        self.w2 = nn.Parameter(torch.rand(NofUnits, NofUnits, requires_grad=True))
        self.b2 = nn.Parameter(torch.zeros(NofUnits, requires_grad=True))

        ## output layer
        self.w3 = nn.Parameter(torch.rand(NofUnits, 1, requires_grad=True))
        self.b3 = nn.Parameter(torch.zeros(1, requires_grad=True))

        ## activation function
        self.act_fun = activation_fun

    def forward(self,x):
        z = torch.matmul(x, self.w1)+self.b1
        z = self.act_fun(z)
        z = torch.matmul(z, self.w2)+self.b2
        z = self.act_fun(z)
        z = torch.matmul(z, self.w3)+self.b3
        return z
```

#### Process the  dataset for training and testing

```python
n_samples = 2000
##
x = torch.linspace(-0.5*math.pi, 1.5*math.pi, steps=n_samples, requires_grad=False)
y = torch.cos(x)
```

```python
## Shuffle the indices
import numpy as np
indices = np.arange(0,n_samples)
np.random.shuffle(indices) # shuffle the indicies

index_split = math.floor(0.8*n_samples)
indices_train = indices[0:index_split]
indices_test  = indices[index_split:-1]

## create a train part and a test part, no overlappling data
x = torch.reshape(x, (-1, 1))

x_train = x[indices_train]
y_train = y[indices_train]

x_test = x[indices_test]
y_test = y[indices_test]

x_train, y_train, x_test, y_test = map(torch.tensor, (x_train, y_train, x_test, y_test))

##
print(x_train.size())
print(x_test.size())
```

    torch.Size([1600, 1])
    torch.Size([399, 1])

#### Building the ANN model

```python
NofIn    = 1
NofOut   = 1
NofNodes = 10
model    = NeuralNetworkLow(NofIn,NofOut,NofNodes,sigmoid)
```

#### Before training

```python
# test the model
y_test_pred = model.forward(x_test)
print(y_test_pred.size())
print(x_test.size())

plt.figure(1)
plt.scatter(x_test.detach(),y_test.detach(),label="True value")
plt.scatter(x_test.detach(),y_test_pred.detach(),label='Predicted value')
plt.legend()
```

#### Implement Training

```python
# setting the random seed for reproducibility
torch.manual_seed(0)

#  the learning rate
learning_rate = 1e-2
optimizer     = torch.optim.Adam(model.parameters(),lr=learning_rate)
#optimizer     = torch.optim.SGD(model.parameters(),lr=learning_rate)

loss = torch.nn.MSELoss()

epoch = 1000
bat_size = 50
n_items = len(x_train)
batches_per_epoch = n_items // bat_size
max_batches = epoch * batches_per_epoch
loss_hist = []

for b in range(max_batches):
    curr_bat = np.random.choice(n_items, bat_size,
          replace=False)
    batchX = x_train[curr_bat]
    batchY = y_train[curr_bat].view(bat_size,1)

    # clear the gradients
    optimizer.zero_grad()

    # evaluate the function
    batchy_pred = model.forward(batchX)

    # compute the loss function
    loss_obj = loss(batchy_pred, batchY)

    # compute the gradient of the model parameters
    loss_obj.backward()

    # update the parameters
    optimizer.step()

#     with torch.no_grad():
#         model.w1 -=learning_rate*model.w1.grad
#         model.b1 -=learning_rate*model.b1.grad
#         model.w2 -=learning_rate*model.w2.grad
#         model.b2 -=learning_rate*model.b2.grad
#         model.w3 -=learning_rate*model.w3.grad
#         model.b3 -=learning_rate*model.b3.grad

#         model.w1.grad = None
#         model.b1.grad = None
#         model.w2.grad = None
#         model.b2.grad = None
#         model.w3.grad = None
#         model.b3.grad = None

    #print("@epoch : ", b, " #Loss : ", loss_obj.item())
    loss_hist.append(loss_obj.item())

    if b % (max_batches // 10) == 0:
        print("batch = %6d" % b, end="")
        print("  batch loss = %10.8f" % loss_obj.item(), end="")
        print("\n")
```

    batch =      0  batch loss = 27.24151611

    batch =   3200  batch loss = 0.00217584

    batch =   6400  batch loss = 0.00000962

    batch =   9600  batch loss = 0.00009042

    batch =  12800  batch loss = 0.00000123

    batch =  16000  batch loss = 0.00000487

    batch =  19200  batch loss = 0.00001036

    batch =  22400  batch loss = 0.00002155

    batch =  25600  batch loss = 0.00000245

    batch =  28800  batch loss = 0.00000445

**plot the convergence history**

```python
plt.plot(np.log(loss_hist),'r')
plt.xlabel('iterations')
plt.ylabel('log(MSE)')
plt.title('Training loss history')
```

#### Evalutation the ANN After training

```python
# test the model
y_test_pred = model.forward(x_test)

plt.figure(1)
plt.scatter(x_test.detach(),y_test.detach(),label="y=\cos(x)")
plt.scatter(x_test.detach(),y_test_pred.detach(),label='y=\ANN(x)')
plt.grid()
plt.legend()
```

**Check out weights and biases**

```python
print('w1:',model.w1)
print('w1.grad:',model.w1.grad)
print('b1',model.b1)
print('b1.grad:',model.b1)
```

    w1: Parameter containing:
    tensor([[ 0.4740,  0.6952,  0.4000, -0.4287,  2.2885,  0.4281,  2.5096,  2.4806,
              0.3971, -0.9570]], requires_grad=True)
    w1.grad: tensor([[-2.3528e-03, -3.3645e-03, -2.3356e-03,  4.2953e-04,  6.5348e-04,
             -1.3221e-03,  1.0777e-04,  8.0633e-06, -2.2606e-03, -1.0999e-04]])
    b1 Parameter containing:
    tensor([-1.6598, -2.8322, -0.7158,  0.0601, -5.3458, -0.3070, -3.4470, -1.2011,
            -0.8182, -1.3173], requires_grad=True)
    b1.grad: Parameter containing:
    tensor([-1.6598, -2.8322, -0.7158,  0.0601, -5.3458, -0.3070, -3.4470, -1.2011,
            -0.8182, -1.3173], requires_grad=True)

### Version B:  ANNs using Pytorch's high level APIs

```python
import torch
import torch.nn as nn

class NeuralNetworkHigh(nn.Module):

    def __init__(self, in_features=1,out_features=1,neurons=2, actvfun = nn.Sigmoid):
        super(NeuralNetworkHigh, self).__init__()
        ## the input layer
        self.layer1=nn.Linear(in_features, neurons)
        ## hidden layer
        self.layer2=nn.Linear(neurons, neurons)
        ## hidden layer
        self.layer3=nn.Linear(neurons, out_features)
        ## activation function
        self.actvfun=actvfun()

        ## put all the layers together
        self.fnn = nn.Sequential(self.layer1,self.actvfun,
                   self.layer2,self.actvfun,self.layer3)
    def forward(self, x):
        y = self.fnn(x)
        return y

```

#### Process the  dataset for training and testing

```python
import math
import matplotlib.pyplot as plt
n_samples = 2000
##
x = torch.linspace(-0.5*math.pi, 1.5*math.pi, steps=n_samples, requires_grad=False)
y = torch.cos(x)

# x.detach return the array for the matplot
plt.plot(x.detach(),y.detach())
plt.xlabel('$x$')
plt.ylabel('$y$')
plt.title('$y=\cos(x)$')
plt.grid()
print(x.size())
```

```python
## Shuffle the indices
import numpy as np
indices = np.arange(0,n_samples)
np.random.shuffle(indices) # shuffle the indicies

index_split = math.floor(0.8*n_samples)
indices_train = indices[0:index_split]
indices_test  = indices[index_split:-1]

## create a train part and a test part, no overlappling data
x = torch.reshape(x, (-1, 1))

x_train = x[indices_train]
y_train = y[indices_train]

x_test = x[indices_test]
y_test = y[indices_test]

##
print(x_train.size())
print(x_test.size())

```

    torch.Size([1600, 1])
    torch.Size([399, 1])

#### Building the ANN model

```python
NofIn    = 1
NofOut   = 1
NofNodes = 10

#initialize ANN
model    = NeuralNetworkHigh(NofIn,NofOut,NofNodes,torch.nn.Sigmoid)
#initialize loss function
loss_mse = torch.nn.MSELoss()

print(model)
```

    NeuralNetworkHigh(
      (layer1): Linear(in_features=1, out_features=10, bias=True)
      (layer2): Linear(in_features=10, out_features=10, bias=True)
      (layer3): Linear(in_features=10, out_features=1, bias=True)
      (actvfun): Sigmoid()
      (fnn): Sequential(
        (0): Linear(in_features=1, out_features=10, bias=True)
        (1): Sigmoid()
        (2): Linear(in_features=10, out_features=10, bias=True)
        (3): Sigmoid()
        (4): Linear(in_features=10, out_features=1, bias=True)
      )
    )

#### Before training

```python
# test the model
y_test_pred = model.forward(x_test)
plt.figure(1)
plt.scatter(x_test.detach(),y_test.detach(),label="True value")
plt.scatter(x_test.detach(),y_test_pred.detach(),label='Predicted value')
plt.legend()
```

without batchsize, it is difficult to train the ANN**.

#### Implement Training

```python
# setting the random seed for reproducibility
torch.manual_seed(0)

#  the learning rate
learning_rate = 1e-2
optimizer     = torch.optim.Adam(model.parameters(),lr=learning_rate)
loss = torch.nn.MSELoss()

epoch    = 1000
bat_size = 50
n_items  = len(x_train)
batches_per_epoch = n_items // bat_size
max_batches = epoch * batches_per_epoch
loss_hist = []

for b in range(max_batches):
    curr_bat = np.random.choice(n_items, bat_size,
          replace=False)
    batchX = x_train[curr_bat]
    batchY = y_train[curr_bat].view(bat_size,1)

    # clear the gradients
    optimizer.zero_grad()

    # evaluate the function
    batchy_pred = model.forward(batchX)

    # compute the loss function
    loss_obj = loss(batchy_pred, batchY)

    # compute the gradient of the model parameters
    loss_obj.backward()

    # update the parameters
    optimizer.step()

    #print("@epoch : ", b, " #Loss : ", loss_obj.item())
    loss_hist.append(loss_obj.item())

    if b % (max_batches // 10) == 0:
        print("batch = %6d" % b, end="")
        print("  batch loss = %10.8f" % loss_obj.item(), end="")
        print("\n")
```

    batch =      0  batch loss = 0.59832925

    batch =   3200  batch loss = 0.00007870

    batch =   6400  batch loss = 0.00008452

    batch =   9600  batch loss = 0.00000642

    batch =  12800  batch loss = 0.00003712

    batch =  16000  batch loss = 0.00058147

    batch =  19200  batch loss = 0.00000177

    batch =  22400  batch loss = 0.00000193

    batch =  25600  batch loss = 0.00000015

    batch =  28800  batch loss = 0.00000193

**plot the convergence history**

```python
plt.plot(np.log(loss_hist),'r')
plt.xlabel('iterations')
plt.ylabel('log(MSE)')
plt.title('Training loss history')
```

#### Evalutation the ANN After training

```python
# test the model
y_test_pred = model.forward(x_test)

plt.figure(1)
plt.scatter(x_test.detach(),y_test.detach(),label="True value")
plt.scatter(x_test.detach(),y_test_pred.detach(),label='Predicted value')
plt.grid()
plt.legend()
```

```python
print('model.layer1.weight:',model.layer1.weight)
print('model.layer1.bias:',model.layer1.bias)
print('model.layer1.weight.grad:',model.layer1.weight.grad)
```

    model.layer1.weight: Parameter containing:
    tensor([[ 1.8948],
            [ 1.6971],
            [-2.0708],
            [-1.6560],
            [-1.6397],
            [ 2.7532],
            [ 1.2229],
            [ 0.8471],
            [-2.1784],
            [ 0.9251]], requires_grad=True)
    model.layer1.bias: Parameter containing:
    tensor([-1.7189, -4.5297,  0.7479,  1.4470,  2.4407, -0.8972,  2.2323,  1.2852,
             0.7073, -4.4120], requires_grad=True)
    model.layer1.weight.grad: tensor([[ 3.3816e-05],
            [ 2.2467e-04],
            [-3.2189e-05],
            [-1.1313e-04],
            [-1.8500e-04],
            [ 8.1450e-06],
            [-6.7456e-05],
            [-5.0231e-05],
            [-3.5657e-05],
            [-1.1312e-03]])

#### Save and load model

```python
# save model to a file
model_file = 'model.pth'
torch.save(model, model_file)
```

```python
# load model from a file
model_loaded = torch.load(model_file)
```

```python
y_test_pred = model_loaded.forward(x_test)
```

```python
plt.figure(1)
plt.scatter(x_test.detach(),y_test.detach(),label="True value")
plt.scatter(x_test.detach(),y_test_pred.detach(),label='Predicted value (Loaded)')
plt.grid()
plt.legend()
```

**Implement the model on a GPU**

```python
if torch.cuda.is_available():
    print(f"CUDA version: {torch.version.cuda}")
```

    CUDA version: 11.3

```python
print(x_test.device)
print(x_test.size())
```

    cpu
    torch.Size([399, 1])

```python
x_test_cuda = x_test.to('cuda')
print(x_test_cuda.device)
print(x_test_cuda.size())
```

    cuda:0
    torch.Size([399, 1])

```python
# load model from a file
model_cpu = torch.load(model_file)
model_cuda=model_cpu.to(device='cuda')
```

```python
y_pred_cuda = model_cuda(x_test_cuda)
print('y_pred_cuda.device is',y_pred_cuda.device)
```

    y_pred_cuda.device is cuda:0

What if model and Tensor are not on the same device?

```python
model_cpu = torch.load(model_file)
y_pred_xx = model_cpu(x_test_cuda)
```