.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "beginner/examples_nn/polynomial_nn.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_beginner_examples_nn_polynomial_nn.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_beginner_examples_nn_polynomial_nn.py:


PyTorch: nn
-----------

A third order polynomial, trained to predict :math:`y=\sin(x)` from :math:`-\pi`
to :math:`pi` by minimizing squared Euclidean distance.

This implementation uses the nn package from PyTorch to build the network.
PyTorch autograd makes it easy to define computational graphs and take gradients,
but raw autograd can be a bit too low-level for defining complex neural networks;
this is where the nn package can help. The nn package defines a set of Modules,
which you can think of as a neural network layer that produces output from
input and may have some trainable weights.

.. GENERATED FROM PYTHON SOURCE LINES 16-85




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    99 240.86277770996094
    199 167.79660034179688
    299 117.86258697509766
    399 83.69758605957031
    499 60.295040130615234
    599 44.246192932128906
    699 33.227760314941406
    799 25.654376983642578
    899 20.443077087402344
    999 16.853191375732422
    1099 14.37750244140625
    1199 12.668405532836914
    1299 11.487274169921875
    1399 10.670136451721191
    1499 10.104262351989746
    1599 9.71200942993164
    1699 9.439839363098145
    1799 9.25082015991211
    1899 9.119425773620605
    1999 9.028006553649902
    Result: y = 0.013691586442291737 + 0.8503276705741882 x + -0.002362025436013937 x^2 + -0.09241817146539688 x^3






|

.. code-block:: default

    import torch
    import math


    # Create Tensors to hold input and outputs.
    x = torch.linspace(-math.pi, math.pi, 2000)
    y = torch.sin(x)

    # For this example, the output y is a linear function of (x, x^2, x^3), so
    # we can consider it as a linear layer neural network. Let's prepare the
    # tensor (x, x^2, x^3).
    p = torch.tensor([1, 2, 3])
    xx = x.unsqueeze(-1).pow(p)

    # In the above code, x.unsqueeze(-1) has shape (2000, 1), and p has shape
    # (3,), for this case, broadcasting semantics will apply to obtain a tensor
    # of shape (2000, 3) 

    # Use the nn package to define our model as a sequence of layers. nn.Sequential
    # is a Module which contains other Modules, and applies them in sequence to
    # produce its output. The Linear Module computes output from input using a
    # linear function, and holds internal Tensors for its weight and bias.
    # The Flatten layer flatens the output of the linear layer to a 1D tensor,
    # to match the shape of `y`.
    model = torch.nn.Sequential(
        torch.nn.Linear(3, 1),
        torch.nn.Flatten(0, 1)
    )

    # The nn package also contains definitions of popular loss functions; in this
    # case we will use Mean Squared Error (MSE) as our loss function.
    loss_fn = torch.nn.MSELoss(reduction='sum')

    learning_rate = 1e-6
    for t in range(2000):

        # Forward pass: compute predicted y by passing x to the model. Module objects
        # override the __call__ operator so you can call them like functions. When
        # doing so you pass a Tensor of input data to the Module and it produces
        # a Tensor of output data.
        y_pred = model(xx)

        # Compute and print loss. We pass Tensors containing the predicted and true
        # values of y, and the loss function returns a Tensor containing the
        # loss.
        loss = loss_fn(y_pred, y)
        if t % 100 == 99:
            print(t, loss.item())

        # Zero the gradients before running the backward pass.
        model.zero_grad()

        # Backward pass: compute gradient of the loss with respect to all the learnable
        # parameters of the model. Internally, the parameters of each Module are stored
        # in Tensors with requires_grad=True, so this call will compute gradients for
        # all learnable parameters in the model.
        loss.backward()

        # Update the weights using gradient descent. Each parameter is a Tensor, so
        # we can access its gradients like we did before.
        with torch.no_grad():
            for param in model.parameters():
                param -= learning_rate * param.grad

    # You can access the first layer of `model` like accessing the first item of a list
    linear_layer = model[0]

    # For linear layer, its parameters are stored as `weight` and `bias`.
    print(f'Result: y = {linear_layer.bias.item()} + {linear_layer.weight[:, 0].item()} x + {linear_layer.weight[:, 1].item()} x^2 + {linear_layer.weight[:, 2].item()} x^3')


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  0.819 seconds)


.. _sphx_glr_download_beginner_examples_nn_polynomial_nn.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example


    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: polynomial_nn.py <polynomial_nn.py>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: polynomial_nn.ipynb <polynomial_nn.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_