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fix tutorials latex and links (#261)

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Dario Coscia
2024-03-10 10:23:35 +01:00
committed by GitHub
parent 4f911f88ca
commit ada9643c11
15 changed files with 84 additions and 284 deletions
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85
docs/source/_rst/tutorials/tutorial2/tutorial.rst
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@@ -31,12 +31,17 @@ The problem definition
----------------------
The two-dimensional Poisson problem is mathematically written as:
:raw-latex:`\begin{equation}
\begin{cases}
\Delta u = \sin{(\pi x)} \sin{(\pi y)} \text{ in } D, \\
u = 0 \text{ on } \Gamma_1 \cup \Gamma_2 \cup \Gamma_3 \cup \Gamma_4,
\end{cases}
\end{equation}` where :math:`D` is a square domain :math:`[0,1]^2`, and
.. math::
\begin{equation}
\begin{cases}
\Delta u = \sin{(\pi x)} \sin{(\pi y)} \text{ in } D, \\
u = 0 \text{ on } \Gamma_1 \cup \Gamma_2 \cup \Gamma_3 \cup \Gamma_4,
\end{cases}
\end{equation}
where :math:`D` is a square domain :math:`[0,1]^2`, and
:math:`\Gamma_i`, with :math:`i=1,...,4`, are the boundaries of the
square.
@@ -112,19 +117,6 @@ These parameters can be modified as desired. We use the
# train
trainer.train()
.. parsed-literal::
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs
.. parsed-literal::
Epoch 999: : 1it [00:00, 158.53it/s, v_num=3, gamma1_loss=5.29e-5, gamma2_loss=4.09e-5, gamma3_loss=4.73e-5, gamma4_loss=4.18e-5, D_loss=0.00134, mean_loss=0.000304]
.. parsed-literal::
`Trainer.fit` stopped: `max_epochs=1000` reached.
@@ -158,9 +150,11 @@ is now defined, with an additional input variable, named extra-feature,
which coincides with the forcing term in the Laplace equation. The set
of input variables to the neural network is:
:raw-latex:`\begin{equation}
[x, y, k(x, y)], \text{ with } k(x, y)=\sin{(\pi x)}\sin{(\pi y)},
\end{equation}`
.. math::
\begin{equation}
[x, y, k(x, y)], \text{ with } k(x, y)=\sin{(\pi x)}\sin{(\pi y)},
\end{equation}
where :math:`x` and :math:`y` are the spatial coordinates and
:math:`k(x, y)` is the added feature.
@@ -203,19 +197,6 @@ new extra feature.
# train
trainer_feat.train()
.. parsed-literal::
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs
.. parsed-literal::
Epoch 999: : 1it [00:00, 111.88it/s, v_num=4, gamma1_loss=2.54e-7, gamma2_loss=2.17e-7, gamma3_loss=1.94e-7, gamma4_loss=2.69e-7, D_loss=9.2e-6, mean_loss=2.03e-6]
.. parsed-literal::
`Trainer.fit` stopped: `max_epochs=1000` reached.
@@ -249,9 +230,11 @@ Another way to exploit the extra features is the addition of learnable
parameter inside them. In this way, the added parameters are learned
during the training phase of the neural network. In this case, we use:
:raw-latex:`\begin{equation}
k(x, \mathbf{y}) = \beta \sin{(\alpha x)} \sin{(\alpha y)},
\end{equation}`
.. math::
\begin{equation}
k(x, \mathbf{y}) = \beta \sin{(\alpha x)} \sin{(\alpha y)},
\end{equation}
where :math:`\alpha` and :math:`\beta` are the abovementioned
parameters. Their implementation is quite trivial: by using the class
@@ -289,19 +272,6 @@ need, and they are managed by ``autograd`` module!
# train
trainer_learn.train()
.. parsed-literal::
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs
.. parsed-literal::
Epoch 999: : 1it [00:00, 119.29it/s, v_num=5, gamma1_loss=3.26e-8, gamma2_loss=7.84e-8, gamma3_loss=1.13e-7, gamma4_loss=3.02e-8, D_loss=2.66e-6, mean_loss=5.82e-7]
.. parsed-literal::
`Trainer.fit` stopped: `max_epochs=1000` reached.
@@ -338,19 +308,6 @@ removing all the hidden layers in the ``FeedForward``, keeping only the
# train
trainer_learn.train()
.. parsed-literal::
GPU available: False, used: False
TPU available: False, using: 0 TPU cores
IPU available: False, using: 0 IPUs
HPU available: False, using: 0 HPUs
.. parsed-literal::
Epoch 0: : 0it [00:00, ?it/s]Epoch 999: : 1it [00:00, 131.20it/s, v_num=6, gamma1_loss=2.55e-16, gamma2_loss=4.76e-17, gamma3_loss=2.55e-16, gamma4_loss=4.76e-17, D_loss=1.74e-13, mean_loss=3.5e-14]
.. parsed-literal::
`Trainer.fit` stopped: `max_epochs=1000` reached.