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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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docs/source/_rst/tutorials/tutorial3/tutorial.rst
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@@ -25,13 +25,14 @@ The problem definition
The problem is written in the following form:
:raw-latex:`\begin{equation}
\begin{cases}
\Delta u(x,y,t) = \frac{\partial^2}{\partial t^2} u(x,y,t) \quad \text{in } D, \\\\
u(x, y, t=0) = \sin(\pi x)\sin(\pi y), \\\\
u(x, y, t) = 0 \quad \text{on } \Gamma_1 \cup \Gamma_2 \cup \Gamma_3 \cup \Gamma_4,
\end{cases}
\end{equation}`
.. math::
\begin{equation}
\begin{cases}
\Delta u(x,y,t) = \frac{\partial^2}{\partial t^2} u(x,y,t) \quad \text{in } D, \\\\
u(x, y, t=0) = \sin(\pi x)\sin(\pi y), \\\\
u(x, y, t) = 0 \quad \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
@@ -136,20 +137,6 @@ approximately 3 minutes.
trainer = Trainer(pinn, max_epochs=1000, accelerator='cpu', enable_model_summary=False) # we train on CPU and avoid model summary at beginning of training (optional)
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
Missing logger folder: /Users/dariocoscia/Desktop/PINA/tutorials/tutorial3/lightning_logs
.. parsed-literal::
Epoch 999: : 1it [00:00, 84.47it/s, v_num=0, gamma1_loss=0.000, gamma2_loss=0.000, gamma3_loss=0.000, gamma4_loss=0.000, t0_loss=0.0419, D_loss=0.0307, mean_loss=0.0121]
.. parsed-literal::
`Trainer.fit` stopped: `max_epochs=1000` reached.
@@ -214,7 +201,7 @@ progress the solution get worse…. Can we do better?
A valid option is to impose the initial condition as hard constraint as
well. Specifically, our solution is written as:
.. math:: u_{\rm{pinn}} = xy(1-x)(1-y)\cdot NN(x, y, t)\cdot t + \cos(\sqrt{2}\pi t)sin(\pi x)\sin(\pi y),
.. math:: u_{\rm{pinn}} = xy(1-x)(1-y)\cdot NN(x, y, t)\cdot t + \cos(\sqrt{2}\pi t)\sin(\pi x)\sin(\pi y),
Let us build the network first
@@ -252,18 +239,6 @@ Now let’s train with the same configuration as thre previous test
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 0: : 0it [00:00, ?it/s]Epoch 999: : 1it [00:00, 52.10it/s, v_num=1, gamma1_loss=1.97e-15, gamma2_loss=0.000, gamma3_loss=2.14e-15, gamma4_loss=0.000, t0_loss=0.000, D_loss=1.25e-7, mean_loss=2.09e-8]
.. parsed-literal::
`Trainer.fit` stopped: `max_epochs=1000` reached.