tutorial validation (#185)

Co-authored-by: Ben Volokh <89551265+benv123@users.noreply.github.com>

docs/source/_rst/tutorial5/tutorial.rst

@@ -21,6 +21,13 @@ First of all we import the modules needed for the tutorial. Importing
     from pina.problem import AbstractProblem
     import matplotlib.pyplot as plt
 
+
+.. parsed-literal::
+
+    /opt/sissa/apps/intelpython/2022.0.2/intelpython/latest/lib/python3.9/site-packages/scipy/__init__.py:138: UserWarning: A NumPy version >=1.16.5 and <1.23.0 is required for this version of SciPy (detected version 1.26.0)
+      warnings.warn(f"A NumPy version >={np_minversion} and <{np_maxversion} is required for this version of "
+
+
 Data Generation
 ---------------
 
@@ -52,7 +59,7 @@ taken from the authors original reference.
     x = torch.tensor(data['x'], dtype=torch.float)[0]
     y = torch.tensor(data['y'], dtype=torch.float)[0]
 
-Let’s visualize some data
+Let's visualize some data
 
 .. code:: ipython3
 
@@ -66,7 +73,7 @@ Let’s visualize some data
 
 
 
-.. image:: tutorial_files/tutorial_6_0.png
+.. image:: output_6_0.png
 
 
 We now create the neural operator class. It is a very simple class,
@@ -107,10 +114,19 @@ training using supervised learning.
 
 .. parsed-literal::
 
-    GPU available: False, used: False
+    /u/n/ndemo/.local/lib/python3.9/site-packages/torch/cuda/__init__.py:611: UserWarning: Can't initialize NVML
+      warnings.warn("Can't initialize NVML")
+    GPU available: True (cuda), used: True
     TPU available: False, using: 0 TPU cores
     IPU available: False, using: 0 IPUs
     HPU available: False, using: 0 HPUs
+    Missing logger folder: /u/n/ndemo/PINA/tutorials/tutorial5/lightning_logs
+    2023-10-17 10:41:03.316644: I tensorflow/core/util/port.cc:110] oneDNN custom operations are on. You may see slightly different numerical results due to floating-point round-off errors from different computation orders. To turn them off, set the environment variable `TF_ENABLE_ONEDNN_OPTS=0`.
+    2023-10-17 10:41:03.333768: I tensorflow/tsl/cuda/cudart_stub.cc:28] Could not find cuda drivers on your machine, GPU will not be used.
+    2023-10-17 10:41:03.383188: I tensorflow/core/platform/cpu_feature_guard.cc:182] This TensorFlow binary is optimized to use available CPU instructions in performance-critical operations.
+    To enable the following instructions: AVX2 AVX512F AVX512_VNNI FMA, in other operations, rebuild TensorFlow with the appropriate compiler flags.
+    2023-10-17 10:41:07.712785: W tensorflow/compiler/tf2tensorrt/utils/py_utils.cc:38] TF-TRT Warning: Could not find TensorRT
+    LOCAL_RANK: 0 - CUDA_VISIBLE_DEVICES: [0]
     
       | Name        | Type    | Params
     ----------------------------------------
@@ -123,21 +139,20 @@ training using supervised learning.
     0.002     Total estimated model params size (MB)
 
 
-.. parsed-literal::
-
-    Epoch 99: : 1it [00:00, 15.95it/s, v_num=85, mean_loss=0.105]
 
 .. parsed-literal::
 
+    Training: 0it [00:00, ?it/s]
+
+
+.. parsed-literal::
+
+    /u/n/ndemo/.local/lib/python3.9/site-packages/torch/_tensor.py:1386: UserWarning: The use of `x.T` on tensors of dimension other than 2 to reverse their shape is deprecated and it will throw an error in a future release. Consider `x.mT` to transpose batches of matrices or `x.permute(*torch.arange(x.ndim - 1, -1, -1))` to reverse the dimensions of a tensor. (Triggered internally at ../aten/src/ATen/native/TensorShape.cpp:3614.)
+      ret = func(*args, **kwargs)
     `Trainer.fit` stopped: `max_epochs=100` reached.
 
 
-.. parsed-literal::
-
-    Epoch 99: : 1it [00:00, 15.53it/s, v_num=85, mean_loss=0.105]
-
-
-The final loss is pretty high… We can calculate the error by importing
+The final loss is pretty high... We can calculate the error by importing
 ``LpLoss``.
 
 .. code:: ipython3
@@ -157,8 +172,8 @@ The final loss is pretty high… We can calculate the error by importing
 
 .. parsed-literal::
 
-    Final error training 56.06%
-    Final error testing 55.95%
+    Final error training 56.86%
+    Final error testing 56.82%
 
 
 Solving the problem with a Fuorier Neural Operator (FNO)
@@ -191,10 +206,11 @@ operator this approach is better suited, as we shall see.
 
 .. parsed-literal::
 
-    GPU available: False, used: False
+    GPU available: True (cuda), used: True
     TPU available: False, using: 0 TPU cores
     IPU available: False, using: 0 IPUs
     HPU available: False, using: 0 HPUs
+    LOCAL_RANK: 0 - CUDA_VISIBLE_DEVICES: [0]
     
       | Name        | Type    | Params
     ----------------------------------------
@@ -207,22 +223,19 @@ operator this approach is better suited, as we shall see.
     2.364     Total estimated model params size (MB)
 
 
+
 .. parsed-literal::
 
-    Epoch 19: : 1it [00:02,  2.65s/it, v_num=84, mean_loss=0.0294]
+    Training: 0it [00:00, ?it/s]
+
 
 .. parsed-literal::
 
     `Trainer.fit` stopped: `max_epochs=20` reached.
 
 
-.. parsed-literal::
-
-    Epoch 19: : 1it [00:02,  2.67s/it, v_num=84, mean_loss=0.0294]
-
-
 We can clearly see that with 1/3 of the total epochs the loss is lower.
-Let’s see in testing.. Notice that the number of parameters is way
+Let's see in testing.. Notice that the number of parameters is way
 higher than a ``FeedForward`` network. We suggest to use GPU or TPU for
 a speed up in training.
 
@@ -237,13 +250,13 @@ a speed up in training.
 
 .. parsed-literal::
 
-    Final error training 26.05%
-    Final error testing 25.58%
+    Final error training 26.19%
+    Final error testing 25.89%
 
 
 As we can see the loss is way lower!
 
-What’s next?
+What's next?
 ------------
 
 We have made a very simple example on how to use the ``FNO`` for