Update tutorials (#463)

---------

Co-authored-by: Dario Coscia <93731561+dario-coscia@users.noreply.github.com>

tutorials/tutorial9/tutorial.py

@@ -28,17 +28,20 @@ if IN_COLAB:
 
 import torch
 import matplotlib.pyplot as plt
-plt.style.use('tableau-colorblind10')
-from pina import Condition, Plotter
+import warnings
+
+from pina import Condition
 from pina.problem import SpatialProblem
-from pina.operators import laplacian
+from pina.operator import laplacian
 from pina.model import FeedForward
-from pina.model.layers import PeriodicBoundaryEmbedding  # The PBC module
-from pina.solvers import PINN
+from pina.model.block import PeriodicBoundaryEmbedding  # The PBC module
+from pina.solver import PINN
 from pina.trainer import Trainer
 from pina.domain import CartesianDomain
 from pina.equation import Equation
 
+warnings.filterwarnings('ignore')
+
 
 # ## The problem definition
 # 
@@ -63,7 +66,7 @@ from pina.equation import Equation
 # and $f(x)=-6\pi^2\sin(3\pi x)\cos(\pi x)$ which give a solution that can be
 # computed analytically $u(x) = \sin(\pi x)\cos(3\pi x)$.
 
-# In[ ]:
+# In[2]:
 
 
 class Helmholtz(SpatialProblem):
@@ -139,23 +142,52 @@ model = torch.nn.Sequential(PeriodicBoundaryEmbedding(input_dimension=1,
 # for all dimensions using a dictionary, e.g. `periods={'x':2, 'y':3, ...}`
 # would indicate a periodicity of $2$ in $x$, $3$ in $y$, and so on...
 # 
-# We will now solve the problem as usually with the `PINN` and `Trainer` class.
+# We will now solve the problem as usually with the `PINN` and `Trainer` class, then we will look at the losses using the `MetricTracker` callback from `pina.callback`.
 
-# In[ ]:
+# In[4]:
 
 
-pinn = PINN(problem=problem, model=model)
-trainer = Trainer(pinn, max_epochs=5000, accelerator='cpu', enable_model_summary=False) # we train on CPU and avoid model summary at beginning of training (optional)
+from pina.callback import MetricTracker
+from pina.optim import TorchOptimizer
+
+pinn = PINN(problem=problem, model=model, optimizer=TorchOptimizer(torch.optim.Adam, lr=0.001))
+trainer = Trainer(pinn, max_epochs=5000, accelerator='cpu', enable_model_summary=False, # we train on CPU and avoid model summary at beginning of training (optional)
+                  logger=True,
+                  callbacks=[MetricTracker()],
+                  train_size=1.0,
+                  val_size=0.0,
+                  test_size=0.0)
 trainer.train()
 
 
+# In[5]:
+
+
+#plot loss
+trainer_metrics = trainer.callbacks[0].metrics
+print(trainer.callbacks[0].metrics)
+loss = trainer_metrics['train_loss']
+epochs = range(len(loss))
+plt.plot(epochs, loss.cpu())
+# plotting
+plt.xlabel('epoch')
+plt.ylabel('loss')
+plt.yscale('log') 
+
+
 # We are going to plot the solution now!
 
 # In[6]:
 
 
-pl = Plotter()
-pl.plot(pinn)
+pts = pinn.problem.spatial_domain.sample(256, 'grid', variables='x')
+predicted_output = pinn.forward(pts).extract('u').as_subclass(torch.Tensor).cpu().detach()
+true_output = pinn.problem.truth_solution(pts).cpu().detach()
+pts = pts.cpu()
+fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(8, 8))
+ax.plot(pts.extract(['x']), predicted_output, label='Neural Network solution')
+ax.plot(pts.extract(['x']), true_output, label='True solution')
+plt.legend()
 
 
 # Great, they overlap perfectly! This seems a good result, considering the simple neural network used to some this (complex) problem. We will now test the neural network on the domain $[-4, 4]$ without retraining. In principle the periodicity should be present since the $v$ function ensures the periodicity in $(-\infty, \infty)$.
@@ -201,5 +233,3 @@ with torch.no_grad():
 # 3. Exploit extrafeature training ?
 # 
 # 4. Many more...
-
-#