Update tutorials 1 through 12 to current version 0.2
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Nicola Demo
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tutorials/tutorial5/tutorial.ipynb
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tutorials/tutorial5/tutorial.ipynb
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tutorials/tutorial5/tutorial.py
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tutorials/tutorial5/tutorial.py
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@@ -9,7 +9,7 @@
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# In this tutorial we are going to solve the Darcy flow problem in two dimensions, presented in [*Fourier Neural Operator for
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# Parametric Partial Differential Equation*](https://openreview.net/pdf?id=c8P9NQVtmnO). First of all we import the modules needed for the tutorial. Importing `scipy` is needed for input-output operations.
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# In[ ]:
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# In[1]:
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## routine needed to run the notebook on Google Colab
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@@ -30,7 +30,7 @@ from scipy import io
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import torch
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from pina.model import FNO, FeedForward # let's import some models
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from pina import Condition, LabelTensor
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from pina.solvers import SupervisedSolver
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from pina.solver import SupervisedSolver
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from pina.trainer import Trainer
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from pina.problem import AbstractProblem
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import matplotlib.pyplot as plt
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@@ -74,33 +74,23 @@ y = torch.tensor(data['y'], dtype=torch.float)[0]
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plt.subplot(1, 2, 1)
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plt.title('permeability')
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plt.imshow(k_train.squeeze(-1)[0])
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plt.imshow(k_train.squeeze(-1).tensor[0])
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plt.subplot(1, 2, 2)
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plt.title('field solution')
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plt.imshow(u_train.squeeze(-1)[0])
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plt.show()
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# We now create the neural operator class. It is a very simple class, inheriting from `AbstractProblem`.
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# In[4]:
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u_train.labels[3]['dof']
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# We now create the neural operator class. It is a very simple class, inheriting from `AbstractProblem`.
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# In[ ]:
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class NeuralOperatorSolver(AbstractProblem):
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input_variables = k_train.labels[3]['dof']
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output_variables = u_train.labels[3]['dof']
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domains = {
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'pts': k_train
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}
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conditions = {'data' : Condition(domain='pts', #not among allowed pairs!!!
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input_variables = k_train.full_labels[3]['dof']
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output_variables = u_train.full_labels[3]['dof']
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conditions = {'data' : Condition(input_points=k_train,
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output_points=u_train)}
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# make problem
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problem = NeuralOperatorSolver()
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@@ -109,7 +99,7 @@ problem = NeuralOperatorSolver()
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#
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# We will first solve the problem using a Feedforward neural network. We will use the `SupervisedSolver` for solving the problem, since we are training using supervised learning.
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# In[6]:
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# In[5]:
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# make model
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@@ -127,7 +117,7 @@ trainer.train()
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# The final loss is pretty high... We can calculate the error by importing `LpLoss`.
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# In[7]:
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# In[6]:
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from pina.loss import LpLoss
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@@ -135,7 +125,7 @@ from pina.loss import LpLoss
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# make the metric
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metric_err = LpLoss(relative=True)
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model = solver.models[0]
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model = solver.model
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err = float(metric_err(u_train.squeeze(-1), model(k_train).squeeze(-1)).mean())*100
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print(f'Final error training {err:.2f}%')
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@@ -147,7 +137,7 @@ print(f'Final error testing {err:.2f}%')
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#
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# We will now move to solve the problem using a FNO. Since we are learning operator this approach is better suited, as we shall see.
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# In[8]:
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# In[7]:
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# make model
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@@ -171,10 +161,10 @@ trainer.train()
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# We can clearly see that the final loss is lower. 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, when many data samples are used.
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# In[9]:
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# In[8]:
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model = solver.models[0]
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model = solver.model
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err = float(metric_err(u_train.squeeze(-1), model(k_train).squeeze(-1)).mean())*100
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print(f'Final error training {err:.2f}%')
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