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Update Condition notation & domains import in tutorials

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This commit is contained in:
MatteoB30
2025-02-07 15:08:42 +01:00
committed by Nicola Demo
parent 195224794f
commit c6f1aafdec
18 changed files with 224 additions and 256 deletions
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35
tutorials/tutorial12/tutorial.py vendored
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@@ -26,7 +26,7 @@
#
# In the class that models this problem we will see in action the `Equation` class and one of its inherited classes, the `FixedValue` class.
# In[7]:
# In[1]:
## routine needed to run the notebook on Google Colab
@@ -40,14 +40,15 @@ if IN_COLAB:
#useful imports
from pina.problem import SpatialProblem, TimeDependentProblem
from pina.equation import Equation, FixedValue, FixedGradient, FixedFlux
from pina.equation import Equation, FixedValue
from pina.domain import CartesianDomain
import torch
from pina.operators import grad, laplacian
from pina import Condition
# In[6]:
# In[2]:
class Burgers1D(TimeDependentProblem, SpatialProblem):
@@ -74,17 +75,17 @@ class Burgers1D(TimeDependentProblem, SpatialProblem):
# problem condition statement
conditions = {
'gamma1': Condition(location=CartesianDomain({'x': -1, 't': [0, 1]}), equation=FixedValue(0.)),
'gamma2': Condition(location=CartesianDomain({'x': 1, 't': [0, 1]}), equation=FixedValue(0.)),
't0': Condition(location=CartesianDomain({'x': [-1, 1], 't': 0}), equation=Equation(initial_condition)),
'D': Condition(location=CartesianDomain({'x': [-1, 1], 't': [0, 1]}), equation=Equation(burger_equation)),
'bound_cond1': Condition(domain=CartesianDomain({'x': -1, 't': [0, 1]}), equation=FixedValue(0.)),
'bound_cond2': Condition(domain=CartesianDomain({'x': 1, 't': [0, 1]}), equation=FixedValue(0.)),
'time_cond': Condition(domain=CartesianDomain({'x': [-1, 1], 't': 0}), equation=Equation(initial_condition)),
'phys_cond': Condition(domain=CartesianDomain({'x': [-1, 1], 't': [0, 1]}), equation=Equation(burger_equation)),
}
#
# The `Equation` class takes as input a function (in this case it happens twice, with `initial_condition` and `burger_equation`) which computes a residual of an equation, such as a PDE. In a problem class such as the one above, the `Equation` class with such a given input is passed as a parameter in the specified `Condition`.
#
# The `FixedValue` class takes as input a value of same dimensions of the output functions; this class can be used to enforced a fixed value for a specific condition, e.g. Dirichlet boundary conditions, as it happens for instance in our example.
# The `FixedValue` class takes as input a value of same dimensions of the output functions; this class can be used to enforce a fixed value for a specific condition, e.g. Dirichlet boundary conditions, as it happens for instance in our example.
#
# Once the equations are set as above in the problem conditions, the PINN solver will aim to minimize the residuals described in each equation in the training phase.
@@ -98,7 +99,7 @@ class Burgers1D(TimeDependentProblem, SpatialProblem):
# `Equation` classes can be also inherited to define a new class. As example, we can see how to rewrite the above problem introducing a new class `Burgers1D`; during the class call, we can pass the viscosity parameter $\nu$:
# In[13]:
# In[3]:
class Burgers1DEquation(Equation):
@@ -113,7 +114,9 @@ class Burgers1DEquation(Equation):
self.nu = nu
def equation(input_, output_):
return grad(output_, input_, d='t') + output_*grad(output_, input_, d='x') - self.nu*laplacian(output_, input_, d='x')
return grad(output_, input_, d='t') +\
output_*grad(output_, input_, d='x') -\
self.nu*laplacian(output_, input_, d='x')
super().__init__(equation)
@@ -121,7 +124,7 @@ class Burgers1DEquation(Equation):
# Now we can just pass the above class as input for the last condition, setting $\nu= \frac{0.01}{\pi}$:
# In[14]:
# In[4]:
class Burgers1D(TimeDependentProblem, SpatialProblem):
@@ -138,16 +141,16 @@ class Burgers1D(TimeDependentProblem, SpatialProblem):
# problem condition statement
conditions = {
'gamma1': Condition(location=CartesianDomain({'x': -1, 't': [0, 1]}), equation=FixedValue(0.)),
'gamma2': Condition(location=CartesianDomain({'x': 1, 't': [0, 1]}), equation=FixedValue(0.)),
't0': Condition(location=CartesianDomain({'x': [-1, 1], 't': 0}), equation=Equation(initial_condition)),
'D': Condition(location=CartesianDomain({'x': [-1, 1], 't': [0, 1]}), equation=Burgers1DEquation(0.01/torch.pi)),
'bound_cond1': Condition(domain=CartesianDomain({'x': -1, 't': [0, 1]}), equation=FixedValue(0.)),
'bound_cond2': Condition(domain=CartesianDomain({'x': 1, 't': [0, 1]}), equation=FixedValue(0.)),
'time_cond': Condition(domain=CartesianDomain({'x': [-1, 1], 't': 0}), equation=Equation(initial_condition)),
'phys_cond': Condition(domain=CartesianDomain({'x': [-1, 1], 't': [0, 1]}), equation=Burgers1DEquation(0.01/torch.pi)),
}
# # What's next?
# Congratulations on completing the `Equation` class tutorial of **PINA**! As we have seen, you can build new classes that inherits `Equation` to store more complex equations, as the Burgers 1D equation, only requiring to pass the characteristic coefficients of the problem.
# Congratulations on completing the `Equation` class tutorial of **PINA**! As we have seen, you can build new classes that inherit `Equation` to store more complex equations, as the Burgers 1D equation, only requiring to pass the characteristic coefficients of the problem.
# From now on, you can:
# - define additional complex equation classes (e.g. `SchrodingerEquation`, `NavierStokeEquation`..)
# - define more `FixedOperator` (e.g. `FixedCurl`)