fix old codes
This commit is contained in:
Your Name
@@ -12,7 +12,8 @@ The problem is written as: :raw-latex:`\begin{equation}
|
||||
\Delta u = \sin{(\pi x)} \sin{(\pi y)} \text{ in } D, \\
|
||||
u = 0 \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
|
||||
\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
|
||||
square.
|
||||
|
||||
@@ -56,11 +57,16 @@ be compared with the predicted one.
|
||||
return output_['u'] - value
|
||||
|
||||
conditions = {
|
||||
'gamma1': Condition(Span({'x': bounds_x, 'y': bounds_y[-1]}), nil_dirichlet),
|
||||
'gamma2': Condition(Span({'x': bounds_x, 'y': bounds_y[0]}), nil_dirichlet),
|
||||
'gamma3': Condition(Span({'x': bounds_x[-1], 'y': bounds_y}), nil_dirichlet),
|
||||
'gamma4': Condition(Span({'x': bounds_x[0], 'y': bounds_y}), nil_dirichlet),
|
||||
'D': Condition(Span({'x': bounds_x, 'y': bounds_y}), laplace_equation),
|
||||
'gamma1': Condition(
|
||||
Span({'x': bounds_x, 'y': bounds_y[-1]}), nil_dirichlet),
|
||||
'gamma2': Condition(
|
||||
Span({'x': bounds_x, 'y': bounds_y[0]}), nil_dirichlet),
|
||||
'gamma3': Condition(
|
||||
Span({'x': bounds_x[-1], 'y': bounds_y}), nil_dirichlet),
|
||||
'gamma4': Condition(
|
||||
Span({'x': bounds_x[0], 'y': bounds_y}), nil_dirichlet),
|
||||
'D': Condition(
|
||||
Span({'x': bounds_x, 'y': bounds_y}), laplace_equation),
|
||||
}
|
||||
def poisson_sol(self, x, y):
|
||||
return -(np.sin(x*np.pi)*np.sin(y*np.pi))/(2*np.pi**2)
|
||||
@@ -91,19 +97,13 @@ training phase of the PINN.
|
||||
input_variables=poisson_problem.input_variables)
|
||||
|
||||
pinn = PINN(poisson_problem, model, lr=0.003, regularizer=1e-8)
|
||||
pinn.span_pts(20, 'grid', ['D'])
|
||||
pinn.span_pts(20, 'grid', ['gamma1', 'gamma2', 'gamma3', 'gamma4'])
|
||||
pinn.span_pts(20, 'grid', locations=['gamma1', 'gamma2', 'gamma3', 'gamma4'])
|
||||
pinn.span_pts(20, 'grid', locations=['D'])
|
||||
pinn.train(5000, 100)
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
2.384537034558816e-05
|
||||
|
||||
|
||||
|
||||
The loss trend is saved in a dedicated txt file located in
|
||||
*tutorial1_files*.
|
||||
|
||||
@@ -160,8 +160,8 @@ the cell below is also in this case the final loss of PINN.
|
||||
super(myFeature, self).__init__()
|
||||
|
||||
def forward(self, x):
|
||||
return (torch.sin(x['x']*torch.pi) *
|
||||
torch.sin(x['y']*torch.pi))
|
||||
return LabelTensor(torch.sin(x.extract(['x'])*torch.pi) *
|
||||
torch.sin(x.extract(['y'])*torch.pi), 'k')
|
||||
|
||||
feat = [myFeature()]
|
||||
model_feat = FeedForward(layers=[10, 10],
|
||||
@@ -170,18 +170,13 @@ the cell below is also in this case the final loss of PINN.
|
||||
extra_features=feat)
|
||||
|
||||
pinn_feat = PINN(poisson_problem, model_feat, lr=0.003, regularizer=1e-8)
|
||||
pinn_feat.span_pts(20, 'grid', ['D'])
|
||||
pinn_feat.span_pts(20, 'grid', ['gamma1', 'gamma2', 'gamma3', 'gamma4'])
|
||||
pinn_feat.span_pts(20, 'grid', locations=['gamma1', 'gamma2', 'gamma3', 'gamma4'])
|
||||
pinn.feat_span_pts(20, 'grid', locations=['D'])
|
||||
pinn_feat.train(5000, 100)
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
7.93498870023341e-07
|
||||
|
||||
|
||||
|
||||
The losses are saved in a txt file as for the basic Poisson case.
|
||||
|
||||
@@ -208,8 +203,8 @@ represented below.
|
||||
The problem solution with learnable extra-features
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
Another way to predict the solution is to add a parametric forcing term
|
||||
of the Laplace equation as an extra-feature. The parameters added in the
|
||||
Another way to predict the solution is to add a parametric extra-feature.
|
||||
The parameters added in the
|
||||
expression of the extra-feature are learned during the training phase of
|
||||
the neural network. For example, considering two parameters, the
|
||||
parameteric extra-feature is written as:
|
||||
@@ -218,75 +213,26 @@ parameteric extra-feature is written as:
|
||||
\mathbf{k}(\mathbf{x}, \mathbf{y}) = \beta \sin{(\alpha \mathbf{x})} \sin{(\alpha \mathbf{y})}
|
||||
\end{equation}`
|
||||
|
||||
The new Poisson problem is defined in the dedicated class
|
||||
*ParametricPoisson*, where the domain is no more only spatial, but
|
||||
includes the parameters’ space. In our case, the parameters’ bounds are
|
||||
0 and 30.
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
from pina.problem import ParametricProblem
|
||||
|
||||
class ParametricPoisson(SpatialProblem, ParametricProblem):
|
||||
bounds_x = [0, 1]
|
||||
bounds_y = [0, 1]
|
||||
bounds_alpha = [0, 30]
|
||||
bounds_beta = [0, 30]
|
||||
spatial_variables = ['x', 'y']
|
||||
parameters = ['alpha', 'beta']
|
||||
output_variables = ['u']
|
||||
domain = Span({'x': bounds_x, 'y': bounds_y})
|
||||
|
||||
def laplace_equation(input_, output_):
|
||||
force_term = (torch.sin(input_['x']*torch.pi) *
|
||||
torch.sin(input_['y']*torch.pi))
|
||||
return nabla(output_['u'], input_).flatten() - force_term
|
||||
|
||||
def nil_dirichlet(input_, output_):
|
||||
value = 0.0
|
||||
return output_['u'] - value
|
||||
|
||||
conditions = {
|
||||
'gamma1': Condition(
|
||||
Span({'x': bounds_x, 'y': bounds_y[1], 'alpha': bounds_alpha, 'beta': bounds_beta}),
|
||||
nil_dirichlet),
|
||||
'gamma2': Condition(
|
||||
Span({'x': bounds_x, 'y': bounds_y[0], 'alpha': bounds_alpha, 'beta': bounds_beta}),
|
||||
nil_dirichlet),
|
||||
'gamma3': Condition(
|
||||
Span({'x': bounds_x[1], 'y': bounds_y, 'alpha': bounds_alpha, 'beta': bounds_beta}),
|
||||
nil_dirichlet),
|
||||
'gamma4': Condition(
|
||||
Span({'x': bounds_x[0], 'y': bounds_y, 'alpha': bounds_alpha, 'beta': bounds_beta}),
|
||||
nil_dirichlet),
|
||||
'D': Condition(
|
||||
Span({'x': bounds_x, 'y': bounds_y, 'alpha': bounds_alpha, 'beta': bounds_beta}),
|
||||
laplace_equation),
|
||||
}
|
||||
|
||||
def poisson_sol(self, x, y):
|
||||
return -(np.sin(x*np.pi)*np.sin(y*np.pi))/(2*np.pi**2)
|
||||
|
||||
|
||||
Here, as done for the other cases, the new parametric feature is defined
|
||||
and the neural network is re-initialized and trained, considering as two
|
||||
additional parameters :math:`\alpha` and :math:`\beta`.
|
||||
and the neural network is re-initialized and trained.
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
param_poisson_problem = ParametricPoisson()
|
||||
|
||||
class myFeature(torch.nn.Module):
|
||||
class LearnableFeature(torch.nn.Module):
|
||||
"""
|
||||
"""
|
||||
def __init__(self):
|
||||
super(myFeature, self).__init__()
|
||||
self.beta = torch.nn.Parameter(torch.Tensor([1.0]))
|
||||
self.alpha = torch.nn.Parameter(torch.Tensor([1.0]))
|
||||
|
||||
def forward(self, x):
|
||||
return (x['beta']*torch.sin(x['alpha']*x['x']*torch.pi)*
|
||||
torch.sin(x['alpha']*x['y']*torch.pi))
|
||||
return LabelTensor(
|
||||
self.beta*torch.sin(self.alpha*x.extract(['x'])*torch.pi)*
|
||||
torch.sin(self.alpha*x.extract(['y'])*torch.pi),
|
||||
'k')
|
||||
|
||||
feat = [myFeature()]
|
||||
feat = [LearnableFeature()]
|
||||
model_learn = FeedForward(layers=[10, 10],
|
||||
output_variables=param_poisson_problem.output_variables,
|
||||
input_variables=param_poisson_problem.input_variables,
|
||||
@@ -300,12 +246,6 @@ additional parameters :math:`\alpha` and :math:`\beta`.
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
3.265163986679126e-06
|
||||
|
||||
|
||||
|
||||
The losses are saved as for the other two cases trained above.
|
||||
|
||||
.. code:: ipython3
|
||||
@@ -316,7 +256,7 @@ The losses are saved as for the other two cases trained above.
|
||||
pinn_learn.save_state('tutorial1_files/pina.poisson_learn_feat')
|
||||
|
||||
Here the plots for the prediction error (below on the right) shows that
|
||||
the prediction coming from the **parametric PINN** is more accurate than
|
||||
the prediction coming from the latter version is more accurate than
|
||||
the one of the basic version of PINN.
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
Reference in New Issue
Block a user