folivo/PINA
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Adding new problems to problem.zoo (#484)

Browse Source 
* adding problems
* add tests
* update doc + formatting

---------

Co-authored-by: Dario Coscia <dariocos99@gmail.com>
This commit is contained in:
Giovanni Canali
2025-03-12 10:42:16 +01:00
committed by Nicola Demo
parent 2ae4a94e49
commit f67467e5bd
21 changed files with 570 additions and 168 deletions
Download Patch File Download Diff File Expand all files Collapse all files

62
pina/problem/zoo/inverse_poisson_2d_square.py
View File

@@ -1,17 +1,23 @@
"""Definition of the inverse Poisson problem on a square domain."""
"""Formulation of the inverse Poisson problem in a square domain."""
import os
import torch
from pina import Condition, LabelTensor
from pina.problem import SpatialProblem, InverseProblem
from pina.operator import laplacian
from pina.domain import CartesianDomain
from pina.equation.equation import Equation
from pina.equation.equation_factory import FixedValue
from ... import Condition
from ...operator import laplacian
from ...domain import CartesianDomain
from ...equation import Equation, FixedValue
from ...problem import SpatialProblem, InverseProblem
def laplace_equation(input_, output_, params_):
"""
Implementation of the laplace equation.
:param LabelTensor input_: Input data of the problem.
:param LabelTensor output_: Output data of the problem.
:param dict params_: Parameters of the problem.
:return: The residual of the laplace equation.
:rtype: LabelTensor
"""
force_term = torch.exp(
-2 * (input_.extract(["x"]) - params_["mu1"]) ** 2
@@ -21,17 +27,34 @@ def laplace_equation(input_, output_, params_):
return delta_u - force_term
# Absolute path to the data directory
data_dir = os.path.abspath(
os.path.join(
os.path.dirname(__file__), "../../../tutorials/tutorial7/data/"
)
)
# Load input data
input_data = torch.load(
f=os.path.join(data_dir, "pts_0.5_0.5"), weights_only=False
).extract(["x", "y"])
# Load output data
output_data = torch.load(
f=os.path.join(data_dir, "pinn_solution_0.5_0.5"), weights_only=False
)
class InversePoisson2DSquareProblem(SpatialProblem, InverseProblem):
"""
Implementation of the inverse 2-dimensional Poisson problem
on a square domain, with parameter domain [-1, 1] x [-1, 1].
r"""
Implementation of the inverse 2-dimensional Poisson problem in the square
domain :math:`[0, 1] \times [0, 1]`,
with unknown parameter domain :math:`[-1, 1] \times [-1, 1]`.
"""
output_variables = ["u"]
x_min, x_max = -2, 2
y_min, y_max = -2, 2
data_input = LabelTensor(torch.rand(10, 2), ["x", "y"])
data_output = LabelTensor(torch.rand(10, 1), ["u"])
spatial_domain = CartesianDomain({"x": [x_min, x_max], "y": [y_min, y_max]})
unknown_parameter_domain = CartesianDomain({"mu1": [-1, 1], "mu2": [-1, 1]})
@@ -44,13 +67,10 @@ class InversePoisson2DSquareProblem(SpatialProblem, InverseProblem):
}
conditions = {
"nil_g1": Condition(domain="g1", equation=FixedValue(0.0)),
"nil_g2": Condition(domain="g2", equation=FixedValue(0.0)),
"nil_g3": Condition(domain="g3", equation=FixedValue(0.0)),
"nil_g4": Condition(domain="g4", equation=FixedValue(0.0)),
"laplace_D": Condition(domain="D", equation=Equation(laplace_equation)),
"data": Condition(
input=data_input.extract(["x", "y"]),
target=data_output,
),
"g1": Condition(domain="g1", equation=FixedValue(0.0)),
"g2": Condition(domain="g2", equation=FixedValue(0.0)),
"g3": Condition(domain="g3", equation=FixedValue(0.0)),
"g4": Condition(domain="g4", equation=FixedValue(0.0)),
"D": Condition(domain="D", equation=Equation(laplace_equation)),
"data": Condition(input=input_data, target=output_data),
}