f67467e5bd
* adding problems * add tests * update doc + formatting --------- Co-authored-by: Dario Coscia <dariocos99@gmail.com>
77 lines
2.6 KiB
Python
77 lines
2.6 KiB
Python
"""Formulation of the inverse Poisson problem in a square domain."""
|
|
|
|
import os
|
|
import torch
|
|
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
|
|
- 2 * (input_.extract(["y"]) - params_["mu2"]) ** 2
|
|
)
|
|
delta_u = laplacian(output_, input_, components=["u"], d=["x", "y"])
|
|
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):
|
|
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
|
|
spatial_domain = CartesianDomain({"x": [x_min, x_max], "y": [y_min, y_max]})
|
|
unknown_parameter_domain = CartesianDomain({"mu1": [-1, 1], "mu2": [-1, 1]})
|
|
|
|
domains = {
|
|
"g1": CartesianDomain({"x": [x_min, x_max], "y": y_max}),
|
|
"g2": CartesianDomain({"x": [x_min, x_max], "y": y_min}),
|
|
"g3": CartesianDomain({"x": x_max, "y": [y_min, y_max]}),
|
|
"g4": CartesianDomain({"x": x_min, "y": [y_min, y_max]}),
|
|
"D": CartesianDomain({"x": [x_min, x_max], "y": [y_min, y_max]}),
|
|
}
|
|
|
|
conditions = {
|
|
"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),
|
|
}
|