a0cbf1c44a
* Reimplement conditions * Refactor datasets and implement LabelBatch --------- Co-authored-by: Dario Coscia <dariocos99@gmail.com>
57 lines
2.1 KiB
Python
57 lines
2.1 KiB
Python
"""Definition of the inverse Poisson problem on a square domain."""
|
|
|
|
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
|
|
|
|
|
|
def laplace_equation(input_, output_, params_):
|
|
"""
|
|
Implementation of the laplace equation.
|
|
"""
|
|
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
|
|
|
|
|
|
class InversePoisson2DSquareProblem(SpatialProblem, InverseProblem):
|
|
"""
|
|
Implementation of the inverse 2-dimensional Poisson problem
|
|
on a square domain, with parameter domain [-1, 1] x [-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]})
|
|
|
|
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 = {
|
|
"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,
|
|
),
|
|
}
|