Create Problem

import torch
from pina import Condition, LabelTensor
from pina.problem import BaseProblem

input_data = LabelTensor(torch.randn(100, 1), "x")
target_data = LabelTensor(torch.randn(100, 1), "y")

class MySupervisedProblem(BaseProblem):
    input_variables = ["x"]
    output_variables = ["y"]
    conditions = {
        "data": Condition(input=input_data, target=target_data),
    }

problem = MySupervisedProblem()

from pina.problem import SpatialProblem
from pina.domain import CartesianDomain
from pina import Condition
from pina.equation import Equation
from pina.equation.zoo import FixedValue

class MySpatialProblem(SpatialProblem):
    output_variables = ["u"]
    spatial_domain = CartesianDomain({"x": [0, 1], "y": [0, 1]})

    domains = {
        "D": spatial_domain,
        "boundary": spatial_domain.partial(),
    }

    conditions = {
        "boundary": Condition(domain="boundary", equation=FixedValue(0.0)),
        "D": Condition(domain="D", equation=Equation(my_pde)),
    }

    def solution(self, pts):
        ...

from pina.problem import SpatialProblem, TimeDependentProblem
from pina.domain import CartesianDomain
from pina import Condition
from pina.equation import Equation
from pina.equation.zoo import FixedValue

class MySpaceTimeProblem(TimeDependentProblem, SpatialProblem):
    output_variables = ["u"]
    spatial_domain = CartesianDomain({"x": [-1, 1]})
    temporal_domain = CartesianDomain({"t": [0, 1]})

    domains = {
        "D": spatial_domain.update(temporal_domain),
        "ic": spatial_domain.update(CartesianDomain({"t": 0})),
        "boundary": spatial_domain.partial().update(temporal_domain),
    }

    conditions = {
        "boundary": Condition(domain="boundary", equation=FixedValue(0.0)),
        "ic": Condition(domain="ic", equation=Equation(initial_cond)),
        "D": Condition(domain="D", equation=Equation(my_pde)),
    }

    def solution(self, pts):
        ...

from pina.problem import SpatialProblem, InverseProblem
from pina.domain import CartesianDomain
from pina import Condition
from pina.equation import Equation
from pina.equation.zoo import FixedValue

class MyInverseProblem(SpatialProblem, InverseProblem):
    output_variables = ["u"]
    spatial_domain = CartesianDomain({"x": [-2, 2], "y": [-2, 2]})
    unknown_parameter_domain = CartesianDomain({"mu1": [-1, 1], "mu2": [-1, 1]})

    domains = {
        "D": spatial_domain,
        "boundary": spatial_domain.partial(),
    }

    conditions = {
        "boundary": Condition(domain="boundary", equation=FixedValue(0.0)),
        "D": Condition(domain="D", equation=Equation(laplace_equation)),
        "data": Condition(input=input_data, target=target_data),
    }

from pina.problem import SpatialProblem, ParametricProblem
from pina.domain import CartesianDomain

class MyParametricProblem(SpatialProblem, ParametricProblem):
    output_variables = ["u"]
    spatial_domain = CartesianDomain({"x": [0, 1]})
    parameter_domain = CartesianDomain({"mu": [0.5, 2.0]})

    domains = {
        "D": spatial_domain.update(parameter_domain),
        ...
    }
    ...