Source code for pina.problem.spatial_problem
"""Module for the SpatialProblem class"""
from abc import abstractmethod
from .abstract_problem import AbstractProblem
[docs]
class SpatialProblem(AbstractProblem):
"""
The class for the definition of spatial problems, i.e., for problems
with spatial input variables.
Here's an example of a spatial 1-dimensional ODE problem.
:Example:
>>> from pina.problem import SpatialProblem
>>> from pina.operators import grad
>>> from pina.equation import Equation, FixedValue
>>> from pina import Condition
>>> from pina.geometry import CartesianDomain
>>> import torch
>>>
>>>
>>> class SpatialODE(SpatialProblem:
>>>
>>> output_variables = ['u']
>>> spatial_domain = CartesianDomain({'x': [0, 1]})
>>>
>>> def ode_equation(input_, output_):
>>> u_x = grad(output_, input_, components=['u'], d=['x'])
>>> u = output_.extract(['u'])
>>> return u_x - u
>>>
>>> conditions = {
>>> 'x0': Condition(CartesianDomain({'x': 0, 'alpha':[1, 10]}), FixedValue(1.)),
>>> 'D': Condition(CartesianDomain({'x': [0, 1], 'alpha':[1, 10]}), Equation(ode_equation))}
"""
[docs]
@abstractmethod
def spatial_domain(self):
"""
The spatial domain of the problem.
"""
pass
@property
def spatial_variables(self):
"""
The spatial input variables of the problem.
"""
return self.spatial_domain.variables