SpatialProblem

Module for the SpatialProblem class

class SpatialProblem

Bases: 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))}

abstract spatial_domain()

The spatial domain of the problem.

property spatial_variables

The spatial input variables of the problem.