ParametricProblem

Module for the ParametricProblem class

class ParametricProblem

Bases: AbstractProblem

The class for the definition of parametric problems, i.e., problems with parameters among the input variables.

Here’s an example of a spatial parametric ODE problem, i.e., a spatial ODE problem with an additional parameter alpha as coefficient of the derivative term.

Example:

>>> from pina.problem import SpatialProblem, ParametricProblem
>>> from pina.operators import grad
>>> from pina.equations import Equation, FixedValue
>>> from pina import Condition
>>> from pina.geometry import CartesianDomain
>>> import torch
>>>
>>>
>>> class ParametricODE(SpatialProblem, ParametricProblem):
>>>
>>>     output_variables = ['u']
>>>     spatial_domain = CartesianDomain({'x': [0, 1]})
>>>     parameter_domain = CartesianDomain({'alpha': [1, 10]})
>>>
>>>     def ode_equation(input_, output_):
>>>         u_x = grad(output_, input_, components=['u'], d=['x'])
>>>         u = output_.extract(['u'])
>>>         alpha = input_.extract(['alpha'])
>>>         return alpha * 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 parameter_domain()

The parameters’ domain of the problem.

property parameters

The parameters’ variables of the problem.