83 lines
2.9 KiB
Python
83 lines
2.9 KiB
Python
"""Module for the ParametricProblem class"""
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import torch
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from abc import abstractmethod
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from .abstract_problem import AbstractProblem
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class InverseProblem(AbstractProblem):
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"""
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The class for the definition of inverse problems, i.e., problems
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with unknown parameters that have to be learned during the training process
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from given data.
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Here's an example of a spatial inverse ODE problem, i.e., a spatial
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ODE problem with an unknown parameter `alpha` as coefficient of the
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derivative term.
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:Example:
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>>> from pina.problem import SpatialProblem, InverseProblem
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>>> from pina.operator import grad
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>>> from pina.equation import ParametricEquation, FixedValue
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>>> from pina import Condition
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>>> from pina.geometry import CartesianDomain
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>>> import torch
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>>>
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>>> class InverseODE(SpatialProblem, InverseProblem):
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>>>
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>>> output_variables = ['u']
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>>> spatial_domain = CartesianDomain({'x': [0, 1]})
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>>> unknown_parameter_domain = CartesianDomain({'alpha': [1, 10]})
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>>>
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>>> def ode_equation(input_, output_, params_):
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>>> u_x = grad(output_, input_, components=['u'], d=['x'])
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>>> u = output_.extract(['u'])
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>>> return params_.extract(['alpha']) * u_x - u
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>>>
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>>> def solution_data(input_, output_):
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>>> x = input_.extract(['x'])
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>>> solution = torch.exp(x)
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>>> return output_ - solution
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>>>
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>>> conditions = {
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>>> 'x0': Condition(CartesianDomain({'x': 0}), FixedValue(1.0)),
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>>> 'D': Condition(CartesianDomain({'x': [0, 1]}), ParametricEquation(ode_equation)),
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>>> 'data': Condition(CartesianDomain({'x': [0, 1]}), Equation(solution_data))
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"""
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def __init__(self):
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super().__init__()
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# storing unknown_parameters for optimization
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self.unknown_parameters = {}
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for i, var in enumerate(self.unknown_variables):
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range_var = self.unknown_parameter_domain.range_[var]
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tensor_var = (
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torch.rand(1, requires_grad=True) * range_var[1] + range_var[0]
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)
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self.unknown_parameters[var] = torch.nn.Parameter(tensor_var)
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@abstractmethod
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def unknown_parameter_domain(self):
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"""
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The parameters' domain of the problem.
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"""
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pass
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@property
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def unknown_variables(self):
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"""
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The parameters of the problem.
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"""
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return self.unknown_parameter_domain.variables
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@property
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def unknown_parameters(self):
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"""
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The parameters of the problem.
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"""
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return self.__unknown_parameters
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@unknown_parameters.setter
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def unknown_parameters(self, value):
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self.__unknown_parameters = value
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