f67467e5bd
* adding problems * add tests * update doc + formatting --------- Co-authored-by: Dario Coscia <dariocos99@gmail.com>
108 lines
3.2 KiB
Python
108 lines
3.2 KiB
Python
"""Formulation of the advection problem."""
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import torch
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from ... import Condition
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from ...operator import grad
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from ...equation import Equation
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from ...domain import CartesianDomain
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from ...utils import check_consistency
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from ...problem import SpatialProblem, TimeDependentProblem
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class AdvectionEquation(Equation):
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"""
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Implementation of the advection equation.
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"""
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def __init__(self, c):
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"""
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Initialize the advection equation.
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:param c: The advection velocity parameter.
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:type c: float | int
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"""
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self.c = c
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check_consistency(self.c, (float, int))
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def equation(input_, output_):
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"""
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Implementation of the advection equation.
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:param LabelTensor input_: Input data of the problem.
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:param LabelTensor output_: Output data of the problem.
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:return: The residual of the advection equation.
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:rtype: LabelTensor
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"""
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u_x = grad(output_, input_, components=["u"], d=["x"])
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u_t = grad(output_, input_, components=["u"], d=["t"])
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return u_t + self.c * u_x
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super().__init__(equation)
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def initial_condition(input_, output_):
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"""
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Implementation of the initial condition.
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:param LabelTensor input_: Input data of the problem.
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:param LabelTensor output_: Output data of the problem.
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:return: The residual of the initial condition.
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:rtype: LabelTensor
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"""
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return output_ - torch.sin(input_.extract("x"))
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class AdvectionProblem(SpatialProblem, TimeDependentProblem):
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r"""
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Implementation of the advection problem in the spatial interval
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:math:`[0, 2 \pi]` and temporal interval :math:`[0, 1]`.
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.. seealso::
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**Original reference**: Wang, Sifan, et al. *An expert's guide to
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training physics-informed neural networks*.
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arXiv preprint arXiv:2308.08468 (2023).
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DOI: `arXiv:2308.08468 <https://arxiv.org/abs/2308.08468>`_.
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"""
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output_variables = ["u"]
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spatial_domain = CartesianDomain({"x": [0, 2 * torch.pi]})
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temporal_domain = CartesianDomain({"t": [0, 1]})
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domains = {
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"D": CartesianDomain({"x": [0, 2 * torch.pi], "t": [0, 1]}),
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"t0": CartesianDomain({"x": [0, 2 * torch.pi], "t": 0.0}),
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}
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conditions = {
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"t0": Condition(domain="t0", equation=Equation(initial_condition)),
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}
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def __init__(self, c=1.0):
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"""
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Initialize the advection problem.
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:param c: The advection velocity parameter.
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:type c: float | int
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"""
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super().__init__()
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self.c = c
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check_consistency(self.c, (float, int))
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self.conditions["D"] = Condition(
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domain="D", equation=AdvectionEquation(self.c)
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)
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def solution(self, pts):
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"""
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Implementation of the analytical solution of the advection problem.
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:param LabelTensor pts: Points where the solution is evaluated.
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:return: The analytical solution of the advection problem.
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:rtype: LabelTensor
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"""
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sol = torch.sin(pts.extract("x") - self.c * pts.extract("t"))
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sol.labels = self.output_variables
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return sol
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