75 lines
2.3 KiB
Python
75 lines
2.3 KiB
Python
"""Formulation of the Allen Cahn problem."""
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import torch
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from ... import Condition
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from ...problem import SpatialProblem, TimeDependentProblem
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from ...equation import Equation, AllenCahn
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from ...utils import check_consistency
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from ...domain import CartesianDomain
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def initial_condition(input_, output_):
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"""
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Definition of the initial condition of the Allen Cahn problem.
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:param LabelTensor input_: The input data of the problem.
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:param LabelTensor output_: The 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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x = input_.extract("x")
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u_0 = x**2 * torch.cos(torch.pi * x)
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return output_ - u_0
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class AllenCahnProblem(TimeDependentProblem, SpatialProblem):
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r"""
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Implementation of the Allen Cahn problem in the spatial interval
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:math:`[-1, 1]` and temporal interval :math:`[0, 1]`.
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.. seealso::
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**Original reference**: Sokratis J. Anagnostopoulos, Juan D. Toscano,
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Nikolaos Stergiopulos, and George E. Karniadakis.
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*Residual-based attention and connection to information
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bottleneck theory in PINNs*.
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Computer Methods in Applied Mechanics and Engineering 421 (2024): 116805
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DOI: `10.1016/
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j.cma.2024.116805 <https://doi.org/10.1016/j.cma.2024.116805>`_.
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:Example:
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>>> problem = AllenCahnProblem()
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"""
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output_variables = ["u"]
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spatial_domain = CartesianDomain({"x": [-1, 1]})
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temporal_domain = CartesianDomain({"t": [0, 1]})
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domains = {
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"D": CartesianDomain({"x": [-1, 1], "t": [0, 1]}),
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"t0": CartesianDomain({"x": [-1, 1], "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, alpha=1e-4, beta=5):
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"""
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Initialization of the :class:`AllenCahnProblem`.
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:param alpha: The diffusion coefficient.
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:type alpha: float | int
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:param beta: The reaction coefficient.
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:type beta: float | int
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"""
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super().__init__()
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check_consistency(alpha, (float, int))
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check_consistency(beta, (float, int))
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self.alpha = alpha
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self.beta = beta
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self.conditions["D"] = Condition(
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domain="D",
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equation=AllenCahn(alpha=self.alpha, beta=self.beta),
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)
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