f67467e5bd
* adding problems * add tests * update doc + formatting --------- Co-authored-by: Dario Coscia <dariocos99@gmail.com>
67 lines
2.2 KiB
Python
67 lines
2.2 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 ...equation import Equation
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from ...domain import CartesianDomain
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from ...operator import grad, laplacian
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from ...problem import SpatialProblem, TimeDependentProblem
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def allen_cahn_equation(input_, output_):
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"""
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Implementation of the Allen Cahn 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 Allen Cahn equation.
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:rtype: LabelTensor
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"""
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u_t = grad(output_, input_, components=["u"], d=["t"])
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u_xx = laplacian(output_, input_, components=["u"], d=["x"])
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return u_t - 0.0001 * u_xx + 5 * output_**3 - 5 * output_
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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_: 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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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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"""
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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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"D": Condition(domain="D", equation=Equation(allen_cahn_equation)),
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"t0": Condition(domain="t0", equation=Equation(initial_condition)),
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}
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