Source code for pina.problem.zoo.allen_cahn

"""Formulation of the Allen Cahn problem."""

import torch
from ... import Condition
from ...problem import SpatialProblem, TimeDependentProblem
from ...equation import Equation, AllenCahn
from ...utils import check_consistency
from ...domain import CartesianDomain


def initial_condition(input_, output_):
    """
    Definition of the initial condition of the Allen Cahn problem.

    :param LabelTensor input_: The input data of the problem.
    :param LabelTensor output_: The output data of the problem.
    :return: The residual of the initial condition.
    :rtype: LabelTensor
    """
    x = input_.extract("x")
    u_0 = x**2 * torch.cos(torch.pi * x)
    return output_ - u_0


[docs] class AllenCahnProblem(TimeDependentProblem, SpatialProblem): r""" Implementation of the Allen Cahn problem in the spatial interval :math:`[-1, 1]` and temporal interval :math:`[0, 1]`. .. seealso:: **Original reference**: Sokratis J. Anagnostopoulos, Juan D. Toscano, Nikolaos Stergiopulos, and George E. Karniadakis. *Residual-based attention and connection to information bottleneck theory in PINNs*. Computer Methods in Applied Mechanics and Engineering 421 (2024): 116805 DOI: `10.1016/ j.cma.2024.116805 <https://doi.org/10.1016/j.cma.2024.116805>`_. :Example: >>> problem = AllenCahnProblem() """ output_variables = ["u"] spatial_domain = CartesianDomain({"x": [-1, 1]}) temporal_domain = CartesianDomain({"t": [0, 1]}) domains = { "D": CartesianDomain({"x": [-1, 1], "t": [0, 1]}), "t0": CartesianDomain({"x": [-1, 1], "t": 0.0}), } conditions = { "t0": Condition(domain="t0", equation=Equation(initial_condition)), } def __init__(self, alpha=1e-4, beta=5): """ Initialization of the :class:`AllenCahnProblem`. :param alpha: The diffusion coefficient. :type alpha: float | int :param beta: The reaction coefficient. :type beta: float | int """ super().__init__() check_consistency(alpha, (float, int)) check_consistency(beta, (float, int)) self.alpha = alpha self.beta = beta self.conditions["D"] = Condition( domain="D", equation=AllenCahn(alpha=self.alpha, beta=self.beta), )