f67467e5bd
* adding problems * add tests * update doc + formatting --------- Co-authored-by: Dario Coscia <dariocos99@gmail.com>
102 lines
3.3 KiB
Python
102 lines
3.3 KiB
Python
"""Formulation of the diffusion-reaction problem."""
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import torch
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from ... import Condition
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from ...domain import CartesianDomain
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from ...operator import grad, laplacian
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from ...equation import Equation, FixedValue
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from ...problem import SpatialProblem, TimeDependentProblem
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def diffusion_reaction(input_, output_):
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"""
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Implementation of the diffusion-reaction 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 diffusion-reaction equation.
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:rtype: LabelTensor
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"""
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x = input_.extract("x")
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t = input_.extract("t")
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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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r = torch.exp(-t) * (
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1.5 * torch.sin(2 * x)
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+ (8 / 3) * torch.sin(3 * x)
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+ (15 / 4) * torch.sin(4 * x)
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+ (63 / 8) * torch.sin(8 * x)
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)
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return u_t - u_xx - r
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def initial_condition(input_, output_):
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"""
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Definition of the initial condition of the diffusion-reaction 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 = (
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torch.sin(x)
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+ (1 / 2) * torch.sin(2 * x)
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+ (1 / 3) * torch.sin(3 * x)
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+ (1 / 4) * torch.sin(4 * x)
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+ (1 / 8) * torch.sin(8 * x)
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)
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return output_ - u_0
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class DiffusionReactionProblem(TimeDependentProblem, SpatialProblem):
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r"""
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Implementation of the diffusion-reaction problem in the spatial interval
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:math:`[-\pi, \pi]` and temporal interval :math:`[0, 1]`.
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.. seealso::
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**Original reference**: Si, Chenhao, et al. *Complex Physics-Informed
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Neural Network.* arXiv preprint arXiv:2502.04917 (2025).
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DOI: `arXiv:2502.04917 <https://arxiv.org/abs/2502.04917>`_.
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"""
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output_variables = ["u"]
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spatial_domain = CartesianDomain({"x": [-torch.pi, torch.pi]})
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temporal_domain = CartesianDomain({"t": [0, 1]})
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domains = {
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"D": CartesianDomain({"x": [-torch.pi, torch.pi], "t": [0, 1]}),
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"g1": CartesianDomain({"x": -torch.pi, "t": [0, 1]}),
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"g2": CartesianDomain({"x": torch.pi, "t": [0, 1]}),
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"t0": CartesianDomain({"x": [-torch.pi, torch.pi], "t": 0.0}),
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}
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conditions = {
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"D": Condition(domain="D", equation=Equation(diffusion_reaction)),
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"g1": Condition(domain="g1", equation=FixedValue(0.0)),
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"g2": Condition(domain="g2", equation=FixedValue(0.0)),
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"t0": Condition(domain="t0", equation=Equation(initial_condition)),
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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 diffusion-reaction
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problem.
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:param LabelTensor pts: Points where the solution is evaluated.
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:return: The analytical solution of the diffusion-reaction problem.
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:rtype: LabelTensor
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"""
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t = pts.extract("t")
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x = pts.extract("x")
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sol = torch.exp(-t) * (
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torch.sin(x)
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+ (1 / 2) * torch.sin(2 * x)
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+ (1 / 3) * torch.sin(3 * x)
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+ (1 / 4) * torch.sin(4 * x)
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+ (1 / 8) * torch.sin(8 * x)
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)
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sol.labels = self.output_variables
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return sol
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