Update Laplace class and add unit tests (#645)
This commit is contained in:
Giovanni Canali
@@ -6,9 +6,26 @@ __all__ = [
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"FixedValue",
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"FixedGradient",
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"FixedFlux",
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"FixedLaplacian",
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"Laplace",
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"Advection",
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"AllenCahn",
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"DiffusionReaction",
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"Helmholtz",
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"Poisson",
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]
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from .equation import Equation
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from .equation_factory import FixedFlux, FixedGradient, Laplace, FixedValue
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from .equation_factory import (
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FixedFlux,
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FixedGradient,
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FixedLaplacian,
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FixedValue,
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Laplace,
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Advection,
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AllenCahn,
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DiffusionReaction,
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Helmholtz,
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Poisson,
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)
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from .system_equation import SystemEquation
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@@ -1,7 +1,10 @@
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"""Module for defining various general equations."""
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from typing import Callable
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import torch
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from .equation import Equation
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from ..operator import grad, div, laplacian
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from ..utils import check_consistency
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class FixedValue(Equation):
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@@ -110,9 +113,53 @@ class FixedFlux(Equation):
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super().__init__(equation)
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class Laplace(Equation):
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class FixedLaplacian(Equation):
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"""
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Equation to enforce a fixed laplacian for a specific condition.
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"""
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def __init__(self, value, components=None, d=None):
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"""
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Initialization of the :class:`FixedLaplacian` class.
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:param float value: The fixed value to be enforced to the laplacian.
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:param list[str] components: The name of the output variables for which
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the fixed laplace condition is applied. It should be a subset of the
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output labels. If ``None``, all output variables are considered.
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Default is ``None``.
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:param list[str] d: The name of the input variables on which the
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laplacian is computed. It should be a subset of the input labels.
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If ``None``, all the input variables are considered.
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Default is ``None``.
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"""
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def equation(input_, output_):
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"""
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Definition of the equation to enforce a fixed laplacian.
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:param LabelTensor input_: Input points where the equation is
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evaluated.
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:param LabelTensor output_: Output tensor, eventually produced by a
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:class:`torch.nn.Module` instance.
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:return: The computed residual of the equation.
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:rtype: LabelTensor
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"""
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return (
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laplacian(output_, input_, components=components, d=d) - value
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)
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super().__init__(equation)
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class Laplace(FixedLaplacian):
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"""
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Equation to enforce a null laplacian for a specific condition.
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The equation is defined as follows:
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.. math::
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\delta u = 0
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"""
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def __init__(self, components=None, d=None):
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@@ -128,18 +175,277 @@ class Laplace(Equation):
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If ``None``, all the input variables are considered.
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Default is ``None``.
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"""
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super().__init__(0.0, components=components, d=d)
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class Advection(Equation):
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r"""
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Implementation of the N-dimensional advection equation with constant
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velocity parameter. The equation is defined as follows:
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.. math::
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\frac{\partial u}{\partial t} + c \cdot \nabla u = 0
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Here, :math:`c` is the advection velocity parameter.
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"""
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def __init__(self, c):
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"""
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Initialization of the :class:`Advection` class.
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:param c: The advection velocity. If a scalar is provided, the same
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velocity is applied to all spatial dimensions. If a list is
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provided, it must contain one value per spatial dimension.
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:type c: float | int | List[float] | List[int]
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:raises ValueError: If ``c`` is an empty list.
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"""
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# Check consistency
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check_consistency(c, (float, int, list))
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if isinstance(c, list):
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all(check_consistency(ci, (float, int)) for ci in c)
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if len(c) < 1:
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raise ValueError("'c' cannot be an empty list.")
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else:
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c = [c]
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# Store advection velocity parameter
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self.c = torch.tensor(c).unsqueeze(0)
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def equation(input_, output_):
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"""
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Definition of the equation to enforce a null laplacian.
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Implementation of the advection equation.
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:param LabelTensor input_: Input points where the equation is
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evaluated.
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:param LabelTensor output_: Output tensor, eventually produced by a
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:class:`torch.nn.Module` instance.
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:return: The computed residual of the equation.
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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 advection equation.
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:rtype: LabelTensor
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:raises ValueError: If the ``input_`` labels do not contain the time
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variable 't'.
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:raises ValueError: If ``c`` is a list and its length is not
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consistent with the number of spatial dimensions.
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"""
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return laplacian(output_, input_, components=components, d=d)
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# Store labels
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input_lbl = input_.labels
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spatial_d = [di for di in input_lbl if di != "t"]
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# Ensure time is passed as input
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if "t" not in input_lbl:
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raise ValueError(
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"The ``input_`` labels must contain the time 't' variable."
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)
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# Ensure consistency of c length
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if len(self.c) != (len(input_lbl) - 1) and len(self.c) > 1:
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raise ValueError(
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"If 'c' is passed as a list, its length must be equal to "
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"the number of spatial dimensions."
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)
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# Repeat c to ensure consistent shape for advection
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self.c = self.c.repeat(output_.shape[0], 1)
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if self.c.shape[1] != (len(input_lbl) - 1):
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self.c = self.c.repeat(1, len(input_lbl) - 1)
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# Add a dimension to c for the following operations
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self.c = self.c.unsqueeze(-1)
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# Compute the time derivative and the spatial gradient
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time_der = grad(output_, input_, components=None, d="t")
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grads = grad(output_=output_, input_=input_, d=spatial_d)
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# Reshape and transpose
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tmp = grads.reshape(*output_.shape, len(spatial_d))
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tmp = tmp.transpose(-1, -2)
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# Compute advection term
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adv = (tmp * self.c).sum(dim=tmp.tensor.ndim - 2)
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return time_der + adv
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super().__init__(equation)
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class AllenCahn(Equation):
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r"""
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Implementation of the N-dimensional Allen-Cahn equation, defined as follows:
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.. math::
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\frac{\partial u}{\partial t} - \alpha \Delta u + \beta(u^3 - u) = 0
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Here, :math:`\alpha` and :math:`\beta` are parameters of the equation.
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"""
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def __init__(self, alpha, beta):
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"""
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Initialization of the :class:`AllenCahn` class.
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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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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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def equation(input_, output_):
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"""
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Implementation of the Allen-Cahn equation.
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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 Allen-Cahn equation.
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:rtype: LabelTensor
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:raises ValueError: If the ``input_`` labels do not contain the time
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variable 't'.
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"""
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# Ensure time is passed as input
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if "t" not in input_.labels:
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raise ValueError(
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"The ``input_`` labels must contain the time 't' variable."
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)
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# Compute the time derivative and the spatial laplacian
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u_t = grad(output_, input_, d=["t"])
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u_xx = laplacian(
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output_, input_, d=[di for di in input_.labels if di != "t"]
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)
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return u_t - self.alpha * u_xx + self.beta * (output_**3 - output_)
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super().__init__(equation)
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class DiffusionReaction(Equation):
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r"""
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Implementation of the N-dimensional Diffusion-Reaction equation,
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defined as follows:
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.. math::
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\frac{\partial u}{\partial t} - \alpha \Delta u - f = 0
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Here, :math:`\alpha` is a parameter of the equation, while :math:`f` is the
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reaction term.
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"""
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def __init__(self, alpha, forcing_term):
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"""
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Initialization of the :class:`DiffusionReaction` class.
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:param alpha: The diffusion coefficient.
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:type alpha: float | int
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:param Callable forcing_term: The forcing field function, taking as
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input the points on which evaluation is required.
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"""
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check_consistency(alpha, (float, int))
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check_consistency(forcing_term, (Callable))
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self.alpha = alpha
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self.forcing_term = forcing_term
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def equation(input_, output_):
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"""
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Implementation of the Diffusion-Reaction equation.
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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 Diffusion-Reaction equation.
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:rtype: LabelTensor
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:raises ValueError: If the ``input_`` labels do not contain the time
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variable 't'.
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"""
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# Ensure time is passed as input
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if "t" not in input_.labels:
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raise ValueError(
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"The ``input_`` labels must contain the time 't' variable."
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)
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# Compute the time derivative and the spatial laplacian
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u_t = grad(output_, input_, d=["t"])
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u_xx = laplacian(
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output_, input_, d=[di for di in input_.labels if di != "t"]
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)
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return u_t - self.alpha * u_xx - self.forcing_term(input_)
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super().__init__(equation)
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class Helmholtz(Equation):
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r"""
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Implementation of the Helmholtz equation, defined as follows:
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.. math::
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\Delta u + k u - f = 0
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Here, :math:`k` is a parameter of the equation, while :math:`f` is the
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forcing term.
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"""
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def __init__(self, k, forcing_term):
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"""
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Initialization of the :class:`Helmholtz` class.
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:param k: The parameter of the equation.
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:type k: float | int
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:param Callable forcing_term: The forcing field function, taking as
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input the points on which evaluation is required.
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"""
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check_consistency(k, (int, float))
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check_consistency(forcing_term, (Callable))
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self.k = k
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self.forcing_term = forcing_term
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def equation(input_, output_):
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"""
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Implementation of the Helmholtz equation.
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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 Helmholtz equation.
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:rtype: LabelTensor
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"""
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lap = laplacian(output_, input_)
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return lap + self.k * output_ - self.forcing_term(input_)
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super().__init__(equation)
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class Poisson(Equation):
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r"""
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Implementation of the Poisson equation, defined as follows:
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.. math::
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\Delta u - f = 0
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Here, :math:`f` is the forcing term.
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"""
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def __init__(self, forcing_term):
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"""
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Initialization of the :class:`Poisson` class.
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:param Callable forcing_term: The forcing field function, taking as
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input the points on which evaluation is required.
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"""
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check_consistency(forcing_term, (Callable))
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self.forcing_term = forcing_term
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def equation(input_, output_):
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"""
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Implementation of the Poisson equation.
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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 Poisson equation.
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:rtype: LabelTensor
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"""
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lap = laplacian(output_, input_)
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return lap - self.forcing_term(input_)
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super().__init__(equation)
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