"""Module for the Fourier Neural Operator Block class."""
import torch
from torch import nn
from ...utils import check_consistency
from .spectral import (
SpectralConvBlock1D,
SpectralConvBlock2D,
SpectralConvBlock3D,
)
[docs]
class FourierBlock1D(nn.Module):
"""
The inner block of the Fourier Neural Operator for 1-dimensional input
tensors.
The module computes the spectral convolution of the input with a linear
kernel in the fourier space, and then it maps the input back to the physical
space. The output is then added to a Linear tranformation of the input in
the physical space. Finally an activation function is applied to the output.
.. seealso::
**Original reference**: Li, Z., Kovachki, N., Azizzadenesheli, K.,
Liu, B., Bhattacharya, K., Stuart, A., & Anandkumar, A. (2020).
*Fourier neural operator for parametric partial differential equations*.
DOI: `arXiv preprint arXiv:2010.08895.
<https://arxiv.org/abs/2010.08895>`_
"""
def __init__(
self,
input_numb_fields,
output_numb_fields,
n_modes,
activation=torch.nn.Tanh,
):
r"""
Initialization of the :class:`FourierBlock1D` class.
:param int input_numb_fields: The number of channels for the input.
:param int output_numb_fields: The number of channels for the output.
:param n_modes: The number of modes to select for each dimension.
It must be at most equal to :math:`\floor(Nx/2)+1`.
:type n_modes: list[int] | tuple[int]
:param torch.nn.Module activation: The activation function.
Default is :class:`torch.nn.Tanh`.
"""
super().__init__()
# check type consistency
check_consistency(activation(), nn.Module)
# assign variables
self._spectral_conv = SpectralConvBlock1D(
input_numb_fields=input_numb_fields,
output_numb_fields=output_numb_fields,
n_modes=n_modes,
)
self._activation = activation()
self._linear = nn.Conv1d(input_numb_fields, output_numb_fields, 1)
[docs]
def forward(self, x):
"""
Forward pass of the block. It performs a spectral convolution and a
linear transformation of the input. Then, it sums the results.
:param torch.Tensor x: The input tensor for performing the computation.
:return: The output tensor.
:rtype: torch.Tensor
"""
return self._activation(self._spectral_conv(x) + self._linear(x))
[docs]
class FourierBlock2D(nn.Module):
"""
The inner block of the Fourier Neural Operator for 2-dimensional input
tensors.
The module computes the spectral convolution of the input with a linear
kernel in the fourier space, and then it maps the input back to the physical
space. The output is then added to a Linear tranformation of the input in
the physical space. Finally an activation function is applied to the output.
.. seealso::
**Original reference**: Li, Z., Kovachki, N., Azizzadenesheli, K.,
Liu, B., Bhattacharya, K., Stuart, A., & Anandkumar, A. (2020).
*Fourier neural operator for parametric partial differential equations*.
DOI: `arXiv preprint arXiv:2010.08895.
<https://arxiv.org/abs/2010.08895>`_
"""
def __init__(
self,
input_numb_fields,
output_numb_fields,
n_modes,
activation=torch.nn.Tanh,
):
r"""
Initialization of the :class:`FourierBlock2D` class.
:param int input_numb_fields: The number of channels for the input.
:param int output_numb_fields: The number of channels for the output.
:param n_modes: The number of modes to select for each dimension.
It must be at most equal to :math:`\floor(Nx/2)+1`,
:math:`\floor(Ny/2)+1`.
:type n_modes: list[int] | tuple[int]
:param torch.nn.Module activation: The activation function.
Default is :class:`torch.nn.Tanh`.
"""
super().__init__()
# check type consistency
check_consistency(activation(), nn.Module)
# assign variables
self._spectral_conv = SpectralConvBlock2D(
input_numb_fields=input_numb_fields,
output_numb_fields=output_numb_fields,
n_modes=n_modes,
)
self._activation = activation()
self._linear = nn.Conv2d(input_numb_fields, output_numb_fields, 1)
[docs]
def forward(self, x):
"""
Forward pass of the block. It performs a spectral convolution and a
linear transformation of the input. Then, it sums the results.
:param torch.Tensor x: The input tensor for performing the computation.
:return: The output tensor.
:rtype: torch.Tensor
"""
return self._activation(self._spectral_conv(x) + self._linear(x))
[docs]
class FourierBlock3D(nn.Module):
"""
The inner block of the Fourier Neural Operator for 3-dimensional input
tensors.
The module computes the spectral convolution of the input with a linear
kernel in the fourier space, and then it maps the input back to the physical
space. The output is then added to a Linear tranformation of the input in
the physical space. Finally an activation function is applied to the output.
.. seealso::
**Original reference**: Li, Z., Kovachki, N., Azizzadenesheli, K.,
Liu, B., Bhattacharya, K., Stuart, A., & Anandkumar, A. (2020).
*Fourier neural operator for parametric partial differential equations*.
DOI: `arXiv preprint arXiv:2010.08895.
<https://arxiv.org/abs/2010.08895>`_
"""
def __init__(
self,
input_numb_fields,
output_numb_fields,
n_modes,
activation=torch.nn.Tanh,
):
r"""
Initialization of the :class:`FourierBlock3D` class.
:param int input_numb_fields: The number of channels for the input.
:param int output_numb_fields: The number of channels for the output.
:param n_modes: The number of modes to select for each dimension.
It must be at most equal to :math:`\floor(Nx/2)+1`,
:math:`\floor(Ny/2)+1`, :math:`\floor(Nz/2)+1`.
:type n_modes: list[int] | tuple[int]
:param torch.nn.Module activation: The activation function.
Default is :class:`torch.nn.Tanh`.
"""
super().__init__()
# check type consistency
check_consistency(activation(), nn.Module)
# assign variables
self._spectral_conv = SpectralConvBlock3D(
input_numb_fields=input_numb_fields,
output_numb_fields=output_numb_fields,
n_modes=n_modes,
)
self._activation = activation()
self._linear = nn.Conv3d(input_numb_fields, output_numb_fields, 1)
[docs]
def forward(self, x):
"""
Forward pass of the block. It performs a spectral convolution and a
linear transformation of the input. Then, it sums the results.
:param torch.Tensor x: The input tensor for performing the computation.
:return: The output tensor.
:rtype: torch.Tensor
"""
return self._activation(self._spectral_conv(x) + self._linear(x))
