import torch
import torch.nn as nn
from ...utils import check_consistency
from pina.model.layers import (
SpectralConvBlock1D,
SpectralConvBlock2D,
SpectralConvBlock3D,
)
[docs]
class FourierBlock1D(nn.Module):
"""
Fourier block implementation for three dimensional
input tensor. The combination of Fourier blocks
make up the Fourier Neural Operator
.. 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,
):
super().__init__()
"""
PINA implementation of Fourier block one dimension. 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.
The block expects an input of size ``[batch, input_numb_fields, N]``
and returns an output of size ``[batch, output_numb_fields, N]``.
: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 list | tuple n_modes: Number of modes to select for each dimension.
It must be at most equal to the ``floor(N/2)+1``.
:param torch.nn.Module activation: The activation function.
"""
# 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 computation for Fourier Block. It performs a spectral
convolution and a linear transformation of the input and sum the
results.
:param x: The input tensor for fourier block, expect of size
``[batch, input_numb_fields, x]``.
:type x: torch.Tensor
:return: The output tensor obtained from the
fourier block of size ``[batch, output_numb_fields, x]``.
:rtype: torch.Tensor
"""
return self._activation(self._spectral_conv(x) + self._linear(x))
[docs]
class FourierBlock2D(nn.Module):
"""
Fourier block implementation for two dimensional
input tensor. The combination of Fourier blocks
make up the Fourier Neural Operator
.. seealso::
**Original reference**: Li, Zongyi, et al.
*Fourier neural operator for parametric partial
differential equations*. arXiv preprint
arXiv:2010.08895 (2020)
<https://arxiv.org/abs/2010.08895.pdf>`_.
"""
def __init__(
self,
input_numb_fields,
output_numb_fields,
n_modes,
activation=torch.nn.Tanh,
):
"""
PINA implementation of Fourier block two dimensions. 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.
The block expects an input of size ``[batch, input_numb_fields, Nx, Ny]``
and returns an output of size ``[batch, output_numb_fields, Nx, Ny]``.
: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 list | tuple n_modes: Number of modes to select for each dimension.
It must be at most equal to the ``floor(Nx/2)+1`` and ``floor(Ny/2)+1``.
:param torch.nn.Module activation: The activation function.
"""
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 computation for Fourier Block. It performs a spectral
convolution and a linear transformation of the input and sum the
results.
:param x: The input tensor for fourier block, expect of size
``[batch, input_numb_fields, x, y]``.
:type x: torch.Tensor
:return: The output tensor obtained from the
fourier block of size ``[batch, output_numb_fields, x, y, z]``.
:rtype: torch.Tensor
"""
return self._activation(self._spectral_conv(x) + self._linear(x))
[docs]
class FourierBlock3D(nn.Module):
"""
Fourier block implementation for three dimensional
input tensor. The combination of Fourier blocks
make up the Fourier Neural Operator
.. seealso::
**Original reference**: Li, Zongyi, et al.
*Fourier neural operator for parametric partial
differential equations*. arXiv preprint
arXiv:2010.08895 (2020)
<https://arxiv.org/abs/2010.08895.pdf>`_.
"""
def __init__(
self,
input_numb_fields,
output_numb_fields,
n_modes,
activation=torch.nn.Tanh,
):
"""
PINA implementation of Fourier block three dimensions. 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.
The block expects an input of size ``[batch, input_numb_fields, Nx, Ny, Nz]``
and returns an output of size ``[batch, output_numb_fields, Nx, Ny, Nz]``.
: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 list | tuple n_modes: Number of modes to select for each dimension.
It must be at most equal to the ``floor(Nx/2)+1``, ``floor(Ny/2)+1``
and ``floor(Nz/2)+1``.
:param torch.nn.Module activation: The activation function.
"""
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 computation for Fourier Block. It performs a spectral
convolution and a linear transformation of the input and sum the
results.
:param x: The input tensor for fourier block, expect of size
``[batch, input_numb_fields, x, y, z]``.
:type x: torch.Tensor
:return: The output tensor obtained from the
fourier block of size ``[batch, output_numb_fields, x, y, z]``.
:rtype: torch.Tensor
"""
return self._activation(self._spectral_conv(x) + self._linear(x))
