"""Module for spectral convolution blocks."""
import torch
from torch import nn
from ...utils import check_consistency
######## 1D Spectral Convolution ###########
[docs]
class SpectralConvBlock1D(nn.Module):
"""
Spectral Convolution Block for one-dimensional tensors.
This class 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 block expects an input of size [``batch``, ``input_numb_fields``, ``N``]
and returns an output of size [``batch``, ``output_numb_fields``, ``N``].
"""
def __init__(self, input_numb_fields, output_numb_fields, n_modes):
r"""
Initialization of the :class:`SpectralConvBlock1D` 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 int n_modes: The number of modes to select for each dimension.
It must be at most equal to :math:`\floor(Nx/2)+1`.
"""
super().__init__()
# check type consistency
check_consistency(input_numb_fields, int)
check_consistency(output_numb_fields, int)
# assign variables
self._modes = n_modes
self._input_channels = input_numb_fields
self._output_channels = output_numb_fields
# scaling factor
scale = 1.0 / (self._input_channels * self._output_channels)
self._weights = nn.Parameter(
scale
* torch.rand(
self._input_channels,
self._output_channels,
self._modes,
dtype=torch.cfloat,
)
)
def _compute_mult1d(self, input, weights):
"""
Compute the matrix multiplication of the input and the linear kernel
weights.
:param torch.Tensor input: The input tensor. Expected of size
[``batch``, ``input_numb_fields``, ``N``].
:param torch.Tensor weights: The kernel weights. Expected of size
[``input_numb_fields``, ``output_numb_fields``, ``N``].
:return: The result of the matrix multiplication.
:rtype: torch.Tensor
"""
return torch.einsum("bix,iox->box", input, weights)
[docs]
def forward(self, x):
"""
Forward pass.
:param torch.Tensor x: The input tensor. Expected of size
[``batch``, ``input_numb_fields``, ``N``].
:return: The input tensor. Expected of size
[``batch``, ``output_numb_fields``, ``N``].
:rtype: torch.Tensor
"""
batch_size = x.shape[0]
# Compute Fourier transform of the input
x_ft = torch.fft.rfft(x)
# Multiply relevant Fourier modes
out_ft = torch.zeros(
batch_size,
self._output_channels,
x.size(-1) // 2 + 1,
device=x.device,
dtype=torch.cfloat,
)
out_ft[:, :, : self._modes] = self._compute_mult1d(
x_ft[:, :, : self._modes], self._weights
)
# Return to physical space
return torch.fft.irfft(out_ft, n=x.size(-1))
######## 2D Spectral Convolution ###########
[docs]
class SpectralConvBlock2D(nn.Module):
"""
Spectral Convolution Block for two-dimensional tensors.
This class 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 block expects an input of size
[``batch``, ``input_numb_fields``, ``Nx``, ``Ny``]
and returns an output of size
[``batch``, ``output_numb_fields``, ``Nx``, ``Ny``].
"""
def __init__(self, input_numb_fields, output_numb_fields, n_modes):
r"""
Initialization of the :class:`SpectralConvBlock2D` 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]
:raises ValueError: If the number of modes is not consistent.
:raises ValueError: If the number of modes is not a list or tuple.
"""
super().__init__()
# check type consistency
check_consistency(input_numb_fields, int)
check_consistency(output_numb_fields, int)
check_consistency(n_modes, int)
if isinstance(n_modes, (tuple, list)):
if len(n_modes) != 2:
raise ValueError(
"Expected n_modes to be a list or tuple of len two, "
"with each entry corresponding to the number of modes "
"for each dimension "
)
elif isinstance(n_modes, int):
n_modes = [n_modes] * 2
else:
raise ValueError(
"Expected n_modes to be a list or tuple of len two, "
"with each entry corresponding to the number of modes "
"for each dimension; or an int value representing the "
"number of modes for all dimensions"
)
# assign variables
self._modes = n_modes
self._input_channels = input_numb_fields
self._output_channels = output_numb_fields
# scaling factor
scale = 1.0 / (self._input_channels * self._output_channels)
self._weights1 = nn.Parameter(
scale
* torch.rand(
self._input_channels,
self._output_channels,
self._modes[0],
self._modes[1],
dtype=torch.cfloat,
)
)
self._weights2 = nn.Parameter(
scale
* torch.rand(
self._input_channels,
self._output_channels,
self._modes[0],
self._modes[1],
dtype=torch.cfloat,
)
)
def _compute_mult2d(self, input, weights):
"""
Compute the matrix multiplication of the input and the linear kernel
weights.
:param torch.Tensor input: The input tensor. Expected of size
[``batch``, ``input_numb_fields``, ``Nx``, ``Ny``].
:param torch.Tensor weights: The kernel weights. Expected of size
[``input_numb_fields``, ``output_numb_fields``, ``Nx``, ``Ny``].
:return: The result of the matrix multiplication.
:rtype: torch.Tensor
"""
return torch.einsum("bixy,ioxy->boxy", input, weights)
[docs]
def forward(self, x):
"""
Forward pass.
:param torch.Tensor x: The input tensor. Expected of size
[``batch``, ``input_numb_fields``, ``Nx``, ``Ny``].
:return: The input tensor. Expected of size
[``batch``, ``output_numb_fields``, ``Nx``, ``Ny``].
:rtype: torch.Tensor
"""
batch_size = x.shape[0]
# Compute Fourier transform of the input
x_ft = torch.fft.rfft2(x)
# Multiply relevant Fourier modes
out_ft = torch.zeros(
batch_size,
self._output_channels,
x.size(-2),
x.size(-1) // 2 + 1,
device=x.device,
dtype=torch.cfloat,
)
out_ft[:, :, : self._modes[0], : self._modes[1]] = self._compute_mult2d(
x_ft[:, :, : self._modes[0], : self._modes[1]], self._weights1
)
out_ft[:, :, -self._modes[0] :, : self._modes[1] :] = (
self._compute_mult2d(
x_ft[:, :, -self._modes[0] :, : self._modes[1]], self._weights2
)
)
# Return to physical space
return torch.fft.irfft2(out_ft, s=(x.size(-2), x.size(-1)))
######## 3D Spectral Convolution ###########
[docs]
class SpectralConvBlock3D(nn.Module):
"""
Spectral Convolution Block for three-dimensional tensors.
This class 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 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``].
"""
def __init__(self, input_numb_fields, output_numb_fields, n_modes):
r"""
Initialization of the :class:`SpectralConvBlock3D` 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]
:raises ValueError: If the number of modes is not consistent.
:raises ValueError: If the number of modes is not a list or tuple.
"""
super().__init__()
# check type consistency
check_consistency(input_numb_fields, int)
check_consistency(output_numb_fields, int)
check_consistency(n_modes, int)
if isinstance(n_modes, (tuple, list)):
if len(n_modes) != 3:
raise ValueError(
"Expected n_modes to be a list or tuple of len three, "
"with each entry corresponding to the number of modes "
"for each dimension "
)
elif isinstance(n_modes, int):
n_modes = [n_modes] * 3
else:
raise ValueError(
"Expected n_modes to be a list or tuple of len three, "
"with each entry corresponding to the number of modes "
"for each dimension; or an int value representing the "
"number of modes for all dimensions"
)
# assign variables
self._modes = n_modes
self._input_channels = input_numb_fields
self._output_channels = output_numb_fields
# scaling factor
scale = 1.0 / (self._input_channels * self._output_channels)
self._weights1 = nn.Parameter(
scale
* torch.rand(
self._input_channels,
self._output_channels,
self._modes[0],
self._modes[1],
self._modes[2],
dtype=torch.cfloat,
)
)
self._weights2 = nn.Parameter(
scale
* torch.rand(
self._input_channels,
self._output_channels,
self._modes[0],
self._modes[1],
self._modes[2],
dtype=torch.cfloat,
)
)
self._weights3 = nn.Parameter(
scale
* torch.rand(
self._input_channels,
self._output_channels,
self._modes[0],
self._modes[1],
self._modes[2],
dtype=torch.cfloat,
)
)
self._weights4 = nn.Parameter(
scale
* torch.rand(
self._input_channels,
self._output_channels,
self._modes[0],
self._modes[1],
self._modes[2],
dtype=torch.cfloat,
)
)
def _compute_mult3d(self, input, weights):
"""
Compute the matrix multiplication of the input and the linear kernel
weights.
:param torch.Tensor input: The input tensor. Expected of size
[``batch``, ``input_numb_fields``, ``Nx``, ``Ny``, ``Nz``].
:param torch.Tensor weights: The kernel weights. Expected of size
[``input_numb_fields``, ``output_numb_fields``, ``Nx``, ``Ny``,
``Nz``].
:return: The result of the matrix multiplication.
:rtype: torch.Tensor
"""
return torch.einsum("bixyz,ioxyz->boxyz", input, weights)
[docs]
def forward(self, x):
"""
Forward pass.
:param torch.Tensor x: The input tensor. Expected of size
[``batch``, ``input_numb_fields``, ``Nx``, ``Ny``, ``Nz``].
:return: The input tensor. Expected of size
[``batch``, ``output_numb_fields``, ``Nx``, ``Ny``, ``Nz``].
:rtype: torch.Tensor
"""
batch_size = x.shape[0]
# Compute Fourier transform of the input
x_ft = torch.fft.rfftn(x, dim=[-3, -2, -1])
# Multiply relevant Fourier modes
out_ft = torch.zeros(
batch_size,
self._output_channels,
x.size(-3),
x.size(-2),
x.size(-1) // 2 + 1,
device=x.device,
dtype=torch.cfloat,
)
slice0 = (
slice(None),
slice(None),
slice(self._modes[0]),
slice(self._modes[1]),
slice(self._modes[2]),
)
out_ft[slice0] = self._compute_mult3d(x_ft[slice0], self._weights1)
slice1 = (
slice(None),
slice(None),
slice(self._modes[0]),
slice(-self._modes[1], None),
slice(self._modes[2]),
)
out_ft[slice1] = self._compute_mult3d(x_ft[slice1], self._weights2)
slice2 = (
slice(None),
slice(None),
slice(-self._modes[0], None),
slice(self._modes[1]),
slice(self._modes[2]),
)
out_ft[slice2] = self._compute_mult3d(x_ft[slice2], self._weights3)
slice3 = (
slice(None),
slice(None),
slice(-self._modes[0], None),
slice(-self._modes[1], None),
slice(self._modes[2]),
)
out_ft[slice3] = self._compute_mult3d(x_ft[slice3], self._weights4)
# Return to physical space
return torch.fft.irfftn(out_ft, s=(x.size(-3), x.size(-2), x.size(-1)))
