Spectral Convolution Block#

class SpectralConvBlock1D(input_numb_fields, output_numb_fields, n_modes)[source]#

Bases: 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].

Example:

>>> import torch
>>> from pina.model.block import SpectralConvBlock1D
>>> block = SpectralConvBlock1D(
...     input_numb_fields=2, output_numb_fields=2, n_modes=16
... )
>>> x = torch.randn(10, 2, 50)
>>> out = block(x)

Initialization of the SpectralConvBlock1D class.

Parameters:

input_numb_fields (int) – The number of channels for the input.
output_numb_fields (int) – The number of channels for the output.
n_modes (int) – The number of modes to select for each dimension. It must be at most equal to \(\floor(Nx/2)+1\).

forward(x)[source]#

Forward pass.

Parameters:: x (torch.Tensor) – The input tensor. Expected of size [batch, input_numb_fields, N].
Returns:: The input tensor. Expected of size [batch, output_numb_fields, N].
Return type:: torch.Tensor

class SpectralConvBlock2D(input_numb_fields, output_numb_fields, n_modes)[source]#

Bases: 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].

Example:

>>> import torch
>>> from pina.model.block import SpectralConvBlock2D
>>> block = SpectralConvBlock2D(
...     input_numb_fields=2, output_numb_fields=2, n_modes=[8, 8]
... )
>>> x = torch.randn(10, 2, 50, 50)
>>> out = block(x)

Initialization of the SpectralConvBlock2D class.

Parameters:

input_numb_fields (int) – The number of channels for the input.
output_numb_fields (int) – The number of channels for the output.
n_modes (list[int] | tuple[int]) – The number of modes to select for each dimension. It must be at most equal to \(\floor(Nx/2)+1\), \(\floor(Ny/2)+1\).

Raises:

ValueError – If the number of modes is not consistent.
ValueError – If the number of modes is not a list or tuple.

forward(x)[source]#

Forward pass.

Parameters:: x (torch.Tensor) – The input tensor. Expected of size [batch, input_numb_fields, Nx, Ny].
Returns:: The input tensor. Expected of size [batch, output_numb_fields, Nx, Ny].
Return type:: torch.Tensor

class SpectralConvBlock3D(input_numb_fields, output_numb_fields, n_modes)[source]#

Bases: 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].

Example:

>>> import torch
>>> from pina.model.block import SpectralConvBlock3D
>>> block = SpectralConvBlock3D(
...     input_numb_fields=2, output_numb_fields=2, n_modes=[4, 4, 4]
... )
>>> x = torch.randn(10, 2, 20, 20, 20)
>>> out = block(x)

Initialization of the SpectralConvBlock3D class.

Parameters:

input_numb_fields (int) – The number of channels for the input.
output_numb_fields (int) – The number of channels for the output.
n_modes (list[int] | tuple[int]) – The number of modes to select for each dimension. It must be at most equal to \(\floor(Nx/2)+1\), \(\floor(Ny/2)+1\), \(\floor(Nz/2)+1\).

Raises:

ValueError – If the number of modes is not consistent.
ValueError – If the number of modes is not a list or tuple.

forward(x)[source]#

Forward pass.

Parameters:: x (torch.Tensor) – The input tensor. Expected of size [batch, input_numb_fields, Nx, Ny, Nz].
Returns:: The input tensor. Expected of size [batch, output_numb_fields, Nx, Ny, Nz].
Return type:: torch.Tensor