neuralop.layers.differential_conv.FiniteDifferenceConvolution

class neuralop.layers.differential_conv.FiniteDifferenceConvolution(in_channels, out_channels, n_dim, kernel_size=3, groups=1, padding='periodic')[source]

Finite Difference Convolution Layer

This is the finite difference convolution layer introduced in [1].

It computes a finite difference convolution on a regular grid, which converges to a directional derivative as the grid is refined.

Parameters:

in_channelsint

Number of in_channels

out_channelsint

Number of out_channels

n_dimint

Number of dimensions in the input domain

kernel_sizeint, optional

Odd kernel size used for convolutional finite difference stencil, by default 3

groupsint, optional

Splitting number of channels, by default 1

paddingliteral {‘periodic’, ‘replicate’, ‘reflect’, ‘zeros’}, optional

Mode of padding to use on input. Options: ‘periodic’, ‘replicate’, ‘reflect’, ‘zeros’, by default ‘periodic’ See torch.nn.functional.padding.

Methods

forward(x, grid_width)

FiniteDifferenceConvolution's forward pass.

References

[1]

: Liu-Schiaffini, M., et al. (2024). “Neural Operators with Localized Integral and Differential Kernels”. ICML 2024, https://arxiv.org/abs/2402.16845.

forward(x, grid_width)[source]

FiniteDifferenceConvolution’s forward pass. Alternatively, one could center the conv kernel by subtracting the mean pointwise in the kernel: conv(x, kernel - mean(kernel)) / grid_width

Parameters:

xtorch.tensor

input tensor, shape (batch, in_channels, d_1, d_2, …d_n)

grid_widthfloat

discretization size of input grid