sources/neuraloperator/examples/layers/plot_resample.py

"""
Resampling layers
=================

When working with neural operators, we often need to change the resolution of our data.
For some architectures, like the FNO, this is handled automatically due to the 
resolution-invariant nature of the Fourier domain.

However, for other architectures, like the U-Net, we need to explicitly upsample and downsample
the data as it flows through the network. The ``neuralop.layers.resample`` function provides a 
convenient way to do this.

In this example, we'll demonstrate how to use the ``resample`` function to upsample and downsample
a sample from a Gaussian Random Field, which serves as a better visual tool than piecewise
constant data for observing the effects of interpolation.

For 1D and 2D inputs, the ``resample`` function uses PyTorch’s built-in spatial interpolators 
for efficiency, applying linear interpolation for 1D data and bicubic interpolation for 2D data directly 
in the spatial domain. 

For 3D or higher-dimensional inputs, the ``resample`` function switches to a spectral interpolation method 
based on the Fourier transform. The input is transformed into the frequency domain using a real n-dimensional FFT, 
which decomposes the signal into its frequency components. By resizing this frequency representation and 
then applying an inverse FFT, the function achieves smooth, alias-free interpolation 
that preserves the signal’s overall structure.
"""
import torch
import matplotlib.pyplot as plt
from neuralop.layers.resample import resample

# %%
# .. raw:: html
#
#    <div style="margin-top: 3em;"></div>
#
# First, let's generate a data input. We create a high-resolution Gaussian Random Field (GRF), which
# is a smooth, continuous signal, making it ideal for visualizing the effects of resampling.
device = "cpu"


def generate_grf(shape, alpha=2.5, device="cpu"):
    """Generates a 2D Gaussian Random Field.

    Parameters
    ----------
    shape : tuple
        The desired output shape (height, width).
    alpha : float, optional
        A parameter controlling the smoothness of the field.
        Higher alpha leads to smoother fields, by default 2.5.
    device : str, optional
        The device to create the tensor on, by default 'cpu'.

    Returns
    -------
    torch.Tensor
        A 4D tensor of shape (1, 1, height, width) containing the GRF.
    """
    n, m = shape
    freq_x = torch.fft.fftfreq(n, d=1 / n, device=device).view(-1, 1)
    freq_y = torch.fft.fftfreq(m, d=1 / m, device=device).view(1, -1)

    norm_sq = freq_x**2 + freq_y**2
    norm_sq[0, 0] = 1.0  # Avoid division by zero

    # Generate white noise in frequency domain
    noise = torch.randn(n, m, dtype=torch.cfloat, device=device)

    # Apply a power-law filter
    filtered_noise = noise * (norm_sq ** (-alpha / 2.0))

    # Inverse FFT to get the spatial field
    field = torch.fft.ifft2(filtered_noise).real

    # Normalize to [0, 1] for visualization
    field = (field - field.min()) / (field.max() - field.min())

    return field.unsqueeze(0).unsqueeze(0)  # Add batch and channel dims


# Generate a 128x128 sample as our ground truth
high_res = 128
high_res_data = generate_grf((high_res, high_res), device=device)

# Define the low resolution we want to simulate (4x downsampling)
low_res = 32

# %%
# .. raw:: html
#
#    <div style="margin-top: 3em;"></div>
#
# Now, let's use the ``resample`` function to simulate downsampling and upsampling operations.
# This could for instance be used in the encoder and decoder of a U-Net architecture.
# The function takes an input tensor, a `scale_factor`, and a list of
# `axis` dimensions to which the resampling is applied.

# To downsample from 128x128 to 32x32, we need a scale factor of 32/128 = 0.25
downsample_factor = low_res / high_res
downsampled_data = resample(high_res_data, downsample_factor, [2, 3])

# To upsample from 32x32 back to 128x128, we need a scale factor of 128/32 = 4
upsample_factor = high_res / low_res
upsampled_data = resample(downsampled_data, upsample_factor, [2, 3])


# %%
# .. raw:: html
#
#    <div style="margin-top: 3em;"></div>
#
# Finally, let's visualize the results to see the effect of the ``resample`` function.

fig, axs = plt.subplots(1, 3, figsize=(14, 6))
plt.subplots_adjust(wspace=0.04)
fig.suptitle("Resampling a Gaussian Random Field", fontsize=24)

# Plot the original high-resolution data
im1 = axs[0].imshow(high_res_data.squeeze().cpu().numpy(), cmap="viridis", vmin=0, vmax=1)
axs[0].set_title(f"High-Res Data ({high_res}x{high_res})", fontsize=16, fontweight="bold")
cbar1 = fig.colorbar(im1, ax=axs[0], fraction=0.046, pad=0.04, ticks=[0, 0.5, 1])
cbar1.ax.tick_params(labelsize=14)

# Plot the downsampled data
im2 = axs[1].imshow(downsampled_data.squeeze().cpu().numpy(), cmap="viridis", vmin=0, vmax=1)
axs[1].set_title(f"Downsampled (x{downsample_factor}) ({low_res}x{low_res})", fontsize=16, fontweight="bold")
cbar2 = fig.colorbar(im2, ax=axs[1], fraction=0.046, pad=0.04, ticks=[0, 0.5, 1])
cbar2.ax.tick_params(labelsize=14)

# Plot the upsampled data
im3 = axs[2].imshow(upsampled_data.squeeze().cpu().numpy(), cmap="viridis", vmin=0, vmax=1)
axs[2].set_title(f"Upsampled Back (x{upsample_factor:.0f}) ({high_res}x{high_res})", fontsize=16, fontweight="bold")
cbar3 = fig.colorbar(im3, ax=axs[2], fraction=0.046, pad=0.04, ticks=[0, 0.5, 1])
cbar3.ax.tick_params(labelsize=14)

# Hide axis ticks for a cleaner look
for ax in axs.flat:
    ax.set_xticks([])
    ax.set_yticks([])

plt.tight_layout(rect=[0, 0.03, 1, 1.08])
plt.show()

# %%
# .. raw:: html
#
#    <div style="margin-top: 3em;"></div>
#
# The ``resample`` function effectively changes the resolution of the data.
# Notice that the upsampled image on the right is a faithful, if slightly blurrier,
# reconstruction of the original. This is because the downsampling step is lossy;
# high-frequency details are lost and cannot be perfectly recovered.