  Fourier neural operators (FNOs) are invariant with respect to the size of
input images, and thus images with any size can be fed into FNO-based
frameworks without any modification of network architectures, in contrast to
traditional convolutional neural networks (CNNs). Leveraging the advantage of
FNOs, we propose a novel deep-learning framework for classifying images with
varying sizes. Particularly, we simultaneously train the proposed network on
multi-sized images. As a practical application, we consider the problem of
predicting the label (e.g., permeability) of three-dimensional digital porous
media. To construct the framework, an intuitive approach is to connect FNO
layers to a classifier using adaptive max pooling. First, we show that this
approach is only effective for porous media with fixed sizes, whereas it fails
for porous media of varying sizes. To overcome this limitation, we introduce
our approach: instead of using adaptive max pooling, we use static max pooling
with the size of channel width of FNO layers. Since the channel width of the
FNO layers is independent of input image size, the introduced framework can
handle multi-sized images during training. We show the effectiveness of the
introduced framework and compare its performance with the intuitive approach
through the example of the classification of three-dimensional digital porous
media of varying sizes.
