Fourier neural operators for classifying images with varying sizes in one shot training: Applied to 3D digital porous media

Fourier Neural Operators (FNOs) are invariant to the size of input images, allowing them to process images of any size without altering the network architecture, unlike traditional convolutional neural networks (CNNs). Using this advantage of FNOs, we propose a novel deep learning framework designed for classifying images with varying sizes. In this approach, the proposed FNO-based framework is trained on images of multiple sizes simultaneously. As a practical application, we consider predicting permeability of three-dimensional digital porous media. From a computer science perspective, an intuitive approach to construct the desired FNO framework would be to connect the output of FNO layers to a classifier using adaptive max pooling. However, we demonstrate that while this intuitive approach works for porous media with fixed sizes, it fails for those with varying sizes. To overcome this challenge, we introduce our approach: instead of adaptive max pooling, we utilize static max pooling with the channel width of FNO layers. Because the channel width of FNO layers is independent of the input image size, our framework can accommodate images of varying sizes during training. We demonstrate the effectiveness of our proposed framework by comparing its performance with the intuitive approach using the example of classifying three-dimensional digital porous media of different sizes.