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.

翻译：傅里叶神经算子(FNO)对输入图像尺寸具有不变性，因此与传统卷积神经网络(CNN)不同，任何尺寸的图像均可直接输入基于FNO的框架而无需调整网络架构。利用FNO这一优势，我们提出了一种用于分类变尺寸图像的新型深度学习框架。特别地，我们同时对多尺度图像进行网络训练。作为实际应用，我们考虑三维数字多孔介质的标签(如渗透率)预测问题。构建该框架时，直观方法是通过自适应最大池化将FNO层与分类器连接。首先，我们证明该方法仅对固定尺寸多孔介质有效，而对变尺寸多孔介质失效。为克服这一局限，我们提出新方法:采用与FNO层通道宽度等长的静态最大池化替代自适应最大池化。由于FNO层的通道宽度与输入图像尺寸无关，所提框架可在训练过程中处理多尺度图像。通过变尺寸三维数字多孔介质分类实例，我们展示了新框架的有效性，并与直观方法进行了性能对比。