# A novel Fourier neural operator framework for classification of multi-sized images: Application to three dimensional digital porous media

arXiv: https://arxiv.org/abs/2402.11568 · HTML: https://mlsanity.com/paper/2402.11568/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 41 of its 85 references that are in the map.
- First posted on arXiv 18 Feb 2024.

## Builds on (most cited first, 30 of 41)

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- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
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- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
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- [Reliable extrapolation of deep neural operators informed by physics or sparse observations](https://mlsanity.com/paper/2212.06347/) (2022)
- [Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness](https://mlsanity.com/paper/2305.17289/) (2023)
- [Generative Adversarial Neural Operators](https://mlsanity.com/paper/2205.03017/) (2022)
- [Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration](https://mlsanity.com/paper/2303.04778/) (2023)
- [Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network](https://mlsanity.com/paper/2201.02217/) (2022)
- [A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries](https://mlsanity.com/paper/2010.09469/) (2020)
- [On the influence of over-parameterization in manifold based surrogates and deep neural operators](https://mlsanity.com/paper/2203.05071/) (2022)
- [RecFNO: a resolution-invariant flow and heat field reconstruction method from sparse observations via Fourier neural operator](https://mlsanity.com/paper/2302.09808/) (2023)
- [Fourier neural operator for learning solutions to macroscopic traffic flow models: Application to the forward and inverse problems](https://mlsanity.com/paper/2308.07051/) (2023)
- [Fourier neural operator for real-time simulation of 3D dynamic urban microclimate](https://mlsanity.com/paper/2308.03985/) (2023)

## Abstract (arXiv)

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.