2024年12月28日 · In this paper, a multi-scale Fourier neural operator (MscaleFNO) is proposed to reduce the spectral bias of the FNO in learning the mapping between highly oscillatory functions, with application to the nonlinear mapping between the coefficient of …

FNO在机器学习求解偏微分方程领域比较火热，是继 PINN 后一种所谓 "算子学习''的范式，但因为论文中涉及大量数学推导和灵感的阐述让人很难快速理解。 通过阅读源码，我们会发现它的实现其实并不复杂。 本文旨在： 剖析源码中的细节、难点和关键部分，并给出方便进一步深入的参考链接。 原作者代码地址： FNO-Code 论文地址： FNO-Paper. 但是当初看原作者的代码仓库时发现他提供的数据集 (谷歌硬盘上)并不完整，所以没办法直接运行那些程序。 后来看到 L. Lu 在关 …

In this paper, a multi-scale Fourier neural operator (MscaleFNO) is proposed to reduce the spectral bias of the FNO in learning the mapping between highly oscillatory functions, with application to the nonlinear mapping between the coefficient …

由于FNO在github上所提供的代码比较简洁，并且功能齐全，很适合通过复现的方式对该模型进行学习和研究，下面直接进入正题去看代码。 2.代码解析 首先先附上源代码的链接， https:// github.com/zongyi-li/fo urier_neural_operator

2024年12月31日 · In this paper, a multi-scale Fourier neural operator (MscaleFNO) is proposed to reduce the spectral bias of the FNO in learning the mapping between highly oscillatory functions, with application to the nonlinearmappingbetweenthecoeᱏ앍cientoftheHelmholtzequation and its solution.

2022年11月24日 · The FNO seismic simulation is a data-driven method that needs a small amount of training data, especially when using blended source training data. It is a discretization-independent method that is not subject to the limitation of spatial sampling and time steps imposed on traditional numerical solvers, implying that the training data can be ...

2025年1月23日 · The Fourier neural operator (FNO) is one of the workhorses in operator learning. It’s like a superhero that helps in understanding mappings between complex functions. The unique aspect of FNO is that it shifts input functions into the frequency domain—a fancy term for analyzing how those functions behave at different frequencies, like music ...

我们开发了一种基于物理信息傅立叶神经算子 (FNO) 的小数据驱动时域方法，用于在复杂介质中进行快速地震模拟。 与大多数基于 DL 的建模方案不同，这些方案要么通过将物理约束嵌入成本函数来求解波动方程，要么通过将波函数合并到卷积神经网络 (CNN) 中进行基于物理的学习，FNO 使用类似于结构的学习架构分步傅里叶波传播器，它由两个分别在空间域和波数域中表示的 CNN 组成。 空间域 CNN 充当本地可训练的相位屏补偿。 波数域 CNN 表示一个非局部空间卷积算 …

FNO的作者把AI for PDE的方法总结为了Finite-dimensional operators、 Neural-FEM 和 Neural Operators 这三类，要想准确理解这三种分类方式，就需要对欧几里得空间（Euclidean space）和巴拿赫空间（Banach space）等一些数学名词有一定的理性和感性的认知，我在上一篇讲DeepONet文章的 ...

2025年3月18日 · Abstract. In this paper, a multi-scale Fourier neural operator (MscaleFNO) is proposed to reduce the spectral bias of the FNO in learning high-frequency mapping between highly oscillatory functions, with an application to the nonlinear mapping between the coefficient of the Helmholtz equation and its solution.