傅立叶神经算子 该存储库包含该论文的代码： 在这项工作中，我们通过直接在傅立叶空间中对积分内核进行参数化，从而制定了一种新的神经元运算符，从而实现了高效而富有表现力的体系结构。我们对Burgers方程，Darcy流和Navier-Stokes方程（包括湍流状态）进行实验。与现有的神经网络方法相比，我们的傅里叶神经算子显示了最先进的性能，并且与传统的PDE求解器相比，它的速度提高了三个数量级。 它来自以前的作品： 要求 档案文件 代码采用简单脚本的形式。每个脚本应该是独立的并且可以直接运行。 fourier_1d.py是傅立叶神经算子1D的问题，如（与时间无关的）Burgers方程的第5.1节中所讨论的。 fourier_2d.py是傅立叶神经算子的2D问题如达西流在第5.2节中所讨论的。 fourier_2d_time.py是傅立叶神经算子的2D问题诸如在5.3节中讨论的Navier

偏微分方程数值求解 matlab 适合工科研究生博士生参考 也可作为工程人员参考

Partial differential equations (PDEs) and variational methods were introduced into image processing about fifteen years ago. Since then, intensive research has been carried out. The goals of this book are to present a variety of image analysis applications, the precise mathematics involved and how to discretize them. Thus, this book is intended for two audiences. The first is the mathematical community by showing the contribution of mathematics to this domain. It is also the occasion to highlight some unsolved theoretical questions. The second is the computer vision community by presenting a clear, self-contained and global overview of the mathematics involved in image processing problems. This work will serve as a useful source of reference and inspiration for fellow researchers in Applied Mathematics and Computer Vision, as well as being a basis for advanced courses within these fields. During the four years since the publication of the first edition, there has been substantial progress in the range of image processing applications covered by the PDE framework. The main goals of the second edition are to update the first edition by giving a coherent account of some of the recent challenging applications, and to update the existing material. In addition, this book provides the reader with the opportunity to make his own simulations with a minimal effort. To this end, programming tools are made available, which will allow the reader to implement and test easily some classical approaches.

Applied Partial Differential Equations - A Visual Approach - P. Markowich (Springer, 2007) WW.pdf

Partial Differential Equations第四版

文集本身是众多方程领域的数学家为贺法国大家Haim Brezis60岁生日而拿出的祝贺论文的集合。很多文章都是具有很强概括性的综述。But，我也没有详细读过。

任意二维域上的泊松 使用有限元方法求解具有 RHS f 和 Dirichlet 边界条件的任意二维域上的泊松方程。

Functional Analysis Sobolev Spaces And Partial Differential Equations(Brezis)英文版，数分好教材，知乎多人荐之

- py-pde是一个Python软件包，用于求解偏微分方程（PDE）。 该程序包提供了可在其上定义标量和张量字段的网格的类。 关联的微分算子是使用numba编译的有限差分实现来计算的。 这允许定义，检查和求解典型的PDE，例如在物理动力系统研究中出现的PDE。 该软件包的重点在于易于使用，以探索PDE的行为。 但是，可以使用numba透明地编译核心计算，以提高速度。 安装 py-pde在pypi上可用，因此您应该可以通过pip安装它： pip install py-pde 为了使软件包的所有功能可用，您可能还需要安装以下可选软件包： pip install h5py pandas tqdm 此外，需要安装ffmpeg来创建电影。 或者，您可以使用频道通过安装py-pde ： conda install -c conda-forge py-pde 使用conda安装包括所

[Partial differential equations] [L. C. Evans]是数学系 偏微分方程专业的基础课之一，需要好好学习