MD-PINN

[AAAI'24 Accept] An Interpretable Approach to the Solutions of High-Dimensional Partial Differential Equations

This project is a comparative experiment of the article: A program for solving multidimensional PDE(partial differential equations) based on PINN. This program import deepxde as a module, with reference to its example.

本项目是文章的对比实验：基于 PINN 的多维 PDE（偏微分方程）求解程序。本程序导入了deepxde 作为模块，并参考了其示例。

PDE Introduction

There are 3 types of PDE: Advection, Heat and Poission, every PDE have 2 different definitions. We worked out every 2D and 3D solusion of every definition of PDE. Detail materials are shown in .ipynb files.

本次求解的PDE 有 3 种类型：Advection, Heat 和 Poission，每种 PDE 给定 2 种不同的定义。 我们计算出了 每个PDE每个定义的2D和3D解。 更多详细内容在 .ipynb 文件中。

Dataset

Generated test datas ( from Lulu Cao) are put on three floders. In this work, we did not use train data in PINN trainning.

测试数据已生成好（来自曹璐璐），并放在三个文件夹中。 在这项工作中，我们没有在 PINN 训练中使用数据进行训练。

Bibliography

If you find our paper or code helpful, consider citing:

如果您认为这篇文章或这份代码有用, 请引用:

@inproceedings{cao2024interpretable,
  title={An Interpretable Approach to the Solutions of High-Dimensional Partial Differential Equations},
  author={Cao, Lulu and Liu, Yufei and Wang, Zhenzhong and Xu, Dejun and Ye, Kai and Tan, Kay Chen and Jiang, Min},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={38},
  number={18},
  pages={20640--20648},
  year={2024}
}