[PaddlePaddle Hackathon 2] 94. Add Paddle as a new backend of DeepXDE

[TCChenlong]

This ISSUE is a task of PaddlePaddle Hackathon 2. For more information, please see

• PaddlePaddle Hackathon 2
• 【PaddlePaddle Hackathon 第二期】任务总览
• Video (in Chinese)

Task

Description: DeepXDE currently supports TensorFlow 1.x, TensorFlow 2.x, PyTorch, and JAX as backends. In this task, you need to modify DeepXDE to support Paddle as a new backend (the backend name is "paddle"). Specifically, you need to implement the following tasks.

1. Support function approximation

   • Goal: Support the following test examples: func.py, dataset.py
   • Main DeepXDE modules to be modified: dde.backend, dde.nn, dde.optimizers, dde.model

2. Support solving forward ODEs

   • Goal: Support the following test examples: A simple ODE system
   • Main DeepXDE modules to be modified: dde.gradients, dde.icbc

3. Support solving inverse ODEs

   • Goal: Support the following test examples: Inverse problem for the Lorenz system, Inverse problem for the Lorenz system with exogenous input
   • Main DeepXDE modules to be modified: dde.model

4. Update DeepXDE Documentation to add Paddle

Note:

• Please format your code using black.
• Please add sufficient comments for the nontrivial and tricky codes.

Difficulty: Hard

Submission

• Design documentation: Create a PR at PaddlePaddle/community rfcs/DeepXDE folder. In addition to other Hackathon requirements, please discuss:
  • how do you plan to compute the Jacobian, such as which Paddle API to use.
  • any improvement to Paddle should be done in the future in order to better support DeepXDE.
• Code implementation PR

Q&A

• 如果在开发中对于上述任务有任何问题，欢迎在本 ISSUE 下留言交流。
• 对于开发中的共性问题，在活动过程中，会定期组织答疑，请大家关注官网&QQ群的通知，及时参与。

[praksharma]

（此 ISSUE 为 PaddlePaddle Hackathon 第二期活动的任务 ISSUE，更多详见 【PaddlePaddle Hackathon 第二期】任务总览）

【任务内容】

任务说明：DeepXDE目前支持TensorFlow 1.x, TensorFlow 2.x, PyTorch和JAX作为计算的backend。此任务需要增加Paddle作为DeepXDE的backend，以实现以下功能：

1. 使用神经网络进行函数逼近，例如需要Paddle支持代码https://github.com/lululxvi/deepxde/blob/master/examples/function/dataset.py
2. 支持physics-informed neural network (PINN)。 2.1 使用PINN求解PDE的正问题：https://deepxde.readthedocs.io/en/latest/demos/pinn_forward.html 2.2 使用PINN求解PDE的反问题：https://deepxde.readthedocs.io/en/latest/demos/pinn_inverse.html
3. 在DeepXDE的说明文档中加入Paddle相应的内容。

任务难度：困难

【提交内容】

• 设计文档，并提 PR 至 PaddlePaddle/community 的 rfcs/DeepXDE 目录
• 功能实现 PR

【答疑交流】

• 如果在开发中对于上述任务有任何问题，欢迎在本 ISSUE 下留言交流。
• 对于开发中的共性问题，在活动过程中，会定期组织答疑，请大家关注官网&QQ群的通知，及时参与。

Can someone translate this issue into English?

[lululxvi]

This is a hackathon of PaddlePaddle, a deep learning framework developed by Baidu (a Chinese company). The aim of this hackathon is to allow DeepXDE to support the backend Paddle.