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ippqw5 / PINNLearning

Implement PINN with high level APIs of TF2.0, including a solution of coupled PDEs with PINN
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Reference Paper #1

Open idevede opened 2 years ago

idevede commented 2 years ago

Hi @ippqw5,

Thanks for the well-organized repo! I would like to ask about the paper you used for the Jupyter " 7_11_Parabolic耦合pde模型.ipynb". You can directly email me with the address: cdf@pku.edu.cn.

I am looking forward to your response!

Best, Ide

ippqw5 commented 2 years ago

PARTITIONED TIMESTEPPING FOR A PARABOLIC TWO DOMA.pdf It is placed in the folder “04.论文资料”.

idevede commented 2 years ago

Hi @ippqw5,

Thanks for the response!

I am still not sure how PINN can satisfy the schema of solving the coupled PDE. It would be helpful if you can provide more references or intuitions. :)

Best, Ide

ippqw5 commented 2 years ago

Hi @idevede ， I'm sorry for my misunderstanding! I just used the model from the paper "PARTITIONED ..." to implement PINNs.

My strategy is to create two separate neural networks, each representing the respective solution of the two regions. In each epoch, the same training points on Interface are imported into the two networks respectively, so we can obtain the loss_Interface by automatic differentiation.

In addition, the above two neural networks also need to transmit different training points of corresponding regions. So, we can get the loss through pde equations in single region. (In this problem, we have two regions)

Finally, these losses are added to obtain the total LOSS, which means that we can train the above two networks simultaneously by LOSS。

I'm sorry for my poor English,and I hope you can understand my explanation.

The structure of the network is shown by following picture. image

idevede commented 2 years ago

Hi @ippqw5,

Thanks for the clear response! If it is convenient for you, we can add Wechat friend, and feel free to email me with your Wechat ID. :)

Best, Ide