jayroxis / pinns

PyTorch Implementation of Physics-informed Neural Networks

PINNs (Physics-informed Neural Networks)

---

This is a simple implementation of the Physics-informed Neural Networks (PINNs) using PyTorch and Tensorflow.

---

Attribute

Original Work: Maziar Raissi, Paris Perdikaris, and George Em Karniadakis

Github Repo : https://github.com/maziarraissi/PINNs

Link: https://github.com/maziarraissi/PINNs/tree/master/appendix/continuous_time_identification%20(Burgers)

@article{raissi2017physicsI, title={Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations}, author={Raissi, Maziar and Perdikaris, Paris and Karniadakis, George Em}, journal={arXiv preprint arXiv:1711.10561}, year={2017} }

@article{raissi2017physicsII, title={Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations}, author={Raissi, Maziar and Perdikaris, Paris and Karniadakis, George Em}, journal={arXiv preprint arXiv:1711.10566}, year={2017} }

---

Dependencies

Major Dependencies:

• Tensorflow (for Tensorflow Implementation): pip install --upgrade tensorflow
• PyTorch (for PyTorch Implementation): ```pip install --upgrade torch``
• Jupyter Notebook/Lab: pip install jupyterlab (JupyterLab) or pip install notebook

Peripheral Dependencies:

• numpy: pip install numpy
• seaborn: pip install seaborn
• matplotlib: pip install matplotlib
• pyDOE (for Tensorflow Implementation): pip install pyDOE

pinns's Issues

Data Creating Method

Hey Jay,

Thanks so much for creating this repository. It is quite helpful. I was wondering how you created the "burgers_shock.mat" data? Is this data computed by analytically solving the Burgers equation? Would it be possible to have the code you used to generate that?

Best,
-Amir

why two optimizers are needed during the training?

Hello, thanks a lot for your hard work and your sharing.
I would like to ask why two optimizers are needed during the training.
self.optimizer.step(self.loss_func)
self.optimizer_Adam.step()

Thank you so much in advance for your answers.

Unable to visualize data in test code

I am currently trying out the Burgers Identification (PyTorch) code, however, It was able to train, but I cannot visualize the result. Any suggestionn on how to fix it? Thanks

Coefficient (0.01 / math.pi) without parentheses

class Net:
    ...
    def loss_func(self):
        ...
        loss_pde = self.criterion(du_dt + u.squeeze() * du_dx, 0.01 / math.pi * du_dxx)
        ...
        return loss

Here the code of loss_pde = self.criterion(du_dt + u.squeeze() * du_dx, 0.01 / math.pi * du_dxx) of coefficient 0.01 / math.pi need to be (0.01 / math.pi) , and the code will be loss_pde = self.criterion(du_dt + u.squeeze() * du_dx, (0.01 / math.pi) * du_dxx).
Then the result will change. It's so amazing.

Error issue

The L2 test error in the original PINN text is 6.7e-4, but training with the pytorch version yields results of 1e-3~3e-3. What is the reason for this？

OMP: Error in the file named "Burgers Inference (PyTorch).ipynb"

when i run file "Burgers Inference (PyTorch).ipynb" error_u = np.linalg.norm(u_star-u_pred,2)/np.linalg.norm(u_star,2) in the folder “continuous_time_inference (Burgers)”， An error occurred that

OMP: Error #15: Initializing libiomp5md.dll, but found libiomp5md.dll already initialized.
OMP: Hint This means that multiple copies of the OpenMP runtime have been linked into the program. That is dangerous, since it can degrade performance or cause incorrect results. The best thing to do is to ensure that only a single OpenMP runtime is linked into the process, e.g. by avoiding static linking of the OpenMP runtime in any library. As an unsafe, unsupported, undocumented workaround you can set the environment variable KMP_DUPLICATE_LIB_OK=TRUE to allow the program to continue to execute, but that may cause crashes or silently produce incorrect results. For more information, please see http://www.intel.com/software/products/support/.

In the function 'loss_func' of 'Net class' of"Burgers.ipynb", do we need to add 'self.adam.zero_grad()' ?

In the function 'loss_func' of 'Net class' of"Burgers.ipynb", do we need to add 'self.adam.zero_grad()' ?

Burgers inference discrete time

Hi @jayroxis and thank you very much for this useful repository, really appreciated.

I was wondering if by any chance your pytorch implementation for the Burgers Equation inference solution, "time discrete" approach was also available and open to public?

Thank you again!

PS: sorry for asking this in an issue, I could not find your email.