pierremtb / pinns-tf2.0

TensorFlow 2.0 implementation of Maziar Raissi's Physics Informed Neural Networks (PINNs).

PINNs-TF2.0

Implementation in TensorFlow 2.0 of different examples put together by Raissi et al. on their original publication about Physics Informed Neural Networks.

By designing a custom loss function for standard fully-connected deep neural networks, enforcing the known laws of physics governing the different setups, their work showed that it was possible to either solve or discover with surprisingly good accuracy Partial Differential Equations from noisy and scarce data. The very kind that is widespread in real-life applications.

Don’t forget the --recursive flag while cloning, in order to fetch the experiments data put together by Raissi et al:

git clone https://github.com/pierremtb/PINNs-TF2.0 --recursive

Also available on Google Colab (installation-free, GPU-enabled cloud notebooks)

• PINNs for 1D Burgers Equation (TF2.0).ipynb

Authors and citations

For more information, please refer to the following: (https://maziarraissi.github.io/PINNs/)

• Raissi, Maziar, Paris Perdikaris, and George Em Karniadakis. "Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations." arXiv preprint arXiv:1711.10561 (2017).

• Raissi, Maziar, Paris Perdikaris, and George Em Karniadakis. "Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations." arXiv preprint arXiv:1711.10566 (2017).

@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}
}

License

MIT License

Copyright (c) 2019 Pierre Jacquier

pinns-tf2.0's Issues

1dcomplex-schrodinger does not converge

Hay
the 1dcomplex-schrodinger does not converge to results presented in the article.
maybe there is additional commit missing?

ps. I did sanity chack by running 1d-burgers from current commit and it actually worked well in the same environment.

thanks

why importing of .mat file require

Dear Pierra
why the "burgers_shock.mat" file is required to proceed further for solving burger eq,
Is there any alternate way to proceed further.

and how burgers_shock.mat file has generated

"FileNotFoundError: [Errno 2] No such file or directory: 'latex': 'latex'"

Hello, I was running "PINNs-TF2.0/1d-burgers/inf_cont_burgers.py" and meeting a problem is 【 FileNotFoundError: [Errno 2] No such file or directory: 'latex': 'latex'】。Can you help me to solve it?

The question of continuous idenfication and discrete identification

When I run code on colab, I always get errors when running the continuous idenfication and discrete identification modules：

None
—— Starting Adam optimization ——

KeyError Traceback (most recent call last)
in <cell line: 40>()
38 layers[-1] = q
39 pinn = PhysicsInformedNN(layers, tf_optimizer, logger, dt, lb, ub, q, IRK_alpha, IRK_beta)
---> 40 pinn.fit(x_0, u_0, x_1, u_1, tf_epochs)
41 U_0_pred, U_1_pred = pinn.predict(x_star)
42 lambda_1_pred_noisy, lambda_2_pred_noisy = pinn.get_params(numpy=True)

13 frames
/usr/local/lib/python3.10/dist-packages/keras/optimizers/optimizer.py in _update_step(self, gradient, variable)
230 return
231 if self._var_key(variable) not in self._index_dict:
--> 232 raise KeyError(
233 f"The optimizer cannot recognize variable {variable.name}. "
234 "This usually means you are trying to call the optimizer to "

KeyError: in user code:

File "/usr/local/lib/python3.10/dist-packages/keras/optimizers/optimizer.py", line 224, in _update_step_xla  *
    return self._update_step(gradient, variable)
File "/usr/local/lib/python3.10/dist-packages/keras/optimizers/optimizer.py", line 232, in _update_step  **
    raise KeyError(

KeyError: 'The optimizer cannot recognize variable dense_4/kernel:0. This usually means you are trying to call the optimizer to update different parts of the model separately. Please call `optimizer.build(variables)` with the full list of trainable variables before the training loop or use legacy optimizer `tf.keras.optimizers.legacy.Adam.'