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[](https://badge.fury.io/py/fastvpinns)
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<br />
<div align="center">
<a href="https://github.com/cmgcds/fastvpinns">
<img alt="FastVPINNs logo" src="https://raw.githubusercontent.com/cmgcds/fastvpinns/main/Fastvpinns_logo.png" width="500">
</a>
<h3 align="center">Tensor-driven accelerated framework for hp-variational pinns</h3>
<p align="center">
<br />
<a href="https://cmgcds.github.io/fastvpinns"><strong>Link to Documentation 📚</strong></a>
<br />
</p>
</div>
A robust tensor-based deep learning framework for solving partial differential equations using hp-Variational Physics-Informed Neural Networks (hp-VPINNs). The framework is based on the methodology presented in the [FastVPINNs Paper](https://arxiv.org/abs/2404.12063).
*This library is a highly optimised version of the the initial implementation of hp-VPINNs by [Kharazmi et al.](https://github.com/ehsankharazmi/hp-VPINNs). Refer the [hp-VPINNs Paper](https://arxiv.org/abs/2003.05385).*
## Authors 👨💻
---
[Thivin Anandh](https://github.com/thivinanandh), [Divij Ghose](https://divijghose.github.io/), [Sashikumaar Ganesan](https://cds.iisc.ac.in/faculty/sashi)
STARS Lab, Department of Computational and Data Sciences, Indian Institute of Science, Bangalore, India
## Installation 🛠️
---
The build of the code is currently tested on Python versions (3.8, 3.9, 3.10, 3.11), on OS Ubuntu 20.04 and Ubuntu 22.04, MacOS-latest and Windows-latest (refer compatibility build [Compatability check](https://github.com/cmgcds/fastvpinns/actions/workflows/compatibility-tests.yml)).
You can install the package using pip as follows:
```bash
pip install fastvpinns
```
On ubuntu systems with libGL issues caused due to matplotlib or gmsh, please run the following command to install the required dependencies:
```bash
sudo apt-get install -y libglu1-mesa
```
For more information on the installation process, please refer to our documentation [here](https://cmgcds.github.io/fastvpinns/).
## Citing 📜
---
If you use this code in your research, please consider citing the following paper:
```bibtex
@misc{anandh2024fastvpinns,
title={FastVPINNs: Tensor-Driven Acceleration
of VPINNs for Complex Geometries},
author={Thivin Anandh, Divij Ghose, Himanshu Jain
and Sashikumaar Ganesan},
year={2024},
eprint={2404.12063},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
```
## Usage 🚀
---
For detailed usage, please refer to our documentation [here](https://cmgcds.github.io/fastvpinns/).
The package provides a simple API to train and solve PDE using VPINNs. The following code snippet demonstrates how to train a hp-VPINN model for the 2D Poisson equation for a structured grid. We could observe that we can solve a PDE using fastvpinns using 15 lines of code.
```python
#load the geometry
domain = Geometry_2D("quadrilateral", "internal", 100, 100, "./")
cells, boundary_points = domain.generate_quad_mesh_internal(x_limits=[0, 1],y_limits=[0, 1],n_cells_x=4, n_cells_y=4, num_boundary_points=400)
# load the FEspace
fespace = Fespace2D(domain.mesh,cells,boundary_points,domain.mesh_type,fe_order=5,fe_type="jacobi",quad_order=5,quad_type="legendre", fe_transformation_type="bilinear",bound_function_dict=bound_function_dict,bound_condition_dict=bound_condition_dict,
forcing_function=rhs,output_path=i_output_path,generate_mesh_plot=True)
# Instantiate Data handler
datahandler = DataHandler2D(fespace, domain, dtype=tf.float32)
# Instantiate the model with the loss function for the model
model = DenseModel(layer_dims=[2, 30, 30, 30, 1],learning_rate_dict=0.01,params_dict=params_dict,
loss_function=pde_loss_poisson, ## Loss function of poisson2D
input_tensors_list=[in_tensor, dir_in, dir_out],
orig_factor_matrices=[datahandler.shape_val_mat_list,datahandler.grad_x_mat_list, datahandler.grad_y_mat_list],
force_function_list=datahandler.forcing_function_list, tensor_dtype=tf.float32,
use_attention=i_use_attention, ## Archived (not in use)
activation=i_activation,
hessian=False)
# Train the model
for epoch in range(1000):
model.train_step()
```
Note : Supporting functions which define the actual solution and boundary conditions have to be passed to the main code.
## Contributing 🤝
---
This code is currently maintained by the authors as mentioned in the section above. We welcome contributions from the community. Please refer to the [documentation](https://cmgcds.github.io/fastvpinns/) for guidelines on contributing to the project.
## License 📑
---
This project is licensed under the MIT License - see the [LICENSE](LICENSE) file for details.
Raw data
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The framework is based on the methodology presented in the [FastVPINNs Paper](https://arxiv.org/abs/2404.12063).\n\n\n*This library is a highly optimised version of the the initial implementation of hp-VPINNs by [Kharazmi et al.](https://github.com/ehsankharazmi/hp-VPINNs). Refer the [hp-VPINNs Paper](https://arxiv.org/abs/2003.05385).*\n\n## Authors \ud83d\udc68\u200d\ud83d\udcbb\n---\n\n[Thivin Anandh](https://github.com/thivinanandh), [Divij Ghose](https://divijghose.github.io/), [Sashikumaar Ganesan](https://cds.iisc.ac.in/faculty/sashi)\n\nSTARS Lab, Department of Computational and Data Sciences, Indian Institute of Science, Bangalore, India\n\n## Installation \ud83d\udee0\ufe0f\n---\n\nThe build of the code is currently tested on Python versions (3.8, 3.9, 3.10, 3.11), on OS Ubuntu 20.04 and Ubuntu 22.04, MacOS-latest and Windows-latest (refer compatibility build [Compatability check](https://github.com/cmgcds/fastvpinns/actions/workflows/compatibility-tests.yml)).\n\nYou can install the package using pip as follows:\n\n```bash\npip install fastvpinns\n```\n\n On ubuntu systems with libGL issues caused due to matplotlib or gmsh, please run the following command to install the required dependencies:\n```bash\nsudo apt-get install -y libglu1-mesa \n```\n\nFor more information on the installation process, please refer to our documentation [here](https://cmgcds.github.io/fastvpinns/).\n\n## Citing \ud83d\udcdc\n---\n\nIf you use this code in your research, please consider citing the following paper:\n\n```bibtex\n@misc{anandh2024fastvpinns,\n title={FastVPINNs: Tensor-Driven Acceleration\n of VPINNs for Complex Geometries}, \n author={Thivin Anandh, Divij Ghose, Himanshu Jain\n and Sashikumaar Ganesan},\n year={2024},\n eprint={2404.12063},\n archivePrefix={arXiv},\n primaryClass={cs.LG}\n}\n```\n\n## Usage \ud83d\ude80\n---\n\nFor detailed usage, please refer to our documentation [here](https://cmgcds.github.io/fastvpinns/).\n\nThe package provides a simple API to train and solve PDE using VPINNs. The following code snippet demonstrates how to train a hp-VPINN model for the 2D Poisson equation for a structured grid. We could observe that we can solve a PDE using fastvpinns using 15 lines of code.\n\n```python\n#load the geometry \ndomain = Geometry_2D(\"quadrilateral\", \"internal\", 100, 100, \"./\")\ncells, boundary_points = domain.generate_quad_mesh_internal(x_limits=[0, 1],y_limits=[0, 1],n_cells_x=4, n_cells_y=4, num_boundary_points=400)\n\n# load the FEspace\nfespace = Fespace2D(domain.mesh,cells,boundary_points,domain.mesh_type,fe_order=5,fe_type=\"jacobi\",quad_order=5,quad_type=\"legendre\", fe_transformation_type=\"bilinear\",bound_function_dict=bound_function_dict,bound_condition_dict=bound_condition_dict,\nforcing_function=rhs,output_path=i_output_path,generate_mesh_plot=True)\n\n# Instantiate Data handler \ndatahandler = DataHandler2D(fespace, domain, dtype=tf.float32)\n\n# Instantiate the model with the loss function for the model \nmodel = DenseModel(layer_dims=[2, 30, 30, 30, 1],learning_rate_dict=0.01,params_dict=params_dict,\n loss_function=pde_loss_poisson, ## Loss function of poisson2D\n input_tensors_list=[in_tensor, dir_in, dir_out],\n orig_factor_matrices=[datahandler.shape_val_mat_list,datahandler.grad_x_mat_list, datahandler.grad_y_mat_list],\n force_function_list=datahandler.forcing_function_list, tensor_dtype=tf.float32,\n use_attention=i_use_attention, ## Archived (not in use)\n activation=i_activation,\n hessian=False)\n\n# Train the model\nfor epoch in range(1000):\n model.train_step()\n```\n\nNote : Supporting functions which define the actual solution and boundary conditions have to be passed to the main code.\n\n## Contributing \ud83e\udd1d\n---\nThis code is currently maintained by the authors as mentioned in the section above. 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