# 𝕌pdes
𝕌pdes is a general-purpose library for mesh-free PDE simulation and control.
- GitHub project: https://github.com/ddrous/Updes
- Documentation: https://ddrous.github.io/Updes/
## Features
𝕌pdes leverages Radial Basis Functions (RBFs) and JAX to provide the following features:
- User-centric design: no need to re-implement a solver for each new PDE
- Lightning fast mesh-free simulation via Radial Basis Functions
- Robust differentiable simulation via JAX, and portable across CPU, GPU, and TPU
- Support for Dirichlet, Neumann, Robin, and Periodic boundary conditions
- Automatic generation of normals from 2D GMSH meshes
𝕌pdes in incredibly extendable, with additional features added frequently.
## Getting started
The package is available on PyPI. You can install it with
```
pip install updes
```
The example below illustrates how to solve the Laplace equation with Dirichlet and Neumann boundary conditions:
```python
import updes
import jax.numpy as jnp
# Create a mesh-free cloud of points on a unit square
facet_types={"South":"n", "West":"d", "North":"d", "East":"d"}
cloud = updes.SquareCloud(Nx=30, Ny=20, facet_types=facet_types)
# Define the differential operator (left-hand side of the PDE)
def my_diff_operator(x, center, rbf, monomial, fields):
return updes.nodal_laplacian(x, center, rbf, monomial)
# Define the right-hand side of the PDE
def my_rhs_operator(x, centers, rbf, fields):
return 0.0
# Set a sin function as the Dirichlet BC on the North, and zero everywhere else
sine = lambda coord: jnp.sin(jnp.pi * coord[0])
zero = lambda coord: 0.0
boundary_conditions = {"South":zero, "West":zero, "North":sine, "East":zero}
# Solve the Laplace equation with a JIT-compiled solver
sol = updes.pde_solver_jit(diff_operator=my_diff_operator,
rhs_operator=my_rhs_operator,
cloud=cloud,
boundary_conditions=boundary_conditions,
rbf=updes.polyharmonic,
max_degree=1)
# Visualize the solution
cloud.visualize_field(sol.vals, cmap="jet", projection="3d", title="RBF solution")
```
𝕌pdes can handle much complicated cases with little to no modifications to the code above. Check out further notebooks and scripts in the [documentation](https://ddrous.github.io/Updes/) and the folder [`demos`](./demos)!
## Dependencies
- **Core**: JAX - GMSH - Lineax - Matplotlib - Seaborn - Scikit-Learn
- **Optional**: PyVista - FFMPEG - QuartoDoc
See the `pyproject.toml` file the specific versions of the dependencies.
## Cite us !
If you use this software, please cite us with the following BibTeX entry:
```
@inproceedings{nzoyem2023comparison,
title={A comparison of mesh-free differentiable programming and data-driven strategies for optimal control under PDE constraints},
author={Nzoyem Ngueguin, Roussel Desmond and Barton, David AW and Deakin, Tom},
booktitle={Proceedings of the SC'23 Workshops of The International Conference on High Performance Computing, Network, Storage, and Analysis},
pages={21--28},
year={2023}}
```
Raw data
{
"_id": null,
"home_page": null,
"name": "updes",
"maintainer": null,
"docs_url": null,
"requires_python": null,
"maintainer_email": null,
"keywords": "differentiable-programming, radial-basis-function, meshfree, optimisation, differentiable-physics, PDEs",
"author": null,
"author_email": "Roussel Desmond Nzoyem <desmond.ngueguin@gmail.com>",
"download_url": "https://files.pythonhosted.org/packages/1d/57/8a4e9d13c8b1fa52aa8388dbcd8cca976ff95820826f3b99668f30b067bc/updes-1.0.2.post1.tar.gz",
"platform": null,
"description": "# \ud835\udd4cpdes\n\n\ud835\udd4cpdes is a general-purpose library for mesh-free PDE simulation and control.\n- GitHub project: https://github.com/ddrous/Updes\n- Documentation: https://ddrous.github.io/Updes/\n\n\n## Features\n\ud835\udd4cpdes leverages Radial Basis Functions (RBFs) and JAX to provide the following features:\n- User-centric design: no need to re-implement a solver for each new PDE\n- Lightning fast mesh-free simulation via Radial Basis Functions\n- Robust differentiable simulation via JAX, and portable across CPU, GPU, and TPU\n- Support for Dirichlet, Neumann, Robin, and Periodic boundary conditions\n- Automatic generation of normals from 2D GMSH meshes\n\n\ud835\udd4cpdes in incredibly extendable, with additional features added frequently.\n\n\n## Getting started\nThe package is available on PyPI. You can install it with\n```\npip install updes\n```\n\nThe example below illustrates how to solve the Laplace equation with Dirichlet and Neumann boundary conditions:\n```python\nimport updes\nimport jax.numpy as jnp\n\n# Create a mesh-free cloud of points on a unit square\nfacet_types={\"South\":\"n\", \"West\":\"d\", \"North\":\"d\", \"East\":\"d\"}\ncloud = updes.SquareCloud(Nx=30, Ny=20, facet_types=facet_types)\n\n# Define the differential operator (left-hand side of the PDE)\ndef my_diff_operator(x, center, rbf, monomial, fields):\n return updes.nodal_laplacian(x, center, rbf, monomial)\n\n# Define the right-hand side of the PDE\ndef my_rhs_operator(x, centers, rbf, fields):\n return 0.0\n\n# Set a sin function as the Dirichlet BC on the North, and zero everywhere else\nsine = lambda coord: jnp.sin(jnp.pi * coord[0])\nzero = lambda coord: 0.0\nboundary_conditions = {\"South\":zero, \"West\":zero, \"North\":sine, \"East\":zero}\n\n# Solve the Laplace equation with a JIT-compiled solver\nsol = updes.pde_solver_jit(diff_operator=my_diff_operator, \n rhs_operator=my_rhs_operator, \n cloud=cloud, \n boundary_conditions=boundary_conditions, \n rbf=updes.polyharmonic,\n max_degree=1)\n\n# Visualize the solution\ncloud.visualize_field(sol.vals, cmap=\"jet\", projection=\"3d\", title=\"RBF solution\")\n```\n\n\ud835\udd4cpdes can handle much complicated cases with little to no modifications to the code above. Check out further notebooks and scripts in the [documentation](https://ddrous.github.io/Updes/) and the folder [`demos`](./demos)!\n\n\n## Dependencies\n- **Core**: JAX - GMSH - Lineax - Matplotlib - Seaborn - Scikit-Learn\n- **Optional**: PyVista - FFMPEG - QuartoDoc\n\nSee the `pyproject.toml` file the specific versions of the dependencies.\n\n\n## Cite us !\nIf you use this software, please cite us with the following BibTeX entry:\n```\n@inproceedings{nzoyem2023comparison,\n title={A comparison of mesh-free differentiable programming and data-driven strategies for optimal control under PDE constraints},\n author={Nzoyem Ngueguin, Roussel Desmond and Barton, David AW and Deakin, Tom},\n booktitle={Proceedings of the SC'23 Workshops of The International Conference on High Performance Computing, Network, Storage, and Analysis},\n pages={21--28},\n year={2023}}\n```\n",
"bugtrack_url": null,
"license": null,
"summary": "Universal Partial Differential Equations Simulator",
"version": "1.0.2.post1",
"project_urls": {
"Documentation": "https://ddrous.github.io/Updes/",
"Homepage": "https://github.com/ddrous/Updes"
},
"split_keywords": [
"differentiable-programming",
" radial-basis-function",
" meshfree",
" optimisation",
" differentiable-physics",
" pdes"
],
"urls": [
{
"comment_text": "",
"digests": {
"blake2b_256": "e860cb3f2dccd6f122179f8adf008c8de7d63389b6842bfdf10c321ef020c0e4",
"md5": "c30446246d907fd976066f6bdb30976d",
"sha256": "5f7634843f2e7428d9973247bb510acc3980fba76e9bd1e921b358c087338aa0"
},
"downloads": -1,
"filename": "updes-1.0.2.post1-py3-none-any.whl",
"has_sig": false,
"md5_digest": "c30446246d907fd976066f6bdb30976d",
"packagetype": "bdist_wheel",
"python_version": "py3",
"requires_python": null,
"size": 26170,
"upload_time": "2024-06-21T00:47:53",
"upload_time_iso_8601": "2024-06-21T00:47:53.513893Z",
"url": "https://files.pythonhosted.org/packages/e8/60/cb3f2dccd6f122179f8adf008c8de7d63389b6842bfdf10c321ef020c0e4/updes-1.0.2.post1-py3-none-any.whl",
"yanked": false,
"yanked_reason": null
},
{
"comment_text": "",
"digests": {
"blake2b_256": "1d578a4e9d13c8b1fa52aa8388dbcd8cca976ff95820826f3b99668f30b067bc",
"md5": "c5cae5752a82646fede17a7eed878dfc",
"sha256": "421ae8d6234011c501fdbf899ffd88f215cab72ed0cf17ca314a9691404e2459"
},
"downloads": -1,
"filename": "updes-1.0.2.post1.tar.gz",
"has_sig": false,
"md5_digest": "c5cae5752a82646fede17a7eed878dfc",
"packagetype": "sdist",
"python_version": "source",
"requires_python": null,
"size": 26769,
"upload_time": "2024-06-21T00:47:54",
"upload_time_iso_8601": "2024-06-21T00:47:54.854069Z",
"url": "https://files.pythonhosted.org/packages/1d/57/8a4e9d13c8b1fa52aa8388dbcd8cca976ff95820826f3b99668f30b067bc/updes-1.0.2.post1.tar.gz",
"yanked": false,
"yanked_reason": null
}
],
"upload_time": "2024-06-21 00:47:54",
"github": true,
"gitlab": false,
"bitbucket": false,
"codeberg": false,
"github_user": "ddrous",
"github_project": "Updes",
"travis_ci": false,
"coveralls": false,
"github_actions": true,
"lcname": "updes"
}
JSON
