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<p align="center">
<a href="http://mathlab.github.io/PINA/" target="_blank" >
<img alt="Physics-Informed Neural networks for Advanced modeling" src="readme/pina_logo.png" width="200" />
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<h3 align="center">Solve equations, intuitively.</h3>
<p align="center">
A simple framework to solve difficult problems with neural networks.
<br />
<a href="https://mathlab.github.io/PINA/"><strong>Explore the docs »</strong></a>
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<details>
<summary>🏁 Table of Contents</summary>
<ol>
<li><a href="#-introduction">Introduction</a></li>
<li><a href="#-quickstart">Quickstart</a></li>
<li>
<a href="#%EF%B8%8F-solve-your-differential-problem">Solve Your Differential Problem</a>
<ul>
<li><a href="#-1-formulate-the-problem">Formulate the Problem</a></li>
<li><a href="#-2-solve-the-problem">Solve the Problem</a></li>
</ul>
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<br />
# 🤖 Introduction
🤹 PINA is a Python package providing an easy interface to deal with *physics-informed neural networks* (PINN) for the approximation of (differential, nonlinear, ...) functions. Based on Pytorch, PINA offers a simple and intuitive way to formalize a specific problem and solve it using PINN.
- 👨‍💻 Formulate your differential problem in few lines of code, just translating the mathematical equations into Python
- 📄 Training your neural network in order to solve the problem
- 🚀 Use the model to visualize and analyze the solution!
**PINA**: Physics-Informed Neural networks for Advanced modeling
<br>
## Table of contents
* [Description](#description)
* [Problem definition](#problem-definition)
* [Problem solution](#problem-solution)
* [Dependencies and installation](#dependencies-and-installation)
* [Installing via PIP](#installing-via-pip)
* [Installing from source](#installing-from-source)
<!-- * [Documentation](#documentation) -->
<!-- * [Testing](#testing) -->
* [Examples and Tutorials](#examples-and-tutorials)
* [References](#references)
<!-- * [Recent works with PyDMD](#recent-works-with-pydmd) -->
* [Authors and contributors](#authors-and-contributors)
* [How to contribute](#how-to-contribute)
* [Submitting a patch](#submitting-a-patch)
* [License](#license)
# 🤸 Quickstart
## Description
**PINA** is a Python package providing an easy interface to deal with *physics-informed neural networks* (PINN) for the approximation of (differential, nonlinear, ...) functions. Based on Pytorch, PINA offers a simple and intuitive way to formalize a specific problem and solve it using PINN. The approximated solution of a differential equation can be implemented using PINA in a few lines of code thanks to the intuitive and user-friendly interface.
[Install PINA](https://mathlab.github.io/PINA/_rst/installation.html) via
[PyPI](https://pypi.org/project/pina-mathlab/). Python 3 is required:
<p align="center">
<a href="http://mathlab.github.io/PINA/" target="_blank" >
<img alt="PINA interface for solving problems." src="readme/API_color.png" width="400" />
</a>
</p>
```bash
pip install "pina-mathlab"
```
<br>
# 🖼️ Solve Your Differential Problem
#### Physics-informed neural network
PINN is a novel approach that involves neural networks to solve supervised learning tasks while respecting any given law of physics described by general nonlinear differential equations. Proposed in *"Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations"*, such framework aims to solve problems in a continuous and nonlinear settings.
PINN is a novel approach that involves neural networks to solve supervised learning tasks while respecting any given law of physics described by general nonlinear differential equations. Proposed in [Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations](https://www.sciencedirect.com/science/article/pii/S0021999118307125?casa_token=p0BAG8SoAbEAAAAA:3H3r1G0SJ7IdXWm-FYGRJZ0RAb_T1qynSdfn-2VxqQubiSWnot5yyKli9UiH82rqQWY_Wzfq0HVV), such framework aims to solve problems in a continuous and nonlinear settings.
## 🔋 1. Formulate the Problem
#### Problem definition
First step is formalization of the problem in the PINA framework. We take as example here a simple Poisson problem, but PINA is already able to deal with **multi-dimensional**, **parametric**, **time-dependent** problems.
Consider:
$$\begin{cases} \Delta u = \sin(\pi x)\sin(\pi y)\quad& \text{in} \\ D \\\\ u = 0& \text{on} \\ \partial D \end{cases}$$
$$
\begin{cases}
\Delta u = \sin(\pi x)\sin(\pi y)\quad& \text{in}\, D \\
u = 0& \text{on}\, \partial D \end{cases}$$
where $D = [0, 1]^2$ is a square domain, $u$ the unknown field, and $\partial D = \Gamma_1 \cup \Gamma_2 \cup \Gamma_3 \cup \Gamma_4$, where $\Gamma_i$ are the boundaries of the square for $i=1,\cdots,4$. The translation in PINA code becomes a new class containing all the information about the domain, about the `conditions` and nothing more:
@@ -86,7 +193,7 @@ class Poisson(SpatialProblem):
}
```
#### Problem solution
## 👨‍🍳 2. Solve the Problem
After defining it, we want of course to solve such a problem. The only things we need is a `model`, in this case a feed forward network, and some samples of the domain and boundaries, here using a Cartesian grid. In these points we are going to evaluate the residuals, which is nothing but the loss of the network.
```python
@@ -108,68 +215,35 @@ After the training we can infer our model, save it or just plot the PINN approxi
<p align="center">
<img alt="Poisson approximation" src="readme/poisson_plot.png" width="100%" />
</p>
<br>
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## Dependencies and installation
**PINA** requires `numpy`, `scipy`, `matplotlib`, `future`, `torch`, `sphinx` (for the documentation) and `pytest` (for local test). The code is tested for Python 3, while compatibility of Python 2 is not guaranteed anymore. It can be installed using `pip` or directly from the source code.
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### Installing via PIP
Mac and Linux users can install pre-built binary packages using pip.
To install the package just type:
```bash
> pip install git+https://github.com/mathLab/PINA.git
```
To uninstall the package:
```bash
> pip uninstall pina
```
ZenML is managed by a [core team](https://zenml.io/company#CompanyTeam) of
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and you can directly influence the roadmap as follows:
### Installing from source
The official distribution is on GitHub, and you can clone the repository using
```bash
> git clone https://github.com/mathLab/PINA
```
- Vote on your most wanted feature on our [Discussion
board](https://zenml.io/discussion).
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To install the package just type:
```bash
> pip install -e .
```
# 🙌 Contributing and Community
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We would love to develop PINA together with our community! Best way to get
started is to select any issue from the [`good-first-issue`
label](https://github.com/mathLab/PINA/issues?q=is%3Aopen+is%3Aissue+label%3A%22good+first+issue%22). If you
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Guide](CONTRIBUTING.md) for all relevant details.
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## Examples and Tutorials
The directory `Examples` contains some examples showing Poisson and Burgers problems solved in the PINN context.
### References
To implement the package we follow these works:
* Raissi, Maziar, Paris Perdikaris, and George E. Karniadakis.
*Physics-informed neural networks: A deep learning framework for solving
forward and inverse problems involving nonlinear partial differential
equations.* Journal of Computational Physics 378 (2019): 686-707.
## Authors and contributors
We warmly thank all the contributors that have supported PINA!
We warmly thank all the contributors that have supported PINA so far:
<a href="https://github.com/mathLab/PINA/graphs/contributors">
<img src="https://contrib.rocks/image?repo=mathLab/PINA" />
@@ -178,48 +252,18 @@ We warmly thank all the contributors that have supported PINA!
Made with [contrib.rocks](https://contrib.rocks).
## How to contribute
We'd love to accept your patches and contributions to this project. There are just a few small guidelines you need to follow.
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## License
# 📜 License
See the [LICENSE](LICENSE.rst) file for license rights and limitations (MIT).
PINA is distributed under the terms of the MIT License.
A complete version of the license is available in the [LICENSE.rst](LICENSE.rst) file in this repository. Any contribution made to this project will be licensed under the MIT License.