diff --git a/README.md b/README.md index ff118d7..59f2cc8 100644 --- a/README.md +++ b/README.md @@ -1,64 +1,171 @@ -

- - Physics-Informed Neural networks for Advanced modeling + + + +

+ +[![PyPi][pypi-shield]][pypi-url] +[![PyPi][pypiversion-shield]][pypi-url] +[![PyPi][downloads-shield]][downloads-url] +[![License][license-shield]][license-url] + +
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+ + ZenML Logo + + +

Solve equations, intuitively.

+ +

+ A simple framework to solve difficult problems with neural networks. +
+ Explore the docs » +
+ +
+ + +

+
+ + +
+ 🏁 Table of Contents +
    +
  1. Introduction
    2. +
  2. Quickstart
    3. +
  3. + Solve Your Differential Problem + +
    4. + +
  4. Contributing and Community
    5. + +
  5. License
    6. +
+
+ +
+ +# 🤖 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 +
-## 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) - - -* [Examples and Tutorials](#examples-and-tutorials) -* [References](#references) - -* [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: -

- - PINA interface for solving problems. - -

+```bash +pip install "pina-mathlab" +``` +
+# 🖼️ 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

Poisson approximation

+
+ -To install the package just type: -```bash -> pip install -e . -``` +# 🙌 Contributing and Community - - +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 +would like to contribute, please review our [Contributing +Guide](CONTRIBUTING.md) for all relevant details. - - - - - - - - - - - - - - - - - - -## 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: @@ -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. + -## 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.