https://github.com/314arhaam/burger-pinn
A Physics-Informed Neural Network for solving Burgers' equation.
https://github.com/314arhaam/burger-pinn
burgers-equation deep-learning machine-learning neural-network physics-informed-neural-networks
Last synced: 24 days ago
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A Physics-Informed Neural Network for solving Burgers' equation.
- Host: GitHub
- URL: https://github.com/314arhaam/burger-pinn
- Owner: 314arhaam
- License: mit
- Created: 2021-11-05T17:16:18.000Z (over 4 years ago)
- Default Branch: main
- Last Pushed: 2024-03-06T19:52:52.000Z (over 2 years ago)
- Last Synced: 2024-03-06T20:59:57.772Z (over 2 years ago)
- Topics: burgers-equation, deep-learning, machine-learning, neural-network, physics-informed-neural-networks
- Language: Jupyter Notebook
- Homepage:
- Size: 1.18 MB
- Stars: 21
- Watchers: 1
- Forks: 6
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# 🍔 $\textbf{Burger-PINN}$ ⚛️
A Physics-Informed Neural Network to solve **Burgers' equation**.
Reference: [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://arxiv.org/abs/1711.10561)
Author's Github page: https://maziarraissi.github.io/PINNs/
**Check out my other PINN project: [heat-pinn](https://github.com/314arhaam/heat-pinn)**
## Introduction
This work is an implementation of the reference paper above. In this work, a neural network is trained to solve Burgers' equation, a well-known PDE, for a given set of BCs and an IC.
To train this model, certain number of points on the both boundaries and on the initial timestep were sampled, as input data, called **data points**, to compute MSE loss function, in addition to another set of points on the main domain of the problem, or **collocation points** to penalize the network in case the prediction on this set is not consistent with the governing PDE.
### Problem details
The governing PDE is:
### $\partial_{t}{u}+u\partial_{x}{u}-(\frac{0.01}{\pi})\partial_{xx}{u} = 0$
Which is solved in the following spatial and temporal domain:
### $D = \\{ (t, x)\ |\ 0\le t \le +1 \land -1\le x \le +1 \\}$
Regarding the following initial and boundary conditions:
$$
\begin{equation}
\begin{cases}
u(0, x) = -\sin({\pi x})\\
u(t, +1) = 0.0 \\
u(t, -1) = 0.0 \\
\end{cases}
\end{equation}
$$
## Results
$u(t, x)$ profile (Figure 1. in reference or [author's Github page](https://maziarraissi.github.io/assets/img/Burgers_CT_inference.png))
$u(t, x)$ in Cartesian coordinates for $t \in \\{0.25,0.5,0.75\\}$ (Figure 1. in reference or [author's Github page](https://maziarraissi.github.io/assets/img/Burgers_CT_inference.png))
$u(t, x)$ in Cartesian coordinates for more t values
# Note
This implementation is based on [Tensorflow 2.0](https://www.tensorflow.org/guide/effective_tf2) package and made possible by [Google Colabratory](https://colab.research.google.com) GPU.