# DeepXDE
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DeepXDE is a deep learning library on top of [TensorFlow](https://www.tensorflow.org/). Use DeepXDE if you need a deep learning library that
- solves forward and inverse partial differential equations (PDEs) via physics-informed neural network (PINN),
- solves forward and inverse integro-differential equations (IDEs) via PINN,
- solves forward and inverse fractional partial differential equations (fPDEs) via fractional PINN (fPINN),
- approximates functions from multi-fidelity data via multi-fidelity NN (MFNN),
- approximates nonlinear operators via deep operator network (DeepONet),
- approximates functions from a dataset with/without constraints.
**Documentation**: [ReadTheDocs](https://deepxde.readthedocs.io/), [Extended abstract](http://ceur-ws.org/Vol-2587/article_14.pdf), [Short paper](https://ml4physicalsciences.github.io/files/NeurIPS_ML4PS_2019_2.pdf), [Full paper](https://arxiv.org/abs/1907.04502), [Slides](https://lululxvi.github.io/files/talks/2020SIAMMDS_MS70.pdf), [Video](https://www.youtube.com/watch?v=Wfgr1pMA9fY&list=PL1e3Jic2_DwwJQ528agJYMEpA0oMaDSA9&index=13)
**Papers**
- Algorithms & examples
- Solving PDEs and IDEs via PINN: [Extended abstract](http://ceur-ws.org/Vol-2587/article_14.pdf), [Short paper](https://ml4physicalsciences.github.io/files/NeurIPS_ML4PS_2019_2.pdf), [Full paper](https://arxiv.org/abs/1907.04502)
- Solving fPDEs via fPINN: [SIAM J. Sci. Comput.](https://epubs.siam.org/doi/abs/10.1137/18M1229845)
- Solving stochastic PDEs via NN-arbitrary polynomial chaos (NN-aPC): [J. Comput. Phys.](https://www.sciencedirect.com/science/article/pii/S0021999119305340)
- Learning from multi-fidelity data via MFNN: [PNAS](https://www.pnas.org/content/117/13/7052), [J. Comput. Phys.](https://www.sciencedirect.com/science/article/pii/S0021999119307260)
- Learning nonlinear operators via DeepONet: [arXiv](https://arxiv.org/abs/1910.03193)
## Features
DeepXDE supports
- complex domain geometries without tyranny mesh generation. The primitive geometries are interval, triangle, rectangle, polygon, disk, cuboid, and sphere. Other geometries can be constructed as constructive solid geometry (CSG) using three boolean operations: union, difference, and intersection;
- multi-physics, i.e., coupled PDEs;
- 5 types of boundary conditions (BCs): Dirichlet, Neumann, Robin, periodic, and a general BC;
- time-dependent PDEs are solved as easily as time-independent ones by only adding initial conditions;
- residual-based adaptive refinement (RAR);
- uncertainty quantification using dropout;
- two types of neural networks: fully connected neural network, and residual neural network;
- many different losses, metrics, optimizers, learning rate schedules, initializations, regularizations, etc.;
- useful techniques, such as dropout and batch normalization;
- callbacks to monitor the internal states and statistics of the model during training;
- enables the user code to be compact, resembling closely the mathematical formulation.
All the components of DeepXDE are loosely coupled, and thus DeepXDE is well-structured and highly configurable. It is easy to customize DeepXDE to meet new demands.
## Installation
DeepXDE requires [TensorFlow](https://www.tensorflow.org/) to be installed. Both TensorFlow 1 and TensorFlow 2 can be used as the DeepXDE backend, but TensorFlow 1 is recommended, because in my tests TensorFlow 2 is 2x~3x slower than TensorFlow 1.
Then, you can install DeepXDE itself. If you use Python 2, you need to install DeepXDE using `pip`.
- Install the stable version with `pip`:
```
$ pip install deepxde
```
- Install the stable version with `conda`:
```
$ conda install -c conda-forge deepxde
```
- For developers, you should clone the folder to your local machine and put it along with your project scripts.
```
$ git clone https://github.com/lululxvi/deepxde.git
```
- Dependencies
- [Matplotlib](https://matplotlib.org/)
- [NumPy](http://www.numpy.org/)
- [SALib](http://salib.github.io/SALib/)
- [scikit-learn](https://scikit-learn.org)
- [SciPy](https://www.scipy.org/)
- [TensorFlow](https://www.tensorflow.org/)>=1.14.0
## Explore more
- [Examples](https://github.com/lululxvi/deepxde/tree/master/examples)
- [FAQ](https://deepxde.readthedocs.io/en/latest/user/faq.html)
- [Research papers used DeepXDE](https://deepxde.readthedocs.io/en/latest/user/research.html)
## Cite DeepXDE
If you use DeepXDE for academic research, you are encouraged to cite the following paper:
```
@article{lu2019deepxde,
author = {Lu, Lu and Meng, Xuhui and Mao, Zhiping and Karniadakis, George E.},
title = {{DeepXDE}: A deep learning library for solving differential equations},
journal = {arXiv preprint arXiv:1907.04502},
year = {2019}
}
```
## Contributing to DeepXDE
First off, thanks for taking the time to contribute!
- **Reporting bugs.** To report a bug, simply open an issue in the GitHub "Issues" section.
- **Suggesting enhancements.** To submit an enhancement suggestion for DeepXDE, including completely new features and minor improvements to existing functionality, let us know by opening an issue.
- **Pull requests.** If you made improvements to DeepXDE, fixed a bug, or had a new example, feel free to send us a pull-request.
- **Questions.** To get help on how to use DeepXDE or its functionalities, you can as well open an issue.
## License
[Apache license 2.0](https://github.com/lululxvi/deepxde/blob/master/LICENSE)
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资源分类:Python库 所属语言:Python 资源全名:DeepXDE-0.8.4.tar.gz 资源来源:官方 安装方法:https://lanzao.blog.csdn.net/article/details/101784059
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DeepXDE-0.8.4.tar.gz (58个子文件)
DeepXDE-0.8.4
MANIFEST.in 78B
PKG-INFO 9KB
LICENSE 11KB
setup.cfg 79B
requirements.txt 61B
setup.py 2KB
README.md 6KB
DeepXDE.egg-info
PKG-INFO 9KB
requires.txt 61B
SOURCES.txt 1KB
top_level.txt 8B
dependency_links.txt 1B
deepxde
real.py 732B
display.py 2KB
callbacks.py 12KB
utils.py 5KB
data
helper.py 362B
ide.py 5KB
func_constraint.py 2KB
pde.py 7KB
op_dataset.py 2KB
mf.py 6KB
dataset.py 2KB
func.py 1KB
__init__.py 514B
fpde.py 24KB
data.py 566B
train.py 2KB
metrics.py 1KB
maps
resnet.py 2KB
fnn.py 4KB
map.py 2KB
regularizers.py 532B
activations.py 1KB
__init__.py 211B
opnn.py 7KB
mfnn.py 4KB
pfnn.py 4KB
initializers.py 6KB
math_ops.py 1KB
losses.py 2KB
__init__.py 762B
external_optimizer.py 16KB
postprocessing.py 4KB
boundary_conditions.py 5KB
geometry
timedomain.py 4KB
geometry_3d.py 3KB
geometry_1d.py 4KB
__init__.py 760B
geometry_2d.py 15KB
geometry_nd.py 5KB
geometry.py 3KB
csg.py 7KB
model.py 15KB
config.py 151B
array_ops.py 2KB
initial_condition.py 806B
backend.py 792B
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