1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
|
%global _empty_manifest_terminate_build 0
Name: python-DeepXDE
Version: 1.8.4
Release: 1
Summary: A library for scientific machine learning
License: LGPL-2.1
URL: https://github.com/lululxvi/deepxde
Source0: https://mirrors.nju.edu.cn/pypi/web/packages/87/81/ab8ce53a2a1785394554a8674f8e5cfe6e5cb7bcb9d02ecab6e7b2951c80/DeepXDE-1.8.4.tar.gz
BuildArch: noarch
Requires: python3-matplotlib
Requires: python3-numpy
Requires: python3-scikit-learn
Requires: python3-scikit-optimize
Requires: python3-scipy
%description
# DeepXDE
[](https://github.com/lululxvi/deepxde/actions/workflows/build.yml)
[](https://deepxde.readthedocs.io/en/latest/?badge=latest)
[](https://www.codacy.com/gh/lululxvi/deepxde/dashboard?utm_source=github.com&utm_medium=referral&utm_content=lululxvi/deepxde&utm_campaign=Badge_Grade)
[](https://badge.fury.io/py/DeepXDE)
[](https://pepy.tech/project/deepxde)
[](https://anaconda.org/conda-forge/deepxde)
[](https://anaconda.org/conda-forge/deepxde)
[](https://github.com/lululxvi/deepxde/blob/master/LICENSE)
DeepXDE is a library for scientific machine learning and physics-informed learning. DeepXDE includes the following algorithms:
- physics-informed neural network (PINN)
- solving different problems
- solving forward/inverse ordinary/partial differential equations (ODEs/PDEs) [[SIAM Rev.](https://doi.org/10.1137/19M1274067)]
- solving forward/inverse integro-differential equations (IDEs) [[SIAM Rev.](https://doi.org/10.1137/19M1274067)]
- fPINN: solving forward/inverse fractional PDEs (fPDEs) [[SIAM J. Sci. Comput.](https://doi.org/10.1137/18M1229845)]
- NN-arbitrary polynomial chaos (NN-aPC): solving forward/inverse stochastic PDEs (sPDEs) [[J. Comput. Phys.](https://doi.org/10.1016/j.jcp.2019.07.048)]
- PINN with hard constraints (hPINN): solving inverse design/topology optimization [[SIAM J. Sci. Comput.](https://doi.org/10.1137/21M1397908)]
- improving PINN accuracy
- residual-based adaptive sampling [[SIAM Rev.](https://doi.org/10.1137/19M1274067), [Comput. Methods Appl. Mech. Eng.](https://doi.org/10.1016/j.cma.2022.115671)]
- gradient-enhanced PINN (gPINN) [[Comput. Methods Appl. Mech. Eng.](https://doi.org/10.1016/j.cma.2022.114823)]
- PINN with multi-scale Fourier features [[Comput. Methods Appl. Mech. Eng.](https://doi.org/10.1016/j.cma.2021.113938)]
- [Slides](https://github.com/lululxvi/tutorials/blob/master/20211210_pinn/pinn.pdf), [Video](https://www.youtube.com/watch?v=Wfgr1pMA9fY&list=PL1e3Jic2_DwwJQ528agJYMEpA0oMaDSA9&index=13), [Video in Chinese](http://tianyuan.xmu.edu.cn/cn/minicourses/637.html)
- (physics-informed) deep operator network (DeepONet)
- DeepONet: learning operators [[Nat. Mach. Intell.](https://doi.org/10.1038/s42256-021-00302-5)]
- DeepONet extensions, e.g., POD-DeepONet [[Comput. Methods Appl. Mech. Eng.](https://doi.org/10.1016/j.cma.2022.114778)]
- MIONet: learning multiple-input operators [[SIAM J. Sci. Comput.](https://doi.org/10.1137/22M1477751)]
- Fourier-MIONet [[arXiv](https://arxiv.org/abs/2303.04778)]
- physics-informed DeepONet [[Sci. Adv.](https://doi.org/10.1126/sciadv.abi8605)]
- multifidelity DeepONet [[Phys. Rev. Research](https://doi.org/10.1103/PhysRevResearch.4.023210)]
- DeepM&Mnet: solving multiphysics and multiscale problems [[J. Comput. Phys.](https://doi.org/10.1016/j.jcp.2021.110296), [J. Comput. Phys.](https://doi.org/10.1016/j.jcp.2021.110698)]
- Reliable extrapolation [[arXiv](https://arxiv.org/abs/2212.06347)]
- multifidelity neural network (MFNN)
- learning from multifidelity data [[J. Comput. Phys.](https://doi.org/10.1016/j.jcp.2019.109020), [PNAS](https://doi.org/10.1073/pnas.1922210117)]
DeepXDE supports five tensor libraries as backends: TensorFlow 1.x (`tensorflow.compat.v1` in TensorFlow 2.x), TensorFlow 2.x, PyTorch, JAX, and PaddlePaddle. For how to select one, see [Working with different backends](https://deepxde.readthedocs.io/en/latest/user/installation.html#working-with-different-backends).
**Documentation**: [ReadTheDocs](https://deepxde.readthedocs.io)
## Features
DeepXDE has implemented many algorithms as shown above and supports many features:
- enables the user code to be compact, resembling closely the mathematical formulation.
- **complex domain geometries** without tyranny mesh generation. The primitive geometries are interval, triangle, rectangle, polygon, disk, ellipse, cuboid, sphere, hypercube, and hypersphere. Other geometries can be constructed as constructive solid geometry (CSG) using three boolean operations: union, difference, and intersection. DeepXDE also supports a geometry represented by a point cloud.
- 5 types of **boundary conditions** (BCs): Dirichlet, Neumann, Robin, periodic, and a general BC, which can be defined on an arbitrary domain or on a point set.
- different **neural networks**: fully connected neural network (FNN), stacked FNN, residual neural network, (spatio-temporal) multi-scale Fourier feature networks, etc.
- many **sampling methods**: uniform, pseudorandom, Latin hypercube sampling, Halton sequence, Hammersley sequence, and Sobol sequence. The training points can keep the same during training or be resampled (adaptively) every certain iterations.
- 4 **function spaces**: power series, Chebyshev polynomial, Gaussian random field (1D/2D).
- different **optimizers**: Adam, L-BFGS, etc.
- conveniently **save** the model during training, and **load** a trained model.
- **callbacks** to monitor the internal states and statistics of the model during training: early stopping, etc.
- **uncertainty quantification** using dropout.
- **float16**, **float32**, and **float64**.
- many other useful features: different (weighted) losses, learning rate schedules, metrics, etc.
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 one of the following backend-specific dependencies to be installed:
- TensorFlow 1.x: [TensorFlow](https://www.tensorflow.org)>=2.7.0
- TensorFlow 2.x: [TensorFlow](https://www.tensorflow.org)>=2.2.0, [TensorFlow Probability](https://www.tensorflow.org/probability)>=0.10.0
- PyTorch: [PyTorch](https://pytorch.org)>=1.9.0
- JAX: [JAX](https://jax.readthedocs.io), [Flax](https://flax.readthedocs.io), [Optax](https://optax.readthedocs.io)
- PaddlePaddle: [PaddlePaddle](https://www.paddlepaddle.org.cn/en) ([develop version](https://www.paddlepaddle.org.cn/en/install/quick?docurl=/documentation/docs/en/develop/install/pip/linux-pip_en.html))
Then, you can install DeepXDE itself.
- 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
```
## Explore more
- [Install and Setup](https://deepxde.readthedocs.io/en/latest/user/installation.html)
- [Demos of function approximation](https://deepxde.readthedocs.io/en/latest/demos/function.html)
- [Demos of forward problems](https://deepxde.readthedocs.io/en/latest/demos/pinn_forward.html)
- [Demos of inverse problems](https://deepxde.readthedocs.io/en/latest/demos/pinn_inverse.html)
- [Demos of operator learning](https://deepxde.readthedocs.io/en/latest/demos/operator.html)
- [FAQ](https://deepxde.readthedocs.io/en/latest/user/faq.html)
- [Research papers used DeepXDE](https://deepxde.readthedocs.io/en/latest/user/research.html)
- [API](https://deepxde.readthedocs.io/en/latest/modules/deepxde.html)
## Cite DeepXDE
If you use DeepXDE for academic research, you are encouraged to cite the following paper:
```
@article{lu2021deepxde,
author = {Lu, Lu and Meng, Xuhui and Mao, Zhiping and Karniadakis, George Em},
title = {{DeepXDE}: A deep learning library for solving differential equations},
journal = {SIAM Review},
volume = {63},
number = {1},
pages = {208-228},
year = {2021},
doi = {10.1137/19M1274067}
}
```
## 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](https://github.com/lululxvi/deepxde/issues).
- **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 in the GitHub [Issues](https://github.com/lululxvi/deepxde/issues).
- **Pull requests.** If you made improvements to DeepXDE, fixed a bug, or had a new example, feel free to send us a pull-request.
- **Asking questions.** To get help on how to use DeepXDE or its functionalities, you can open a discussion in the GitHub [Discussions](https://github.com/lululxvi/deepxde/discussions).
- **Answering questions.** If you know the answer to any question in the [Discussions](https://github.com/lululxvi/deepxde/discussions), you are welcomed to answer.
**Slack.** The DeepXDE Slack hosts a primary audience of moderate to experienced DeepXDE users and developers for general chat, online discussions, collaboration, etc. If you need a slack invite, please send me an email.
## The Team
DeepXDE was developed by [Lu Lu](https://lu.seas.upenn.edu) under the supervision of Prof. [George Karniadakis](https://www.brown.edu/research/projects/crunch/george-karniadakis) at [Brown University](https://www.brown.edu) from the summer of 2018 to 2020, supported by [PhILMs](https://www.pnnl.gov/computing/philms). DeepXDE was originally self-hosted in Subversion at Brown University, under the name SciCoNet (Scientific Computing Neural Networks). On Feb 7, 2019, SciCoNet was moved from Subversion to GitHub, renamed to DeepXDE.
DeepXDE is currently maintained by [Lu Lu](https://lu.seas.upenn.edu) at [University of Pennsylvania](https://www.upenn.edu) with major contributions coming from several talented individuals in various forms and means. A non-exhaustive but growing list needs to mention: [Zongren Zou](https://github.com/ZongrenZou), [Zhongyi Jiang](https://github.com/Jerry-Jzy), [Shunyuan Mao](https://github.com/smao-astro), [Paul Escapil-Inchauspé](https://github.com/pescap).
## License
[LGPL-2.1 License](https://github.com/lululxvi/deepxde/blob/master/LICENSE)
%package -n python3-DeepXDE
Summary: A library for scientific machine learning
Provides: python-DeepXDE
BuildRequires: python3-devel
BuildRequires: python3-setuptools
BuildRequires: python3-pip
%description -n python3-DeepXDE
# DeepXDE
[](https://github.com/lululxvi/deepxde/actions/workflows/build.yml)
[](https://deepxde.readthedocs.io/en/latest/?badge=latest)
[](https://www.codacy.com/gh/lululxvi/deepxde/dashboard?utm_source=github.com&utm_medium=referral&utm_content=lululxvi/deepxde&utm_campaign=Badge_Grade)
[](https://badge.fury.io/py/DeepXDE)
[](https://pepy.tech/project/deepxde)
[](https://anaconda.org/conda-forge/deepxde)
[](https://anaconda.org/conda-forge/deepxde)
[](https://github.com/lululxvi/deepxde/blob/master/LICENSE)
DeepXDE is a library for scientific machine learning and physics-informed learning. DeepXDE includes the following algorithms:
- physics-informed neural network (PINN)
- solving different problems
- solving forward/inverse ordinary/partial differential equations (ODEs/PDEs) [[SIAM Rev.](https://doi.org/10.1137/19M1274067)]
- solving forward/inverse integro-differential equations (IDEs) [[SIAM Rev.](https://doi.org/10.1137/19M1274067)]
- fPINN: solving forward/inverse fractional PDEs (fPDEs) [[SIAM J. Sci. Comput.](https://doi.org/10.1137/18M1229845)]
- NN-arbitrary polynomial chaos (NN-aPC): solving forward/inverse stochastic PDEs (sPDEs) [[J. Comput. Phys.](https://doi.org/10.1016/j.jcp.2019.07.048)]
- PINN with hard constraints (hPINN): solving inverse design/topology optimization [[SIAM J. Sci. Comput.](https://doi.org/10.1137/21M1397908)]
- improving PINN accuracy
- residual-based adaptive sampling [[SIAM Rev.](https://doi.org/10.1137/19M1274067), [Comput. Methods Appl. Mech. Eng.](https://doi.org/10.1016/j.cma.2022.115671)]
- gradient-enhanced PINN (gPINN) [[Comput. Methods Appl. Mech. Eng.](https://doi.org/10.1016/j.cma.2022.114823)]
- PINN with multi-scale Fourier features [[Comput. Methods Appl. Mech. Eng.](https://doi.org/10.1016/j.cma.2021.113938)]
- [Slides](https://github.com/lululxvi/tutorials/blob/master/20211210_pinn/pinn.pdf), [Video](https://www.youtube.com/watch?v=Wfgr1pMA9fY&list=PL1e3Jic2_DwwJQ528agJYMEpA0oMaDSA9&index=13), [Video in Chinese](http://tianyuan.xmu.edu.cn/cn/minicourses/637.html)
- (physics-informed) deep operator network (DeepONet)
- DeepONet: learning operators [[Nat. Mach. Intell.](https://doi.org/10.1038/s42256-021-00302-5)]
- DeepONet extensions, e.g., POD-DeepONet [[Comput. Methods Appl. Mech. Eng.](https://doi.org/10.1016/j.cma.2022.114778)]
- MIONet: learning multiple-input operators [[SIAM J. Sci. Comput.](https://doi.org/10.1137/22M1477751)]
- Fourier-MIONet [[arXiv](https://arxiv.org/abs/2303.04778)]
- physics-informed DeepONet [[Sci. Adv.](https://doi.org/10.1126/sciadv.abi8605)]
- multifidelity DeepONet [[Phys. Rev. Research](https://doi.org/10.1103/PhysRevResearch.4.023210)]
- DeepM&Mnet: solving multiphysics and multiscale problems [[J. Comput. Phys.](https://doi.org/10.1016/j.jcp.2021.110296), [J. Comput. Phys.](https://doi.org/10.1016/j.jcp.2021.110698)]
- Reliable extrapolation [[arXiv](https://arxiv.org/abs/2212.06347)]
- multifidelity neural network (MFNN)
- learning from multifidelity data [[J. Comput. Phys.](https://doi.org/10.1016/j.jcp.2019.109020), [PNAS](https://doi.org/10.1073/pnas.1922210117)]
DeepXDE supports five tensor libraries as backends: TensorFlow 1.x (`tensorflow.compat.v1` in TensorFlow 2.x), TensorFlow 2.x, PyTorch, JAX, and PaddlePaddle. For how to select one, see [Working with different backends](https://deepxde.readthedocs.io/en/latest/user/installation.html#working-with-different-backends).
**Documentation**: [ReadTheDocs](https://deepxde.readthedocs.io)
## Features
DeepXDE has implemented many algorithms as shown above and supports many features:
- enables the user code to be compact, resembling closely the mathematical formulation.
- **complex domain geometries** without tyranny mesh generation. The primitive geometries are interval, triangle, rectangle, polygon, disk, ellipse, cuboid, sphere, hypercube, and hypersphere. Other geometries can be constructed as constructive solid geometry (CSG) using three boolean operations: union, difference, and intersection. DeepXDE also supports a geometry represented by a point cloud.
- 5 types of **boundary conditions** (BCs): Dirichlet, Neumann, Robin, periodic, and a general BC, which can be defined on an arbitrary domain or on a point set.
- different **neural networks**: fully connected neural network (FNN), stacked FNN, residual neural network, (spatio-temporal) multi-scale Fourier feature networks, etc.
- many **sampling methods**: uniform, pseudorandom, Latin hypercube sampling, Halton sequence, Hammersley sequence, and Sobol sequence. The training points can keep the same during training or be resampled (adaptively) every certain iterations.
- 4 **function spaces**: power series, Chebyshev polynomial, Gaussian random field (1D/2D).
- different **optimizers**: Adam, L-BFGS, etc.
- conveniently **save** the model during training, and **load** a trained model.
- **callbacks** to monitor the internal states and statistics of the model during training: early stopping, etc.
- **uncertainty quantification** using dropout.
- **float16**, **float32**, and **float64**.
- many other useful features: different (weighted) losses, learning rate schedules, metrics, etc.
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 one of the following backend-specific dependencies to be installed:
- TensorFlow 1.x: [TensorFlow](https://www.tensorflow.org)>=2.7.0
- TensorFlow 2.x: [TensorFlow](https://www.tensorflow.org)>=2.2.0, [TensorFlow Probability](https://www.tensorflow.org/probability)>=0.10.0
- PyTorch: [PyTorch](https://pytorch.org)>=1.9.0
- JAX: [JAX](https://jax.readthedocs.io), [Flax](https://flax.readthedocs.io), [Optax](https://optax.readthedocs.io)
- PaddlePaddle: [PaddlePaddle](https://www.paddlepaddle.org.cn/en) ([develop version](https://www.paddlepaddle.org.cn/en/install/quick?docurl=/documentation/docs/en/develop/install/pip/linux-pip_en.html))
Then, you can install DeepXDE itself.
- 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
```
## Explore more
- [Install and Setup](https://deepxde.readthedocs.io/en/latest/user/installation.html)
- [Demos of function approximation](https://deepxde.readthedocs.io/en/latest/demos/function.html)
- [Demos of forward problems](https://deepxde.readthedocs.io/en/latest/demos/pinn_forward.html)
- [Demos of inverse problems](https://deepxde.readthedocs.io/en/latest/demos/pinn_inverse.html)
- [Demos of operator learning](https://deepxde.readthedocs.io/en/latest/demos/operator.html)
- [FAQ](https://deepxde.readthedocs.io/en/latest/user/faq.html)
- [Research papers used DeepXDE](https://deepxde.readthedocs.io/en/latest/user/research.html)
- [API](https://deepxde.readthedocs.io/en/latest/modules/deepxde.html)
## Cite DeepXDE
If you use DeepXDE for academic research, you are encouraged to cite the following paper:
```
@article{lu2021deepxde,
author = {Lu, Lu and Meng, Xuhui and Mao, Zhiping and Karniadakis, George Em},
title = {{DeepXDE}: A deep learning library for solving differential equations},
journal = {SIAM Review},
volume = {63},
number = {1},
pages = {208-228},
year = {2021},
doi = {10.1137/19M1274067}
}
```
## 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](https://github.com/lululxvi/deepxde/issues).
- **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 in the GitHub [Issues](https://github.com/lululxvi/deepxde/issues).
- **Pull requests.** If you made improvements to DeepXDE, fixed a bug, or had a new example, feel free to send us a pull-request.
- **Asking questions.** To get help on how to use DeepXDE or its functionalities, you can open a discussion in the GitHub [Discussions](https://github.com/lululxvi/deepxde/discussions).
- **Answering questions.** If you know the answer to any question in the [Discussions](https://github.com/lululxvi/deepxde/discussions), you are welcomed to answer.
**Slack.** The DeepXDE Slack hosts a primary audience of moderate to experienced DeepXDE users and developers for general chat, online discussions, collaboration, etc. If you need a slack invite, please send me an email.
## The Team
DeepXDE was developed by [Lu Lu](https://lu.seas.upenn.edu) under the supervision of Prof. [George Karniadakis](https://www.brown.edu/research/projects/crunch/george-karniadakis) at [Brown University](https://www.brown.edu) from the summer of 2018 to 2020, supported by [PhILMs](https://www.pnnl.gov/computing/philms). DeepXDE was originally self-hosted in Subversion at Brown University, under the name SciCoNet (Scientific Computing Neural Networks). On Feb 7, 2019, SciCoNet was moved from Subversion to GitHub, renamed to DeepXDE.
DeepXDE is currently maintained by [Lu Lu](https://lu.seas.upenn.edu) at [University of Pennsylvania](https://www.upenn.edu) with major contributions coming from several talented individuals in various forms and means. A non-exhaustive but growing list needs to mention: [Zongren Zou](https://github.com/ZongrenZou), [Zhongyi Jiang](https://github.com/Jerry-Jzy), [Shunyuan Mao](https://github.com/smao-astro), [Paul Escapil-Inchauspé](https://github.com/pescap).
## License
[LGPL-2.1 License](https://github.com/lululxvi/deepxde/blob/master/LICENSE)
%package help
Summary: Development documents and examples for DeepXDE
Provides: python3-DeepXDE-doc
%description help
# DeepXDE
[](https://github.com/lululxvi/deepxde/actions/workflows/build.yml)
[](https://deepxde.readthedocs.io/en/latest/?badge=latest)
[](https://www.codacy.com/gh/lululxvi/deepxde/dashboard?utm_source=github.com&utm_medium=referral&utm_content=lululxvi/deepxde&utm_campaign=Badge_Grade)
[](https://badge.fury.io/py/DeepXDE)
[](https://pepy.tech/project/deepxde)
[](https://anaconda.org/conda-forge/deepxde)
[](https://anaconda.org/conda-forge/deepxde)
[](https://github.com/lululxvi/deepxde/blob/master/LICENSE)
DeepXDE is a library for scientific machine learning and physics-informed learning. DeepXDE includes the following algorithms:
- physics-informed neural network (PINN)
- solving different problems
- solving forward/inverse ordinary/partial differential equations (ODEs/PDEs) [[SIAM Rev.](https://doi.org/10.1137/19M1274067)]
- solving forward/inverse integro-differential equations (IDEs) [[SIAM Rev.](https://doi.org/10.1137/19M1274067)]
- fPINN: solving forward/inverse fractional PDEs (fPDEs) [[SIAM J. Sci. Comput.](https://doi.org/10.1137/18M1229845)]
- NN-arbitrary polynomial chaos (NN-aPC): solving forward/inverse stochastic PDEs (sPDEs) [[J. Comput. Phys.](https://doi.org/10.1016/j.jcp.2019.07.048)]
- PINN with hard constraints (hPINN): solving inverse design/topology optimization [[SIAM J. Sci. Comput.](https://doi.org/10.1137/21M1397908)]
- improving PINN accuracy
- residual-based adaptive sampling [[SIAM Rev.](https://doi.org/10.1137/19M1274067), [Comput. Methods Appl. Mech. Eng.](https://doi.org/10.1016/j.cma.2022.115671)]
- gradient-enhanced PINN (gPINN) [[Comput. Methods Appl. Mech. Eng.](https://doi.org/10.1016/j.cma.2022.114823)]
- PINN with multi-scale Fourier features [[Comput. Methods Appl. Mech. Eng.](https://doi.org/10.1016/j.cma.2021.113938)]
- [Slides](https://github.com/lululxvi/tutorials/blob/master/20211210_pinn/pinn.pdf), [Video](https://www.youtube.com/watch?v=Wfgr1pMA9fY&list=PL1e3Jic2_DwwJQ528agJYMEpA0oMaDSA9&index=13), [Video in Chinese](http://tianyuan.xmu.edu.cn/cn/minicourses/637.html)
- (physics-informed) deep operator network (DeepONet)
- DeepONet: learning operators [[Nat. Mach. Intell.](https://doi.org/10.1038/s42256-021-00302-5)]
- DeepONet extensions, e.g., POD-DeepONet [[Comput. Methods Appl. Mech. Eng.](https://doi.org/10.1016/j.cma.2022.114778)]
- MIONet: learning multiple-input operators [[SIAM J. Sci. Comput.](https://doi.org/10.1137/22M1477751)]
- Fourier-MIONet [[arXiv](https://arxiv.org/abs/2303.04778)]
- physics-informed DeepONet [[Sci. Adv.](https://doi.org/10.1126/sciadv.abi8605)]
- multifidelity DeepONet [[Phys. Rev. Research](https://doi.org/10.1103/PhysRevResearch.4.023210)]
- DeepM&Mnet: solving multiphysics and multiscale problems [[J. Comput. Phys.](https://doi.org/10.1016/j.jcp.2021.110296), [J. Comput. Phys.](https://doi.org/10.1016/j.jcp.2021.110698)]
- Reliable extrapolation [[arXiv](https://arxiv.org/abs/2212.06347)]
- multifidelity neural network (MFNN)
- learning from multifidelity data [[J. Comput. Phys.](https://doi.org/10.1016/j.jcp.2019.109020), [PNAS](https://doi.org/10.1073/pnas.1922210117)]
DeepXDE supports five tensor libraries as backends: TensorFlow 1.x (`tensorflow.compat.v1` in TensorFlow 2.x), TensorFlow 2.x, PyTorch, JAX, and PaddlePaddle. For how to select one, see [Working with different backends](https://deepxde.readthedocs.io/en/latest/user/installation.html#working-with-different-backends).
**Documentation**: [ReadTheDocs](https://deepxde.readthedocs.io)
## Features
DeepXDE has implemented many algorithms as shown above and supports many features:
- enables the user code to be compact, resembling closely the mathematical formulation.
- **complex domain geometries** without tyranny mesh generation. The primitive geometries are interval, triangle, rectangle, polygon, disk, ellipse, cuboid, sphere, hypercube, and hypersphere. Other geometries can be constructed as constructive solid geometry (CSG) using three boolean operations: union, difference, and intersection. DeepXDE also supports a geometry represented by a point cloud.
- 5 types of **boundary conditions** (BCs): Dirichlet, Neumann, Robin, periodic, and a general BC, which can be defined on an arbitrary domain or on a point set.
- different **neural networks**: fully connected neural network (FNN), stacked FNN, residual neural network, (spatio-temporal) multi-scale Fourier feature networks, etc.
- many **sampling methods**: uniform, pseudorandom, Latin hypercube sampling, Halton sequence, Hammersley sequence, and Sobol sequence. The training points can keep the same during training or be resampled (adaptively) every certain iterations.
- 4 **function spaces**: power series, Chebyshev polynomial, Gaussian random field (1D/2D).
- different **optimizers**: Adam, L-BFGS, etc.
- conveniently **save** the model during training, and **load** a trained model.
- **callbacks** to monitor the internal states and statistics of the model during training: early stopping, etc.
- **uncertainty quantification** using dropout.
- **float16**, **float32**, and **float64**.
- many other useful features: different (weighted) losses, learning rate schedules, metrics, etc.
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 one of the following backend-specific dependencies to be installed:
- TensorFlow 1.x: [TensorFlow](https://www.tensorflow.org)>=2.7.0
- TensorFlow 2.x: [TensorFlow](https://www.tensorflow.org)>=2.2.0, [TensorFlow Probability](https://www.tensorflow.org/probability)>=0.10.0
- PyTorch: [PyTorch](https://pytorch.org)>=1.9.0
- JAX: [JAX](https://jax.readthedocs.io), [Flax](https://flax.readthedocs.io), [Optax](https://optax.readthedocs.io)
- PaddlePaddle: [PaddlePaddle](https://www.paddlepaddle.org.cn/en) ([develop version](https://www.paddlepaddle.org.cn/en/install/quick?docurl=/documentation/docs/en/develop/install/pip/linux-pip_en.html))
Then, you can install DeepXDE itself.
- 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
```
## Explore more
- [Install and Setup](https://deepxde.readthedocs.io/en/latest/user/installation.html)
- [Demos of function approximation](https://deepxde.readthedocs.io/en/latest/demos/function.html)
- [Demos of forward problems](https://deepxde.readthedocs.io/en/latest/demos/pinn_forward.html)
- [Demos of inverse problems](https://deepxde.readthedocs.io/en/latest/demos/pinn_inverse.html)
- [Demos of operator learning](https://deepxde.readthedocs.io/en/latest/demos/operator.html)
- [FAQ](https://deepxde.readthedocs.io/en/latest/user/faq.html)
- [Research papers used DeepXDE](https://deepxde.readthedocs.io/en/latest/user/research.html)
- [API](https://deepxde.readthedocs.io/en/latest/modules/deepxde.html)
## Cite DeepXDE
If you use DeepXDE for academic research, you are encouraged to cite the following paper:
```
@article{lu2021deepxde,
author = {Lu, Lu and Meng, Xuhui and Mao, Zhiping and Karniadakis, George Em},
title = {{DeepXDE}: A deep learning library for solving differential equations},
journal = {SIAM Review},
volume = {63},
number = {1},
pages = {208-228},
year = {2021},
doi = {10.1137/19M1274067}
}
```
## 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](https://github.com/lululxvi/deepxde/issues).
- **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 in the GitHub [Issues](https://github.com/lululxvi/deepxde/issues).
- **Pull requests.** If you made improvements to DeepXDE, fixed a bug, or had a new example, feel free to send us a pull-request.
- **Asking questions.** To get help on how to use DeepXDE or its functionalities, you can open a discussion in the GitHub [Discussions](https://github.com/lululxvi/deepxde/discussions).
- **Answering questions.** If you know the answer to any question in the [Discussions](https://github.com/lululxvi/deepxde/discussions), you are welcomed to answer.
**Slack.** The DeepXDE Slack hosts a primary audience of moderate to experienced DeepXDE users and developers for general chat, online discussions, collaboration, etc. If you need a slack invite, please send me an email.
## The Team
DeepXDE was developed by [Lu Lu](https://lu.seas.upenn.edu) under the supervision of Prof. [George Karniadakis](https://www.brown.edu/research/projects/crunch/george-karniadakis) at [Brown University](https://www.brown.edu) from the summer of 2018 to 2020, supported by [PhILMs](https://www.pnnl.gov/computing/philms). DeepXDE was originally self-hosted in Subversion at Brown University, under the name SciCoNet (Scientific Computing Neural Networks). On Feb 7, 2019, SciCoNet was moved from Subversion to GitHub, renamed to DeepXDE.
DeepXDE is currently maintained by [Lu Lu](https://lu.seas.upenn.edu) at [University of Pennsylvania](https://www.upenn.edu) with major contributions coming from several talented individuals in various forms and means. A non-exhaustive but growing list needs to mention: [Zongren Zou](https://github.com/ZongrenZou), [Zhongyi Jiang](https://github.com/Jerry-Jzy), [Shunyuan Mao](https://github.com/smao-astro), [Paul Escapil-Inchauspé](https://github.com/pescap).
## License
[LGPL-2.1 License](https://github.com/lululxvi/deepxde/blob/master/LICENSE)
%prep
%autosetup -n DeepXDE-1.8.4
%build
%py3_build
%install
%py3_install
install -d -m755 %{buildroot}/%{_pkgdocdir}
if [ -d doc ]; then cp -arf doc %{buildroot}/%{_pkgdocdir}; fi
if [ -d docs ]; then cp -arf docs %{buildroot}/%{_pkgdocdir}; fi
if [ -d example ]; then cp -arf example %{buildroot}/%{_pkgdocdir}; fi
if [ -d examples ]; then cp -arf examples %{buildroot}/%{_pkgdocdir}; fi
pushd %{buildroot}
if [ -d usr/lib ]; then
find usr/lib -type f -printf "/%h/%f\n" >> filelist.lst
fi
if [ -d usr/lib64 ]; then
find usr/lib64 -type f -printf "/%h/%f\n" >> filelist.lst
fi
if [ -d usr/bin ]; then
find usr/bin -type f -printf "/%h/%f\n" >> filelist.lst
fi
if [ -d usr/sbin ]; then
find usr/sbin -type f -printf "/%h/%f\n" >> filelist.lst
fi
touch doclist.lst
if [ -d usr/share/man ]; then
find usr/share/man -type f -printf "/%h/%f.gz\n" >> doclist.lst
fi
popd
mv %{buildroot}/filelist.lst .
mv %{buildroot}/doclist.lst .
%files -n python3-DeepXDE -f filelist.lst
%dir %{python3_sitelib}/*
%files help -f doclist.lst
%{_docdir}/*
%changelog
* Fri May 05 2023 Python_Bot <Python_Bot@openeuler.org> - 1.8.4-1
- Package Spec generated
|
