ai4xde 0.1.5

AI4XDE is a library for scientific machine learning and physics-informed learning

AI4XDE

Description

AI4XDE is a comprehensive library for scientific machine learning and physical information networks. AI4XDE aims to decouple specific algorithms from specific examples, using examples as input parameters for neural networks, so that all examples can be calculated in one programming operation. Writing neural network algorithms and examples according to the interface paradigm used in the AI4XDE library can quickly test the stability of algorithms on different examples and accelerate experimental progress; At the same time, it can also enable the completion of calculation examples, which can be tested and compared on different neural network algorithms.

Currently, AI4XDE supports the following algorithms:

1. PINN
2. Uniform
3. Random_ R
4. RAR_ D
5. RAR_ G
6. RAD
7. R3Sampling
8. HPO

Currently, AI4XDE supports the following examples:

1. Formula based approximate function calculation example
2. Data based formula approximation examples
3. Burgers equation
4. Heat equation
5. Allen Cahn equation
6. Diffusion equation
7. Diffusion-reaction equation
8. Klein-Gordon equation
9. Wave equation
10. Diffusion_ Action_ Reverse equation
11. A simple ODE calculation example
12. Lotka Volterra equation
13. Second Order ODE
14. Poisson equation in 1D with Dirichlet boundary conditions
15. Poisson equation in 1D with Dirichlet/Neumann boundary conditions
16. Poisson equation in 1D with Dirichlet/Robin boundary conditions
17. Poisson equation in 1D with Dirichlet/Periodic boundary conditions
18. Poisson equation in 1D with Dirichlet/PointSetOperator boundary conditions
19. Poisson equation in 1D with hard boundary conditions
20. Poisson equation in 1D with Multi-scale Fourier feature networks
21. Poisson equation over L-shaped domain
22. Laplace equation on a disk
23. Helmholtz equation over a 2D square domain
24. Helmholtz equation over a 2D square domain with a hole
25. Helmholtz sound-hard scattering problem with absorbing boundary conditions
26. Kovasznay_Flow
27. Euler Beam
28. Integro-differential equation
29. Volterra IDE
30. Fractional Poisson equation in 1D
31. Fractional Poisson equation in 2D
32. Fractional Poisson equation in 3D
33. Fractional_Diffusion_1D

Installation

Since AI4XDE is based on the DeepXDE library, you need to first install the DeepXDE library.

DeepXDE requires one of the following dependencies to be installed:

• TensorFlow 1.x: TensorFlow>=2.7.0
• TensorFlow 2.x: TensorFlow>=2.2.0, TensorFlow Probability>=0.10.0
• PyTorch: PyTorch>=1.9.0
• JAX: JAX, Flax, Optax
• PaddlePaddle: PaddlePaddle (develop version)

Please install the above dependencies as a baseline before installing DeepXDE

Subsequently, you can use the following method to install AI4XDE

• Install using 'pip':

$ pip install ai4xde

• Install using 'conda':

$ conda install -c xuelanghanbao ai4xde

• For developers, you should clone the folder to your local machine and put it along with your project scripts:

$ git clone https://gitee.com/xuelanghanbao/AI4XDE.git

Instructions

AI4XDE separates algorithms from examples, where algorithm templates are stored in the solver folder, and specific algorithms implemented based on algorithm templates (such as PINN, R3Sampling, etc.) are stored in the algorithms folder. The calculation template and specific calculation examples (such as Burgers, AllenCahn, etc.) are stored in the cases folder.

Contribution

1. Fork the repository
2. Create Feat_xxx branch
3. Commit your code
4. Create Pull Request