ai4xde 0.4.1

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
9. gPINN
10. FI-PINN
11. FBPINN

Currently, AI4XDE supports the following examples:

1. Formula based approximate function calculation example
2. Data based formula approximation examples
3. A simple ODE calculation example
4. Lotka Volterra equation
5. Second Order ODE
6. Poisson equation in 1D with Dirichlet boundary conditions
7. Poisson equation in 1D with Dirichlet/Neumann boundary conditions
8. Poisson equation in 1D with Dirichlet/Robin boundary conditions
9. Poisson equation in 1D with Dirichlet/Periodic boundary conditions
10. Poisson equation in 1D with Dirichlet/PointSetOperator boundary conditions
11. Poisson equation in 1D with hard boundary conditions
12. Poisson equation in 1D with Multi-scale Fourier feature networks
13. Poisson equation over L-shaped domain
14. Inverse problem for the Poisson equation with unknown forcing field
15. Inverse problem for the fractional Poisson equation in 1D
16. Inverse problem for the fractional Poisson equation in 2D
17. Poisson equation in 2D peak problem
18. Laplace equation on a disk
19. Euler Beam
20. Helmholtz equation over a 2D square domain
21. Helmholtz equation over a 2D square domain with a hole
22. Helmholtz sound-hard scattering problem with absorbing boundary conditions
23. Kovasznay Flow
24. Burgers equation
25. Heat equation
26. Diffusion equation
27. Diffusion-reaction equation
28. Allen Cahn equation
29. Klein-Gordon equation
30. Beltrami flow
31. Schrodinger equation
32. Wave propagation with spatio-temporal multi-scale Fourier feature architecture
33. Wave equation
34. Integro-differential equation
35. Volterra IDE
36. Fractional Poisson equation in 1D
37. Fractional Poisson equation in 2D
38. Fractional Poisson equation in 3D
39. Fractional_Diffusion_1D
40. Inverse problem for the Lorenz system
41. Inverse problem for the Lorenz system with exogenous input
42. Inverse problem for Brinkman-Forchheimer model
43. Inverse problem for the diffusion equation
44. Inverse problem for the Diffusion-reaction equation
45. Inverse problem for the Navier-Stokes equation of incompressible flow around cylinder
46. Bimodal in 2D
47. Flow in a Lid-Driven Cavity
48. Convection equation in 1D with Periodic boundary conditions
49. Harmonic Oscillator 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