Package: ai4xde
AI4XDEDescriptionAI4XDE 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:PINNUniformRandom_ RRAR_ DRAR_ GRADR3SamplingHPOgPINNFI-PINNFBPINNCurrently,  AI4XDE supports the following examples:Formula based approximate function calculation exampleData based formula approximation examplesA simple ODE calculation exampleLotka Volterra equationSecond Order ODEPoisson equation in 1D with Dirichlet boundary conditionsPoisson equation in 1D with Dirichlet/Neumann boundary conditionsPoisson equation in 1D with Dirichlet/Robin boundary conditionsPoisson equation in 1D with Dirichlet/Periodic boundary conditionsPoisson equation in 1D with Dirichlet/PointSetOperator boundary conditionsPoisson equation in 1D with hard boundary conditionsPoisson equation in 1D with Multi-scale Fourier feature networksPoisson equation over L-shaped domainInverse problem for the Poisson equation with unknown forcing fieldInverse problem for the fractional Poisson equation in 1DInverse problem for the fractional Poisson equation in 2DPoisson equation in 2D peak problemLaplace equation on a diskEuler BeamHelmholtz equation over a 2D square domainHelmholtz equation over a 2D square domain with a holeHelmholtz sound-hard scattering problem with absorbing boundary conditionsKovasznay FlowBurgers equationHeat equationDiffusion equationDiffusion-reaction equationAllen Cahn equationKlein-Gordon equationBeltrami flowSchrodinger equationWave propagation with spatio-temporal multi-scale Fourier feature architectureWave equationIntegro-differential equationVolterra IDEFractional Poisson equation in 1DFractional Poisson equation in 2DFractional Poisson equation in 3DFractional_Diffusion_1DInverse problem for the Lorenz systemInverse problem for the Lorenz system with exogenous inputInverse problem for Brinkman-Forchheimer modelInverse problem for the diffusion equationInverse problem for the Diffusion-reaction equationInverse problem for the Navier-Stokes equation of incompressible flow around cylinderBimodal in 2DFlow in a Lid-Driven CavityConvection equation in 1D with Periodic boundary conditionsHarmonic Oscillator 1DInstallationSince 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>=2.7.0TensorFlow 2.x:TensorFlow>=2.2.0,TensorFlow Probability>=0.10.0PyTorch:PyTorch>=1.9.0JAX:JAX,Flax,OptaxPaddlePaddle:PaddlePaddle(develop version)Please install the above dependencies as a baseline before installing DeepXDESubsequently, you can use the following method to install AI4XDEInstall using 'pip':$ pip install ai4xdeInstall using 'conda':$ conda install -c xuelanghanbao ai4xdeFor 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.gitInstructionsAI4XDE separates algorithms from examples, where algorithm templates are stored in thesolverfolder, and specific algorithms implemented based on algorithm templates (such as PINN, R3Sampling, etc.) are stored in thealgorithmsfolder. The calculation template and specific calculation examples (such as Burgers, AllenCahn, etc.) are stored in thecasesfolder.ContributionFork the repositoryCreate Feat_xxx branchCommit your codeCreate Pull Request