NeuralPDE.jl: Scientific Machine Learning for Partial Differential Equations

NeuralPDE.jl is a solver package which consists of neural network solvers for partial differential equations using scientific machine learning (SciML) techniques such as physics-informed neural networks (PINNs) and deep BSDE solvers. This package utilizes deep neural networks and neural stochastic differential equations to solve high-dimensional PDEs at a greatly reduced cost and greatly increased generality compared with classical methods.

Features

  • Physics-Informed Neural Networks for automated PDE solving
  • Forward-Backwards Stochastic Differential Equation (FBSDE) methods for parabolic PDEs
  • Deep-learning-based solvers for optimal stopping time and Kolmogorov backwards equations

Citation

If you use NeuralPDE.jl in your research, please cite this paper:

@article{zubov2021neuralpde,
  title={NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with Error Approximations},
  author={Zubov, Kirill and McCarthy, Zoe and Ma, Yingbo and Calisto, Francesco and Pagliarino, Valerio and Azeglio, Simone and Bottero, Luca and Luj{\'a}n, Emmanuel and Sulzer, Valentin and Bharambe, Ashutosh and others},
  journal={arXiv preprint arXiv:2107.09443},
  year={2021}
}