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.


  • 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


If you use NeuralPDE.jl in your work, please cite:

 author = {Rackauckas, Christopher and Nie, Qing},
 doi = {10.5334/jors.151},
 journal = {The Journal of Open Research Software},
 keywords = {Applied Mathematics},
 note = {Exported from on 2019/05/05},
 number = {1},
 pages = {},
 title = {DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia},
 url = { and},
 volume = {5},
 year = {2017}