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Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
| Date | Stars |
|---|---|
| 2026-07-24 | 1209 |
| 2026-07-25 | 1209 |
| 2026-07-28 | 1209 |
| 2026-07-30 | 1209 |
| 2026-07-31 | 1213 |
| 2026-08-02 | 1213 |
| 2026-08-03 | 1213 |
| 2026-08-04 | 1214 |
| 2026-08-06 | 1214 |
Today
— stars today
This week
+5 stars this week
This month
— stars this month
Momentum
20.0
growth rate 0.41%/day
# NeuralPDE
[](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged)
[](https://docs.sciml.ai/NeuralPDE/stable/)
[](https://codecov.io/gh/SciML/NeuralPDE.jl)
[](https://github.com/SciML/NeuralPDE.jl/actions?query=workflow%3ATests)
[](https://buildkite.com/julialang/neuralpde-dot-jl)
[](https://github.com/SciML/ColPrac)
[](https://github.com/SciML/SciMLStyle)
NeuralPDE.jl is a solver package which consists of neural network solvers for
partial differential equations using physics-informed neural networks (PINNs). This package utilizes
neural stochastic differential equations to solve PDEs at a greatly increased generality
compared with classical methods.
## Installation
Assuming that you already have Julia correctly installed, it suffices to install NeuralPDE.jl in the standard way, that is, by typing `] add NeuralPDE`. Note:
to exit the Pkg REPL-mode, just press <kbd>Backspace</kbd> or <kbd>Ctrl</kbd> + <kbd>C</kbd>.
## Tutorials and Documentation
For information on using the package,
[see the stable documentation](https://docs.sciml.ai/NeuralPDE/stable/). Use the
[in-development documentation](https://docs.sciml.ai/NeuralPDE/dev/) for the version of
the documentation, which contains the unreleased features.
## Features
- Physics-Informed Neural Networks for ODE, SDE, RODE, and PDE solving
- Ability to define extra loss functions to mix xDE solving with data fitting (scientific machine learning)
- Automated construction of Physics-Informed loss functions from a high level symbolic interface
- Sophisticated techniques like quadrature training strategies, adaptive loss functions, and neural adapters
to accelerate training
- Integrated logging suite for handling connections to TensorBoard
- Handling of (partial) integro-differential equations and various stochastic equations
- Specialized forms for solving `ODEProblem`s with neural networks
- Compatibility with [Flux.jl](https://fluxml.ai/) and [Lux.jl](https://lux.csail.mit.edu/)
for all of the GPU-powered machine learning layers available from those libraries.
- Compatibility with [NeuralOperators.jl](https://docs.sciml.ai/NeuralOperators/stable/) for
mixing DeepONets and other neural operators (Fourier Neural Operators, Graph Neural Operators,
etc.) with physics-informed loss functions
## Example: Solving 2D Poisson Equation via Physics-Informed Neural Networks
```julia
using NeuralPDE, Lux, ModelingToolkit, Optimization, OptimizationOptimisers
import DomainSets: Interval, infimum, supremum
@parameters x y
@variables u(..)
Dxx = Differential(x)^2
Dyy = Differential(y)^2
# 2D PDE
eq = Dxx(u(x, y)) + Dyy(u(x, y)) ~ -sin(pi * x) * sin(pi * y)
# Boundary conditions
bcs = [u(0, y) ~ 0.0, u(1, y) ~ 0,
u(x, 0) ~ 0.0, u(x, 1) ~ 0]
# Space and time domains
domains = [x ∈ Interval(0.0, 1.0),
y ∈ Interval(0.0, 1.0)]
# Discretization
dx = 0.1
# Neural network
dim = 2 # number of dimensions
chain = Lux.Chain(Dense(dim, 16, Lux.σ), Dense(16, 16, Lux.σ), Dense(16, 1))
discretization = PhysicsInformedNN(chain, QuadratureTraining())
@named pde_system = PDESystem(eq, bcs, domains, [x, y], [u(x, y)])
prob = discretize(pde_system, discretization)
callback = function (p, Excerpt of 5,598 characters
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Would you bet a product on this? Bounded 0–100 and slow moving.
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