NeuralPDE.jl Scientific Machine Learning Solvers in JuliaNew

What it is

NeuralPDE.jl expresses physics-ML problems through the SciML stack: define the PDE symbolically in ModelingToolkit, then train PINN, DeepONet or NeuralOperator variants with Lux/Flux - all inside Julia.

Key strengths

• Symbolic PDE definition -> automatic symbolic differentiation of residuals
• Interoperability with DifferentialEquations.jl solvers (e.g. as data generators)
• Distributed and GPU training through Julia native tooling
• Hybrid workflows: classical solvers and neural solvers in one language

Learning path

1. Set up Julia + NeuralPDE.jl; run the official 1-D Poisson PINN
2. Define a custom PDE via ModelingToolkit and train it
3. Use an ODE solver to generate reference data; fit a DeepONet
4. Explore GPU training for larger 2-D problems

Choose it when

• Your team already runs Julia for modeling or controls
• You want one language from classical simulation to neural training