Partial Differential Equations (PDEs)

Solving partial differential equations (PDEs) using SciML/MethodOfLines.jl, a finite difference method (FDM).

Other PDE packages

• Ferrite-FEM/Ferrite.jl (Finite Element method)

• gridap/Gridap.jl and its tutorials

• trixi-framework/Trixi.jl

• WaterLily-jl/WaterLily.jl for fluid dynamics.

PDE courses

• Solving partial differential equations in parallel on GPUs

Using neural networks to solve differential equations

Universal Differential Equations (UDEs) are hybrids of differential equations and neural networks.

• Universal Differential Equations (UDEs): SciML/DiffEqFlux.jl

• Physically-informed neural networks (PINNs): SciML/NeuralPDE.jl

DiffEqFlux is generally more efficient than NeuralPDE because NeuralPDE also tries to discover physical rules in the data, which is mentioned in this thread.