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

UDEs

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

• SciML/DiffEqFlux.jl : fusing differential equations (DifferentialEquations.jl) and neural networks (Lux.jl).

• SciML/NeuralPDE.jl : physics-Informed Neural Networks (PINN) Solvers, learning and building the equations from the ground up. NeuralPDE.jl is slower than DiffEqFlux.jl.