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 thanDiffEqFlux.jl
.
Runtime information#
using InteractiveUtils
InteractiveUtils.versioninfo()
Julia Version 1.11.6
Commit 9615af0f269 (2025-07-09 12:58 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 4 × AMD EPYC 7763 64-Core Processor
WORD_SIZE: 64
LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 4 default, 0 interactive, 2 GC (on 4 virtual cores)
Environment:
JULIA_CI = true
JULIA_NUM_THREADS = auto
JULIA_CONDAPKG_BACKEND = Null
JULIA_PATH = /usr/local/julia/
using Pkg
Pkg.status()
Status `/tmp/Project.toml`
[b0b7db55] ComponentArrays v0.15.29
[aae7a2af] DiffEqFlux v4.4.0
[5b8099bc] DomainSets v0.7.15
[7da242da] Enzyme v0.13.61
[d3d80556] LineSearches v7.4.0
[7ed4a6bd] LinearSolve v3.22.0
[b2108857] Lux v1.16.0
[961ee093] ModelingToolkit v10.13.0
[315f7962] NeuralPDE v5.20.0
[7f7a1694] Optimization v4.4.0
[36348300] OptimizationOptimJL v0.4.3
[42dfb2eb] OptimizationOptimisers v0.3.8
[500b13db] OptimizationPolyalgorithms v0.3.0
[1dea7af3] OrdinaryDiffEq v6.101.0
[91a5bcdd] Plots v1.40.17
[37e2e46d] LinearAlgebra v1.11.0
[9a3f8284] Random v1.11.0
This notebook was generated using Literate.jl.