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 1.11.5
Commit 760b2e5b739 (2025-04-14 06:53 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: 2 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
JULIA_CI = true
LD_LIBRARY_PATH = /opt/hostedtoolcache/Python/3.13.3/x64/lib
JULIA_PROJECT = /home/runner/work/jl-ude/jl-ude/Project.toml
JULIA_DEPOT_PATH = /home/runner/.julia:/opt/hostedtoolcache/julia/1.11.5/x64/local/share/julia:/opt/hostedtoolcache/julia/1.11.5/x64/share/julia
JULIA_CONDAPKG_BACKEND = Null
JULIA_NUM_THREADS = 2
JULIA_LOAD_PATH = @:@v#.#:@stdlib
using Pkg
Pkg.status()
Status `~/work/jl-ude/jl-ude/Project.toml`
[b0b7db55] ComponentArrays v0.15.26
[aae7a2af] DiffEqFlux v4.3.0
[7da242da] Enzyme v0.13.38
[d3d80556] LineSearches v7.3.0
[7ed4a6bd] LinearSolve v3.8.0
[b2108857] Lux v1.12.3
[961ee093] ModelingToolkit v9.72.0
[315f7962] NeuralPDE v5.18.1
[7f7a1694] Optimization v4.1.2
[36348300] OptimizationOptimJL v0.4.1
[42dfb2eb] OptimizationOptimisers v0.3.7
[500b13db] OptimizationPolyalgorithms v0.3.0
[1dea7af3] OrdinaryDiffEq v6.93.0
[91a5bcdd] Plots v1.40.13
[37e2e46d] LinearAlgebra v1.11.0
[9a3f8284] Random v1.11.0
This notebook was generated using Literate.jl.