UDEs

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.

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/3.13.5/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 v0.15.28
  [aae7a2af] DiffEqFlux v4.3.0
  [7da242da] Enzyme v0.13.52
  [d3d80556] LineSearches v7.4.0
  [7ed4a6bd] LinearSolve v3.18.2
  [b2108857] Lux v1.13.5
⌅ [961ee093] ModelingToolkit v9.80.6
  [315f7962] NeuralPDE v5.18.1
  [7f7a1694] Optimization v4.4.0
  [36348300] OptimizationOptimJL v0.4.3
  [42dfb2eb] OptimizationOptimisers v0.3.7
  [500b13db] OptimizationPolyalgorithms v0.3.0
  [1dea7af3] OrdinaryDiffEq v6.98.0
  [91a5bcdd] Plots v1.40.14
  [37e2e46d] LinearAlgebra v1.11.0
  [9a3f8284] Random v1.11.0
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`

This notebook was generated using Literate.jl.

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