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 1.12.2
Commit ca9b6662be4 (2025-11-20 16:25 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-18.1.7 (ORCJIT, znver3)
  GC: Built with stock GC
Threads: 4 default, 1 interactive, 4 GC (on 4 virtual cores)
Environment:
  JULIA_CPU_TARGET = generic;icelake-server,clone_all;znver3,clone_all
  JULIA_CONDAPKG_OFFLINE = true
  JULIA_CONDAPKG_BACKEND = Null
  JULIA_CI = true
  LD_LIBRARY_PATH = /opt/hostedtoolcache/Python/3.13.9/x64/lib
  JULIA_NUM_THREADS = auto

using Pkg
Pkg.status()

Status `~/work/jl-ude/jl-ude/Project.toml`
  [b0b7db55] ComponentArrays v0.15.30
⌃ [aae7a2af] DiffEqFlux v4.4.0
  [5b8099bc] DomainSets v0.7.16
  [7da242da] Enzyme v0.13.108
  [f6369f11] ForwardDiff v1.3.0
  [d3d80556] LineSearches v7.5.1
⌃ [b2108857] Lux v1.21.1
  [961ee093] ModelingToolkit v10.30.0
  [315f7962] NeuralPDE v5.20.0
⌅ [7f7a1694] Optimization v4.8.0
⌃ [36348300] OptimizationOptimJL v0.4.5
⌃ [42dfb2eb] OptimizationOptimisers v0.3.11
⌃ [500b13db] OptimizationPolyalgorithms v0.3.1
  [1dea7af3] OrdinaryDiffEq v6.103.0
  [91a5bcdd] Plots v1.41.2
  [37e2e46d] LinearAlgebra v1.12.0
  [9a3f8284] Random v1.11.0
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated`

This notebook was generated using Literate.jl.

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