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 1.11.6
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.

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