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 1.11.2
Commit 5e9a32e7af2 (2024-12-01 20:02 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/3.12.8/x64/lib
  JULIA_PROJECT = /home/runner/work/jl-ude/jl-ude/Project.toml
  JULIA_DEPOT_PATH = /home/runner/.julia:/opt/hostedtoolcache/julia/1.11.2/x64/local/share/julia:/opt/hostedtoolcache/julia/1.11.2/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 v0.15.19
  [aae7a2af] DiffEqFlux v4.1.0
  [7da242da] Enzyme v0.13.22
  [d3d80556] LineSearches v7.3.0
  [7ed4a6bd] LinearSolve v2.38.0
⌃ [b2108857] Lux v1.2.3
  [961ee093] ModelingToolkit v9.58.0
  [315f7962] NeuralPDE v5.17.0
  [7f7a1694] Optimization v4.0.5
  [36348300] OptimizationOptimJL v0.4.1
  [42dfb2eb] OptimizationOptimisers v0.3.6
  [500b13db] OptimizationPolyalgorithms v0.3.0
  [1dea7af3] OrdinaryDiffEq v6.90.1
  [91a5bcdd] Plots v1.40.9
  [37e2e46d] LinearAlgebra v1.11.0
  [9a3f8284] Random v1.11.0
Info Packages marked with ⌃ have new versions available and may be upgradable.

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This notebook was generated using Literate.jl.