NeuralLyapunov.jl
NeuralLyapunov.jl is a library for searching for neural Lyapunov functions in Julia.
This package provides an API for setting up the search for a neural Lyapunov function. Such a search can be formulated as a partial differential inequality, and this library generates a ModelingToolkit.jl PDESystem to be solved using NeuralPDE.jl. Since the Lyapunov conditions can be formulated in several different ways and a neural Lyapunov function can be set up in many different forms, this library presents an extensible interface for users to choose how they wish to set up the search, with useful pre-built options for common setups.
Getting Started
If this is your first time using the library, start by familiarizing yourself with the components of a neural Lyapunov problem in NeuralLyapunov.jl. Then, you can dive in with any of the following demonstrations (the damped simple harmonic oscillator is recommended to begin):
- Damped Simple Harmonic Oscillator
- Estimating the Region of Attraction
- Policy Search on the Driven Inverted Pendulum
- Benchmarking a neural Lyapunov method
When you begin to write your own neural Lyapunov code, especially if you hope to define your own neural Lyapunov formulation, you may find any of the following manual pages useful:
- Components of a Neural Lyapunov Problem
- Solving a Neural Lyapunov Problem
- Lyapunov Minimization Condition
- Lyapunov Decrease Condition
- Structuring a Neural Lyapunov function
- Training for Region of Attraction Identification
- Policy Search and Network-Dependent Dynamics
- Benchmarking neural Lyapunov methods
- Local Lyapunov analysis
Finally, when you wish to test your neural Lyapunov code, you may wish to use one of the built-in example systems:
Contributing
Please refer to the SciML ColPrac: Contributor's Guide on Collaborative Practices for Community Packages for guidance on PRs, issues, and other matters relating to contributing to SciML.
See the SciML Style Guide for common coding practices and other style decisions.
There are a few community forums:
- The #diffeq-bridged and #sciml-bridged channels in the Julia Slack
- The #diffeq-bridged and #sciml-bridged channels in the Julia Zulip
- On the Julia Discourse forums
- See also SciML Community page
Reproducibility
The documentation of this SciML package was built using these direct dependencies,
Status `~/github-runners/demeter4-4/_work/NeuralLyapunov.jl/NeuralLyapunov.jl/docs/Project.toml`
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Julia Version 1.11.9
Commit 53a02c0720c (2026-02-06 00:27 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 64 × AMD EPYC 9354 32-Core Processor
WORD_SIZE: 64
LLVM: libLLVM-16.0.6 (ORCJIT, znver4)
Threads: 1 default, 0 interactive, 1 GC (on 64 virtual cores)
Environment:
JULIA_DEBUG = Documenter
JULIA_DEPOT_PATH = /home/chrisrackauckas/github-runners/demeter4-4/.juliaA more complete overview of all dependencies and their versions is also provided.
Status `~/github-runners/demeter4-4/_work/NeuralLyapunov.jl/NeuralLyapunov.jl/docs/Manifest.toml`
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[89763e89] Libtiff_jll v4.7.2+0
[38a345b3] Libuuid_jll v2.41.3+0
[856f044c] MKL_jll v2025.2.0+0
[e7412a2a] Ogg_jll v1.3.6+0
[9bd350c2] OpenSSH_jll v10.2.1+0
[458c3c95] OpenSSL_jll v3.5.5+0
[efe28fd5] OpenSpecFun_jll v0.5.6+0
[91d4177d] Opus_jll v1.6.1+0
[36c8627f] Pango_jll v1.57.0+0
⌅ [30392449] Pixman_jll v0.44.2+0
⌅ [c0090381] Qt6Base_jll v6.8.2+2
⌅ [629bc702] Qt6Declarative_jll v6.8.2+1
⌅ [ce943373] Qt6ShaderTools_jll v6.8.2+1
⌃ [e99dba38] Qt6Wayland_jll v6.8.2+2
[f50d1b31] Rmath_jll v0.5.1+0
[a44049a8] Vulkan_Loader_jll v1.3.243+0
[a2964d1f] Wayland_jll v1.24.0+0
[ffd25f8a] XZ_jll v5.8.2+0
[f67eecfb] Xorg_libICE_jll v1.1.2+0
[c834827a] Xorg_libSM_jll v1.2.6+0
[4f6342f7] Xorg_libX11_jll v1.8.13+0
[0c0b7dd1] Xorg_libXau_jll v1.0.13+0
[935fb764] Xorg_libXcursor_jll v1.2.4+0
[a3789734] Xorg_libXdmcp_jll v1.1.6+0
[1082639a] Xorg_libXext_jll v1.3.8+0
[d091e8ba] Xorg_libXfixes_jll v6.0.2+0
[a51aa0fd] Xorg_libXi_jll v1.8.3+0
[d1454406] Xorg_libXinerama_jll v1.1.7+0
[ec84b674] Xorg_libXrandr_jll v1.5.6+0
[ea2f1a96] Xorg_libXrender_jll v0.9.12+0
[c7cfdc94] Xorg_libxcb_jll v1.17.1+0
[cc61e674] Xorg_libxkbfile_jll v1.2.0+0
[e920d4aa] Xorg_xcb_util_cursor_jll v0.1.6+0
[12413925] Xorg_xcb_util_image_jll v0.4.1+0
[2def613f] Xorg_xcb_util_jll v0.4.1+0
[975044d2] Xorg_xcb_util_keysyms_jll v0.4.1+0
[0d47668e] Xorg_xcb_util_renderutil_jll v0.3.10+0
[c22f9ab0] Xorg_xcb_util_wm_jll v0.4.2+0
[35661453] Xorg_xkbcomp_jll v1.4.7+0
[33bec58e] Xorg_xkeyboard_config_jll v2.44.0+0
[c5fb5394] Xorg_xtrans_jll v1.6.0+0
[3161d3a3] Zstd_jll v1.5.7+1
[35ca27e7] eudev_jll v3.2.14+0
[214eeab7] fzf_jll v0.61.1+0
[a4ae2306] libaom_jll v3.13.1+0
[0ac62f75] libass_jll v0.17.4+0
[1183f4f0] libdecor_jll v0.2.2+0
[2db6ffa8] libevdev_jll v1.13.4+0
[f638f0a6] libfdk_aac_jll v2.0.4+0
[36db933b] libinput_jll v1.28.1+0
[b53b4c65] libpng_jll v1.6.55+0
[f27f6e37] libvorbis_jll v1.3.8+0
[009596ad] mtdev_jll v1.1.7+0
[1317d2d5] oneTBB_jll v2022.0.0+1
⌅ [1270edf5] x264_jll v10164.0.1+0
[dfaa095f] x265_jll v4.1.0+0
[d8fb68d0] xkbcommon_jll v1.13.0+0
[0dad84c5] ArgTools v1.1.2
[56f22d72] Artifacts v1.11.0
[2a0f44e3] Base64 v1.11.0
[ade2ca70] Dates v1.11.0
[8ba89e20] Distributed v1.11.0
[f43a241f] Downloads v1.6.0
[7b1f6079] FileWatching v1.11.0
[9fa8497b] Future v1.11.0
[b77e0a4c] InteractiveUtils v1.11.0
[4af54fe1] LazyArtifacts v1.11.0
[b27032c2] LibCURL v0.6.4
[76f85450] LibGit2 v1.11.0
[8f399da3] Libdl v1.11.0
[37e2e46d] LinearAlgebra v1.11.0
[56ddb016] Logging v1.11.0
[d6f4376e] Markdown v1.11.0
[a63ad114] Mmap v1.11.0
[ca575930] NetworkOptions v1.2.0
[44cfe95a] Pkg v1.11.0
[de0858da] Printf v1.11.0
[9abbd945] Profile v1.11.0
[3fa0cd96] REPL v1.11.0
[9a3f8284] Random v1.11.0
[ea8e919c] SHA v0.7.0
[9e88b42a] Serialization v1.11.0
[1a1011a3] SharedArrays v1.11.0
[6462fe0b] Sockets v1.11.0
[2f01184e] SparseArrays v1.11.0
[f489334b] StyledStrings v1.11.0
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.3
[a4e569a6] Tar v1.10.0
[8dfed614] Test v1.11.0
[cf7118a7] UUIDs v1.11.0
[4ec0a83e] Unicode v1.11.0
[e66e0078] CompilerSupportLibraries_jll v1.1.1+0
[deac9b47] LibCURL_jll v8.6.0+0
[e37daf67] LibGit2_jll v1.7.2+0
[29816b5a] LibSSH2_jll v1.11.0+1
[c8ffd9c3] MbedTLS_jll v2.28.6+0
[14a3606d] MozillaCACerts_jll v2023.12.12
[4536629a] OpenBLAS_jll v0.3.27+1
[05823500] OpenLibm_jll v0.8.5+0
[efcefdf7] PCRE2_jll v10.42.0+1
[bea87d4a] SuiteSparse_jll v7.7.0+0
[83775a58] Zlib_jll v1.2.13+1
[8e850b90] libblastrampoline_jll v5.11.0+0
[8e850ede] nghttp2_jll v1.59.0+0
[3f19e933] p7zip_jll v17.4.0+2
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 -m`You can also download the manifest file and the project file.