DiffEqFlux: High Level Pre-Built Architectures for Implicit Deep Learning
DiffEqFlux.jl is an implicit deep learning library built using the SciML ecosystem. It is a high-level interface that pulls together all the tools with heuristics and helper functions to make training such deep implicit layer models fast and easy.
DiffEqFlux.jl is only for pre-built architectures and utility functions for deep implicit learning, mixing differential equations with machine learning. For details on automatic differentiation of equation solvers and adjoint techniques, and using these methods for doing things like calibrating models to data, nonlinear optimal control, and PDE-constrained optimization, see SciMLSensitivity.jl.
Pre-Built Architectures
The approach of this package is the easy and efficient training of Neural Ordinary Differential Equations and its variants. DiffEqFlux.jl provides architectures which match the interfaces of machine learning libraries such as Flux.jl and Lux.jl to make it easy to build continuous-time machine learning layers into larger machine learning applications.
The following layer functions exist:
- Neural Ordinary Differential Equations (Neural ODEs)
- Collocation-Based Neural ODEs (Neural ODEs without a solver, by far the fastest way!)
- Multiple Shooting Neural Ordinary Differential Equations
- Neural Stochastic Differential Equations (Neural SDEs)
- Neural Differential-Algebraic Equations (Neural DAEs)
- Neural Delay Differential Equations (Neural DDEs)
- Augmented Neural ODEs
- Hamiltonian Neural Networks (with specialized second order and symplectic integrators)
- Continuous Normalizing Flows (CNF) and FFJORD
Examples of how to build architectures from scratch, with tutorials on things like Graph Neural ODEs, can be found in the SciMLSensitivity.jl documentation.
Flux.jl vs Lux.jl
Both Flux and Lux defined neural networks are supported by DiffEqFlux.jl. However, Lux.jl neural networks are greatly preferred for many correctness reasons. Particularly, a Flux Chain
does not respect Julia's type promotion rules. This causes major problems in that the restructuring of a Flux neural network will not respect the chosen types from the solver. Demonstration:
using Flux, Tracker
x = [0.8; 0.8]
ann = Chain(Dense(2, 10, tanh), Dense(10, 1))
p, re = Flux.destructure(ann)
z = re(Float64.(p))
While one may think this recreates the neural network to act in Float64
precision, it does not and instead its values will silently downgrade everything to Float32
. This is only fixed by Chain(Dense(2, 10, tanh), Dense(10, 1)) |> f64
. Similar cases will lead to dropped gradients with complex numbers. This is not an issue with the automatic differentiation library commonly associated with Flux (Zygote.jl) but rather due to choices in the neural network library's decision for how to approach type handling and precision. Thus when using DiffEqFlux.jl with Flux, the user must be very careful to ensure that the precision of the arguments are correct, and anything that requires alternative types (like TrackerAdjoint
tracked values and ForwardDiffSensitivity
dual numbers) are suspect.
Lux.jl has none of these issues, is simpler to work with due to the parameters in its function calls being explicit rather than implicit global references, and achieves higher performance. It is built on the same foundations as Flux.jl, such as Zygote and NNLib, and thus it supports the same layers underneath and calls the same kernels. The better performance comes from not having the overhead of restructure
required. Thus we highly recommend people use Lux instead and only use the Flux fallbacks for legacy code.
Citation
If you use DiffEqFlux.jl or are influenced by its ideas, please cite:
@article{rackauckas2020universal,
title={Universal differential equations for scientific machine learning},
author={Rackauckas, Christopher and Ma, Yingbo and Martensen, Julius and Warner, Collin and Zubov, Kirill and Supekar, Rohit and Skinner, Dominic and Ramadhan, Ali},
journal={arXiv preprint arXiv:2001.04385},
year={2020}
}
Reproducibility
The documentation of this SciML package was built using these direct dependencies,
Status `/var/lib/buildkite-agent/builds/gpuci-14/julialang/diffeqflux-dot-jl/docs/Project.toml`
[336ed68f] CSV v0.10.14
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[b4f34e82] Distances v0.10.11
[31c24e10] Distributions v0.25.108
[e30172f5] Documenter v1.4.1
[587475ba] Flux v0.14.15
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[c8e1da08] IterTools v1.10.0
[b2108857] Lux v0.5.50
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[7f7a1694] Optimization v3.25.0
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[42dfb2eb] OptimizationOptimisers v0.2.1
[500b13db] OptimizationPolyalgorithms v0.2.0
[1dea7af3] OrdinaryDiffEq v6.77.1
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[de0858da] Printf
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[8dfed614] Test
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`
and using this machine and Julia version.
Julia Version 1.10.3
Commit 0b4590a5507 (2024-04-30 10:59 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 48 × AMD EPYC 7402 24-Core Processor
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
Threads: 1 default, 0 interactive, 1 GC (on 2 virtual cores)
Environment:
JULIA_CPU_THREADS = 2
JULIA_DEBUG = Documenter
JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/64dbdc29-d6e3-4071-807c-a2eda6e09bd8
LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
A more complete overview of all dependencies and their versions is also provided.
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⌃ [0234f1f7] HDF5_jll v1.14.2+1
[2e76f6c2] HarfBuzz_jll v2.8.1+1
[e33a78d0] Hwloc_jll v2.10.0+0
[1d5cc7b8] IntelOpenMP_jll v2024.1.0+0
[aacddb02] JpegTurbo_jll v3.0.3+0
[9c1d0b0a] JuliaNVTXCallbacks_jll v0.2.1+0
[c1c5ebd0] LAME_jll v3.100.2+0
⌅ [88015f11] LERC_jll v3.0.0+1
[dad2f222] LLVMExtra_jll v0.0.29+0
[1d63c593] LLVMOpenMP_jll v15.0.7+0
[dd4b983a] LZO_jll v2.10.2+0
[81d17ec3] L_BFGS_B_jll v3.0.1+0
⌅ [e9f186c6] Libffi_jll v3.2.2+1
[d4300ac3] Libgcrypt_jll v1.8.11+0
[7e76a0d4] Libglvnd_jll v1.6.0+0
[7add5ba3] Libgpg_error_jll v1.49.0+0
[94ce4f54] Libiconv_jll v1.17.0+0
[4b2f31a3] Libmount_jll v2.40.1+0
⌅ [89763e89] Libtiff_jll v4.5.1+1
[38a345b3] Libuuid_jll v2.40.1+0
[856f044c] MKL_jll v2024.1.0+0
[7cb0a576] MPICH_jll v4.2.1+1
[f1f71cc9] MPItrampoline_jll v5.3.3+1
[9237b28f] MicrosoftMPI_jll v10.1.4+2
[e98f9f5b] NVTX_jll v3.1.0+2
[e7412a2a] Ogg_jll v1.3.5+1
[fe0851c0] OpenMPI_jll v5.0.2+0
[458c3c95] OpenSSL_jll v3.0.13+1
[efe28fd5] OpenSpecFun_jll v0.5.5+0
[91d4177d] Opus_jll v1.3.2+0
[32165bc3] PMIx_jll v4.2.9+0
[30392449] Pixman_jll v0.43.4+0
⌅ [c0090381] Qt6Base_jll v6.5.3+1
[f50d1b31] Rmath_jll v0.4.2+0
[a44049a8] Vulkan_Loader_jll v1.3.243+0
[a2964d1f] Wayland_jll v1.21.0+1
[2381bf8a] Wayland_protocols_jll v1.31.0+0
[02c8fc9c] XML2_jll v2.12.7+0
[aed1982a] XSLT_jll v1.1.34+0
[ffd25f8a] XZ_jll v5.4.6+0
[f67eecfb] Xorg_libICE_jll v1.1.1+0
[c834827a] Xorg_libSM_jll v1.2.4+0
[4f6342f7] Xorg_libX11_jll v1.8.6+0
[0c0b7dd1] Xorg_libXau_jll v1.0.11+0
[935fb764] Xorg_libXcursor_jll v1.2.0+4
[a3789734] Xorg_libXdmcp_jll v1.1.4+0
[1082639a] Xorg_libXext_jll v1.3.6+0
[d091e8ba] Xorg_libXfixes_jll v5.0.3+4
[a51aa0fd] Xorg_libXi_jll v1.7.10+4
[d1454406] Xorg_libXinerama_jll v1.1.4+4
[ec84b674] Xorg_libXrandr_jll v1.5.2+4
[ea2f1a96] Xorg_libXrender_jll v0.9.11+0
[14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
[c7cfdc94] Xorg_libxcb_jll v1.15.0+0
[cc61e674] Xorg_libxkbfile_jll v1.1.2+0
[e920d4aa] Xorg_xcb_util_cursor_jll v0.1.4+0
[12413925] Xorg_xcb_util_image_jll v0.4.0+1
[2def613f] Xorg_xcb_util_jll v0.4.0+1
[975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
[0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
[c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
[35661453] Xorg_xkbcomp_jll v1.4.6+0
[33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
[c5fb5394] Xorg_xtrans_jll v1.5.0+0
[3161d3a3] Zstd_jll v1.5.6+0
[35ca27e7] eudev_jll v3.2.9+0
⌅ [214eeab7] fzf_jll v0.43.0+0
[1a1c6b14] gperf_jll v3.1.1+0
[477f73a3] libaec_jll v1.1.2+0
[a4ae2306] libaom_jll v3.9.0+0
[0ac62f75] libass_jll v0.15.1+0
[2db6ffa8] libevdev_jll v1.11.0+0
[1080aeaf] libevent_jll v2.1.13+1
[f638f0a6] libfdk_aac_jll v2.0.2+0
[36db933b] libinput_jll v1.18.0+0
[b53b4c65] libpng_jll v1.6.43+1
[f27f6e37] libvorbis_jll v1.3.7+1
[009596ad] mtdev_jll v1.1.6+0
[1317d2d5] oneTBB_jll v2021.12.0+0
[eb928a42] prrte_jll v3.0.2+0
[1270edf5] x264_jll v2021.5.5+0
[dfaa095f] x265_jll v3.5.0+0
[d8fb68d0] xkbcommon_jll v1.4.1+1
[0dad84c5] ArgTools v1.1.1
[56f22d72] Artifacts
[2a0f44e3] Base64
[ade2ca70] Dates
[8ba89e20] Distributed
[f43a241f] Downloads v1.6.0
[7b1f6079] FileWatching
[9fa8497b] Future
[b77e0a4c] InteractiveUtils
[4af54fe1] LazyArtifacts
[b27032c2] LibCURL v0.6.4
[76f85450] LibGit2
[8f399da3] Libdl
[37e2e46d] LinearAlgebra
[56ddb016] Logging
[d6f4376e] Markdown
[a63ad114] Mmap
[ca575930] NetworkOptions v1.2.0
[44cfe95a] Pkg v1.10.0
[de0858da] Printf
[3fa0cd96] REPL
[9a3f8284] Random
[ea8e919c] SHA v0.7.0
[9e88b42a] Serialization
[1a1011a3] SharedArrays
[6462fe0b] Sockets
[2f01184e] SparseArrays v1.10.0
[10745b16] Statistics v1.10.0
[4607b0f0] SuiteSparse
[fa267f1f] TOML v1.0.3
[a4e569a6] Tar v1.10.0
[8dfed614] Test
[cf7118a7] UUIDs
[4ec0a83e] Unicode
[e66e0078] CompilerSupportLibraries_jll v1.1.1+0
[deac9b47] LibCURL_jll v8.4.0+0
[e37daf67] LibGit2_jll v1.6.4+0
[29816b5a] LibSSH2_jll v1.11.0+1
[c8ffd9c3] MbedTLS_jll v2.28.2+1
[14a3606d] MozillaCACerts_jll v2023.1.10
[4536629a] OpenBLAS_jll v0.3.23+4
[05823500] OpenLibm_jll v0.8.1+2
[efcefdf7] PCRE2_jll v10.42.0+1
[bea87d4a] SuiteSparse_jll v7.2.1+1
[83775a58] Zlib_jll v1.2.13+1
[8e850b90] libblastrampoline_jll v5.8.0+1
[8e850ede] nghttp2_jll v1.52.0+1
[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.