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.

Note

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:

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 similar foundations as Flux.jl, such as Zygote and NNLib. The better performance comes from not having the overhead of restructure required and fusing common operations in LuxLib.jl. 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-1/julialang/diffeqflux-dot-jl/docs/Project.toml`
  [336ed68f] CSV v0.10.15
  [052768ef] CUDA v5.5.2
  [b0b7db55] ComponentArrays v0.15.17
  [124859b0] DataDeps v0.7.13
  [a93c6f00] DataFrames v1.7.0
  [aae7a2af] DiffEqFlux v4.1.0 `/var/lib/buildkite-agent/builds/gpuci-1/julialang/diffeqflux-dot-jl`
  [b4f34e82] Distances v0.10.12
  [31c24e10] Distributions v0.25.113
  [e30172f5] Documenter v1.7.0
  [587475ba] Flux v0.14.25
  [f6369f11] ForwardDiff v0.10.37
  [c8e1da08] IterTools v1.10.0
  [b2108857] Lux v1.2.3
  [d0bbae9a] LuxCUDA v0.3.3
  [eb30cadb] MLDatasets v0.7.18
  [f1d291b0] MLUtils v0.4.4
  [872c559c] NNlib v0.9.24
  [0b1bfda6] OneHotArrays v0.2.5
 [3bd65402] Optimisers v0.3.4
  [7f7a1694] Optimization v4.0.5
  [36348300] OptimizationOptimJL v0.4.1
  [42dfb2eb] OptimizationOptimisers v0.3.4
  [500b13db] OptimizationPolyalgorithms v0.3.0
  [1dea7af3] OrdinaryDiffEq v6.89.0
  [91a5bcdd] Plots v1.40.8
  [37e2e3b7] ReverseDiff v1.15.3
  [0bca4576] SciMLBase v2.58.1
  [1ed8b502] SciMLSensitivity v7.70.0
  [860ef19b] StableRNGs v1.0.2
  [789caeaf] StochasticDiffEq v6.70.0
  [e88e6eb3] Zygote v0.6.72
  [37e2e46d] LinearAlgebra
  [de0858da] Printf
  [9a3f8284] Random
  [10745b16] Statistics v1.10.0
  [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 1.10.6
Commit 67dffc4a8ae (2024-10-28 12:23 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
  JULIA_PKG_SERVER =
A more complete overview of all dependencies and their versions is also provided.
Status `/var/lib/buildkite-agent/builds/gpuci-1/julialang/diffeqflux-dot-jl/docs/Manifest.toml`
  [47edcb42] ADTypes v1.9.0
  [a4c015fc] ANSIColoredPrinters v0.0.1
  [621f4979] AbstractFFTs v1.5.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.38
  [79e6a3ab] Adapt v4.1.1
  [66dad0bd] AliasTables v1.1.3
  [dce04be8] ArgCheck v2.3.0
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.16.0
  [4c555306] ArrayLayouts v1.10.4
  [a9b6321e] Atomix v0.1.0
 [a963bdd2] AtomsBase v0.3.5
  [ab4f0b2a] BFloat16s v0.5.0
  [198e06fe] BangBang v0.4.3
  [9718e550] Baselet v0.1.1
  [e2ed5e7c] Bijections v0.1.9
  [d1d4a3ce] BitFlags v0.1.9
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [4544d5e4] Boltz v1.0.2
  [e1450e63] BufferedStreams v1.2.2
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.6
  [336ed68f] CSV v0.10.15
  [052768ef] CUDA v5.5.2
  [1af6417a] CUDA_Runtime_Discovery v0.3.5
  [7057c7e9] Cassette v0.3.14
  [082447d4] ChainRules v1.71.0
  [d360d2e6] ChainRulesCore v1.25.0
  [46823bd8] Chemfiles v0.10.41
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [944b1d66] CodecZlib v0.7.6
  [35d6a980] ColorSchemes v3.27.0
 [3da002f7] ColorTypes v0.11.5
 [c3611d14] ColorVectorSpace v0.10.0
 [5ae59095] Colors v0.12.11
  [861a8166] Combinatorics v1.0.2
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.16.0
  [b0b7db55] ComponentArrays v0.15.17
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [f0e56b4a] ConcurrentUtilities v2.4.2
  [88cd18e8] ConsoleProgressMonitor v0.1.2
  [187b0558] ConstructionBase v1.5.8
  [6add18c4] ContextVariablesX v0.1.3
  [d38c429a] Contour v0.6.3
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [124859b0] DataDeps v0.7.13
  [a93c6f00] DataFrames v1.7.0
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [244e2a9f] DefineSingletons v0.1.2
  [8bb1440f] DelimitedFiles v1.9.1
  [2b5f629d] DiffEqBase v6.158.3
  [459566f4] DiffEqCallbacks v4.1.0
  [aae7a2af] DiffEqFlux v4.1.0 `/var/lib/buildkite-agent/builds/gpuci-1/julialang/diffeqflux-dot-jl`
  [77a26b50] DiffEqNoiseProcess v5.23.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.6.21
  [8d63f2c5] DispatchDoctor v0.4.17
  [b4f34e82] Distances v0.10.12
  [31c24e10] Distributions v0.25.113
  [ffbed154] DocStringExtensions v0.9.3
  [e30172f5] Documenter v1.7.0
  [5b8099bc] DomainSets v0.7.14
  [7c1d4256] DynamicPolynomials v0.6.0
  [4e289a0a] EnumX v1.0.4
  [7da242da] Enzyme v0.13.14
  [f151be2c] EnzymeCore v0.8.5
  [460bff9d] ExceptionUnwrapping v0.1.10
  [d4d017d3] ExponentialUtilities v1.26.1
  [e2ba6199] ExprTools v0.1.10
 [6b7a57c9] Expronicon v0.8.5
  [c87230d0] FFMPEG v0.4.2
  [cc61a311] FLoops v0.2.2
  [b9860ae5] FLoopsBase v0.1.1
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [29a986be] FastLapackInterface v2.0.4
  [a4df4552] FastPower v1.1.1
  [5789e2e9] FileIO v1.16.4
  [48062228] FilePathsBase v0.9.22
  [1a297f60] FillArrays v1.13.0
  [6a86dc24] FiniteDiff v2.26.0
  [53c48c17] FixedPointNumbers v0.8.5
  [587475ba] Flux v0.14.25
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v0.10.37
  [f62d2435] FunctionProperties v0.1.2
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
 [d9f16b24] Functors v0.4.12
 [0c68f7d7] GPUArrays v10.3.1
 [46192b85] GPUArraysCore v0.1.6
 [61eb1bfa] GPUCompiler v0.27.8
  [28b8d3ca] GR v0.73.8
  [92fee26a] GZip v0.6.2
  [14197337] GenericLinearAlgebra v0.3.14
  [c145ed77] GenericSchur v0.5.4
  [d7ba0133] Git v1.3.1
  [c27321d9] Glob v1.3.1
  [86223c79] Graphs v1.12.0
  [42e2da0e] Grisu v1.0.2
  [f67ccb44] HDF5 v0.17.2
  [cd3eb016] HTTP v1.10.9
  [3e5b6fbb] HostCPUFeatures v0.1.17
  [0e44f5e4] Hwloc v3.3.0
  [34004b35] HypergeometricFunctions v0.3.24
  [b5f81e59] IOCapture v0.2.5
  [7869d1d1] IRTools v0.4.14
  [615f187c] IfElse v0.1.1
  [c817782e] ImageBase v0.1.7
  [a09fc81d] ImageCore v0.10.3
  [4e3cecfd] ImageShow v0.3.8
  [d25df0c9] Inflate v0.1.5
  [22cec73e] InitialValues v0.3.1
  [842dd82b] InlineStrings v1.4.2
  [18e54dd8] IntegerMathUtils v0.1.2
  [7d512f48] InternedStrings v0.7.0
  [8197267c] IntervalSets v0.7.10
  [3587e190] InverseFunctions v0.1.17
  [41ab1584] InvertedIndices v1.3.0
  [92d709cd] IrrationalConstants v0.2.2
  [c8e1da08] IterTools v1.10.0
  [82899510] IteratorInterfaceExtensions v1.0.0
  [033835bb] JLD2 v0.5.8
  [1019f520] JLFzf v0.1.8
  [692b3bcd] JLLWrappers v1.6.1
  [682c06a0] JSON v0.21.4
  [0f8b85d8] JSON3 v1.14.1
  [b14d175d] JuliaVariables v0.2.4
  [ccbc3e58] JumpProcesses v9.14.0
  [ef3ab10e] KLU v0.6.0
  [63c18a36] KernelAbstractions v0.9.29
  [ba0b0d4f] Krylov v0.9.8
  [5be7bae1] LBFGSB v0.4.1
  [929cbde3] LLVM v9.1.3
  [8b046642] LLVMLoopInfo v1.0.0
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.5
  [10f19ff3] LayoutPointers v0.1.17
  [0e77f7df] LazilyInitializedFields v1.3.0
  [5078a376] LazyArrays v2.2.1
  [8cdb02fc] LazyModules v0.3.1
  [1d6d02ad] LeftChildRightSiblingTrees v0.2.0
  [2d8b4e74] LevyArea v1.0.0
  [87fe0de2] LineSearch v0.1.4
  [d3d80556] LineSearches v7.3.0
  [7ed4a6bd] LinearSolve v2.36.2
  [2ab3a3ac] LogExpFunctions v0.3.28
  [e6f89c97] LoggingExtras v1.1.0
  [bdcacae8] LoopVectorization v0.12.171
  [b2108857] Lux v1.2.3
  [d0bbae9a] LuxCUDA v0.3.3
  [bb33d45b] LuxCore v1.1.0
  [82251201] LuxLib v1.3.7
  [23992714] MAT v0.10.7
  [7e8f7934] MLDataDevices v1.5.0
  [eb30cadb] MLDatasets v0.7.18
  [d8e11817] MLStyle v0.4.17
  [f1d291b0] MLUtils v0.4.4
  [3da0fdf6] MPIPreferences v0.1.11
  [1914dd2f] MacroTools v0.5.13
  [d125e4d3] ManualMemory v0.1.8
  [dbb5928d] MappedArrays v0.4.2
  [d0879d2d] MarkdownAST v0.1.2
  [bb5d69b7] MaybeInplace v0.1.4
  [739be429] MbedTLS v1.1.9
  [442fdcdd] Measures v0.3.2
  [128add7d] MicroCollections v0.2.0
  [e1d29d7a] Missings v1.2.0
  [e94cdb99] MosaicViews v0.3.4
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.7
  [d8a4904e] MutableArithmetics v1.5.2
  [d41bc354] NLSolversBase v7.8.3
  [2774e3e8] NLsolve v4.5.1
  [872c559c] NNlib v0.9.24
  [15e1cf62] NPZ v0.4.3
  [5da4648a] NVTX v0.3.4
  [77ba4419] NaNMath v1.0.2
  [71a1bf82] NameResolution v0.1.5
 [8913a72c] NonlinearSolve v3.15.1
  [d8793406] ObjectFile v0.4.2
  [6fe1bfb0] OffsetArrays v1.14.1
  [0b1bfda6] OneHotArrays v0.2.5
  [4d8831e6] OpenSSL v1.4.3
  [429524aa] Optim v1.9.4
 [3bd65402] Optimisers v0.3.4
  [7f7a1694] Optimization v4.0.5
  [bca83a33] OptimizationBase v2.4.0
  [36348300] OptimizationOptimJL v0.4.1
  [42dfb2eb] OptimizationOptimisers v0.3.4
  [500b13db] OptimizationPolyalgorithms v0.3.0
  [bac558e1] OrderedCollections v1.6.3
  [1dea7af3] OrdinaryDiffEq v6.89.0
  [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v1.1.0
  [6ad6398a] OrdinaryDiffEqBDF v1.1.2
  [bbf590c4] OrdinaryDiffEqCore v1.10.0
  [50262376] OrdinaryDiffEqDefault v1.1.0
  [4302a76b] OrdinaryDiffEqDifferentiation v1.1.0
  [9286f039] OrdinaryDiffEqExplicitRK v1.1.0
  [e0540318] OrdinaryDiffEqExponentialRK v1.1.0
  [becaefa8] OrdinaryDiffEqExtrapolation v1.2.1
  [5960d6e9] OrdinaryDiffEqFIRK v1.2.0
  [101fe9f7] OrdinaryDiffEqFeagin v1.1.0
  [d3585ca7] OrdinaryDiffEqFunctionMap v1.1.1
  [d28bc4f8] OrdinaryDiffEqHighOrderRK v1.1.0
  [9f002381] OrdinaryDiffEqIMEXMultistep v1.1.0
  [521117fe] OrdinaryDiffEqLinear v1.1.0
  [1344f307] OrdinaryDiffEqLowOrderRK v1.2.0
  [b0944070] OrdinaryDiffEqLowStorageRK v1.2.1
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.2.2
  [c9986a66] OrdinaryDiffEqNordsieck v1.1.0
  [5dd0a6cf] OrdinaryDiffEqPDIRK v1.1.0
  [5b33eab2] OrdinaryDiffEqPRK v1.1.0
  [04162be5] OrdinaryDiffEqQPRK v1.1.0
  [af6ede74] OrdinaryDiffEqRKN v1.1.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.2.0
  [2d112036] OrdinaryDiffEqSDIRK v1.1.0
  [669c94d9] OrdinaryDiffEqSSPRK v1.2.0
  [e3e12d00] OrdinaryDiffEqStabilizedIRK v1.1.0
  [358294b1] OrdinaryDiffEqStabilizedRK v1.1.0
  [fa646aed] OrdinaryDiffEqSymplecticRK v1.1.0
  [b1df2697] OrdinaryDiffEqTsit5 v1.1.0
  [79d7bb75] OrdinaryDiffEqVerner v1.1.1
  [90014a1f] PDMats v0.11.31
  [65ce6f38] PackageExtensionCompat v1.0.2
  [5432bcbf] PaddedViews v0.5.12
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.1
  [7b2266bf] PeriodicTable v1.2.1
  [fbb45041] Pickle v0.3.5
  [b98c9c47] Pipe v1.3.0
  [ccf2f8ad] PlotThemes v3.3.0
  [995b91a9] PlotUtils v1.4.3
  [91a5bcdd] Plots v1.40.8
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.16
  [1d0040c9] PolyesterWeave v0.2.2
  [f27b6e38] Polynomials v4.0.11
  [2dfb63ee] PooledArrays v1.4.3
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.24
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [8162dcfd] PrettyPrint v0.2.0
  [08abe8d2] PrettyTables v2.4.0
  [27ebfcd6] Primes v0.5.6
  [33c8b6b6] ProgressLogging v0.1.4
  [92933f4c] ProgressMeter v1.10.2
  [43287f4e] PtrArrays v1.2.1
  [1fd47b50] QuadGK v2.11.1
  [74087812] Random123 v1.7.0
  [e6cf234a] RandomNumbers v1.6.0
  [c1ae055f] RealDot v0.1.0
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
  [731186ca] RecursiveArrayTools v3.27.3
  [f2c3362d] RecursiveFactorization v0.2.23
  [189a3867] Reexport v1.2.2
  [2792f1a3] RegistryInstances v0.1.0
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.0
  [ae5879a3] ResettableStacks v1.1.1
  [37e2e3b7] ReverseDiff v1.15.3
  [79098fc4] Rmath v0.8.0
  [47965b36] RootedTrees v2.23.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.43
  [0bca4576] SciMLBase v2.58.1
  [19f34311] SciMLJacobianOperators v0.1.1
  [c0aeaf25] SciMLOperators v0.3.12
  [1ed8b502] SciMLSensitivity v7.70.0
  [53ae85a6] SciMLStructures v1.5.0
  [6c6a2e73] Scratch v1.2.1
  [91c51154] SentinelArrays v1.4.7
  [efcf1570] Setfield v1.1.1
  [605ecd9f] ShowCases v0.1.0
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.2.0
 [727e6d20] SimpleNonlinearSolve v1.12.3
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [a2af1166] SortingAlgorithms v1.2.1
  [9f842d2f] SparseConnectivityTracer v0.6.8
  [47a9eef4] SparseDiffTools v2.23.0
  [dc90abb0] SparseInverseSubset v0.1.2
  [0a514795] SparseMatrixColorings v0.4.8
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.4.0
  [171d559e] SplittablesBase v0.1.15
  [860ef19b] StableRNGs v1.0.2
  [cae243ae] StackViews v0.1.1
  [aedffcd0] Static v1.1.1
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.8
  [1e83bf80] StaticArraysCore v1.4.3
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.3
  [4c63d2b9] StatsFuns v1.3.2
  [789caeaf] StochasticDiffEq v6.70.0
  [7792a7ef] StrideArraysCore v0.5.7
 [4db3bf67] StridedViews v0.2.2
  [69024149] StringEncodings v0.3.7
  [892a3eda] StringManipulation v0.4.0
  [09ab397b] StructArrays v0.6.18
  [53d494c1] StructIO v0.3.1
  [856f2bd8] StructTypes v1.11.0
  [2efcf032] SymbolicIndexingInterface v0.3.34
  [19f23fe9] SymbolicLimits v0.2.2
  [d1185830] SymbolicUtils v3.7.2
  [0c5d862f] Symbolics v6.18.3
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [62fd8b95] TensorCore v0.1.1
  [8ea1fca8] TermInterface v2.0.0
  [5d786b92] TerminalLoggers v0.1.7
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.25
  [9f7883ad] Tracker v0.2.36
  [3bb67fe8] TranscodingStreams v0.11.3
  [28d57a85] Transducers v0.4.84
  [d5829a12] TriangularSolve v0.2.1
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [1986cc42] Unitful v1.21.0
  [a7773ee8] UnitfulAtomic v1.0.0
  [45397f5d] UnitfulLatexify v1.6.4
  [a7c27f48] Unityper v0.1.6
  [013be700] UnsafeAtomics v0.2.1
  [d80eeb9a] UnsafeAtomicsLLVM v0.2.1
  [41fe7b60] Unzip v0.2.0
  [3d5dd08c] VectorizationBase v0.21.71
  [19fa3120] VertexSafeGraphs v0.2.0
  [ea10d353] WeakRefStrings v1.4.2
  [d49dbf32] WeightInitializers v1.0.4
  [76eceee3] WorkerUtilities v1.6.1
  [a5390f91] ZipFile v0.10.1
  [e88e6eb3] Zygote v0.6.72
  [700de1a5] ZygoteRules v0.2.5
  [02a925ec] cuDNN v1.4.0
  [6e34b625] Bzip2_jll v1.0.8+2
  [4ee394cb] CUDA_Driver_jll v0.10.3+0
  [76a88914] CUDA_Runtime_jll v0.15.3+0
  [62b44479] CUDNN_jll v9.4.0+0
  [83423d85] Cairo_jll v1.18.2+1
  [78a364fa] Chemfiles_jll v0.10.4+0
  [ee1fde0b] Dbus_jll v1.14.10+0
  [7cc45869] Enzyme_jll v0.0.163+0
  [2702e6a9] EpollShim_jll v0.0.20230411+0
  [2e619515] Expat_jll v2.6.2+0
 [b22a6f82] FFMPEG_jll v4.4.4+1
  [a3f928ae] Fontconfig_jll v2.13.96+0
  [d7e528f0] FreeType2_jll v2.13.2+0
  [559328eb] FriBidi_jll v1.0.14+0
  [0656b61e] GLFW_jll v3.4.0+1
  [d2c73de3] GR_jll v0.73.8+0
  [78b55507] Gettext_jll v0.21.0+0
  [f8c6e375] Git_jll v2.46.2+0
  [7746bdde] Glib_jll v2.80.5+0
  [3b182d85] Graphite2_jll v1.3.14+0
 [0234f1f7] HDF5_jll v1.14.2+1
  [2e76f6c2] HarfBuzz_jll v8.3.1+0
  [e33a78d0] Hwloc_jll v2.11.2+1
  [1d5cc7b8] IntelOpenMP_jll v2024.2.1+0
  [aacddb02] JpegTurbo_jll v3.0.4+0
  [9c1d0b0a] JuliaNVTXCallbacks_jll v0.2.1+0
  [c1c5ebd0] LAME_jll v3.100.2+0
  [88015f11] LERC_jll v4.0.0+0
  [dad2f222] LLVMExtra_jll v0.0.34+0
  [1d63c593] LLVMOpenMP_jll v18.1.7+0
  [dd4b983a] LZO_jll v2.10.2+1
  [81d17ec3] L_BFGS_B_jll v3.0.1+0
 [e9f186c6] Libffi_jll v3.2.2+1
  [d4300ac3] Libgcrypt_jll v1.11.0+0
  [7e76a0d4] Libglvnd_jll v1.6.0+0
  [7add5ba3] Libgpg_error_jll v1.50.0+0
  [94ce4f54] Libiconv_jll v1.17.0+1
  [4b2f31a3] Libmount_jll v2.40.1+0
  [89763e89] Libtiff_jll v4.7.0+0
  [38a345b3] Libuuid_jll v2.40.1+0
  [856f044c] MKL_jll v2024.2.0+0
  [7cb0a576] MPICH_jll v4.2.3+0
  [f1f71cc9] MPItrampoline_jll v5.5.1+0
  [9237b28f] MicrosoftMPI_jll v10.1.4+2
  [e98f9f5b] NVTX_jll v3.1.0+2
  [e7412a2a] Ogg_jll v1.3.5+1
  [fe0851c0] OpenMPI_jll v5.0.5+0
  [458c3c95] OpenSSL_jll v3.0.15+1
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.3+0
  [36c8627f] Pango_jll v1.54.1+0
  [30392449] Pixman_jll v0.43.4+0
  [c0090381] Qt6Base_jll v6.7.1+1
  [629bc702] Qt6Declarative_jll v6.7.1+2
  [ce943373] Qt6ShaderTools_jll v6.7.1+1
  [e99dba38] Qt6Wayland_jll v6.7.1+1
  [f50d1b31] Rmath_jll v0.5.1+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 v2.13.4+0
  [aed1982a] XSLT_jll v1.1.41+0
  [ffd25f8a] XZ_jll v5.6.3+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 v1.17.0+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+1
  [1e29f10c] demumble_jll v1.3.0+0
  [35ca27e7] eudev_jll v3.2.9+0
  [214eeab7] fzf_jll v0.53.0+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 v0.15.2+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [2db6ffa8] libevdev_jll v1.11.0+0
  [f638f0a6] libfdk_aac_jll v2.0.3+0
  [36db933b] libinput_jll v1.18.0+0
  [b53b4c65] libpng_jll v1.6.44+0
  [f27f6e37] libvorbis_jll v1.3.7+2
  [009596ad] mtdev_jll v1.1.6+0
  [1317d2d5] oneTBB_jll v2021.12.0+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 v5.11.0+0
  [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.