NeuralPDE.jl: Automatic Physics-Informed Neural Networks (PINNs)
NeuralPDE.jl is a solver package which consists of neural network solvers for partial differential equations using physics-informed neural networks (PINNs) and the ability to generate neural networks which both approximate physical laws and real data simultaneously.
Features
- Physics-Informed Neural Networks for ODE, SDE, RODE, and PDE solving.
- Ability to define extra loss functions to mix xDE solving with data fitting (scientific machine learning).
- Automated construction of Physics-Informed loss functions from a high-level symbolic interface.
- Sophisticated techniques like quadrature training strategies, adaptive loss functions, and neural adapters to accelerate training.
- Integrated logging suite for handling connections to TensorBoard.
- Handling of (partial) integro-differential equations and various stochastic equations.
- Specialized forms for solving
ODEProblems with neural networks. - Compatibility with Flux.jl and Lux.jl. for all the GPU-powered machine learning layers available from those libraries.
- Compatibility with NeuralOperators.jl for mixing DeepONets and other neural operators (Fourier Neural Operators, Graph Neural Operators, etc.) with physics-informed loss functions.
Installation
Assuming that you already have Julia correctly installed, it suffices to import NeuralPDE.jl in the standard way:
import Pkg
Pkg.add("NeuralPDE")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
Citation
If you use NeuralPDE.jl in your research, please cite this paper:
@misc{https://doi.org/10.48550/arxiv.2107.09443,
doi = {10.48550/ARXIV.2107.09443},
url = {https://arxiv.org/abs/2107.09443},
author = {Zubov, Kirill and McCarthy, Zoe and Ma, Yingbo and Calisto, Francesco and Pagliarino, Valerio and Azeglio, Simone and Bottero, Luca and Luján, Emmanuel and Sulzer, Valentin and Bharambe, Ashutosh and Vinchhi, Nand and Balakrishnan, Kaushik and Upadhyay, Devesh and Rackauckas, Chris},
keywords = {Mathematical Software (cs.MS), Symbolic Computation (cs.SC), FOS: Computer and information sciences, FOS: Computer and information sciences},
title = {NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with Error Approximations},
publisher = {arXiv},
year = {2021},
copyright = {Creative Commons Attribution Non Commercial Share Alike 4.0 International}
}Flux.jl vs Lux.jl
Both Flux and Lux defined neural networks are supported by NeuralPDE.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, ForwardDiffSensitivity dual numbers, and TaylorDiff.jl differentiation) 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.
Reproducibility
The documentation of this SciML package was built using these direct dependencies,
Status `/var/lib/buildkite-agent/builds/gpuci-7/julialang/neuralpde-dot-jl/docs/Project.toml`
[0bf59076] AdvancedHMC v0.6.1
[b0b7db55] ComponentArrays v0.15.11
[667455a9] Cubature v1.5.1
[2b5f629d] DiffEqBase v6.149.0
[31c24e10] Distributions v0.25.107
[e30172f5] Documenter v1.4.0
⌅ [5b8099bc] DomainSets v0.6.7
[587475ba] Flux v0.14.15
[de52edbc] Integrals v4.4.1
[d3d80556] LineSearches v7.2.0
[b2108857] Lux v0.5.35
[d0bbae9a] LuxCUDA v0.3.2
[94925ecb] MethodOfLines v0.11.0
[961ee093] ModelingToolkit v9.11.0
[0987c9cc] MonteCarloMeasurements v1.1.6
[315f7962] NeuralPDE v5.16.0 `/var/lib/buildkite-agent/builds/gpuci-7/julialang/neuralpde-dot-jl`
[7f7a1694] Optimization v3.24.3
[36348300] OptimizationOptimJL v0.2.3
[42dfb2eb] OptimizationOptimisers v0.2.1
[500b13db] OptimizationPolyalgorithms v0.2.0
[1dea7af3] OrdinaryDiffEq v6.74.1
[91a5bcdd] Plots v1.40.4
[8a4e6c94] QuasiMonteCarlo v0.3.3
[f2b01f46] Roots v2.1.5
[276daf66] SpecialFunctions v2.3.1
[37e2e46d] LinearAlgebra
[9a3f8284] Random
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 1.10.2
Commit bd47eca2c8a (2024-03-01 10:14 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_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/f8da2e12-18ea-4414-879b-afc071467714
LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
JULIA_DEBUG = DocumenterA more complete overview of all dependencies and their versions is also provided.
Status `/var/lib/buildkite-agent/builds/gpuci-7/julialang/neuralpde-dot-jl/docs/Manifest.toml`
[47edcb42] ADTypes v0.2.7
[a4c015fc] ANSIColoredPrinters v0.0.1
[621f4979] AbstractFFTs v1.5.0
[80f14c24] AbstractMCMC v5.2.0
[1520ce14] AbstractTrees v0.4.5
[7d9f7c33] Accessors v0.1.36
[79e6a3ab] Adapt v4.0.4
[0bf59076] AdvancedHMC v0.6.1
[dce04be8] ArgCheck v2.3.0
[ec485272] ArnoldiMethod v0.4.0
[4fba245c] ArrayInterface v7.9.0
[4c555306] ArrayLayouts v1.9.2
[a9b6321e] Atomix v0.1.0
⌃ [13072b0f] AxisAlgorithms v1.0.1
[39de3d68] AxisArrays v0.4.7
[ab4f0b2a] BFloat16s v0.5.0
⌅ [198e06fe] BangBang v0.3.40
[9718e550] Baselet v0.1.1
[e2ed5e7c] Bijections v0.1.6
[d1d4a3ce] BitFlags v0.1.8
[62783981] BitTwiddlingConvenienceFunctions v0.1.5
[fa961155] CEnum v0.5.0
[2a0fbf3d] CPUSummary v0.2.4
[00ebfdb7] CSTParser v3.4.2
[052768ef] CUDA v5.3.0
[1af6417a] CUDA_Runtime_Discovery v0.2.4
[49dc2e85] Calculus v0.5.1
[082447d4] ChainRules v1.63.0
[d360d2e6] ChainRulesCore v1.23.0
[fb6a15b2] CloseOpenIntervals v0.1.12
[944b1d66] CodecZlib v0.7.4
[35d6a980] ColorSchemes v3.24.0
[3da002f7] ColorTypes v0.11.5
[c3611d14] ColorVectorSpace v0.10.0
[5ae59095] Colors v0.12.10
[861a8166] Combinatorics v1.0.2
[a80b9123] CommonMark v0.8.12
[38540f10] CommonSolve v0.2.4
[bbf7d656] CommonSubexpressions v0.3.0
[34da2185] Compat v4.14.0
[b0b7db55] ComponentArrays v0.15.11
[b152e2b5] CompositeTypes v0.1.4
[a33af91c] CompositionsBase v0.1.2
[2569d6c7] ConcreteStructs v0.2.3
[f0e56b4a] ConcurrentUtilities v2.4.1
[88cd18e8] ConsoleProgressMonitor v0.1.2
[187b0558] ConstructionBase v1.5.5
[6add18c4] ContextVariablesX v0.1.3
[d38c429a] Contour v0.6.3
[adafc99b] CpuId v0.3.1
[a8cc5b0e] Crayons v4.1.1
[667455a9] Cubature v1.5.1
[9a962f9c] DataAPI v1.16.0
[a93c6f00] DataFrames v1.6.1
[864edb3b] DataStructures v0.18.19
[e2d170a0] DataValueInterfaces v1.0.0
[244e2a9f] DefineSingletons v0.1.2
[8bb1440f] DelimitedFiles v1.9.1
[2b5f629d] DiffEqBase v6.149.0
[459566f4] DiffEqCallbacks v3.6.1
[77a26b50] DiffEqNoiseProcess v5.21.0
[163ba53b] DiffResults v1.1.0
[b552c78f] DiffRules v1.15.1
[31c24e10] Distributions v0.25.107
[ffbed154] DocStringExtensions v0.9.3
[e30172f5] Documenter v1.4.0
⌅ [5b8099bc] DomainSets v0.6.7
[fa6b7ba4] DualNumbers v0.6.8
[7c1d4256] DynamicPolynomials v0.5.6
[06fc5a27] DynamicQuantities v0.13.2
[4e289a0a] EnumX v1.0.4
⌃ [f151be2c] EnzymeCore v0.6.6
[460bff9d] ExceptionUnwrapping v0.1.10
[d4d017d3] ExponentialUtilities v1.26.1
[e2ba6199] ExprTools v0.1.10
[c87230d0] FFMPEG v0.4.1
[7a1cc6ca] FFTW v1.8.0
[cc61a311] FLoops v0.2.1
[b9860ae5] FLoopsBase v0.1.1
[7034ab61] FastBroadcast v0.2.8
[9aa1b823] FastClosures v0.3.2
[29a986be] FastLapackInterface v2.0.2
[1a297f60] FillArrays v1.10.0
[64ca27bc] FindFirstFunctions v1.2.0
[6a86dc24] FiniteDiff v2.23.0
[53c48c17] FixedPointNumbers v0.8.4
[587475ba] Flux v0.14.15
[1fa38f19] Format v1.3.7
[f6369f11] ForwardDiff v0.10.36
[069b7b12] FunctionWrappers v1.1.3
[77dc65aa] FunctionWrappersWrappers v0.1.3
[d9f16b24] Functors v0.4.10
[0c68f7d7] GPUArrays v10.1.0
[46192b85] GPUArraysCore v0.1.6
[61eb1bfa] GPUCompiler v0.26.4
[28b8d3ca] GR v0.73.3
[c145ed77] GenericSchur v0.5.4
[d7ba0133] Git v1.3.1
[c27321d9] Glob v1.3.1
[86223c79] Graphs v1.10.0
[42e2da0e] Grisu v1.0.2
[19dc6840] HCubature v1.6.0
[cd3eb016] HTTP v1.10.5
[3e5b6fbb] HostCPUFeatures v0.1.16
[34004b35] HypergeometricFunctions v0.3.23
[b5f81e59] IOCapture v0.2.4
[7869d1d1] IRTools v0.4.12
[615f187c] IfElse v0.1.1
[d25df0c9] Inflate v0.1.4
[22cec73e] InitialValues v0.3.1
[842dd82b] InlineStrings v1.4.0
[505f98c9] InplaceOps v0.3.0
[18e54dd8] IntegerMathUtils v0.1.2
[de52edbc] Integrals v4.4.1
⌅ [a98d9a8b] Interpolations v0.14.0
[8197267c] IntervalSets v0.7.10
[3587e190] InverseFunctions v0.1.13
[41ab1584] InvertedIndices v1.3.0
[92d709cd] IrrationalConstants v0.2.2
[c8e1da08] IterTools v1.10.0
[82899510] IteratorInterfaceExtensions v1.0.0
[1019f520] JLFzf v0.1.7
[692b3bcd] JLLWrappers v1.5.0
[682c06a0] JSON v0.21.4
[98e50ef6] JuliaFormatter v1.0.56
[b14d175d] JuliaVariables v0.2.4
[ccbc3e58] JumpProcesses v9.11.1
[ef3ab10e] KLU v0.6.0
[63c18a36] KernelAbstractions v0.9.18
[5ab0869b] KernelDensity v0.6.8
[ba0b0d4f] Krylov v0.9.5
[929cbde3] LLVM v6.6.3
[8b046642] LLVMLoopInfo v1.0.0
[b964fa9f] LaTeXStrings v1.3.1
[2ee39098] LabelledArrays v1.15.1
[984bce1d] LambertW v0.4.6
[23fbe1c1] Latexify v0.16.2
[73f95e8e] LatticeRules v0.0.1
[10f19ff3] LayoutPointers v0.1.15
[0e77f7df] LazilyInitializedFields v1.2.2
[5078a376] LazyArrays v1.9.1
[1d6d02ad] LeftChildRightSiblingTrees v0.2.0
[d3d80556] LineSearches v7.2.0
[7ed4a6bd] LinearSolve v2.28.0
[6fdf6af0] LogDensityProblems v2.1.1
[996a588d] LogDensityProblemsAD v1.7.0
[2ab3a3ac] LogExpFunctions v0.3.27
[e6f89c97] LoggingExtras v1.0.3
[bdcacae8] LoopVectorization v0.12.169
[b2108857] Lux v0.5.35
[d0bbae9a] LuxCUDA v0.3.2
[bb33d45b] LuxCore v0.1.14
[34f89e08] LuxDeviceUtils v0.1.20
[82251201] LuxLib v0.3.12
[c7f686f2] MCMCChains v6.0.6
[be115224] MCMCDiagnosticTools v0.3.10
[e80e1ace] MLJModelInterface v1.9.6
[d8e11817] MLStyle v0.4.17
[f1d291b0] MLUtils v0.4.4
[1914dd2f] MacroTools v0.5.13
[d125e4d3] ManualMemory v0.1.8
[d0879d2d] MarkdownAST v0.1.2
[a3b82374] MatrixFactorizations v2.2.0
[bb5d69b7] MaybeInplace v0.1.2
[739be429] MbedTLS v1.1.9
[442fdcdd] Measures v0.3.2
[94925ecb] MethodOfLines v0.11.0
⌅ [128add7d] MicroCollections v0.1.4
[e1d29d7a] Missings v1.2.0
[961ee093] ModelingToolkit v9.11.0
[4886b29c] MonteCarloIntegration v0.2.0
[0987c9cc] MonteCarloMeasurements v1.1.6
[46d2c3a1] MuladdMacro v0.2.4
[102ac46a] MultivariatePolynomials v0.5.4
[d8a4904e] MutableArithmetics v1.4.2
[d41bc354] NLSolversBase v7.8.3
[872c559c] NNlib v0.9.13
[5da4648a] NVTX v0.3.4
[77ba4419] NaNMath v1.0.2
[71a1bf82] NameResolution v0.1.5
[c020b1a1] NaturalSort v1.0.0
[315f7962] NeuralPDE v5.16.0 `/var/lib/buildkite-agent/builds/gpuci-7/julialang/neuralpde-dot-jl`
[8913a72c] NonlinearSolve v3.10.0
[6fe1bfb0] OffsetArrays v1.14.0
[0b1bfda6] OneHotArrays v0.2.5
[4d8831e6] OpenSSL v1.4.2
[429524aa] Optim v1.9.4
[3bd65402] Optimisers v0.3.3
[7f7a1694] Optimization v3.24.3
[bca83a33] OptimizationBase v0.0.5
[36348300] OptimizationOptimJL v0.2.3
[42dfb2eb] OptimizationOptimisers v0.2.1
[500b13db] OptimizationPolyalgorithms v0.2.0
[bac558e1] OrderedCollections v1.6.3
[1dea7af3] OrdinaryDiffEq v6.74.1
[a7812802] PDEBase v0.1.10
[90014a1f] PDMats v0.11.31
[65ce6f38] PackageExtensionCompat v1.0.2
[d96e819e] Parameters v0.12.3
[69de0a69] Parsers v2.8.1
[570af359] PartialFunctions v1.2.0
[b98c9c47] Pipe v1.3.0
[ccf2f8ad] PlotThemes v3.1.0
[995b91a9] PlotUtils v1.4.1
[91a5bcdd] Plots v1.40.4
[e409e4f3] PoissonRandom v0.4.4
[f517fe37] Polyester v0.7.12
[1d0040c9] PolyesterWeave v0.2.1
[2dfb63ee] PooledArrays v1.4.3
[85a6dd25] PositiveFactorizations v0.2.4
[d236fae5] PreallocationTools v0.4.20
[aea7be01] PrecompileTools v1.2.1
[21216c6a] Preferences v1.4.3
[8162dcfd] PrettyPrint v0.2.0
[08abe8d2] PrettyTables v2.3.1
[27ebfcd6] Primes v0.5.6
[33c8b6b6] ProgressLogging v0.1.4
[92933f4c] ProgressMeter v1.10.0
[1fd47b50] QuadGK v2.9.4
[8a4e6c94] QuasiMonteCarlo v0.3.3
[74087812] Random123 v1.7.0
[e6cf234a] RandomNumbers v1.5.3
[b3c3ace0] RangeArrays v0.3.2
[c84ed2f1] Ratios v0.4.5
[c1ae055f] RealDot v0.1.0
[3cdcf5f2] RecipesBase v1.3.4
[01d81517] RecipesPipeline v0.6.12
[731186ca] RecursiveArrayTools v3.13.0
[f2c3362d] RecursiveFactorization v0.2.22
[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
[79098fc4] Rmath v0.7.1
[f2b01f46] Roots v2.1.5
[7e49a35a] RuntimeGeneratedFunctions v0.5.12
[94e857df] SIMDTypes v0.1.0
[476501e8] SLEEFPirates v0.6.42
[0bca4576] SciMLBase v2.33.0
[c0aeaf25] SciMLOperators v0.3.8
[53ae85a6] SciMLStructures v1.1.0
[30f210dd] ScientificTypesBase v3.0.0
[6c6a2e73] Scratch v1.2.1
[91c51154] SentinelArrays v1.4.1
[efcf1570] Setfield v1.1.1
[605ecd9f] ShowCases v0.1.0
[992d4aef] Showoff v1.0.3
[777ac1f9] SimpleBufferStream v1.1.0
[727e6d20] SimpleNonlinearSolve v1.7.0
[699a6c99] SimpleTraits v0.9.4
[ce78b400] SimpleUnPack v1.1.0
[ed01d8cd] Sobol v1.5.0
[a2af1166] SortingAlgorithms v1.2.1
[47a9eef4] SparseDiffTools v2.17.0
[dc90abb0] SparseInverseSubset v0.1.2
[e56a9233] Sparspak v0.3.9
[276daf66] SpecialFunctions v2.3.1
[171d559e] SplittablesBase v0.1.15
[aedffcd0] Static v0.8.10
[0d7ed370] StaticArrayInterface v1.5.0
[90137ffa] StaticArrays v1.9.3
[1e83bf80] StaticArraysCore v1.4.2
[64bff920] StatisticalTraits v3.2.0
[82ae8749] StatsAPI v1.7.0
[2913bbd2] StatsBase v0.34.3
[4c63d2b9] StatsFuns v1.3.1
[7792a7ef] StrideArraysCore v0.5.5
[892a3eda] StringManipulation v0.3.4
[09ab397b] StructArrays v0.6.18
[2efcf032] SymbolicIndexingInterface v0.3.16
[19f23fe9] SymbolicLimits v0.2.0
[d1185830] SymbolicUtils v1.5.1
[0c5d862f] Symbolics v5.28.0
[3783bdb8] TableTraits v1.0.1
[bd369af6] Tables v1.11.1
[62fd8b95] TensorCore v0.1.1
⌅ [8ea1fca8] TermInterface v0.3.3
[5d786b92] TerminalLoggers v0.1.7
[8290d209] ThreadingUtilities v0.5.2
[a759f4b9] TimerOutputs v0.5.23
[0796e94c] Tokenize v0.5.28
[3bb67fe8] TranscodingStreams v0.10.7
⌃ [28d57a85] Transducers v0.4.80
⌅ [d5829a12] TriangularSolve v0.1.21
[410a4b4d] Tricks v0.1.8
[781d530d] TruncatedStacktraces v1.4.0
[5c2747f8] URIs v1.5.1
[3a884ed6] UnPack v1.0.2
[1cfade01] UnicodeFun v0.4.1
[1986cc42] Unitful v1.19.0
[45397f5d] UnitfulLatexify v1.6.3
[a7c27f48] Unityper v0.1.6
[013be700] UnsafeAtomics v0.2.1
[d80eeb9a] UnsafeAtomicsLLVM v0.1.3
[41fe7b60] Unzip v0.2.0
[3d5dd08c] VectorizationBase v0.21.65
[19fa3120] VertexSafeGraphs v0.2.0
[d49dbf32] WeightInitializers v0.1.7
⌅ [efce3f68] WoodburyMatrices v0.5.6
[e88e6eb3] Zygote v0.6.69
[700de1a5] ZygoteRules v0.2.5
[02a925ec] cuDNN v1.3.1
[6e34b625] Bzip2_jll v1.0.8+1
[4ee394cb] CUDA_Driver_jll v0.8.1+0
[76a88914] CUDA_Runtime_jll v0.12.1+0
[62b44479] CUDNN_jll v9.0.0+1
[83423d85] Cairo_jll v1.18.0+1
[7bc98958] Cubature_jll v1.0.5+0
[2702e6a9] EpollShim_jll v0.0.20230411+0
[2e619515] Expat_jll v2.5.0+0
⌅ [b22a6f82] FFMPEG_jll v4.4.4+1
[f5851436] FFTW_jll v3.3.10+0
[a3f928ae] Fontconfig_jll v2.13.93+0
[d7e528f0] FreeType2_jll v2.13.1+0
[559328eb] FriBidi_jll v1.0.10+0
[0656b61e] GLFW_jll v3.3.9+0
[d2c73de3] GR_jll v0.73.3+0
[78b55507] Gettext_jll v0.21.0+0
[f8c6e375] Git_jll v2.44.0+2
[7746bdde] Glib_jll v2.80.0+0
[3b182d85] Graphite2_jll v1.3.14+0
[2e76f6c2] HarfBuzz_jll v2.8.1+1
[1d5cc7b8] IntelOpenMP_jll v2024.0.2+0
[aacddb02] JpegTurbo_jll v3.0.2+0
[9c1d0b0a] JuliaNVTXCallbacks_jll v0.2.1+0
[c1c5ebd0] LAME_jll v3.100.1+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 v2.10.1+0
⌅ [e9f186c6] Libffi_jll v3.2.2+1
[d4300ac3] Libgcrypt_jll v1.8.7+0
[7e76a0d4] Libglvnd_jll v1.6.0+0
[7add5ba3] Libgpg_error_jll v1.42.0+0
[94ce4f54] Libiconv_jll v1.17.0+0
[4b2f31a3] Libmount_jll v2.39.3+0
⌅ [89763e89] Libtiff_jll v4.5.1+1
[38a345b3] Libuuid_jll v2.39.3+1
[856f044c] MKL_jll v2024.0.0+0
[e98f9f5b] NVTX_jll v3.1.0+2
[e7412a2a] Ogg_jll v1.3.5+1
[458c3c95] OpenSSL_jll v3.0.13+1
[efe28fd5] OpenSpecFun_jll v0.5.5+0
[91d4177d] Opus_jll v1.3.2+0
[30392449] Pixman_jll v0.42.2+0
[c0090381] Qt6Base_jll v6.5.3+1
[f50d1b31] Rmath_jll v0.4.0+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 v2.12.6+0
[aed1982a] XSLT_jll v1.1.34+0
[ffd25f8a] XZ_jll v5.4.6+0
[f67eecfb] Xorg_libICE_jll v1.0.10+1
[c834827a] Xorg_libSM_jll v1.2.3+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 v1.3.4+4
[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 v0.9.10+4
[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
[a4ae2306] libaom_jll v3.4.0+0
[0ac62f75] libass_jll v0.15.1+0
[2db6ffa8] libevdev_jll v1.11.0+0
[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
[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 v1.1.0+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.