SciML: Differentiable Modeling and Simulation Combined with Machine Learning

The SciML organization is a collection of tools for solving equations and modeling systems developed in the Julia programming language with bindings to other languages such as R and Python. The organization provides well-maintained tools which compose together as a coherent ecosystem. It has a coherent development principle, unified APIs over large collections of equation solvers, pervasive differentiability and sensitivity analysis, and features many of the highest performance and parallel implementations one can find.

Scientific Machine Learning (SciML) = Scientific Computing + Machine Learning

Where to Start?

And for diving into the details, use the bar on the top to navigate to the submodule of interest!

Reproducibility

The documentation of the [SciML Showcase](@ref showcase) was built using these direct dependencies,
Status `/var/lib/buildkite-agent/builds/gpuci-13/julialang/scimldocs/docs/Project.toml`
 [0bf59076] AdvancedHMC v0.5.5
  [6e4b80f9] BenchmarkTools v1.3.2
  [336ed68f] CSV v0.10.11
 [052768ef] CUDA v4.4.1
  [b0b7db55] ComponentArrays v0.15.4
  [2445eb08] DataDrivenDiffEq v1.3.0
  [5b588203] DataDrivenSparse v0.1.2
  [a93c6f00] DataFrames v1.6.1
  [aae7a2af] DiffEqFlux v2.4.0
 [071ae1c0] DiffEqGPU v2.5.1
 [0c46a032] DifferentialEquations v7.10.0
  [31c24e10] Distributions v0.25.103
  [e30172f5] Documenter v1.1.2
 [5b8099bc] DomainSets v0.6.7
  [587475ba] Flux v0.14.6
  [f6369f11] ForwardDiff v0.10.36
  [40713840] IncompleteLU v0.2.1
 [de52edbc] Integrals v3.9.0
  [d3d80556] LineSearches v7.2.0
 [7ed4a6bd] LinearSolve v2.10.0
  [b2108857] Lux v0.5.9
  [c7f686f2] MCMCChains v6.0.4
  [eff96d63] Measurements v2.11.0
 [94925ecb] MethodOfLines v0.9.6
 [961ee093] ModelingToolkit v8.70.0
  [87ed4bf0] MultiDocumenter v0.7.0
  [315f7962] NeuralPDE v5.9.0
 [8913a72c] NonlinearSolve v1.10.1
  [7f7a1694] Optimization v3.19.3
  [fd9f6733] OptimizationMOI v0.1.16
  [4e6fcdb7] OptimizationNLopt v0.1.8
  [36348300] OptimizationOptimJL v0.1.13
  [42dfb2eb] OptimizationOptimisers v0.1.6
  [500b13db] OptimizationPolyalgorithms v0.1.2
  [1dea7af3] OrdinaryDiffEq v6.58.2
  [91a5bcdd] Plots v1.39.0
  [afe9f18d] SciMLExpectations v2.1.0
  [1ed8b502] SciMLSensitivity v7.46.0
  [860ef19b] StableRNGs v1.0.0
  [90137ffa] StaticArrays v1.6.5
  [f3b207a7] StatsPlots v0.15.6
  [1986cc42] Unitful v1.17.0
  [e88e6eb3] Zygote v0.6.67
  [76f85450] LibGit2
  [37e2e46d] LinearAlgebra
  [44cfe95a] Pkg v1.9.2
  [de0858da] Printf
  [9a3f8284] Random
  [10745b16] Statistics v1.9.0
Info Packages marked with  and  have new versions available, but those with  are restricted by compatibility constraints from upgrading. To see why use `status --outdated`
and using this machine and Julia version.
Julia Version 1.9.3
Commit bed2cd540a1 (2023-08-24 14:43 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-14.0.6 (ORCJIT, znver2)
  Threads: 1 on 2 virtual cores
Environment:
  JULIA_CPU_THREADS = 2
  JULIA_DEBUG = Documenter
  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/0183cc98-c3b4-4959-aaaa-6c0d5f351407
  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
  JULIA_PKG_SERVER =
  JULIA_IMAGE_THREADS = 1
A more complete overview of all dependencies and their versions is also provided.
Status `/var/lib/buildkite-agent/builds/gpuci-13/julialang/scimldocs/docs/Manifest.toml`
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  [76eceee3] WorkerUtilities v1.6.1
  [e88e6eb3] Zygote v0.6.67
  [700de1a5] ZygoteRules v0.2.4
  [ae81ac8f] ASL_jll v0.1.3+0
 [68821587] Arpack_jll v3.5.1+1
  [6e34b625] Bzip2_jll v1.0.8+0
 [4ee394cb] CUDA_Driver_jll v0.5.0+1
 [76a88914] CUDA_Runtime_jll v0.6.0+0
  [83423d85] Cairo_jll v1.16.1+1
  [7bc98958] Cubature_jll v1.0.5+0
 [7cc45869] Enzyme_jll v0.0.89+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 v3.3.8+0
  [d2c73de3] GR_jll v0.72.10+0
  [78b55507] Gettext_jll v0.21.0+0
  [f8c6e375] Git_jll v2.42.0+0
  [7746bdde] Glib_jll v2.76.5+0
  [3b182d85] Graphite2_jll v1.3.14+0
  [528830af] Gumbo_jll v0.10.2+0
  [2e76f6c2] HarfBuzz_jll v2.8.1+1
  [1d5cc7b8] IntelOpenMP_jll v2023.2.0+0
 [9cc047cb] Ipopt_jll v300.1400.400+0
  [aacddb02] JpegTurbo_jll v2.1.91+0
  [c1c5ebd0] LAME_jll v3.100.1+0
  [88015f11] LERC_jll v3.0.0+1
  [dad2f222] LLVMExtra_jll v0.0.27+0
  [1d63c593] LLVMOpenMP_jll v15.0.4+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 v2.35.0+0
  [89763e89] Libtiff_jll v4.5.1+1
  [38a345b3] Libuuid_jll v2.36.0+0
  [d00139f3] METIS_jll v5.1.2+0
  [856f044c] MKL_jll v2023.2.0+0
 [d7ed1dd3] MUMPS_seq_jll v5.4.1+0
  [079eb43e] NLopt_jll v2.7.1+0
  [e7412a2a] Ogg_jll v1.3.5+1
 [656ef2d0] OpenBLAS32_jll v0.3.21+0
  [458c3c95] OpenSSL_jll v3.0.12+0
  [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
 [fb77eaff] Sundials_jll v5.2.1+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.21.0+1
  [2381bf8a] Wayland_protocols_jll v1.25.0+0
  [02c8fc9c] XML2_jll v2.11.5+0
  [aed1982a] XSLT_jll v1.1.34+0
  [ffd25f8a] XZ_jll v5.4.4+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 v1.5.5+0
  [35ca27e7] eudev_jll v3.2.9+0
 [214eeab7] fzf_jll v0.35.1+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 v1.6.38+0
  [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 v0.6.3
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.9.2
  [de0858da] Printf
  [9abbd945] Profile
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays
  [10745b16] Statistics v1.9.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.0.5+0
  [deac9b47] LibCURL_jll v7.84.0+0
  [29816b5a] LibSSH2_jll v1.10.2+0
  [c8ffd9c3] MbedTLS_jll v2.28.2+0
  [14a3606d] MozillaCACerts_jll v2022.10.11
  [4536629a] OpenBLAS_jll v0.3.21+4
  [05823500] OpenLibm_jll v0.8.1+0
  [efcefdf7] PCRE2_jll v10.42.0+0
  [bea87d4a] SuiteSparse_jll v5.10.1+6
  [83775a58] Zlib_jll v1.2.13+0
  [8e850b90] libblastrampoline_jll v5.8.0+0
  [8e850ede] nghttp2_jll v1.48.0+0
  [3f19e933] p7zip_jll v17.4.0+0
Info Packages marked with  and  have new versions available, 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.