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GlobalSensitivity.jl: Robust, Fast, and Parallel Global Sensitivity Analysis (GSA) in Julia

Global Sensitivity Analysis (GSA) methods are used to quantify the uncertainty in the output of a model with respect to the parameters. These methods allow practitioners to measure both parameter's individual contributions and the contribution of their interactions to the output uncertainty.

Installation

To use this functionality, you must install GlobalSensitivity.jl:

using Pkg
Pkg.add("GlobalSensitivity")

Note: GlobalSensitivity.jl is unrelated to the GlobalSensitivityAnalysis.jl package.

General Interface

The general interface for performing global sensitivity analysis using this package is:

GlobalSensitivity.gsa — Method
gsa(f, method::GSAMethod, param_range; samples, batch=false)

where:

  • y=f(x) is a function that takes in a single vector and spits out a single vector or scalar. If batch=true, then f takes in a matrix where each row is a set of parameters, and returns a matrix where each row is the output for the corresponding row of parameters.
  • method is one of the available GSA methods.
  • param_range is a vector of tuples for the upper and lower bound for the given parameter i.
  • samples is a required keyword argument for the number of samples of parameters for the design matrix. Note that this is not relevant for Fractional Factorial Method and Morris Method.

Additionally,

For Delta Moment-Independent Method, EASI Method and Regression Method input and output matrix-based method as follows is available:

res = gsa(X, Y, method)

where:

  • X is the number of parameters * samples matrix with parameter values.
  • Y is the output dimension * number of samples matrix with are evaluated at X's columns.
  • method is one of the GSA methods below.

For Sobol Method, one can use the following design matrices-based method instead of parameter range-based method discussed earlier:

effects = gsa(f, method, A, B; batch=false)

where A and B are design matrices, with each row being a set of parameters. Note that generate_design_matrices from QuasiMonteCarlo.jl can be used to generate the design matrices.

source

The descriptions of the available methods can be found in the Methods section. The gsa interface allows for utilizing batched functions with the batch kwarg discussed above for parallel computation of GSA results.

Citing

If you use this software in your work, please cite:

@article{dixit2022globalsensitivity,
  title={GlobalSensitivity. jl: Performant and Parallel Global Sensitivity Analysis with Julia},
  author={Dixit, Vaibhav Kumar and Rackauckas, Christopher},
  journal={Journal of Open Source Software},
  volume={7},
  number={76},
  pages={4561},
  year={2022}
}

Reproducibility

The documentation of this SciML package was built using these direct dependencies,
Status `~/work/GlobalSensitivity.jl/GlobalSensitivity.jl/docs/Project.toml`
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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: 4 × AMD EPYC 7763 64-Core Processor
  WORD_SIZE: 64
  LIBM: libopenlibm
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Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
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A more complete overview of all dependencies and their versions is also provided.
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⌅ [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
  [e7412a2a] Ogg_jll v1.3.5+1
  [18a262bb] OpenEXR_jll v3.1.4+0
  [458c3c95] OpenSSL_jll v3.0.13+1
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.2+0
  [36c8627f] Pango_jll v1.52.1+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
  [9a68df92] isoband_jll v0.2.3+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
  [075b6546] libsixel_jll v1.10.3+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
  [8bf52ea8] CRC32c
  [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.