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GlobalSensitivity.jl

GlobalSensitivity.jl package contains implementation of some the most popular GSA methods. Currently it supports Delta Moment-Independent, DGSM, EASI, eFAST, Morris, Mutual Information, Fractional Factorial, RBD-FAST, RSA, Sobol and Regression based sensitivity methods.

Tutorials and Documentation

For information on using the package,see the stable documentation. Use thein-development documentation for the version ofthe documentation, which contains the unreleased features.

Installation

The GlobalSensitivity.jl package can be installed with julia's package manager as shown below:

using PkgPkg.add("GlobalSensitivity")

General Interface

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

res=gsa(f, method, param_range; samples, batch=false)

Example

Sobol method on theIshigami function.

Serial execution

functionishi(X)    A=7    B=0.1sin(X[1])+ A*sin(X[2])^2+ B* X[3]^4*sin(X[1])endn=600000lb=-ones(4)* πub=ones(4)* πsampler=SobolSample()A, B= QuasiMonteCarlo.generate_design_matrices(n, lb, ub, sampler)res1=gsa(ishi,Sobol(order= [0,1,2]), A, B)

Using batching interface

functionishi_batch(X)    A=7    B=0.1@.sin(X[1, :])+ A*sin(X[2, :])^2+ B* X[3, :]^4*sin(X[1, :])endres2=gsa(ishi_batch,Sobol(), A, B, batch=true)

Regression based and Morris method sensitivity analysis of Lotka Volterra model.

using GlobalSensitivity, QuasiMonteCarlo, OrdinaryDiffEq, Statistics, CairoMakiefunctionf(du, u, p, t)    du[1]= p[1]* u[1]- p[2]* u[1]* u[2]#prey    du[2]=-p[3]* u[2]+ p[4]* u[1]* u[2]#predatorendu0= [1.0;1.0]tspan= (0.0,10.0)p= [1.5,1.0,3.0,1.0]prob=ODEProblem(f, u0, tspan, p)t=collect(range(0, stop=10, length=200))f1=function (p)    prob1=remake(prob; p= p)    sol=solve(prob1,Tsit5(); saveat= t)return [mean(sol[1, :]),maximum(sol[2, :])]endbounds= [[1,5], [1,5], [1,5], [1,5]]reg_sens=gsa(f1,RegressionGSA(true), bounds)fig=Figure(resolution= (600,400))ax,hm= CairoMakie.heatmap(fig[1,1], reg_sens.partial_correlation,    figure= (resolution= (300,200),),    axis= (xticksvisible=false,        yticksvisible=false,        yticklabelsvisible=false,        xticklabelsvisible=false,        title="Partial correlation"))Colorbar(fig[1,2], hm)ax,hm= CairoMakie.heatmap(fig[2,1], reg_sens.standard_regression,    figure= (resolution= (300,200),),    axis= (xticksvisible=false,        yticksvisible=false,        yticklabelsvisible=false,        xticklabelsvisible=false,        title="Standard regression"))Colorbar(fig[2,2], hm)fig

using StableRNGs_rng=StableRNG(1234)morris_sens=gsa(f1,Morris(), bounds, rng= _rng)fig=Figure(resolution= (300,200))scatter(fig[1,1], [1,2,3,4], morris_sens.means_star[1, :],    color=:green, axis= (xticksvisible=false,        xticklabelsvisible=false, title="Prey (Morris)"))scatter(fig[1,2], [1,2,3,4], morris_sens.means_star[2, :],    color=:red, axis= (xticksvisible=false,        xticklabelsvisible=false, title="Predator (Morris)"))fig

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}}