GlobalSensitivity.jl
GlobalSensitivity.jl package contains implementation of some the most popular GSA methods. Currently it supports Delta Moment-Independent, DGSM, EASI, eFAST, Morris, Fractional Factorial, RBD-FAST, Sobol and Regression based sensitivity methods.
Tutorials and Documentation
For information on using the package, see the stable documentation. Use the in-development documentation for the version of the documentation, which contains the unreleased features.
Installation
The GlobalSensitivity.jl package can be installed with julia's package manager as shown below:
using Pkg
Pkg.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 the Ishigami function.
Serial execution
function ishi(X)
A = 7
B = 0.1
sin(X[1]) + A * sin(X[2])^2 + B * X[3]^4 * sin(X[1])
end
n = 600000
lb = -ones(4) * π
ub = ones(4) * π
sampler = SobolSample()
A, B = QuasiMonteCarlo.generate_design_matrices(n, lb, ub, sampler)
res1 = gsa(ishi, Sobol(order = [0, 1, 2]), A, B)Using batching interface
function ishi_batch(X)
A = 7
B = 0.1
@. sin(X[1, :]) + A * sin(X[2, :])^2 + B * X[3, :]^4 * sin(X[1, :])
end
res2 = gsa(ishi_batch, Sobol(), A, B, batch = true)Regression based and Morris method sensitivity analysis of Lotka Volterra model.
using GlobalSensitivity, QuasiMonteCarlo, OrdinaryDiffEq, Statistics, CairoMakie
function f(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] #predator
end
u0 = [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,:])]
end
bounds = [[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}
}