Parameter Analysis Utilities

GlobalSensitivity.jl: Global Sensitivity Analysis

Derivatives calculate the local sensitivity of a model, i.e. the change in the simulation's outcome if one were to change the parameter with respect to some chosen part of the parameter space. But how does a simulation's output change “in general” with respect to a given parameter? That is what global sensitivity analysis (GSA) computes, and thus GlobalSensitivity.jl is the way to answer that question. GlobalSensitivity.jl includes a wide array of methods, including:

Morris's method
Sobol's method
Regression methods (PCC, SRC, Pearson)
eFAST
Delta Moment-Independent method
Derivative-based Global Sensitivity Measures (DGSM)
EASI
Fractional Factorial method
Random Balance Design FAST method

StructuralIdentifiability.jl: Identifiability Analysis Made Simple

Performing parameter estimation from a data set means attempting to recover parameters like reaction rates by fitting some model to the data. But how do you know whether you have enough data to even consider getting the “correct” parameters back? StructuralIdentifiability.jl allows for running a structural identifiability analysis on a given model to determine whether it's theoretically possible to recover the correct parameters. It can state whether a given type of output data can be used to globally recover the parameters (i.e. only a unique parameter set for the model produces a given output), whether the parameters are only locally identifiable (i.e. there are finitely many parameter sets which could generate the seen data), or whether it's unidentifiable (there are infinitely many parameters which generate the same output data).

For more information on what StructuralIdentifiability.jl is all about, see the SciMLCon 2022 tutorial video.

MinimallyDisruptiveCurves.jl

MinimallyDisruptiveCurves.jl is a library for finding relationships between parameters of models, finding the curves on which the solution is constant.

Third-Party Libraries to Note

SIAN.jl: Structural Identifiability Analyzer

SIAN.jl is a structural identifiability analysis package which uses an entirely different algorithm from StructuralIdentifiability.jl. For information on the differences between the two approaches, see the Structural Identifiability Tools in Julia tutorial.

DynamicalSystems.jl: A Suite of Dynamical Systems Analysis

DynamicalSystems.jl is an entire ecosystem of dynamical systems analysis methods, for computing measures of chaos (dimension estimation, Lyapunov coefficients), generating delay embeddings, and much more. It uses the SciML tools for its internal equation solving and thus shares much of its API, adding a layer of new tools for extended analyses.

For more information, watch the tutorial Introduction to DynamicalSystems.jl.