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.
SymbolicNumericIntegration.jl is a package computing the solution to symbolic integration problem using numerical methods (numerical integration mixed with sparse regression).
JuliaSymbolics is a sister organization of SciML. It spawned out of the symbolic modeling tools being developed within SciML (ModelingToolkit.jl) to become its own organization dedicated to building a fully-featured Julia-based Computer Algebra System (CAS). As such, the two organizations are closely aligned in terms of its developer community and many of the SciML libraries use Symbolics.jl extensively.
Symbolics.jl is the CAS of the Julia programming language. If something needs to be done symbolically, most likely Symbolics.jl is the answer.
Metatheory.jl is a library for defining e-graph rewriters for use on the common symbolic interface. This can be used to do all sorts of analysis and code transformations, such as improving code performance, numerical stability, and more. See Automated Code Optimization with E-Graphs for more details.
SymbolicUtils.jl is the underlying utility library and rule-based rewriting language on which Symbolics.jl is developed. Symbolics.jl is standardized type and rule definitions built using SymbolicUtils.jl. However, if non-standard types are required, such as symbolic computing over Fock algebras, then SymbolicUtils.jl is the library from which the new symbolic types can be implemented.
SIAN.jl is a structural identifiability analysis package which uses an entirely different algorithm from StructuralIdentifiability.jl. For information on the differences bewteen the two approaches, see the Structural Identifiability Tools in Julia tutoral.