The SciML Interface Libraries
SciMLBase.jl: The SciML Common Interface
SciMLBase.jl defines the core interfaces of the SciML libraries, such as the definitions of abstract types like SciMLProblem, along with their instantiations like ODEProblem. While SciMLBase.jl is insufficient to solve any equations, it holds all of the equation definitions, and thus downstream libraries which wish to allow for using SciML solvers without depending on any solvers can directly depend on SciMLBase.jl.
SciMLOperators.jl: The AbstractSciMLOperator Interface
SciMLOperators.jl defines the interface for how matrix-free linear and affine operators are defined and used throughout the SciML ecosystem.
DiffEqNoiseProcess.jl: The SciML Common Noise Interface
DiffEqNoiseProcess.jl defines the common interface for stochastic noise processes used by the equation solvers of the SciML ecosystem.
CommonSolve.jl: The Common Definition of Solve
CommonSolve.jl is the library that defines the solve, solve!, and init interfaces which are used throughout all of the SciML equation solvers. It's defined as an extremely lightweight library so that other ecosystems can build off of the same solve definition without clashing with SciML when both export.
Static.jl: A Shared Interface for Static Compile-Time Computation
Static.jl is a set of statically parameterized types for performing operations in a statically-defined (compiler-optimized) way with respect to values.
DiffEqBase.jl: A Library of Shared Components for Differential Equation Solvers
DiffEqBase.jl is the core shared component of the DifferentialEquations.jl ecosystem. It's not intended for non-developer users to interface directly with, instead it's used for the common functionality for uniformity of implementation between the solver libraries.
Third Party Libraries to Note
ArrayInterface.jl: Extensions to the Julia AbstractArray Interface
ArrayInterface.jl are traits and functions which extend the Julia Base AbstractArray interface, giving a much larger set of queries to allow for writing high-performance generic code over all array types. For example, functions include can_change_size to know if an AbstractArray type is compatible with resize!, fast_scalar_indexing to know whether direct scalar indexing A[i] is optimized, and functions like findstructralnz to get the structural non-zeros of arbtirary sparse and structured matrices.
Adapt.jl: Conversion to Allow Chip-Generic Programs
Adapt.jl makes it possible to write code that is generic to the compute devices, i.e. code that works on both CPUs and GPUs. It defines the adapt function which acts like convert(T, x), but without the restriction of returning a T. This allows you to "convert" wrapper types like Adjoint to be GPU compatible (for example) without throwing away the wrapper.
Example usage:
adapt(CuArray, ::Adjoint{Array})::Adjoint{CuArray}AbstractFFTs.jl: High Level Shared Interface for Fast Fourier Transformation Libraries
AbstractFFTs.jl defines the common interface for Fast Fourier Transformations (FFTs) in Julia. Similar to SciMLBase.jl, AbstractFFTs.jl is not a solver library but instead a shared API which is extended by solver libraries such as FFTW.jl. Code written using AbstractFFTs.jl can be made compatible with FFT libraries without having an explicit dependency on a solver.
GPUArrays.jl: Common Interface for GPU-Based Array Types
GPUArrays.jl defines the shared higher-level operations for GPU-based array types like CUDA.jl's CuArray and AMDGPU.jl's ROCmArray. Packages in SciML use the designation x isa AbstractGPUArray in order to find out if a user's operation is on the GPU and specialize computations.
RecipesBase.jl: Standard Plotting Recipe Interface
RecipesBase.jl defines the common interface for plotting recipes, composable transformations of Julia data types into simpler data types for visualization with libraries such as Plots.jl and Makie.jl. SciML libraries attempt to always include plot recipes wherever possible for ease of visualization.
Tables.jl: Common Interface for Tablular Data Types
Tables.jl is a common interface for defining tabular data structures, such as DataFrames.jl. SciML's libraries extend the Tables.jl interface to allow for automated conversions into data frame libraries without explicit dependence on any singular implementation.
EllipsisNotation.jl: Implementation of Ellipsis Array Slicing
EllipsisNotation.jl defines the ellipsis array slicing notation for Julia. It uses .. as a catch all for "all dimensions", allow for indexing like [..,1] to mean "[:,:,:,1]` on four dimensional arrays, in a way that is generic to the number of dimensions in the underlying array.