Benchmarking, testing, and development tools for differential equations and scientific machine learning (SciML)

Build and simulate jump equations like Gillespie simulations and jump diffusions with constant and state-dependent rates and mix with differential equations and scientific machine learning (SciML)

A library of noise processes for stochastic systems like stochastic differential equations (SDEs) and other systems that are present in scientific machine learning (SciML)

Linear operators for discretizations of differential equations and scientific machine learning (SciML)

Easy scientific machine learning (SciML) parameter estimation with pre-built loss functions

A library of premade problems for examples and testing differential equation solvers and other SciML scientific machine learning tools

A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.

Fast uncertainty quantification for scientific machine learning (SciML) and differential equations

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differential-algebraic equations (DAEs), and more in Julia.

A simple shared suite of common derivative definitions

Julia package for integer digit manipulation

Tangent bundle, vector space and Submanifold definition

A Julia Package for Inference over Discrete Graphical Models

A Julia package for evaluation of divergences between distributions

A Julia package for describing domains as continuous sets of elements

A Julia wrapper for the DOPRI5 and DOP853 integrators.

Extended precision arithmetic for Julia (deprecated)

Math with more good bits

Filter design, periodograms, window functions, and other digital signal processing functionality

Automatic dualization feature for MathOptInterface.jl

Julia package for representing dual numbers and for performing dual algebra

Award winning software library for nonlinear dynamics and nonlinear timeseries analysis

Dynamic Time Warping (DTW) and related algorithms in Julia, at Julia speeds

Multivariate polynomials implementation of commutative and non-commutative variables

Solve non-linear HJB equations.

Einstein summation notation in Julia

Julia wrapper of the Fortran library for efficiently solving structured matrix eigenvalue problems using unitary core transformations

Julia interface to the Elemental linear algebra library.

Julia-based implementation of ellipsis array indexing notation `..`

Elliptic integral and Jacobi elliptic special functions

Julia package for doing arithmetic on endpoints in array indexing

GJK signed distance algorithm for convex bodies in Julia

Entropic Cone approximation and optimization

A set of functions to estimate entropy from discrete and continuous samples

Derive mathematical relations

A library for graph analysis written Julia.

Error-free transformations are used to get results with extra accuracy.

Several error-free transformations from the scientific literature

A julialang package for DSP related estimation

Working with time-dependent networks in Julia