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.

Bayesian inference with probabilistic programming.

Powerful convenience for Julia visualizations and data analysis

An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physics-informed machine learning and automated transformations of differential equations

Symbolic programming for the next generation of numerical software

Optimization functions for Julia

A Julia package for probability distributions and associated functions.

Forward Mode Automatic Differentiation for Julia

Statically sized arrays for Julia

Macro(s) for vectorizing loops.

Mathematical Optimization in Julia. Local, global, gradient-based and derivative-free. Linear, Quadratic, Convex, Mixed-Integer, and Nonlinear Optimization in one simple, fast, and differentiable interface.

Progress meter for long-running computations

Julia implementation of Data structures

Formatted output of timed sections in Julia

HTTP for Julia

A benchmarking framework for the Julia language

Physical quantities with arbitrary units

Basic statistics for Julia

An opinionated code formatter for Julia. Plot twist - the opinion is your own.

Convert julia objects to LaTeX equations, arrays or other environments.

Symbolic expressions, rewriting and simplification

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

Fast, continuous interpolation of discrete datasets in Julia

An optimized graphs package for the Julia programming language

Julia bindings for the Enzyme automatic differentiator

Forward and reverse mode automatic differentiation primitives for Julia Base + StdLibs

A Julia package for evaluating distances (metrics) between vectors.

Types with default field values, keyword constructors and (un-)pack macros

Print data in formatted tables.

Julia functional programming infrastructures and metaprogramming facilities

A data structure for mathematical optimization problems

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

Manifolds.jl provides a library of manifolds aiming for an easy-to-use and fast implementation.

Heterogeneous programming in Julia

Plotting for Julia based on GR, a framework for visualisation applications

Special mathematical functions in Julia

Root finding functions for Julia

A Julia Basket of Hand-Picked Krylov Methods

Julia solvers for systems of nonlinear equations and mixed complementarity problems

Efficient implementation of struct arrays in Julia