The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems

Lazy arrays and linear algebra in Julia

An interface for tables in Julia

Arrays with arbitrarily nested named components.

Adaptive 1d numerical Gauss–Kronrod integration in Julia

AD-backend agnostic system defining custom forward and reverse mode rules. This is the light weight core to allow you to define rules for your functions in your packages, without depending on any particular AD system.

Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem

Fast non-allocating calculations of gradients, Jacobians, and Hessians with sparsity support

LinearSolve.jl: High-Performance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.

The cheapest threads you can find!

Fast jacobian computation through sparsity exploitation and matrix coloring

Mathematical functions related to statistics.

High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.

Tools for easily handling objects like arrays of arrays and deeper nestings in scientific machine learning (SciML) and other applications

Convenient input and display of LaTeX equation strings for the Julia language

Reduce time-to-first-execution of Julia code

Color manipulation utilities for Julia

Neural Network primitives with multiple backends

Abstract julia interfaces for working with trees

Lazy code loading for Julia

Fortran-like arrays with arbitrary, zero or negative starting indices.

BlockArrays for Julia

Colorschemes, colormaps, gradients, and palettes

Julia package for lazily representing matrices filled with a single entry

Update immutable data

Update deeply nested immutable structs.

An interface to various automatic differentiation backends in Julia.

Julia macro for re-exporting one module from another

Reusable compiler infrastructure for Julia GPU backends.

Simple Traits for Julia

An enhancement to julia piping syntax

Automatic differentiation of Distributions using Tracker, Zygote, ForwardDiff and ReverseDiff

Colored and styled strings for terminals.

Compatibility across Julia versions

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)

Composable Loggers for the Julia Logging StdLib

The dispatch doctor prescribes type stability

Designs for new Base array interface primitives, used widely through scientific machine learning (SciML) and other organizations

The Base interface of the SciML ecosystem

Julia wrapper for the LLVM C API