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.

Main Package for IO, loading all different kind of files

A combinatorics library for Julia

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

Julia interface to Sundials, including a nonlinear solver (KINSOL), ODE's (CVODE and ARKODE), and DAE's (IDA) in a SciML scientific machine learning enabled manner

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

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

Lazy code loading for Julia

BlockArrays for Julia

A Julia package for fast discrete wavelet transforms and utilities

Colorschemes, colormaps, gradients, and palettes

Julia package for lazily representing matrices filled with a single entry

Kernel density estimators for Julia

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

Common functional iterator patterns

Compatibility across Julia versions

Composable Loggers for the Julia Logging StdLib

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)

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

Project Preferences Package

A Julia package for representing banded matrices

One- and multi-dimensional adaptive integration routines for the Julia language

A Julia framework for implementing FFTs