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.

Julia bindings for the Enzyme automatic differentiator

Update immutable data

Implementation of domain-specific language (DSL) for dynamic probabilistic programming

Common functional iterator patterns

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

Symbolic programming for the next generation of numerical software

Symbolic expressions, rewriting and simplification

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.

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

Lightweight and easy generation of quasi-Monte Carlo sequences with a ton of different methods on one API for easy parameter exploration in scientific machine learning (SciML)

Bayesian inference with probabilistic programming.

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

Calculating contour curves for 2D scalar fields in Julia

Print data in formatted tables.

Implementation of variational Bayes inference algorithms

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.

Simple, consistent interfaces for any codec.

Root finding functions for Julia

The Base interface of the SciML ecosystem

Basic interface for manifolds in Julia

Powerful convenience for Julia visualizations and data analysis

Faster `findfirst(==(val), dense_vector)`.

Primitives for construction of objects

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.

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)

High performance nearest neighbor data structures (KDTree and BallTree) and algorithms for 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.

Forward Mode Automatic Differentiation for Julia

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

SciMLOperators.jl: Matrix-Free Operators for the SciML Scientific Machine Learning Common Interface in Julia

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

Julia implementation of Data structures

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

An interface to various automatic differentiation backends in Julia.

A Julia interface to the NLopt nonlinear-optimization library

A structure interface for SciML to give queryable properties from user data and parameters

Julia macro for re-exporting one module from another

Julia bindings to the FFTW library for fast Fourier transforms