A comprehensive open source computer algebra system for computations in algebra, geometry, and number theory.

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.

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.

A fast trajectory optimization library written in Julia

Surrogate modeling and optimization for scientific machine learning (SciML)

Computer vision models for Flux

Julia solvers for systems of nonlinear equations and mixed complementarity problems

Evolutionary & genetic algorithms for Julia

Modeling and simulation of multidomain engineering systems

Efficient implementation of struct arrays in Julia

Simple curve fitting in Julia

Package for writing high-level code for parallel high-performance stencil computations that can be deployed on both GPUs and CPUs

Convex optimization for fun and profit. (Now in Julia!)

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

A Julia package for Gaussian Processes

A differentiable physics engine for robotics

Lazy arrays and linear algebra in Julia

A Julia package to perform Bifurcation Analysis

Julia package for Gaussian quadrature

High accuracy derivatives, estimated via numerical finite differences (formerly FDM.jl)

A JuMP extension for Stochastic Dual Dynamic Programming

Arrays with arbitrarily nested named components.

XGBoost Julia Package

Julia implementation of various rigid body dynamics and kinematics algorithms

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

GPU-acceleration routines for DifferentialEquations.jl and the broader SciML scientific machine learning ecosystem

COSMO: Accelerated ADMM-based solver for convex conic optimisation problems (LP, QP, SOCP, SDP, ExpCP, PowCP). Automatic chordal decomposition of sparse semidefinite programs.

Julia for optimization simulation and modeling of PowerSystems. Part of the Scalable Integrated Infrastructure Planning Initiative at the National Renewable Energy Lab.

StateSpaceModels.jl is a Julia package for time-series analysis using state-space models.

GenX: a configurable power system capacity expansion model for studying low-carbon energy futures. More details at : https://genx.mit.edu

Types and utility functions for summarizing Markov chain Monte Carlo simulations

DeepONets, (Fourier) Neural Operators, Physics-Informed Neural Operators, and more in Julia

A Julia interface to the NLopt nonlinear-optimization library

Propagation of distributions by Monte-Carlo sampling: Real number types with uncertainty represented by samples.

Julia package for automated Bayesian inference on a factor graph with reactive message passing

:rocket: Julia package for orthogonal polynomial transforms :snowboarder:

Markov chain Monte Carlo (MCMC) for Bayesian analysis in julia

An intuitive modeling interface for infinite-dimensional optimization problems.

The JuliaFEM software library is a framework that allows for the distributed processing of large Finite Element Models across clusters of computers using simple programming models. It is designed to scale up from single servers to thousands of machines, each offering local computation and storage.

A toolbox for satellite analysis written in julia language.