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.

Symbolic programming for the next generation of numerical software

Forward Mode Automatic Differentiation for Julia

Award winning software library for nonlinear dynamics and nonlinear timeseries analysis

Statically sized arrays for Julia

Grid-based approximation of partial differential equations in Julia

An optimized graphs package for the Julia programming language

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Julia package for function approximation

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

Error propagation calculator and library for physical measurements. It supports real and complex numbers with uncertainty, arbitrary precision calculations, operations with arrays, and numerical integration.

⟨Grassmann-Clifford-Hodge⟩ multilinear differential geometric algebra

An optimized graphs package for the Julia programming language

Julia package for tensor contractions and related operations

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

Combine ingredients for a plot

Iterative algorithms for solving linear systems, eigensystems, and singular value problems

Computational geometry in Julia

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.

Special mathematical functions in Julia

Geometric Deep Learning for Flux

Taylor polynomial expansions in one and several independent variables.

Root finding functions for Julia

Finite element toolbox for Julia

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

A Julia Basket of Hand-Picked Krylov Methods

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.

Julia solvers for systems of nonlinear equations and mixed complementarity problems

Efficient implementation of struct arrays 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 defining and working with linear maps, also known as linear transformations or linear operators acting on vectors. The only requirement for a LinearMap is that it can act on a vector (by multiplication) efficiently.

Lazy arrays and linear algebra in Julia

Polynomial manipulations in Julia

A Julia package to perform Bifurcation Analysis

Julia package for Gaussian quadrature

Julia package for Gaussian quadrature