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.

A fast and modern CAS for a fast and modern language.

Forward Mode Automatic Differentiation for Julia

Award winning software library for nonlinear dynamics and nonlinear timeseries analysis

An optimized graphs package for the Julia programming language

Statically sized arrays for Julia

Grid-based approximation of partial differential equations in Julia

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Julia package for function approximation

Expression rewriting and simplification

Fast, continuous interpolation of discrete datasets in Julia

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

⟨Leibniz-Grassmann-Clifford⟩ differential geometric algebra / multivector simplicial complex

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.

Efficient transducers for Julia

An optimized graphs package for the Julia programming language

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

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

Julia package for tensor contractions and related operations

Combine ingredients for a plot

Filter design, periodograms, window functions, and other digital signal processing functionality

Geometric Deep Learning for Flux

Special mathematical functions in Julia

Manifolds.jl provides a library of manifolds aiming for an easy-to-use and fast implementation.

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.

Taylor polynomial expansions in one and several independent variables.

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

Julia solvers for systems of nonlinear equations and mixed complementarity problems

Computational geometry and meshing algorithms in Julia

Efficient implementation of struct arrays in Julia

A Julia Basket of Hand-Picked Krylov Methods

Julia package for Gaussian quadrature

Julia package for Gaussian quadrature

XGBoost Julia Package

Root finding functions for Julia

Polynomial manipulations in Julia

Calculus functions in Julia

Lazy arrays and linear algebra in Julia

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.