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

The Base interface of the SciML ecosystem

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

Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software.

Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

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

A standard library of components to model the world and beyond

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.

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

Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization

Documentation for the DiffEq differential equations and scientific machine learning (SciML) ecosystem

SBML differential equation and chemical reaction model (Gillespie simulations) for Julia's SciML ModelingToolkit

Computing reachable states of dynamical systems in Julia

Solve Fractional Differential Equations using high performance numerical methods

Robust, Fast, and Parallel Global Sensitivity Analysis (GSA) in Julia

A library of useful callbacks for hybrid scientific machine learning (SciML) with augmented differential equation solvers

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)

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

Extension functionality which uses Stan.jl, DynamicHMC.jl, and Turing.jl to estimate the parameters to differential equations and perform Bayesian probabilistic scientific machine learning