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.

Bayesian inference with probabilistic programming.

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

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

Solve and estimate Dynamic Stochastic General Equilibrium models (including the New York Fed DSGE)

Universal neural differential equations with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learning (SciML) and physics-informed machine learning methods

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

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

Award winning software library for nonlinear dynamics and nonlinear timeseries analysis

Tutorials for doing scientific machine learning (SciML) and high-performance differential equation solving with open source software.

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.

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.

Library for the numerical simulation of closed as well as open quantum systems.

Expression rewriting and simplification

A Control Systems Toolbox for 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)

Probabilistic programming via source rewriting

Distributed High-Performance symbolic regression in Julia

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

Trixi.jl: Adaptive high-order numerical simulations of hyperbolic PDEs in Julia

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

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

Density-functional toolkit

Modeling and simulation of multidomain engineering systems

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

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

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.

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

A Julia package to perform Bifurcation Analysis

Arrays with arbitrarily nested named components.

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

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

Julia interface to Sundials, including a nonlinear solver (KINSOL), ODE's (CVODE and ARKODE), and DAE's (IDA) in a SciML scientific machine learning enabled manner

Tools for the exploration of chaos and nonlinear dynamics

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.

Robust robotic localization and mapping, together with www.NavAbility.io. Reach out to info@navability.io for help.

Methods to compute sets of states reachable by dynamical systems

A common interface for quadrature and numerical integration for the SciML scientific machine learning organization

Tools for easily handling objects like arrays of arrays and deeper nestings in scientific machine learning (SciML) and other applications