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.

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

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

Pre-built implicit layer architectures with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learning (SciML) and physics-informed machine learning methods

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.

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

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

A Control Systems Toolbox for 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.

Modeling and simulation of multidomain engineering systems

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

Tools for the exploration of chaos and nonlinear dynamics

Implementations of the models from the Statistical Rethinking book with Turing.jl

Automatic Finite Difference PDE solving with Julia SciML

System Identification toolbox, compatible with ControlSystems.jl

A differentiable simulator for scientific machine learning (SciML) with N-body problems, including astrophysical and molecular dynamics

Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

Causal.jl - A modeling and simulation framework adopting causal modeling approach.

State estimation, smoothing and parameter estimation using Kalman and particle filters.

Equation-based modeling and simulations in Julia

Package for dynamical modeling of power grids

MagNav: airborne Magnetic anomaly Navigation

Core functions for the Julia (2nd) edition of the text Fundamentals of Numerical Computation, by Driscoll and Braun.

A framework for simulating viscous incompressible flows about arbitrary body shapes.

FMI.jl is a free-to-use software library for the Julia programming language which integrates FMI (fmi-standard.org): load or create, parameterize, differentiate and simulate FMUs seamlessly inside the Julia programming language!

OrbitalTrajectories.jl is a modern orbital trajectory design, optimisation, and analysis library for Julia, providing methods and tools for designing spacecraft orbits and transfers via high-performance simulations of astrodynamical models.

High level functions for analyzing the output of simulations

A julia package for representing and manipulating model semantics

Modeling and Simulation of 3D systems

A framework for developing multi-scale arrays for use in scientific machine learning (SciML) simulations

The amazing Reaction Mechanism Simulator for simulating large chemical kinetic mechanisms

A Julia package for Deep Backwards Stochastic Differential Equation (Deep BSDE) and Feynman-Kac methods to solve high-dimensional PDEs without the curse of dimensionality

A simple tool for simulating trapped ion systems

Simulation and visualization of articulated rigid body systems in Julia

Global glacier model using Universal Differential Equations for climate-glacier interactions

An open-source framework written in Julia for global integrated assessment models.

An open source model predictive control package for Julia.