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

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

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

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

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

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

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

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 simple tool for simulating trapped ion systems

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

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

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

Atomic graph models for molecules and crystals in Julia

FMIFlux.jl is a free-to-use software library for the Julia programming language, which offers the ability to place FMUs (fmi-standard.org) everywhere inside of your ML topologies and still keep the resulting model trainable with a standard (or custom) FluxML training process.

A Petri net modeling framework for the Julia programming language

An interface for accelerated simulation of high-dimensional collisionless and electrostatic plasmas.

DPFEHM: A Differentiable Subsurface Flow Simulator

Simulation of simple controls problems in Julia

A full stack simulator of quantum hardware, from the low-level analog physics to high-level network dynamics. Includes discrete event simulator, symbolic representation for quantum object, and works with many backend simulators.

A turbulence-convection single column model cloud parameterization.

ParameterEstimation.jl is a Julia package for estimating parameters and initial conditions of ODE models given measurement data.

Stochastic delay differential equations (SDDE) solvers for the SciML scientific machine learning ecosystem

Simulate quantum systems consisting of many spins interacting via dipole-dipole interaction

Tools for the Simulation and Execution of Quantum Annealing Algorithms

A tool to solve optimal control problem

Implementations of Infinitesimal Continuous Normalizing Flows Algorithms in Julia

Astrodynamics with units! Provides common astrodynamics calculations, plotting, and iterative Halo, Kepler, and Lambert solvers.

Piecewise Deterministic Markov Processes in Julia