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.

Grid-based approximation of partial differential equations in Julia

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

A Julia/JuMP Package for Power Network Optimization

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

Julia for optimization simulation and modeling of PowerSystems. Part of the Scalable Integrated Infrastructure Planning Initiative at the National Renewable Energy Lab.

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

Robust robotic localization and mapping, together with NavAbility(TM). Reach out to info@wherewhen.ai for help.

Julia package to run Dynamic Power System simulations. Part of the Scalable Integrated Infrastructure Planning Initiative at the National Renewable Energy Lab.

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

Julia package for simulating Dynamics on Networks

Universal modeling and simulation of fluid mechanics upon machine learning. From the Boltzmann equation, heading towards multiscale and multiphysics flows.

Solve non-linear HJB equations.

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

Package for dynamical modeling of power grids

Parallel distributed-memory version of Gridap

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

Pure Julia Implementation of Geometrically Exact Beam Theory

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 to solve, simulate, and analyze nonlinear DSGE models.

A julia package for representing and manipulating model semantics

Provides a modeling interface for mixed complementarity problems (MCP) and math programs with equilibrium problems (MPEC) via JuMP

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

Clique recycling non-Gaussian (multi-modal) factor graph solver; also see Caesar.jl.

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

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

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

Robot Motion Estimate: Tools, Variables, and Factors for SLAM in robotics; also see Caesar.jl.

Atomic graph models for molecules and crystals in Julia