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

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

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.

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

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

Solution of nonlinear multiphysics partial differential equation systems using the Voronoi finite volume method

A package for binary and continuous, single and multi-material, truss and continuum, 2D and 3D topology optimization on unstructured meshes using automatic differentiation in Julia.

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

Automatic Finite Difference PDE solving with Julia SciML

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

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

Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

SymbolicNumericIntegration.jl: Symbolic-Numerics for Solving Integrals

Equation-based modeling and simulations in Julia

A standard library of components to model the world and beyond

Toolbox for gradient-based and derivative-free non-convex constrained optimization with continuous and/or discrete variables.

Package for dynamical modeling of power grids

Fast contact-implicit model predictive control for robotic systems that make and break contact with their environments.

Macros and functions to work with DSGE models.

A helper tool for visualizing and editing a ModelingToolkit.jl system connections

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 simple domain-specific language (DSL) for defining differential equations for use in scientific machine learning (SciML) and other applications

Preheat your MCMC

The amazing Reaction Mechanism Simulator for simulating large chemical kinetic mechanisms

Bayesian Generalized Linear models using `@formula` syntax.

Generalized mean-field equations in open quantum systems

Taylor-mode automatic differentiation for higher-order derivatives

Turing + Makie = Turkie

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

High-performance simulations of the Porous Electrode Theory for Li-ion batteries

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

CellMLToolkit.jl is a Julia library that connects CellML models to the Scientific Julia ecosystem.

Choo-choo

Conic Augmented Lagrangian Interior-Point SOlver

Differentiable trajectory optimization in Julia.

Efficient, Accurate, and Streamlined Training of Physics-Informed Neural Networks

A Julia package for solving nonlinear differential equations using the harmonic balance method.