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

Symbolic programming for the next generation of numerical software

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.

Symbolic expressions, rewriting and simplification

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.

Probabilistic programming via source rewriting

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 Julia package for solving systems of polynomials via homotopy continuation.

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

Algorithms and data structures for game theory in Julia

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

Sum of Squares Programming for Julia

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.

Spin dynamics and generalization to SU(N) coherent states

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

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

Taylor-mode automatic differentiation for higher-order derivatives

Turing + Makie = Turkie