Equation-based modeling and simulations in Julia

Programs modeled after "Numerical Methods for Engineers" by D.V. Griffiths and I.M. Smith

Bayesian inference with probabilistic programming.

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

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

Common interface bindings for the MATLAB ODE solvers via MATLAB.jl for the SciML Scientific Machine Learning ecosystem

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

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

Example problems for GeometricIntegrators.jl

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

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

Package for dynamical modeling of power grids

The amazing Reaction Mechanism Simulator for simulating large chemical kinetic mechanisms

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

Julia Catalyst.jl importers for various reaction network file formats like BioNetGen and stoichiometry matrices

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

Comparing performance and results of mcmc options using Julia

Develop tools for ensemble Kalman filter

Drift diffusion simulator for semiconductor devices

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

Marginalized log-probability functions in Julia

A fast and flexible Structural Equation Modelling Framework

Finite Element Module for Julia that focusses on gradient-robust discretisations and multiphysics problems

Generalized mean-field equations in open quantum systems

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

Common functions in actuarial and financial routines

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.

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A three-way bridge between ExpressionTreeForge.jl, PartitionedStructures.jl and PartiallySeparableSolvers.jl

Trust-region methods with partitioned quasi-Newton approximations

Julia implementation of Path Weight Sampling (PWS) to compute information transmission rates

EHT Image domain analysis through template matching.

Package for the Rigorous Computation of Invariant Measures

Finds relationships between the parameters of a mathematical model

Composable contracts, models, and functions that allow for modeling of both simple and complex financial instruments

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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.

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

Methods for computational information geometry