Algorithms from circuit theory to predict connectivity in heterogeneous landscapes

ODE integration using Taylor's method, and more, 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

Probabilistic Numerical Differential Equation solvers via Bayesian filtering and smoothing

Algebraic Multigrid in Julia

SymbolicNumericIntegration.jl: Symbolic-Numerics for Solving Integrals

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

State estimation, smoothing and parameter estimation using Kalman and particle filters.

A standard library of components to model the world and beyond

Equation-based modeling and simulations in Julia

Assorted basic Ordinary Differential Equation solvers for scientific machine learning (SciML). Deprecated: Use DifferentialEquations.jl instead.

Package for dynamical modeling of power grids

Lightweight and easy generation of quasi-Monte Carlo sequences with a ton of different methods on one API for easy parameter exploration in scientific machine learning (SciML)

MagNav: airborne Magnetic anomaly Navigation

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

A framework for simulating viscous incompressible flows about arbitrary body shapes.

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

A library of useful callbacks for hybrid scientific machine learning (SciML) with augmented differential equation solvers

Rigorous floating-point calculations with interval arithmetic in Julia

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.

Julia Library for Interatomic Potentials

Solve Fractional Differential Equations using high performance numerical methods

High level functions for analyzing the output of simulations

ClimaAtmos.jl is a library for building atmospheric circulation models that is designed from the outset to leverage data assimilation and machine learning tools. We welcome contributions!

A julia package for representing and manipulating model semantics

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

WIP successor to Soss.jl

Modeling and Simulation of 3D systems

A framework for developing multi-scale arrays for use in scientific machine learning (SciML) simulations

Julia toolkit for open quantum system simulation.

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

Simulation and visualization of articulated rigid body systems in Julia

Generalized mean-field equations in open quantum systems

DIVAnd performs an n-dimensional variational analysis of arbitrarily located observations

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