Equation-based modeling and simulations in Julia

Julia package for function approximation

Unitary and Lindbladian evolution in Julia

Julia package for solving singular integral equations

A Control Systems Toolbox for Julia

A Julia implementation of Bayesian linear regression using marginal likelihood for hyperparameter optimization, as presented in Chris Bishop's book.

Calculate oscillatory integrals using Julia

Calculate equilibrium measures from potentials

Supports approximating functions and solving differential equations on various higher dimensional domains such as disks and triangles

A Julia package for solving Riemann–Hilbert problems

Solve and estimate Dynamic Stochastic General Equilibrium models (including the New York Fed DSGE)

Piecewise Deterministic Markov Processes in Julia

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

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

Simulate quantum systems consisting of many spins interacting via dipole-dipole interaction

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.

Learning Dynamic Movement Primitives in Julia

Julia Library for Interatomic Potentials

Geometric Numerical Integration in Julia

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

A unified interface for simulations of the Bio-Energetic model on food webs

Julia package for transfer operator spectral methods

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

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

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

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

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.

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

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

Delay differential equation (DDE) solvers in Julia for the SciML scientific machine learning ecosystem. Covers neutral and retarded delay differential equations, and differential-algebraic equations.

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

Algorithms from circuit theory to predict connectivity in heterogeneous landscapes

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

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

Modeling and simulation of multidomain engineering systems

Boundary value problem (BVP) solvers for scientific machine learning (SciML)

Piecewise Deterministic Sampler library (Bouncy particle sampler, Zig Zag sampler, ...)

A library for building differential equations arising from physical problems for physics-informed and scientific machine learning (SciML)