SBML differential equation and chemical reaction model (Gillespie simulations) for Julia's SciML ModelingToolkit

Fast and differentiable implementations of matrix exponentials, Krylov exponential matrix-vector multiplications ("expmv"), KIOPS, ExpoKit functions, and more. All your exponential needs in SciML form.

The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems

Computing reachable states of dynamical systems in Julia

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

High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.

Solve Fractional Differential Equations using high performance numerical methods

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

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

A standard library of components to model the world and beyond

Robust, Fast, and Parallel Global Sensitivity Analysis (GSA) in Julia

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

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

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.

Fast and simple nonlinear solvers for the SciML common interface. Newton, Broyden, Bisection, Falsi, and more rootfinders on a standard interface.

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

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

Simulaciones numéricas en módelos de ecuaciones diferenciales

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

LinearSolve.jl: High-Performance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.