Tools for building non-allocating pre-cached functions in Julia, allowing for GC-free usage of automatic differentiation in complex codes

Fast and automatic structural identifiability software for ODE systems

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

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)

Functions generated at runtime without world-age issues or overhead

A scientific machine learning (SciML) wrapper for the FEniCS Finite Element library in the Julia programming language

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

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.

Julia-based implementation of ellipsis array indexing notation `..`

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

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

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

Fast uncertainty quantification for scientific machine learning (SciML) and differential equations

Fast uncertainty quantification for scientific machine learning (SciML) and differential equations

A library of noise processes for stochastic systems like stochastic differential equations (SDEs) and other systems that are present in scientific machine learning (SciML)

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

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

Easy scientific machine learning (SciML) parameter estimation with pre-built loss functions

Automatic detection of sparsity in pure Julia functions for sparsity-enabled scientific machine learning (SciML)

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.

A library of premade problems for examples and testing differential equation solvers and other SciML scientific machine learning tools

Static types useful for dispatch and generated functions.

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

Implicit Layer Machine Learning via Deep Equilibrium Networks, O(1) backpropagation with accelerated convergence.

Finds relationships between the parameters of a mathematical model

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

Benchmarking, testing, and development tools for differential equations and scientific machine learning (SciML)

This package contains a macro for converting expressions to use muladd calls and fused-multiply-add (FMA) operations for high-performance in the SciML scientific machine learning ecosystem

No need to train, he's a smooth operator

SciMLOperators.jl: Matrix-Free Operators for the SciML Scientific Machine Learning Common Interface in Julia

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

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

Helicopter Scientific Machine Learning (SciML) Challenge Problem

Repository for automatic differentiation backend types

A collection of functionality around rooted trees to generate order conditions for Runge-Kutta methods in Julia for differential equations and scientific machine learning (SciML)

Workshop materials for training in scientific computing and scientific machine learning

High-level model-order reduction to automate the acceleration of large-scale simulations

Solves stiff differential algebraic equations (DAE) using variable stepsize backwards finite difference formula (BDF) in the SciML scientific machine learning organization

Solving difference equations with DifferenceEquations.jl and the SciML ecosystem.