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

A Julia package to construct orthogonal polynomials, their quadrature rules, and use it with polynomial chaos expansions.

Fast Poisson Random Numbers in pure Julia for scientific machine learning (SciML)

A library of systems of partial differential equations, as defined with ModelingToolkit.jl in Julia

Common types and interface for discretizers of ModelingToolkit PDESystems.

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

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

The base package for Optimization.jl, containing the structs and basic functions for it.

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.

No need to train, he's a smooth operator

Adds the common API onto ODEInterface classic Fortran methods for the SciML Scientific Machine Learning organization

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

Wrappers for MINPACK into the SciML Common Interface

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

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

DeepONets, (Fourier) Neural Operators, Physics-Informed Neural Operators, and more in Julia

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

A differentiable simulator for scientific machine learning (SciML) with N-body problems, including astrophysical and molecular dynamics

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

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

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

A standard library of components to model the world and beyond

Symbolic-Numeric Universal Differential Equations for Automating 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

Finds relationships between the parameters of a mathematical model

Automatic Finite Difference PDE solving with Julia SciML

Rewrite Inplace Operations to be OOP if needed

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

Julia MathML parser

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.

Arrays which also have a label for each element for easy scientific machine learning (SciML)

Build and simulate jump equations like Gillespie simulations and jump diffusions with constant and state-dependent rates and mix with differential equations and scientific machine learning (SciML)

Implicit Runge-Kutta Gauss-Legendre 16th order (Julia)

A common interface for quadrature and numerical integration for the SciML scientific machine learning organization

Under some conditions you may need this function

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

Helicopter Scientific Machine Learning (SciML) Challenge Problem

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

Differential equation solvers with global error estimation

Wrappers for GeometricIntegrators.jl into the SciML common interface for scientific machine learning (SciML)