Documentation for the DiffEq differential equations and scientific machine learning (SciML) ecosystem
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Updated
Jun 4, 2024 - Julia
Documentation for the DiffEq differential equations and scientific machine learning (SciML) ecosystem
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.
Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
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
High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)
Pre-built implicit layer architectures with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learning (SciML) and physics-informed machine learning methods
The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
Julia interface to Sundials, including a nonlinear solver (KINSOL), ODE's (CVODE and ARKODE), and DAE's (IDA) in a SciML scientific machine learning enabled manner
Linear operators for discretizations of differential equations and scientific machine learning (SciML)
Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software.
Surrogate modeling and optimization for scientific machine learning (SciML)
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.
Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem
Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization
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.
Assorted basic Ordinary Differential Equation solvers for scientific machine learning (SciML). Deprecated: Use DifferentialEquations.jl instead.
A library of useful callbacks for hybrid scientific machine learning (SciML) with augmented differential equation solvers
High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.
DeepONets, (Fourier) Neural Operators, Physics-Informed Neural Operators, and more in Julia
Benchmarking, testing, and development tools for differential equations and scientific machine learning (SciML)
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