High level functions for analyzing the output of simulations

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

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.

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

Faster `findfirst(==(val), dense_vector)`.

Finite State Projection algorithms for chemical reaction networks

Solver for two-dimensional conservation equations using the finite volume method in Julia.

Implementation of the finite volume method in 1D.

A SciML symbolic-numeric compiler tool for investigating functions in order to perform optimizations

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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.

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

Differential equation solvers with global error estimation

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

Helicopter Scientific Machine Learning (SciML) Challenge Problem

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

Under some conditions you may need this function

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

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

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)

Arrays which also have a label for each element for easy 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.

Julia MathML parser

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

Rewrite Inplace Operations to be OOP if needed

Automatic Finite Difference PDE solving with Julia SciML

Finds relationships between the parameters of a mathematical model

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

Symbolic-Numeric Universal Differential Equations for Automating Scientific Machine Learning (SciML)

A standard library of components to model the world and beyond

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

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

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

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

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

Wrappers for MINPACK into the SciML Common Interface