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Top 23 Julia Sciml Projects

DifferentialEquations.jl
Multilanguage suite for highperformance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differentialalgebraic equations (DAEs), and more in Julia.
Project mention: Startups are building with the Julia Programming Language  news.ycombinator.com  20221213This lists some of its unique abilities:
https://docs.sciml.ai/DiffEqDocs/stable/
The routines are sufficiently generic, with regard to Julia’s type system, to allow the solvers to automatically compose with other packages and to seamlessly use types other than Numbers. For example, instead of handling just functions Number→Number, you can define your ODE in terms of quantities with physical dimensions, uncertainties, quaternions, etc., and it will just work (for example, propagating uncertainties correctly to the solution¹). Recent developments involve research into the automated selection of solution routines based on the properties of the ODE, something that seems really nextlevel to me.

ModelingToolkit.jl
An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physicsinformed machine learning and automated transformations of differential equations
I'd use a modeling tool like https://mtk.sciml.ai/dev/ Using the standard library, you wouldn't need to come up with all equations yourself. Depending on the details of your use case, system identification as suggested before might be a faster approach though.

SonarLint
Clean code begins in your IDE with SonarLint. Up your coding game and discover issues early. SonarLint is a free plugin that helps you find & fix bugs and security issues from the moment you start writing code. Install from your favorite IDE marketplace today.

NeuralPDE.jl
PhysicsInformed Neural Networks (PINN) and Deep BSDE Solvers of Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
The documentation has a manifest associated with it: https://docs.sciml.ai/NeuralPDE/dev/#Reproducibility. Instantiating the manifest will give you all of the exact versions used for the documentation build (https://github.com/SciML/NeuralPDE.jl/blob/ghpages/v5.7.0/assets/Manifest.toml). You just ]instantiate folder_of_manifest. Or you can use the Project.toml.

Optimization.jl
Mathematical Optimization in Julia. Local, global, gradientbased and derivativefree. Linear, Quadratic, Convex, MixedInteger, and Nonlinear Optimization in one simple, fast, and differentiable interface.
Project mention: SciPy: Interested in adopting PRIMA, but little appetite for more Fortran code  news.ycombinator.com  20230518Interesting response. I develop the Julia SciML organization https://sciml.ai/ and we'd be more than happy to work with you to get wrappers for PRIMA into Optimization.jl's general interface (https://docs.sciml.ai/Optimization/stable/). Please get in touch and we can figure out how to set this all up. I personally would be curious to try this out and do some benchmarks against nlopt methods.

Project mention: Symbolicregression.jl – HighPerformance Symbolic Regression in Julia and Python  news.ycombinator.com  20230715

DataDrivenDiffEq.jl
Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization
If you are looking to infer the actual structure (not just parameters) of an ODE given some data, there is DataDrivenDiffEq.jl. https://github.com/SciML/DataDrivenDiffEq.jl

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

InfluxDB
Collect and Analyze Billions of Data Points in Real Time. Manage all types of time series data in a single, purposebuilt database. Run at any scale in any environment in the cloud, onpremises, or at the edge.


SciMLSensitivity.jl
A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimizethendiscretize, discretizethenoptimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.

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

StochasticDiffEq.jl
Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem
For stochastic processes you have to work a little bit more. However maybe the StochasticDiffEq.jl package can give some guiding there https://github.com/SciML/StochasticDiffEq.jl/tree/master/test


RecursiveArrayTools.jl
Tools for easily handling objects like arrays of arrays and deeper nestings in scientific machine learning (SciML) and other applications
You're not really supposed to be using StaticArraysCore anymore, but here's a somewhat older PR that shows the siginificance of moving StaticArray functionality on a smaller library, moving it from 6228ms to 292ms load time (https://github.com/SciML/RecursiveArrayTools.jl/pull/217).


Project mention: Please help me make a case to implement Julia in enterprise  /r/Julia  20221107
You might be interested in MethodOfLines.jl, a symbolic automatic partial differential equation discretizer based on the ModelingToolkit and DiffEq stack.

NonlinearSolve.jl
Highperformance and differentiationenabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and NewtonKrylov support.
I would highly suggest using NonlinearSolve.jl instead as it's more maintained. For this, the solution object is documented here: https://docs.sciml.ai/NonlinearSolve/stable/basics/NonlinearSolution/

NBodySimulator.jl
A differentiable simulator for scientific machine learning (SciML) with Nbody problems, including astrophysical and molecular dynamics



ParameterizedFunctions.jl
A simple domainspecific language (DSL) for defining differential equations for use in scientific machine learning (SciML) and other applications

Project mention: WorldDynamics.jl: A modern implemention of famous integrated assessment models  /r/collapse  20221006

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

MuladdMacro.jl
This package contains a macro for converting expressions to use muladd calls and fusedmultiplyadd (FMA) operations for highperformance in the SciML scientific machine learning ecosystem

Mergify
Updating dependencies is timeconsuming.. Solutions like Dependabot or Renovate update but don't merge dependencies. You need to do it manually while it could be fully automated! Add a Merge Queue to your workflow and stop caring about PR management & merging. Try Mergify for free.
Julia Sciml related posts
 Good linear algebra libraries
 Julia's latency: Past, present and future
 Please help me make a case to implement Julia in enterprise
 How much useful are RungeKutta methods of order 9 and higher within doubleprecision arithmetic/floating point accuracy?
 Interpolant Coefficients for the BS5 RungeKutta method
 “Why I still recommend Julia”
 Why Fortran is easy to learn

A note from our sponsor  Mergify
blog.mergify.com  30 Sep 2023
Index
What are some of the best opensource Sciml projects in Julia? This list will help you:
Project  Stars  

1  DifferentialEquations.jl  2,622 
2  ModelingToolkit.jl  1,256 
3  NeuralPDE.jl  813 
4  Optimization.jl  568 
5  SymbolicRegression.jl  458 
6  DataDrivenDiffEq.jl  384 
7  Catalyst.jl  366 
8  Surrogates.jl  287 
9  SciMLSensitivity.jl  273 
10  DiffEqBase.jl  262 
11  StochasticDiffEq.jl  219 
12  ReservoirComputing.jl  180 
13  RecursiveArrayTools.jl  177 
14  SciMLStyle  152 
15  MethodOfLines.jl  133 
16  NonlinearSolve.jl  128 
17  NBodySimulator.jl  119 
18  LatticeQCD.jl  117 
19  ModelingToolkitStandardLibrary.jl  83 
20  ParameterizedFunctions.jl  73 
21  WorldDynamics.jl  53 
22  DiffEqDevTools.jl  43 
23  MuladdMacro.jl  42 