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Top 21 Julia differential-equation Projects
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DifferentialEquations.jl
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.
Another up-and-coming solution is Julia's simulation ecosystem [1]. It is powered by the commercial organization behind the Julia programming language, which has received DARPA funding [2] to build out these tools. This ecosystem unifies researchers in numerical methods [3], scalable compute, and domain experts in modeling engineering systems (electrical, mechanical, etc.) I believe this is where simulation is headed.
[1] https://juliahub.com/products/juliasim
[2] https://news.ycombinator.com/item?id=26425659
[3] https://docs.sciml.ai/DiffEqDocs/stable/
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InfluxDB
InfluxDB high-performance time series database. Collect, organize, and act on massive volumes of high-resolution data to power real-time intelligent systems.
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ModelingToolkit.jl
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
JuliaSim looks interesting! From my understanding, it's 100% proprietary/commercial, but built on top of the open source https://github.com/SciML/ModelingToolkit.jl?
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NeuralPDE.jl
Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation
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DiffEqFlux.jl
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
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OrdinaryDiffEq.jl
High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)
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Catalyst.jl
Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and O(1) solvers in open source software.
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DataDrivenDiffEq.jl
Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization
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SciMLSensitivity.jl
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.
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DiffEqBase.jl
The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems
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DiffEqGPU.jl
GPU-acceleration routines for DifferentialEquations.jl and the broader SciML scientific machine learning ecosystem
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StochasticDiffEq.jl
Solvers for stochastic differential equations which connect with the scientific machine learning (SciML) ecosystem
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NonlinearSolve.jl
High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity and Newton-Krylov support.
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ParameterizedFunctions.jl
A simple domain-specific language (DSL) for defining differential equations for use in scientific machine learning (SciML) and other applications
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DiffEqDevTools.jl
Benchmarking, testing, and development tools for differential equations and scientific machine learning (SciML)
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SimpleDiffEq.jl
Simple differential equation solvers in native Julia for scientific machine learning (SciML)
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SciPyDiffEq.jl
Wrappers for the SciPy differential equation solvers for the SciML Scientific Machine Learning organization
Project mention: SciML: Open-Source Software for Scientific Machine Learning | news.ycombinator.com | 2025-04-20 -
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NOTE:
The open source projects on this list are ordered by number of github stars.
The number of mentions indicates repo mentiontions in the last 12 Months or
since we started tracking (Dec 2020).
Julia differential-equations discussion
Julia differential-equations related posts
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SciML: Open-Source Software for Scientific Machine Learning
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Building a compile-time SIMD optimized smoothing filter
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2023 was the year that GPUs stood still
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Automatically install huge number of dependency?
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Good linear algebra libraries
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Can Fortran survive another 15 years?
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Why Fortran is a scientific powerhouse
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A note from our sponsor - CodeRabbit
coderabbit.ai | 26 Apr 2025
Index
What are some of the best open-source differential-equation projects in Julia? This list will help you:
| # | Project | Stars |
|---|---|---|
| 1 | DifferentialEquations.jl | 2,938 |
| 2 | ModelingToolkit.jl | 1,502 |
| 3 | NeuralPDE.jl | 1,066 |
| 4 | DiffEqFlux.jl | 890 |
| 5 | OrdinaryDiffEq.jl | 584 |
| 6 | Catalyst.jl | 478 |
| 7 | DataDrivenDiffEq.jl | 415 |
| 8 | SciMLSensitivity.jl | 348 |
| 9 | Surrogates.jl | 342 |
| 10 | DiffEqBase.jl | 327 |
| 11 | ComponentArrays.jl | 313 |
| 12 | DiffEqGPU.jl | 296 |
| 13 | StochasticDiffEq.jl | 277 |
| 14 | NonlinearSolve.jl | 261 |
| 15 | ReservoirComputing.jl | 213 |
| 16 | ModelingToolkitStandardLibrary.jl | 140 |
| 17 | ParameterizedFunctions.jl | 76 |
| 18 | DiffEqDevTools.jl | 52 |
| 19 | BoundaryValueDiffEq.jl | 48 |
| 20 | SimpleDiffEq.jl | 24 |
| 21 | SciPyDiffEq.jl | 22 |
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