# SciML/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

Repository: https://github.com/SciML/ModelingToolkit.jl
Canonical: https://ross.abutalabs.com/products/modelingtoolkitjl
Homepage: https://docs.sciml.ai/ModelingToolkit/stable/
Language: Julia
License: NOASSERTION
License Family: other
Topics: differential-equations, ode, dae, ordinary-differential-equations, pde, sde, dde, stochastic-differential-equations, delay-differential-equations, julia, symbolic, symbolic-computation, symbolic-numerics, computer-algebra, sciml, scientific-machine-learning, optimization, nonlinear-programming, acausal, equation-based
Last push: 2026-08-26T19:13:30+00:00

## Health v2 (maintenance only)
Score: 95/100 (v2, computed 2026-09-03T02:39:23.370411+00:00)
- activity 99, release rhythm 87, longevity 100
- inputs: {"age_days": 3110, "days_push": 7, "days_rel": 7, "gap_med": 0.0, "n_releases_24m": 277}
- flags: no_license
- formula: round(0.45*activity + 0.35*rhythm + 0.20*longevity); archived -> min(score, 10)

## Adoption (not part of the score)
Stars 1661, forks 264 (observed 2026-08-28T04:05:18.542575+00:00)

## What it is
ModelingToolkit.jl is a Julia-based acausal, equation-based modeling framework and computer algebra system for symbolic-numeric computation in scientific machine learning. It lets users describe models at a high level, then automatically applies symbolic transformations (index reduction, simplification, sparsification, parallelization) and generates fast functions like Jacobians and Hessians for numerical solvers.

## Use cases
- model and simulate systems of differential equations symbolically in Julia
- automatically generate fast Jacobians and Hessians for ODE solvers
- convert DAEs into optimization problems and vice versa
- build acausal physics-based component models like Modelica or Simulink
- parallelize and sparsify large scientific models automatically
- perform index reduction on differential-algebraic equations
- physics-informed machine learning with symbolic preprocessing

## When to choose
- you need high-performance symbolic-numeric modeling in the Julia ecosystem
- you want acausal equation-based modeling with automatic transformations
- you need to bridge differential equations and optimization problems
- you want automatically parallelized, sparsity-aware model code generation

## When to avoid
- you need a general-purpose CAS like SymPy or Mathematica outside scientific modeling
- your project is in Python, MATLAB, or another non-Julia language
- you only need to numerically solve standard ODEs without symbolic preprocessing
- you require a mature GUI-based modeling environment like Simulink

## Facets
- artifact type: library
- maturity: active
- function: simulation, math, compiler, machine-learning, data-science
- domain: machine-learning, mathematics, simulation
- platform: cross-platform
- tags: acausal-modeling, symbolic-computation, differential-equations, computer-algebra, scientific-machine-learning, ode, dae, pde, equation-based-modeling, julia, scientific-computing, algorithms

## Member repositories
- SciML/ModelingToolkit.jl (main) score 95

## Provenance
- Observed fields: from GitHub, fetched 2026-08-28T04:05:18.542575+00:00.
- Health v2: computed from the inputs above; adoption is never an input.
- Inferred fields (summary, facets, guidance): AI-extracted, prompt v1, taxonomy v1, on 2026-08-30T03:44:36.606569+00:00, confidence not recorded.
  - readme: https://github.com/SciML/ModelingToolkit.jl (fetched 2026-08-28T04:05:18.542575+00:00, sha 9c96637f0d12)
  - homepage: https://docs.sciml.ai/ModelingToolkit/stable/ (fetched 2026-08-29T11:16:57.884589+00:00, sha 0ec8554458d1)
  - site_page: https://docs.sciml.ai/DiffEqDocs (fetched 2026-08-29T11:16:57.888866+00:00, sha 82260832e07c)
  - site_page: https://docs.sciml.ai/DiffEqDevDocs (fetched 2026-08-29T11:16:57.891134+00:00, sha db0de492634b)
  - site_page: https://docs.sciml.ai/ModelingToolkit/stable/basics/FAQ (fetched 2026-08-29T11:16:57.893203+00:00, sha f81cc9903902)
  - site_page: https://docs.sciml.ai/Symbolics/stable (fetched 2026-08-29T11:16:57.895377+00:00, sha 5b363fc32024)
  - site_page: https://docs.sciml.ai/DiffEqDocs/stable (fetched 2026-08-29T11:16:57.897551+00:00, sha cd446df7f51e)
- Data as of 2026-08-30T08:39:29.467469+00:00.