ModelingToolkit.jl: High-Performance Symbolic-Numeric Equation-Based Modeling

ModelingToolkit.jl is a modeling language for high-performance symbolic-numeric computation in scientific computing and scientific machine learning. It then mixes ideas from symbolic computational algebra systems with causal and acausal equation-based modeling frameworks to give an extendable and parallel modeling system. It allows for users to give a high-level description of a model for symbolic preprocessing to analyze and enhance the model. Automatic symbolic transformations, such as index reduction of differential-algebraic equations, make it possible to solve equations that are impossible to solve with a purely numeric-based technique.

Installation

To install ModelingToolkit.jl, use the Julia package manager:

using Pkg
Pkg.add("ModelingToolkit")

Citation

If you use ModelingToolkit in your work, please cite the following:

@misc{ma2021modelingtoolkit,
      title={ModelingToolkit: A Composable Graph Transformation System For Equation-Based Modeling},
      author={Yingbo Ma and Shashi Gowda and Ranjan Anantharaman and Chris Laughman and Viral Shah and Chris Rackauckas},
      year={2021},
      eprint={2103.05244},
      archivePrefix={arXiv},
      primaryClass={cs.MS}
}

Feature Summary

ModelingToolkit version 11

ModelingToolkit version 11 just released. Please refer to the changelog for a summary of the changes. Some documentation pages may be broken while downstream packages update to the new version.

ModelingToolkit.jl is a symbolic-numeric modeling package. Thus it combines some of the features from symbolic computing packages like SymPy or Mathematica with the ideas of equation-based modeling systems like the causal Simulink and the acausal Modelica. It bridges the gap between many different kinds of equations, allowing one to quickly and easily transform systems of DAEs into optimization problems, or vice-versa, and then simplify and parallelize the resulting expressions before generating code.

Feature List

Causal and acausal modeling (Simulink/Modelica)
Automated model transformation, simplification, and composition
Automatic conversion of numerical models into symbolic models
Composition of models through the components, a lazy connection system, and tools for expanding/flattening
Pervasive parallelism in symbolic computations and generated functions
Transformations like alias elimination and tearing of nonlinear systems for efficiently numerically handling large-scale systems of equations
The ability to use the entire Symbolics.jl Computer Algebra System (CAS) as part of the modeling process.
Import models from common formats like SBML, CellML, BioNetGen, and more.
Extensibility: the whole system is written in pure Julia, so adding new functions, simplification rules, and model transformations has no barrier.

For information on how to use the Symbolics.jl CAS system that ModelingToolkit.jl is built on, consult the Symbolics.jl documentation

Equation Types

Ordinary differential equations
Stochastic differential equations
Partial differential equations
Nonlinear systems
Optimization problems
Continuous-Time Markov Chains
Chemical Reactions (via Catalyst.jl)
Nonlinear Optimal Control

Standard Library

For quick development, ModelingToolkit.jl includes ModelingToolkitStandardLibrary.jl, a standard library of prebuilt components for the ModelingToolkit ecosystem.

Model Import Formats

CellMLToolkit.jl: Import CellML models into ModelingToolkit
- Repository of more than a thousand pre-made models
- Focus on biomedical models in areas such as: Calcium Dynamics, Cardiovascular Circulation, Cell Cycle, Cell Migration, Circadian Rhythms, Electrophysiology, Endocrine, Excitation-Contraction Coupling, Gene Regulation, Hepatology, Immunology, Ion Transport, Mechanical Constitutive Laws, Metabolism, Myofilament Mechanics, Neurobiology, pH Regulation, PKPD, Protein Modules, Signal Transduction, and Synthetic Biology.
SBMLToolkit.jl: Import SBML models into ModelingToolkit
- Uses the robust libsbml library for parsing and transforming the SBML
ReactionNetworkImporters.jl: Import various models into ModelingToolkit
- Supports the BioNetGen .net file
- Supports importing networks specified by stoichiometric matrices

Extension Libraries

Because ModelingToolkit.jl is the core foundation of an equation-based modeling ecosystem, there is a large set of libraries adding features to this system. Below is an incomplete list of extension libraries one may want to be aware of:

Catalyst.jl: Symbolic representations of chemical reactions
- Symbolically build and represent large systems of chemical reactions
- Generate code for ODEs, SDEs, continuous-time Markov Chains, and more
- Simulate the models using the SciML ecosystem with O(1) Gillespie methods
DataDrivenDiffEq.jl: Automatic identification of equations from data
- Automated construction of ODEs and DAEs from data
- Representations of Koopman operators and Dynamic Mode Decomposition (DMD)
MomentClosure.jl: Automatic transformation of ReactionSystems into deterministic systems
- Generates Systems for the moment closures
- Allows for geometrically-distributed random reaction rates
ReactionMechanismSimulator.jl: Simulating and analyzing large chemical reaction mechanisms
- Ideal gas and dilute liquid phases.
- Constant T and P and constant V adiabatic ideal gas reactors.
- Constant T and V dilute liquid reactors.
- Diffusion limited rates. Sensitivity analysis for all reactors.
- Flux diagrams with molecular images (if molecular information is provided).
NumCME.jl: High-performance simulation of chemical master equations (CME)
- Transient solution of the CME
- Dynamic state spaces
- Accepts reaction systems defined using Catalyst.jl DSL.
FiniteStateProjection.jl: High-performance simulation of chemical master equations (CME) via finite state projections
- Accepts reaction systems defined using Catalyst.jl DSL.

Compatible Numerical Solvers

All of the symbolic systems have a direct conversion to a numerical system, which can then be handled through the SciML interfaces. For example, after building a model and performing symbolic manipulations, a System can be converted into an ODEProblem to then be solved by a numerical ODE solver. Below is a list of the solver libraries which are the numerical targets of the ModelingToolkit system:

DifferentialEquations.jl
- Multi-package interface of high performance numerical solvers for System, SDESystem, and JumpSystem
NonlinearSolve.jl
- High performance numerical solving of NonlinearSystem
Optimization.jl
- Multi-package interface for numerical solving OptimizationSystem
NeuralPDE.jl
- Physics-Informed Neural Network (PINN) training on PDESystem
MethodOfLines.jl
- Automated finite difference method (FDM) discretization of PDESystem

Contributing

Please refer to the SciML ColPrac: Contributor's Guide on Collaborative Practices for Community Packages for guidance on PRs, issues, and other matters relating to contributing to SciML.
See the SciML Style Guide for common coding practices and other style decisions.
There are a few community forums:
- The #diffeq-bridged and #sciml-bridged channels in the Julia Slack
- The #diffeq-bridged and #sciml-bridged channels in the Julia Zulip
- On the Julia Discourse forums
- See also SciML Community page

Reproducibility

The documentation of this SciML package was built using these direct dependencies,

Status `~/work/ModelingToolkit.jl/ModelingToolkit.jl/docs/Project.toml`
⌅ [f3fd9213] Attractors v1.38.4
  [6e4b80f9] BenchmarkTools v1.8.0
  [0f109fa4] BifurcationKit v0.8.7
  [13f3f980] CairoMakie v0.15.15
  [38540f10] CommonSolve v0.2.14
  [aaaaaaaa] ControlSystemsBase v1.22.0
  [687d7614] ControlSystemsMTK v2.8.1
⌅ [82cc6244] DataInterpolations v9.5.0
  [31c24e10] Distributions v0.25.131
  [e30172f5] Documenter v1.19.0
  [06fc5a27] DynamicQuantities v1.13.0
⌅ [14a09403] FMI v0.14.3
  [86223c79] Graphs v1.15.0
  [20393b10] InfiniteOpt v0.6.3
  [b6b21f68] Ipopt v1.16.0
  [ccbc3e58] JumpProcesses v9.33.1
  [961ee093] ModelingToolkit v11.45.3 `~/work/ModelingToolkit.jl/ModelingToolkit.jl`
  [7771a370] ModelingToolkitBase v1.77.2 `~/work/ModelingToolkit.jl/ModelingToolkit.jl/lib/ModelingToolkitBase`
  [16a59e39] ModelingToolkitStandardLibrary v2.29.8
  [6bb917b9] ModelingToolkitTearing v1.20.6
  [8913a72c] NonlinearSolve v4.32.0
  [429524aa] Optim v2.3.2
  [7f7a1694] Optimization v5.9.1
  [36348300] OptimizationOptimJL v0.4.21
  [1dea7af3] OrdinaryDiffEq v7.8.1
  [d3585ca7] OrdinaryDiffEqFunctionMap v2.3.0
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v2.9.9
  [43230ef6] OrdinaryDiffEqRosenbrock v2.7.5
  [2d112036] OrdinaryDiffEqSDIRK v2.9.7
  [91a5bcdd] Plots v1.41.7
  [d236fae5] PreallocationTools v1.7.1
  [91a8cdf1] SciCompDSL v1.0.4 `~/work/ModelingToolkit.jl/ModelingToolkit.jl/lib/SciCompDSL`
  [53ae85a6] SciMLStructures v1.10.5
  [efcf1570] Setfield v1.1.2
  [64909d44] StateSelection v1.11.1
  [789caeaf] StochasticDiffEq v7.2.0
  [2efcf032] SymbolicIndexingInterface v0.3.55
  [d1185830] SymbolicUtils v4.48.0
  [0c5d862f] Symbolics v7.41.1
  [37e2e46d] LinearAlgebra
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`

and using this machine and Julia version.

Julia Version 1.10.12
Commit d93beab124c (2026-08-15 10:29 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 9V74 80-Core Processor
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
  JULIA_DEBUG = Documenter

A more complete overview of all dependencies and their versions is also provided.

Status `~/work/ModelingToolkit.jl/ModelingToolkit.jl/docs/Manifest.toml`
  [47edcb42] ADTypes v1.24.0
  [14f7f29c] AMD v0.5.4
  [a4c015fc] ANSIColoredPrinters v0.0.1
  [621f4979] AbstractFFTs v1.5.0
  [6e696c72] AbstractPlutoDingetjes v1.4.1
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.45
  [79e6a3ab] Adapt v4.7.1
  [35492f91] AdaptivePredicates v1.2.0
  [66dad0bd] AliasTables v1.1.3
  [27a7e980] Animations v0.4.2
  [ec485272] ArnoldiMethod v0.4.0
⌅ [7d9fca2a] Arpack v0.5.3
  [4fba245c] ArrayInterface v7.30.2
  [4c555306] ArrayLayouts v1.13.0
⌅ [f3fd9213] Attractors v1.38.4
  [67c07d97] Automa v1.2.0
  [13072b0f] AxisAlgorithms v1.1.0
  [39de3d68] AxisArrays v0.4.8
  [aae01518] BandedMatrices v1.13.0
  [198e06fe] BangBang v0.4.9
  [18cc8868] BaseDirs v1.4.0
  [6e4b80f9] BenchmarkTools v1.8.0
  [0e736298] Bessels v0.2.8
  [0f109fa4] BifurcationKit v0.8.7
  [e2ed5e7c] Bijections v0.2.2
  [b2a6c25c] BinaryHeaps v1.1.0
  [caf10ac8] BipartiteGraphs v0.1.14
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [a134a8b2] BlackBoxOptim v0.6.12
  [8e7c35d0] BlockArrays v1.10.0
  [70df07ce] BracketingNonlinearSolve v1.12.8
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.7
  [96374032] CRlibm v1.0.2
  [159f3aea] Cairo v1.1.1
  [13f3f980] CairoMakie v0.15.15
  [d360d2e6] ChainRulesCore v1.26.1
  [ae650224] ChunkSplitters v3.2.0
  [aaaa29a8] Clustering v0.15.8
  [523fee87] CodecBzip2 v0.8.5
  [944b1d66] CodecZlib v0.7.9
  [6b39b394] CodecZstd v0.8.7
  [a2cac450] ColorBrewer v0.4.2
  [35d6a980] ColorSchemes v3.31.0
  [3da002f7] ColorTypes v0.12.3
  [c3611d14] ColorVectorSpace v0.11.0
  [5ae59095] Colors v0.13.2
⌅ [861a8166] Combinatorics v1.0.2
  [38540f10] CommonSolve v0.2.14
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.2.2
  [34da2185] Compat v4.18.1
  [ab4b797d] ComplexityMeasures v3.11.0
  [b0b7db55] ComponentArrays v0.15.50
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [95dc2771] ComputePipeline v0.1.8
  [2569d6c7] ConcreteStructs v0.2.8
  [88cd18e8] ConsoleProgressMonitor v0.1.2
  [187b0558] ConstructionBase v1.6.0
  [d38c429a] Contour v0.6.3
  [aaaaaaaa] ControlSystemsBase v1.22.0
  [687d7614] ControlSystemsMTK v2.8.1
  [b7a15901] CoreMath v0.1.0
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.2.0
  [717857b8] DSP v0.8.6
  [9a962f9c] DataAPI v1.16.0
⌅ [82cc6244] DataInterpolations v9.5.0
  [864edb3b] DataStructures v0.19.6
  [e2d170a0] DataValueInterfaces v1.0.0
  [927a84f5] DelaunayTriangulation v1.6.7
  [5732040d] DelayEmbeddings v2.9.0
  [8bb1440f] DelimitedFiles v1.9.1
  [a81e2ce2] DescriptorSystems v1.5.0
  [2b5f629d] DiffEqBase v7.21.3
  [459566f4] DiffEqCallbacks v4.19.4
  [77a26b50] DiffEqNoiseProcess v5.36.4
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.16.0
  [a0c0ee7d] DifferentiationInterface v0.7.21
  [8d63f2c5] DispatchDoctor v0.4.29
  [b4f34e82] Distances v0.10.12
  [31c24e10] Distributions v0.25.131
  [ffbed154] DocStringExtensions v0.9.5
  [e30172f5] Documenter v1.19.0
  [5b8099bc] DomainSets v0.8.3
  [7c1d4256] DynamicPolynomials v0.6.8
  [06fc5a27] DynamicQuantities v1.13.0
  [6e36e845] DynamicalSystemsBase v3.19.3
  [4e289a0a] EnumX v1.0.7
  [f151be2c] EnzymeCore v0.8.21
  [429591f6] ExactPredicates v2.2.9
  [e2ba6199] ExprTools v0.1.11
  [55351af7] ExproniconLite v0.10.14
  [8f5d6c58] EzXML v1.2.3
  [c87230d0] FFMPEG v0.4.6
  [b86e33f2] FFTA v0.3.1
  [7a1cc6ca] FFTW v1.10.0
⌅ [14a09403] FMI v0.14.3
  [900ee838] FMIBase v1.5.0
  [8af89139] FMICore v1.2.0
⌅ [31b88311] FMIExport v0.4.1
  [9fcbc62e] FMIImport v1.3.1
  [7034ab61] FastBroadcast v1.4.0
  [9aa1b823] FastClosures v0.3.2
  [442a2c76] FastGaussQuadrature v1.3.0
  [a4df4552] FastPower v1.5.0
  [5789e2e9] FileIO v1.20.0
  [8fc22ac5] FilePaths v0.9.0
  [48062228] FilePathsBase v0.9.24
  [1a297f60] FillArrays v1.17.1
  [64ca27bc] FindFirstFunctions v3.4.0
  [6a86dc24] FiniteDiff v2.33.0
⌅ [53c48c17] FixedPointNumbers v0.8.6
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v1.4.6
  [b38be410] FreeType v4.1.1
  [663a7486] FreeTypeAbstraction v0.10.8
  [a85aefff] FunctionMaps v0.1.2
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v1.13.0
  [d9f16b24] Functors v0.5.3
  [46192b85] GPUArraysCore v0.2.1
  [28b8d3ca] GR v0.73.27
⌃ [a0844989] Gamma v1.1.0
  [c145ed77] GenericSchur v0.5.8
  [5c1252a2] GeometryBasics v0.5.13
  [d7ba0133] Git v1.5.0
  [a2bd30eb] Graphics v1.1.3
  [86223c79] Graphs v1.15.0
  [3955a311] GridLayoutBase v0.11.3
  [076d061b] HashArrayMappedTries v0.2.0
  [3e5b6fbb] HostCPUFeatures v0.1.18
  [e91730f6] Hungarian v0.7.0
  [34004b35] HypergeometricFunctions v0.3.30
  [b5f81e59] IOCapture v1.0.0
  [615f187c] IfElse v0.1.1
  [2803e5a7] ImageAxes v0.6.12
  [c817782e] ImageBase v0.1.7
  [a09fc81d] ImageCore v0.10.5
  [82e4d734] ImageIO v0.6.10
  [bc367c6b] ImageMetadata v0.9.10
  [3263718b] ImplicitDiscreteSolve v2.3.0
  [9b13fd28] IndirectArrays v1.0.0
  [20393b10] InfiniteOpt v0.6.3
  [d25df0c9] Inflate v0.1.5
  [22cec73e] InitialValues v0.3.1
  [18e54dd8] IntegerMathUtils v0.1.4
  [a98d9a8b] Interpolations v0.16.3
  [d1acc4aa] IntervalArithmetic v1.0.12
  [8197267c] IntervalSets v0.7.14
  [3587e190] InverseFunctions v0.1.17
  [b6b21f68] Ipopt v1.16.0
  [92d709cd] IrrationalConstants v0.2.6
  [f1662d9f] Isoband v0.1.1
  [c8e1da08] IterTools v1.10.0
  [42fd0dbc] IterativeSolvers v0.9.4
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.11
  [692b3bcd] JLLWrappers v1.8.0
  [682c06a0] JSON v1.10.0
  [ae98c720] Jieko v0.2.1
  [b835a17e] JpegTurbo v0.1.6
  [4076af6c] JuMP v1.31.2
  [ccbc3e58] JumpProcesses v9.33.1
  [5ab0869b] KernelDensity v0.6.12
  [ba0b0d4f] Krylov v0.10.10
  [0b1a1467] KrylovKit v0.10.4
  [2faa5264] LHLFactorization v2.2.2
  [b964fa9f] LaTeXStrings v1.4.1
  [23fbe1c1] Latexify v0.16.12
  [10f19ff3] LayoutPointers v0.1.17
  [0e77f7df] LazilyInitializedFields v1.3.0
  [8cdb02fc] LazyModules v0.3.1
  [1d6d02ad] LeftChildRightSiblingTrees v0.3.0
  [87fe0de2] LineSearch v0.1.19
  [d3d80556] LineSearches v7.8.2
  [7a12625a] LinearMaps v3.11.4
  [7ed4a6bd] LinearSolve v5.18.2
⌅ [2ab3a3ac] LogExpFunctions v0.3.29
  [e6f89c97] LoggingExtras v1.2.0
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.16
  [ee78f7c6] Makie v0.24.15
  [d125e4d3] ManualMemory v0.1.8
  [dbb5928d] MappedArrays v0.4.3
  [d0879d2d] MarkdownAST v0.1.3
  [b8f27783] MathOptInterface v1.54.0
  [0a4f8689] MathTeXEngine v0.6.9
  [99c1a7ee] MatrixEquations v2.6.7
  [a3b82374] MatrixFactorizations v3.1.3
  [48965c70] MatrixPencils v1.9.1
  [bb5d69b7] MaybeInplace v0.1.8
  [442fdcdd] Measures v0.3.3
  [e1d29d7a] Missings v1.2.0
  [961ee093] ModelingToolkit v11.45.3 `~/work/ModelingToolkit.jl/ModelingToolkit.jl`
  [7771a370] ModelingToolkitBase v1.77.2 `~/work/ModelingToolkit.jl/ModelingToolkit.jl/lib/ModelingToolkitBase`
  [16a59e39] ModelingToolkitStandardLibrary v2.29.8
  [6bb917b9] ModelingToolkitTearing v1.20.6
  [0987c9cc] MonteCarloMeasurements v1.5.2
  [e94cdb99] MosaicViews v0.3.4
⌅ [2e0e35c7] Moshi v0.3.9
  [46d2c3a1] MuladdMacro v0.2.7
  [102ac46a] MultivariatePolynomials v0.5.20
  [d8a4904e] MutableArithmetics v1.8.1
  [d41bc354] NLSolversBase v8.0.1
  [77ba4419] NaNMath v1.1.4
  [b8a86587] NearestNeighbors v0.4.29
  [645ca80c] Neighborhood v0.2.5
  [f09324ee] Netpbm v1.1.1
  [8913a72c] NonlinearSolve v4.32.0
  [be0214bd] NonlinearSolveBase v2.54.0
  [5959db7a] NonlinearSolveFirstOrder v2.10.0
  [9a2c21bd] NonlinearSolveQuasiNewton v1.15.3
  [26075421] NonlinearSolveSpectralMethods v1.8.3
  [510215fc] Observables v0.5.5
  [6fe1bfb0] OffsetArrays v1.17.0
  [67456a42] OhMyThreads v0.8.6
  [52e1d378] OpenEXR v0.3.3
  [429524aa] Optim v2.3.2
  [7f7a1694] Optimization v5.9.1
  [bca83a33] OptimizationBase v5.7.0
  [36348300] OptimizationOptimJL v0.4.21
⌅ [bac558e1] OrderedCollections v1.8.2
  [1dea7af3] OrdinaryDiffEq v7.8.1
  [6ad6398a] OrdinaryDiffEqBDF v2.4.12
  [bbf590c4] OrdinaryDiffEqCore v4.18.1
  [50262376] OrdinaryDiffEqDefault v2.6.2
  [4302a76b] OrdinaryDiffEqDifferentiation v3.12.4
  [d3585ca7] OrdinaryDiffEqFunctionMap v2.3.0
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v2.9.9
  [43230ef6] OrdinaryDiffEqRosenbrock v2.7.5
  [b4bd8bb3] OrdinaryDiffEqRosenbrockTableaus v2.4.2
  [2d112036] OrdinaryDiffEqSDIRK v2.9.7
  [b1df2697] OrdinaryDiffEqTsit5 v2.1.5
  [79d7bb75] OrdinaryDiffEqVerner v2.4.2
  [90014a1f] PDMats v0.11.41
  [f57f5aa1] PNGFiles v0.4.5
  [65ce6f38] PackageExtensionCompat v1.0.2
  [19eb6ba3] Packing v0.5.1
  [5432bcbf] PaddedViews v0.5.12
⌅ [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v3.0.0
  [eebad327] PkgVersion v0.3.3
  [ccf2f8ad] PlotThemes v3.3.0
  [995b91a9] PlotUtils v1.5.0
  [91a5bcdd] Plots v1.41.7
  [e409e4f3] PoissonRandom v0.4.13
  [647866c9] PolygonOps v0.1.2
  [f27b6e38] Polynomials v4.1.3
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v1.7.1
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.6.0
  [08abe8d2] PrettyTables v3.5.0
  [27ebfcd6] Primes v0.5.7
  [33c8b6b6] ProgressLogging v0.1.6
  [92933f4c] ProgressMeter v1.11.0
  [43287f4e] PtrArrays v1.4.0
  [0c0d3e7f] PureKLU v1.6.0
  [4b34888f] QOI v1.0.2
  [1fd47b50] QuadGK v2.11.3
  [b3c3ace0] RangeArrays v0.3.2
  [c84ed2f1] Ratios v0.4.5
  [988b38a3] ReadOnlyArrays v0.2.0
  [795d4caa] ReadOnlyDicts v1.0.1
⌅ [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
  [731186ca] RecursiveArrayTools v4.5.3
  [189a3867] Reexport v1.2.2
  [2792f1a3] RegistryInstances v0.1.0
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.1
  [ae5879a3] ResettableStacks v1.4.0
  [9fe22ead] RespecializeParams v1.3.0
  [79098fc4] Rmath v0.9.0
  [21fd56a4] RobustAndOptimalControl v0.4.52
  [f2b01f46] Roots v3.0.8
  [5eaf0fd0] RoundingEmulator v0.2.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.27
  [9dfe8606] SCCNonlinearSolve v1.15.4
  [fdea26ae] SIMD v3.7.2
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.46
  [91a8cdf1] SciCompDSL v1.0.4 `~/work/ModelingToolkit.jl/ModelingToolkit.jl/lib/SciCompDSL`
  [0bca4576] SciMLBase v3.57.0
  [19f34311] SciMLJacobianOperators v0.1.19
  [a6db7da4] SciMLLogging v2.1.0
  [c0aeaf25] SciMLOperators v1.30.1
  [431bcebd] SciMLPublic v1.3.0
  [53ae85a6] SciMLStructures v1.10.5
  [7e506255] ScopedValues v1.6.2
  [6c6a2e73] Scratch v1.3.0
  [efcf1570] Setfield v1.1.2
  [65257c39] ShaderAbstractions v0.5.1
  [992d4aef] Showoff v1.1.1
  [73760f76] SignedDistanceFields v0.4.1
  [727e6d20] SimpleNonlinearSolve v2.14.6
  [699a6c99] SimpleTraits v0.9.6
  [45858cf5] Sixel v0.1.5
  [ed01d8cd] Sobol v1.5.0
  [a2af1166] SortingAlgorithms v1.2.3
  [a57abbd0] SparseColumnPivotedQR v2.1.8
  [9f842d2f] SparseConnectivityTracer v1.2.3
  [0a514795] SparseMatrixColorings v0.4.28
  [276daf66] SpecialFunctions v2.9.0
  [91464d47] StableTasks v0.1.7
  [cae243ae] StackViews v0.1.2
  [0c0c59c1] StarAlgebras v0.3.0
  [64909d44] StateSelection v1.11.1
  [40b095a5] StateSpaceSets v2.5.5
  [aedffcd0] Static v1.4.6
  [0d7ed370] StaticArrayInterface v1.10.0
  [90137ffa] StaticArrays v1.9.22
  [1e83bf80] StaticArraysCore v1.4.4
  [82ae8749] StatsAPI v1.8.0
  [2913bbd2] StatsBase v0.34.13
⌅ [4c63d2b9] StatsFuns v1.5.3
  [789caeaf] StochasticDiffEq v7.2.0
  [19c5a474] StochasticDiffEqCore v2.2.3
  [0520c28c] StochasticDiffEqHighOrder v2.2.0
  [ebf54054] StochasticDiffEqIIF v2.1.0
  [5080b986] StochasticDiffEqImplicit v2.2.1
  [aefaaa88] StochasticDiffEqLeaping v2.1.0
  [90dbc90e] StochasticDiffEqLevyArea v2.1.1
  [d15fe365] StochasticDiffEqLowOrder v2.0.5
  [8c95a807] StochasticDiffEqMilstein v2.1.1
  [db241ea8] StochasticDiffEqROCK v2.1.1
  [49714585] StochasticDiffEqRODE v2.2.0
  [af2a2fcd] StochasticDiffEqWeak v2.2.1
  [892a3eda] StringManipulation v0.6.1
  [09ab397b] StructArrays v0.7.3
  [ec057cc2] StructUtils v2.9.2
  [f489334b] StyledStrings v1.0.3
  [2efcf032] SymbolicIndexingInterface v0.3.55
  [19f23fe9] SymbolicLimits v1.2.1
  [d1185830] SymbolicUtils v4.48.0
  [0c5d862f] Symbolics v7.41.1
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.14.0
  [ed4db957] TaskLocalValues v0.1.3
  [62fd8b95] TensorCore v0.1.1
  [8ea1fca8] TermInterface v2.0.0
  [5d786b92] TerminalLoggers v0.1.8
  [1c621080] TestItems v1.1.0
  [731e570b] TiffImages v0.11.9
  [a759f4b9] TimerOutputs v1.2.2
  [3bb67fe8] TranscodingStreams v0.11.3
  [410a4b4d] Tricks v0.1.13
  [981d1d27] TriplotBase v0.1.0
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.7.0
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [1986cc42] Unitful v1.29.0
  [41fe7b60] Unzip v0.2.0
⌅ [409d34a3] VectorInterface v0.6.1
  [3d5dd08c] VectorizationBase v0.21.74
  [29a6e085] Wavelets v0.10.2
  [d30d5f5c] WeakCacheSets v0.1.0
  [e3aaa7dc] WebP v0.1.3
  [efce3f68] WoodburyMatrices v1.1.0
  [a5390f91] ZipFile v0.10.1
  [ae81ac8f] ASL_jll v0.1.5+0
⌅ [68821587] Arpack_jll v3.5.2+0
  [6e34b625] Bzip2_jll v1.0.9+0
  [4e9b3aee] CRlibm_jll v1.0.1+0
  [83423d85] Cairo_jll v1.18.7+0
  [a38c48d9] CoreMath_jll v0.1.0+0
  [ee1fde0b] Dbus_jll v1.16.2+0
⌅ [5ae413db] EarCut_jll v2.2.4+0
  [2702e6a9] EpollShim_jll v0.0.20230411+1
  [2e619515] Expat_jll v2.8.4+0
  [b22a6f82] FFMPEG_jll v9.0.1+0
  [f5851436] FFTW_jll v3.3.12+0
  [a3f928ae] Fontconfig_jll v2.17.1+0
  [d7e528f0] FreeType2_jll v2.14.3+1
  [559328eb] FriBidi_jll v1.0.17+0
  [0656b61e] GLFW_jll v3.5.1+0
  [d2c73de3] GR_jll v0.73.27+0
⌅ [b0724c58] GettextRuntime_jll v0.22.4+0
  [61579ee1] Ghostscript_jll v9.55.1+0
  [59f7168a] Giflib_jll v6.1.3+0
  [020c3dae] Git_LFS_jll v3.7.1+0
  [f8c6e375] Git_jll v2.56.0+0
  [7746bdde] Glib_jll v2.88.3+0
  [3b182d85] Graphite2_jll v1.3.16+0
  [2e76f6c2] HarfBuzz_jll v100.14004.0+0
  [e33a78d0] Hwloc_jll v2.14.1+0
  [905a6f67] Imath_jll v3.2.2+0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
⌅ [9cc047cb] Ipopt_jll v300.1400.1902+0
  [aacddb02] JpegTurbo_jll v3.2.0+1
  [c1c5ebd0] LAME_jll v3.100.3+0
  [88015f11] LERC_jll v4.2.0+0
  [1d63c593] LLVMOpenMP_jll v23.1.1+0
⌅ [e9f186c6] Libffi_jll v3.4.7+0
  [7e76a0d4] Libglvnd_jll v1.7.1+1
  [94ce4f54] Libiconv_jll v1.18.0+0
  [4b2f31a3] Libmount_jll v2.42.0+0
  [89763e89] Libtiff_jll v4.7.3+0
  [38a345b3] Libuuid_jll v2.42.0+0
  [d00139f3] METIS_jll v5.1.4+0
  [856f044c] MKL_jll v2025.2.0+0
  [d7ed1dd3] MUMPS_seq_jll v500.900.100+0
  [e7412a2a] Ogg_jll v1.3.6+0
⌅ [656ef2d0] OpenBLAS32_jll v0.3.24+0
⌅ [6cdc7f73] OpenBLASConsistentFPCSR_jll v0.3.29+0
  [18a262bb] OpenEXR_jll v3.4.15+0
  [9bd350c2] OpenSSH_jll v10.5.1+0
  [458c3c95] OpenSSL_jll v3.5.8+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [91d4177d] Opus_jll v1.6.1+0
  [36c8627f] Pango_jll v1.58.2+0
  [30392449] Pixman_jll v0.46.4+0
  [c0090381] Qt6Base_jll v6.10.2+2
  [629bc702] Qt6Declarative_jll v6.10.2+2
  [ce943373] Qt6ShaderTools_jll v6.10.2+1
  [6de9746b] Qt6Svg_jll v6.10.2+0
  [e99dba38] Qt6Wayland_jll v6.10.2+1
  [f50d1b31] Rmath_jll v0.5.2+0
  [319450e9] SPRAL_jll v2025.9.18+1
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.24.0+0
  [02c8fc9c] XML2_jll v2.15.4+0
  [ffd25f8a] XZ_jll v5.8.4+0
  [f67eecfb] Xorg_libICE_jll v1.1.2+0
  [c834827a] Xorg_libSM_jll v1.2.6+0
  [4f6342f7] Xorg_libX11_jll v1.8.13+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.13+0
  [935fb764] Xorg_libXcursor_jll v1.2.4+0
  [a3789734] Xorg_libXdmcp_jll v1.1.6+0
  [1082639a] Xorg_libXext_jll v1.3.8+0
  [d091e8ba] Xorg_libXfixes_jll v6.0.2+0
  [a51aa0fd] Xorg_libXi_jll v1.8.4+0
  [d1454406] Xorg_libXinerama_jll v1.1.7+0
  [ec84b674] Xorg_libXrandr_jll v1.5.6+0
  [ea2f1a96] Xorg_libXrender_jll v0.9.12+0
  [a65dc6b1] Xorg_libpciaccess_jll v0.19.0+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.1+0
  [cc61e674] Xorg_libxkbfile_jll v1.2.0+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.6+0
  [12413925] Xorg_xcb_util_image_jll v0.4.1+0
  [2def613f] Xorg_xcb_util_jll v0.4.1+0
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.1+0
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.10+0
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.2+0
  [35661453] Xorg_xkbcomp_jll v1.4.7+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.47.0+2
  [c5fb5394] Xorg_xtrans_jll v1.6.0+0
  [3161d3a3] Zstd_jll v1.5.7+1
  [35ca27e7] eudev_jll v3.2.14+0
⌅ [214eeab7] fzf_jll v0.61.1+0
  [9a68df92] isoband_jll v0.2.3+0
  [a4ae2306] libaom_jll v3.15.1+0
  [0ac62f75] libass_jll v0.17.5+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [8e53e030] libdrm_jll v2.4.134+0
  [2db6ffa8] libevdev_jll v1.13.4+0
  [f638f0a6] libfdk_aac_jll v2.0.4+0
  [36db933b] libinput_jll v1.28.1+0
  [b53b4c65] libpng_jll v1.6.58+0
  [075b6546] libsixel_jll v1.10.5+0
  [9a156e7d] libva_jll v2.23.0+0
  [f27f6e37] libvorbis_jll v1.3.8+0
  [c5f90fcd] libwebp_jll v1.6.1+0
  [009596ad] mtdev_jll v1.1.7+0
  [1317d2d5] oneTBB_jll v2022.3.0+0
⌅ [1270edf5] x264_jll v10164.0.1+0
  [dfaa095f] x265_jll v4.1.0+0
  [d8fb68d0] xkbcommon_jll v1.13.0+0
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [8bf52ea8] CRC32c
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.10.0
  [de0858da] Printf
  [9abbd945] Profile
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.1.2+1
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.1010+0
  [14a3606d] MozillaCACerts_jll v2025.12.2
  [4536629a] OpenBLAS_jll v0.3.23+5
  [05823500] OpenLibm_jll v0.8.5+0
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.6.1+0
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`

You can also download the manifest file and the project file.