ModelingToolkit

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

https://github.com/sciml/modelingtoolkit.jl

Science Score: 64.0%

This score indicates how likely this project is to be science-related based on various indicators:

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CITATION.cff file
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Links to: arxiv.org
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15 of 137 committers (10.9%) from academic institutions
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Scientific vocabulary similarity
Low similarity (16.3%) to scientific vocabulary

Keywords

acausal computer-algebra dae dde delay-differential-equations differential-equations equation-based julia nonlinear-programming ode optimization ordinary-differential-equations pde scientific-machine-learning sciml sde stochastic-differential-equations symbolic symbolic-computation symbolic-numerics

Keywords from Contributors

julialang numerical differentialequations neural-ode programming-language partial-differential-equations neural-differential-equations differential-algebraic-equations matrix-exponential automatic-differentiation

Last synced: 4 months ago · JSON representation ·

Repository

Basic Info

Host: GitHub
Owner: SciML
License: other
Language: Julia
Default Branch: master
Homepage: https://mtk.sciml.ai/dev/
Size: 1010 MB

Statistics

Stars: 1,549
Watchers: 27
Forks: 232
Open Issues: 502
Releases: 452

Topics

Created almost 8 years ago · Last pushed 4 months ago

Metadata Files

Readme Changelog Contributing License Citation

README.md

ModelingToolkit.jl

ModelingToolkit.jl is a modeling framework for high-performance symbolic-numeric computation in scientific computing and scientific machine learning. It allows for users to give a high-level description of a model for symbolic preprocessing to analyze and enhance the model. ModelingToolkit can automatically generate fast functions for model components like Jacobians and Hessians, along with automatically sparsifying and parallelizing the computations. Automatic transformations, such as index reduction, can be applied to the model to make it easier for numerical solvers to handle.

For information on using the package, see the stable documentation. Use the in-development documentation for the version of the documentation which contains the unreleased features.

Standard Library

For a standard library of ModelingToolkit components and blocks, check out the ModelingToolkitStandardLibrary

High-Level Examples

First, let's define a second order riff on the Lorenz equations, symbolically lower it to a first order system, symbolically generate the Jacobian function for the numerical integrator, and solve it.

```julia using OrdinaryDiffEqDefault, ModelingToolkit using ModelingToolkit: tnounits as t, Dnounits as D

@parameters σ ρ β @variables x(t) y(t) z(t)

eqs = [D(D(x)) ~ σ * (y - x), D(y) ~ x * (ρ - z) - y, D(z) ~ x * y - β * z]

@mtkcompile sys = System(eqs, t)

u0 = [D(x) => 2.0, x => 1.0, y => 0.0, z => 0.0]

p = [σ => 28.0, ρ => 10.0, β => 8 / 3]

tspan = (0.0, 100.0) prob = ODEProblem(sys, u0, tspan, p, jac = true) sol = solve(prob) using Plots plot(sol, idxs = (x, y)) ```

Lorenz2

This automatically will have generated fast Jacobian functions, making it more optimized than directly building a function. In addition, we can then use ModelingToolkit to compose multiple ODE subsystems. Now, let's define two interacting Lorenz equations and simulate the resulting Differential-Algebraic Equation (DAE):

```julia using DifferentialEquations, ModelingToolkit using ModelingToolkit: tnounits as t, Dnounits as D

@parameters σ ρ β @variables x(t) y(t) z(t)

eqs = [D(x) ~ σ * (y - x), D(y) ~ x * (ρ - z) - y, D(z) ~ x * y - β * z]

@named lorenz1 = System(eqs, t) @named lorenz2 = System(eqs, t)

@variables a(t) @parameters γ connections = [0 ~ lorenz1.x + lorenz2.y + a * γ] @mtkcompile connected = System(connections, t, systems = [lorenz1, lorenz2])

u0 = [lorenz1.x => 1.0, lorenz1.y => 0.0, lorenz1.z => 0.0, lorenz2.x => 0.0, lorenz2.y => 1.0, lorenz2.z => 0.0, a => 2.0]

p = [lorenz1.σ => 10.0, lorenz1.ρ => 28.0, lorenz1.β => 8 / 3, lorenz2.σ => 10.0, lorenz2.ρ => 28.0, lorenz2.β => 8 / 3, γ => 2.0]

tspan = (0.0, 100.0) prob = ODEProblem(connected, u0, tspan, p) sol = solve(prob)

using Plots plot(sol, idxs = (a, lorenz1.x, lorenz2.z)) ```

Citation

If you use ModelingToolkit.jl in your research, please cite this paper:

@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} }

Owner

Name: SciML Open Source Scientific Machine Learning
Login: SciML
Kind: organization
Email: contact@chrisrackauckas.com

Website: https://sciml.ai
Twitter: SciML_Org
Repositories: 170
Profile: https://github.com/SciML

Open source software for scientific machine learning

Citation (CITATION.bib)

@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}
}

@article{DifferentialEquations.jl-2017,
 author = {Rackauckas, Christopher and Nie, Qing},
 doi = {10.5334/jors.151},
 journal = {The Journal of Open Research Software},
 keywords = {Applied Mathematics},
 note = {Exported from https://app.dimensions.ai on 2019/05/05},
 number = {1},
 pages = {},
 title = {DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia},
 url = {https://app.dimensions.ai/details/publication/pub.1085583166 and http://openresearchsoftware.metajnl.com/articles/10.5334/jors.151/galley/245/download/},
 volume = {5},
 year = {2017}
}

Committers

Last synced: 8 months ago

All Time

Total Commits: 6,206
Total Committers: 137
Avg Commits per committer: 45.299
Development Distribution Score (DDS): 0.769

Past Year

Commits: 2,063
Committers: 37
Avg Commits per committer: 55.757
Development Distribution Score (DDS): 0.54

Top Committers

Name	Email	Commits
Yingbo Ma	m**5@g**m	1,432
Christopher Rackauckas	a**s@c**m	1,214
Aayush Sabharwal	a**l@g**m	1,137
vyudu	v**n@g**m	286
Shashi Gowda	g**a@m**u	261
Samuel Isaacson	i****s	235
Herman Sletmoen	h**n@g**m	164
Fredrik Bagge Carlson	b**n@g**m	129
Harrison Grodin	h**n@g**m	113
Venkateshprasad	3****k	100
Torkel	t**n@g**m	83
Benjamin Chung	c**e@g**m	73
Lucas Morton	2****n	60
Valentin Kaisermayer	v**r@b**u	53
ArnoStrouwen	a**n@t**e	52
CompatHelper Julia	c**y@j**g	51
Keno Fischer	k**o@j**m	46
Sebastian Micluța-Câmpeanu	s**5@p**e	40
Mason Protter	m**r@i**m	37
anand jain	a**j@u**u	35
Brad Carman	b**n@i**m	32
contradict	c**t@g**m	30
github-actions[bot]	4****]	28
Vaibhav Dixit	v**t@g**m	27
dd	dd	24
Pepijn de Vos	p**s@g**m	21
Sharan Yalburgi	s**i@g**m	19
xtalax	a**y@g**m	19
Chris Elrod	e**c@g**m	18
Dan Padilha	d**d@g**p	16
and 107 more...

Committer Domains (Top 20 + Academic)

juliacomputing.com: 4 outlook.de: 1 tool-temp.ch: 1 iitbhu.ac.in: 1 inria.fr: 1 simons-rock.edu: 1 colmryan.org: 1 jpsamaroo.me: 1 qq.com: 1 umich.edu: 1 fas.harvard.edu: 1 mailbox.tu-dresden.de: 1 tapscott.me: 1 wuerfel.io: 1 juliahub.com: 1 unibas.ch: 1 tae.com: 1 g.ecc.u-tokyo.ac.jp: 1 instron.com: 1 uchicago.edu: 1 mit.edu: 1 gtri.gatech.edu: 1 stonybrook.edu: 1 slcu.cam.ac.uk: 1 vt.edu: 1 stud.uni-goettingen.de: 1

Issues and Pull Requests

Last synced: 4 months ago

All Time

Total issues: 911
Total pull requests: 1,761
Average time to close issues: 9 months
Average time to close pull requests: 23 days
Total issue authors: 235
Total pull request authors: 73
Average comments per issue: 3.37
Average comments per pull request: 1.54
Merged pull requests: 1,304
Bot issues: 1
Bot pull requests: 134

Past Year

Issues: 345
Pull requests: 916
Average time to close issues: 13 days
Average time to close pull requests: 5 days
Issue authors: 94
Pull request authors: 40
Average comments per issue: 1.7
Average comments per pull request: 1.57
Merged pull requests: 702
Bot issues: 1
Bot pull requests: 59

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Top Authors

Issue Authors

TorkelE (114)
baggepinnen (90)
hersle (50)
ChrisRackauckas (39)
bradcarman (30)
isaacsas (25)
AayushSabharwal (24)
YingboMa (21)
B-LIE (20)
SebastianM-C (17)
cstjean (15)
Datseris (13)
ArnoStrouwen (13)
hexaeder (11)
mtiller-jh (10)

Pull Request Authors

AayushSabharwal (683)
ChrisRackauckas (153)
YingboMa (123)
github-actions[bot] (116)
baggepinnen (88)
hersle (73)
ven-k (56)
vyudu (56)
ArnoStrouwen (31)
BenChung (25)
SebastianM-C (24)
TorkelE (23)
contradict (21)
devmotion (21)
isaacsas (20)

Top Labels

Issue Labels

bug (436) question (43) discrete-time (26) arrays (19) control (12) initialization (11) enhancement (10) events (6) usability (6) documentation (5) good first issue (5) input-output (4) linearization (3) transform (2) analysis (1) feature (1) modelingtoolkitize (1) symbolic performance (1) wontfix (1) juliasimcompiler (1)

Pull Request Labels

dependencies (18) discrete-time (7) v10 (4) github_actions (1)

Packages

Total packages: 3
Total downloads:
- julia 1,911 total

Total dependent packages: 90
(may contain duplicates)
Total dependent repositories: 14
(may contain duplicates)
Total versions: 1,359

juliahub.com: ModelingToolkit

Homepage: https://mtk.sciml.ai/dev/
Documentation: https://docs.juliahub.com/General/ModelingToolkit/stable/
License: MIT
Latest release: 10.20.0
published 5 months ago

Versions: 451
Dependent Packages: 90
Dependent Repositories: 14
Downloads: 1,911 Total

Rankings

Stargazers count: 0.3%

Forks count: 0.4%

Dependent packages count: 0.9%

Average: 1.0%

Dependent repos count: 2.4%

Last synced: 4 months ago

proxy.golang.org: github.com/SciML/ModelingToolkit.jl

Documentation: https://pkg.go.dev/github.com/SciML/ModelingToolkit.jl#section-documentation
License: other
Latest release: v10.21.0+incompatible
published 4 months ago

Versions: 454
Dependent Packages: 0
Dependent Repositories: 0

Rankings

Dependent packages count: 7.0%

Average: 8.2%

Dependent repos count: 9.3%

Last synced: 4 months ago

proxy.golang.org: github.com/sciml/modelingtoolkit.jl

Documentation: https://pkg.go.dev/github.com/sciml/modelingtoolkit.jl#section-documentation
License: other
Latest release: v10.21.0+incompatible
published 4 months ago

Versions: 454
Dependent Packages: 0
Dependent Repositories: 0

Rankings

Dependent packages count: 7.0%

Average: 8.2%

Dependent repos count: 9.3%

Last synced: 4 months ago

Dependencies

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