ImplicitDiscreteSolve

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

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

Science Score: 54.0%

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

  • CITATION.cff file
    Found CITATION.cff file
  • codemeta.json file
    Found codemeta.json file
  • .zenodo.json file
    Found .zenodo.json file
  • DOI references
  • Academic publication links
  • Committers with academic emails
    23 of 156 committers (14.7%) from academic institutions
  • Institutional organization owner
  • JOSS paper metadata
  • Scientific vocabulary similarity
    Low similarity (13.3%) to scientific vocabulary

Keywords

adaptive differential-equations differentialequations event-handling hacktoberfest high-performance julia ode ordinary-differential-equations scientific-machine-learning sciml

Keywords from Contributors

sde dae dde pde neural-ode stochastic-differential-equations partial-differential-equations delay-differential-equations neural-differential-equations neural-sde
Last synced: 6 months ago · JSON representation ·

Repository

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

Basic Info
Statistics
  • Stars: 604
  • Watchers: 17
  • Forks: 233
  • Open Issues: 381
  • Releases: 490
Topics
adaptive differential-equations differentialequations event-handling hacktoberfest high-performance julia ode ordinary-differential-equations scientific-machine-learning sciml
Created over 9 years ago · Last pushed 6 months ago
Metadata Files
Readme Contributing License Citation

README.md

OrdinaryDiffEq.jl

Join the chat at https://julialang.zulipchat.com #sciml-bridged Global Docs

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ColPrac: Contributor's Guide on Collaborative Practices for Community Packages SciML Code Style

OrdinaryDiffEq.jl is a component package in the DifferentialEquations ecosystem. It holds the ordinary differential equation solvers and utilities. While completely independent and usable on its own, users interested in using this functionality should check out DifferentialEquations.jl.

Installation

Assuming that you already have Julia correctly installed, it suffices to import OrdinaryDiffEq.jl in the standard way:

julia import Pkg; Pkg.add("OrdinaryDiffEq");

API

OrdinaryDiffEq.jl is part of the SciML common interface, but can be used independently of DifferentialEquations.jl. The only requirement is that the user passes an OrdinaryDiffEq.jl algorithm to solve. For example, we can solve the ODE tutorial from the docs using the Tsit5() algorithm:

julia using OrdinaryDiffEq f(u, p, t) = 1.01 * u u0 = 1 / 2 tspan = (0.0, 1.0) prob = ODEProblem(f, u0, tspan) sol = solve(prob, Tsit5(), reltol = 1e-8, abstol = 1e-8) using Plots plot(sol, linewidth = 5, title = "Solution to the linear ODE with a thick line", xaxis = "Time (t)", yaxis = "u(t) (in μm)", label = "My Thick Line!") # legend=false plot!(sol.t, t -> 0.5 * exp(1.01t), lw = 3, ls = :dash, label = "True Solution!")

That example uses the out-of-place syntax f(u,p,t), while the inplace syntax (more efficient for systems of equations) is shown in the Lorenz example:

julia using OrdinaryDiffEq function lorenz!(du, u, p, t) du[1] = 10.0(u[2] - u[1]) du[2] = u[1] * (28.0 - u[3]) - u[2] du[3] = u[1] * u[2] - (8 / 3) * u[3] end u0 = [1.0; 0.0; 0.0] tspan = (0.0, 100.0) prob = ODEProblem(lorenz!, u0, tspan) sol = solve(prob, Tsit5()) using Plots; plot(sol, idxs = (1, 2, 3))

Very fast static array versions can be specifically compiled to the size of your model. For example:

julia using OrdinaryDiffEq, StaticArrays function lorenz(u, p, t) SA[10.0(u[2] - u[1]), u[1] * (28.0 - u[3]) - u[2], u[1] * u[2] - (8 / 3) * u[3]] end u0 = SA[1.0; 0.0; 0.0] tspan = (0.0, 100.0) prob = ODEProblem(lorenz, u0, tspan) sol = solve(prob, Tsit5())

For "refined ODEs", like dynamical equations and SecondOrderODEProblems, refer to the DiffEqDocs. For example, in DiffEqTutorials.jl we show how to solve equations of motion using symplectic methods:

julia function HH_acceleration!(dv, v, u, p, t) x, y = u dx, dy = dv dv[1] = -x - 2x * y dv[2] = y^2 - y - x^2 end initial_positions = [0.0, 0.1] initial_velocities = [0.5, 0.0] prob = SecondOrderODEProblem(HH_acceleration!, initial_velocities, initial_positions, tspan) sol2 = solve(prob, KahanLi8(), dt = 1 / 10);

Other refined forms are IMEX and semi-linear ODEs (for exponential integrators).

Available Solvers

For the list of available solvers, please refer to the DifferentialEquations.jl ODE Solvers, Dynamical ODE Solvers, and the Split ODE Solvers pages.

Owner

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

Open source software for scientific machine learning

Citation (CITATION.bib)

@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: 8,151
  • Total Committers: 156
  • Avg Commits per committer: 52.25
  • Development Distribution Score (DDS): 0.605
Past Year
  • Commits: 1,957
  • Committers: 36
  • Avg Commits per committer: 54.361
  • Development Distribution Score (DDS): 0.661
Top Committers
Name Email Commits
Christopher Rackauckas a****s@c****m 3,220
Yingbo Ma m****5@g****m 785
ParamThakkar123 p****4@g****m 571
jClugstor j****n@g****m 367
oscarddssmith o****h@j****m 305
David Widmann d****b@d****e 238
Xingjian Guo x****3@n****u 215
Utkarsh r****0@g****m 213
Hendrik Ranocha m****l@r****e 209
Kanav Gupta k****0@g****m 173
deeepeshthakur d****r@g****m 145
Shreyas Ekanathan s****9@g****m 139
sipah00 s****0@g****m 116
ArnoStrouwen a****n@t****e 104
Saurabh Agarwal s****l@g****m 97
CompatHelper Julia c****y@j****g 80
Vedant Puri v****i@g****m 68
Biswajit Ghosh b****8@i****n 58
ErikQQY 2****3@q****m 53
Collin Wittenstein c****s@s****e 51
Chris Elrod e****c@g****m 48
Junpeng j****x@g****m 48
Diogo Netto d****n@g****m 44
hlw h****n@i****m 40
Henry Langner 1****r 38
Gerd Steinebach G****h@h****e 36
Gaurav Arya g****2@g****m 32
Konstantin Althaus k****s@t****e 29
Pepijn de Vos p****s@j****m 25
Aayush Sabharwal a****l@g****m 25
and 126 more...

Issues and Pull Requests

Last synced: 6 months ago

All Time
  • Total issues: 265
  • Total pull requests: 1,177
  • Average time to close issues: 6 months
  • Average time to close pull requests: about 2 months
  • Total issue authors: 128
  • Total pull request authors: 85
  • Average comments per issue: 9.97
  • Average comments per pull request: 1.95
  • Merged pull requests: 808
  • Bot issues: 0
  • Bot pull requests: 197
Past Year
  • Issues: 92
  • Pull requests: 476
  • Average time to close issues: 7 days
  • Average time to close pull requests: 5 days
  • Issue authors: 57
  • Pull request authors: 42
  • Average comments per issue: 2.33
  • Average comments per pull request: 1.63
  • Merged pull requests: 329
  • Bot issues: 0
  • Bot pull requests: 35
Top Authors
Issue Authors
  • ChrisRackauckas (29)
  • ranocha (18)
  • oscardssmith (15)
  • topolarity (8)
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  • ArnoStrouwen (6)
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  • hersle (5)
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  • Ickaser (4)
  • cwittens (4)
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  • jClugstor (3)
  • homocomputeris (3)
Pull Request Authors
  • ChrisRackauckas (304)
  • oscardssmith (193)
  • github-actions[bot] (186)
  • ParamThakkar123 (52)
  • jClugstor (47)
  • AayushSabharwal (34)
  • ChrisRackauckas-Claude (25)
  • Shreyas-Ekanathan (22)
  • ranocha (19)
  • termi-official (16)
  • ArnoStrouwen (16)
  • ErikQQY (15)
  • vyudu (14)
  • gstein3m (13)
  • cwittens (13)
Top Labels
Issue Labels
bug (121) new-algorithm (23) help wanted (4) question (3) easy (2) DAE (2) low-priority (1) high-priority (1) GSoC (1)
Pull Request Labels
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Packages

  • Total packages: 36
  • Total downloads:
    • julia 166,249 total
  • Total dependent packages: 137
    (may contain duplicates)
  • Total dependent repositories: 59
    (may contain duplicates)
  • Total versions: 699
juliahub.com: OrdinaryDiffEq

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 388
  • Dependent Packages: 137
  • Dependent Repositories: 59
  • Downloads: 5,372 Total
Rankings
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Dependent packages count: 0.6%
Dependent repos count: 0.8%
Average: 0.8%
Stargazers count: 1.5%
Last synced: 6 months ago
juliahub.com: OrdinaryDiffEqCore

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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  • Dependent Packages: 0
  • Dependent Repositories: 0
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Dependent packages count: 16.3%
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juliahub.com: OrdinaryDiffEqDifferentiation

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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  • Dependent Packages: 0
  • Dependent Repositories: 0
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Dependent repos count: 3.2%
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Dependent packages count: 16.3%
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juliahub.com: OrdinaryDiffEqRosenbrock

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 22
  • Dependent Packages: 0
  • Dependent Repositories: 0
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Dependent packages count: 16.3%
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juliahub.com: OrdinaryDiffEqBDF

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 14
  • Dependent Packages: 0
  • Dependent Repositories: 0
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juliahub.com: OrdinaryDiffEqSDIRK

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 7
  • Dependent Packages: 0
  • Dependent Repositories: 0
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Dependent repos count: 3.2%
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Dependent packages count: 16.3%
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juliahub.com: OrdinaryDiffEqFIRK

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 17
  • Dependent Packages: 0
  • Dependent Repositories: 0
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Dependent repos count: 3.2%
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Dependent packages count: 16.3%
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juliahub.com: OrdinaryDiffEqExtrapolation

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 10
  • Dependent Packages: 0
  • Dependent Repositories: 0
  • Downloads: 4,987 Total
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Dependent repos count: 3.2%
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Dependent packages count: 16.3%
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juliahub.com: OrdinaryDiffEqExponentialRK

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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  • Dependent Packages: 0
  • Dependent Repositories: 0
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juliahub.com: OrdinaryDiffEqIMEXMultistep

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 7
  • Dependent Packages: 0
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juliahub.com: OrdinaryDiffEqStabilizedIRK

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 6
  • Dependent Packages: 0
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Dependent packages count: 16.3%
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juliahub.com: OrdinaryDiffEqPDIRK

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 7
  • Dependent Packages: 0
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juliahub.com: OrdinaryDiffEqDefault

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 8
  • Dependent Packages: 0
  • Dependent Repositories: 0
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Dependent packages count: 16.3%
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juliahub.com: OrdinaryDiffEqNonlinearSolve

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 22
  • Dependent Packages: 0
  • Dependent Repositories: 0
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Dependent packages count: 16.3%
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juliahub.com: OrdinaryDiffEqTsit5

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 6
  • Dependent Packages: 0
  • Dependent Repositories: 0
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juliahub.com: OrdinaryDiffEqLowOrderRK

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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  • Dependent Packages: 0
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Dependent repos count: 3.2%
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Dependent packages count: 16.3%
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juliahub.com: OrdinaryDiffEqVerner

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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  • Dependent Packages: 0
  • Dependent Repositories: 0
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juliahub.com: OrdinaryDiffEqFunctionMap

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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juliahub.com: OrdinaryDiffEqLowStorageRK

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 9
  • Dependent Packages: 0
  • Dependent Repositories: 0
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juliahub.com: OrdinaryDiffEqStabilizedRK

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 7
  • Dependent Packages: 0
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juliahub.com: OrdinaryDiffEqSSPRK

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 7
  • Dependent Packages: 0
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juliahub.com: OrdinaryDiffEqExplicitRK

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 4
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juliahub.com: OrdinaryDiffEqRKN

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 6
  • Dependent Packages: 0
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juliahub.com: OrdinaryDiffEqNordsieck

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 4
  • Dependent Packages: 0
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juliahub.com: OrdinaryDiffEqAdamsBashforthMoulton

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 6
  • Dependent Packages: 0
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juliahub.com: OrdinaryDiffEqQPRK

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 5
  • Dependent Packages: 0
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juliahub.com: OrdinaryDiffEqHighOrderRK

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 6
  • Dependent Packages: 0
  • Dependent Repositories: 0
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juliahub.com: OrdinaryDiffEqLinear

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 6
  • Dependent Packages: 0
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Dependent repos count: 3.2%
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juliahub.com: OrdinaryDiffEqSymplecticRK

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 7
  • Dependent Packages: 0
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juliahub.com: OrdinaryDiffEqFeagin

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 5
  • Dependent Packages: 0
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juliahub.com: OrdinaryDiffEqPRK

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 5
  • Dependent Packages: 0
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juliahub.com: OrdinaryDiffEqFIRKGenerator

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 2
  • Dependent Packages: 0
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Dependent packages count: 16.3%
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juliahub.com: OrdinaryDiffEqSIMDRK

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 2
  • Dependent Packages: 0
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  • Downloads: 2 Total
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Stargazers count: 1.1%
Dependent repos count: 8.2%
Average: 11.2%
Dependent packages count: 35.2%
Last synced: 6 months ago
juliahub.com: OrdinaryDiffEqTaylorSeries

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 4
  • Dependent Packages: 0
  • Dependent Repositories: 0
Rankings
Dependent repos count: 8.2%
Average: 21.8%
Dependent packages count: 35.4%
Last synced: 6 months ago
juliahub.com: SimpleImplicitDiscreteSolve

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 4
  • Dependent Packages: 0
  • Dependent Repositories: 0
Rankings
Dependent repos count: 8.4%
Average: 22.4%
Dependent packages count: 36.3%
Last synced: 6 months ago
juliahub.com: ImplicitDiscreteSolve

High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differential equations (neural ODEs) and scientific machine learning (SciML)

  • Versions: 7
  • Dependent Packages: 0
  • Dependent Repositories: 0
  • Downloads: 1,093 Total
Rankings
Dependent repos count: 8.5%
Average: 22.5%
Dependent packages count: 36.6%
Last synced: 6 months ago

Dependencies

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