DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia
By Christopher Rackauckas, Qing Nie. Journal of Open Research Software, 2017
1,698 citations recorded by the source corpus.
DifferentialEquations.jl is a package for solving differential equations in Julia. It covers discrete equations (function maps, discrete stochastic (Gillespie/Markov) simulations), ordinary differential equations, stochastic differential equations, algebraic differential equations, delay differential equations, hybrid differential equations, jump diffusions, and (stochastic) partial differential equations. Through extensive use of multiple dispatch, metaprogramming, plot recipes, foreign function interfaces (FFI), and call-overloading, DifferentialEquations.jl offers a unified user interface to solve and analyze various forms of differential equations while not sacrificing features or performance. Many modern features are integrated into the solvers, such as allowing arbitrary user-defined number systems for high-precision and arithmetic with physical units, built-in multithreading and parallelism, and symbolic calculation of Jacobians. Integrated into the package is an algorithm testing and benchmarking suite to both ensure accuracy and serve as an easy way for researchers to develop and distribute their own methods. Together, these features build a highly extendable suite which is feature-rich and highly performant. Funding statement: This work was partially supported by NIH grants P50GM76516 and R01GM107264 and NSF grants DMS1562176 and DMS1161621. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1321846, the National Academies of Science, Engineering, and Medicine via the Ford Foundation, and the National Institutes of Health Award T32 EB009418. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the NIH.
Subfields: Computer Networks and Communications, Plant Science
View Paper: https://www.semanticscholar.org/paper/34473be212082c64ee6c944758988fd64c9c9ef4
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Citations in the corpus
- Optim: A mathematical optimization package for Julia (2018, background): “…academic research, including optimal con-trol (Riseth, Dewynne, and Farmer 2017; Riseth 2017a), parameter estimation (Riseth and Taylor-King 2017; Rackauckas and Nie 2017; and Dony, He, and Stumpf 2018), quantum physics (Damle, Levitt, and Lin 2018), crystalline modelling (Chen and Ortner 2017;…”
- Universal Differential Equations for Scientific Machine Learning (2020, methodology): “[35] Christopher Rackauckas and Qing Nie.”
- Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers (2020, background): “Over the last two decades the SUNDIALS codes have been used in a number of applications on small to large-scale computing systems [22, 28, 29, 33–35, 51, 56, 73, 76] as well as in other mathematical libraries and frameworks [3–5, 54, 61, 67, 75, 76], garnering more than 90,000 downloads in 2020.”
- Gotta Go Fast When Generating Data with Score-Based Models (2021, methodology): “…Platen, 1992] 1.0 Yes Did not converge ImplicitRKMil [Kloeden and Platen, 1992] 1.0 Yes Did not converge ISSEM 0.5 Yes Did not converge Here, we report the preliminary experiments we ran with the DifferentialEquations.jl Julia package [Rackauckas and Nie, 2017a] before devising our own SDE solver.”