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2019

DiffEqFlux.jl - A Julia Library for Neural Differential Equations

Rackauckas, Chris, Innes, Mike, Ma, Yingbo et al.

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DiffEqFlux.jl is a library for fusing neural networks and differential equations.

In this work we describe differential equations from the viewpoint of data science and discuss the complementary nature between machine learning models and differential equations.
We demonstrate the ability to incorporate DifferentialEquations.jl-defined differential equation problems into a Flux-defined neural network, and vice versa.
The advantages of being able to use the entire DifferentialEquations.jl suite for this purpose is demonstrated by counter examples where simple integration strategies fail, but the sophisticated integration strategies provided by the DifferentialEquations.jl library succeed.

DiffEqFlux.jl - A Julia Library for Neural Differential Equations · Around

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Forward-Mode Automatic Differentiation in Julia
Original
Jarrett Revels, Miles Lubin, and Theodore Papamarkou · 2016
Earlier work this paper cites.
DifferentialEquations.jl - A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia
Christopher Rackauckas and Qing Nie · 2017
Earlier work this paper cites.
Neural Ordinary Differential Equations
Original
Ricky T. Q. Chen, Yulia Rubanova, Jesse Bettencourt, and David Duvenaud · 2018
Earlier work this paper cites.

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Christopher Rackauckas, Yingbo Ma, Vaibhav Dixit, Xingjian Guo, Mike Innes, Jarrett Revels, Joakim Nyberg, and Vijay Ivaturi · 2018
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Then

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Later among the works it cites.

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