DiffEqFlux.jl - A Julia Library for Neural Differential Equations

TL;DR

DiffEqFlux.jl is a Julia library that integrates neural networks with differential equations, enabling advanced modeling and solving techniques for data science applications, including neural differential equations and stochastic models.

Contribution

It introduces a Julia library that seamlessly combines differential equations with neural networks, leveraging DifferentialEquations.jl for robust solutions in machine learning contexts.

Findings

Successful integration of differential equations into neural networks.

Demonstrated handling of delay and stochastic differential equations within neural models.

Showcased advanced adjoint methods for efficient backpropagation.

Abstract

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. This is followed by a demonstration of delay differential equations and stochastic differential equations inside of neural networks. We show high-level functionality for defining neural ordinary differential equations (neural networks embedded into the differential equation) and describe the extra models in the Flux model zoo which includes neural stochastic differential equations. We conclude by discussing the various adjoint methods used for backpropogation of the differential equation solvers. DiffEqFlux.jl is an important contribution to the area, as it allows the full weight of the differential equation solvers developed from decades of research in the scientific computing field to be readily applied to the challenges posed by machine learning and data science.