www.Autodiff.org - Publication: Automatic differentiation and the optimization of differential equation models in biology

Automatic differentiation and the optimization of differential equation models in biology

- Article in a journal -

Area
Ordinary Differential Equations

Published in
Frontiers in Ecology and Evolution

Year
2022

Abstract
A computational revolution unleashed the power of artificial neural networks. At the heart of that revolution is automatic differentiation, which calculates the derivative of a performance measure relative to a large number of parameters. Differentiation enhances the discovery of improved performance in large models, an achievement that was previously difficult or impossible. Recently, a second computational advance optimizes the temporal trajectories traced by differential equations. Optimization requires differentiating a measure of performance over a trajectory, such as the closeness of tracking the environment, with respect to the parameters of the differential equations. Because model trajectories are usually calculated numerically by multistep algorithms, such as Runge-Kutta, the automatic differentiation must be passed through the numerical algorithm. This article explains how such automatic differentiation of trajectories is achieved. It also discusses why such computational breakthroughs are likely to advance theoretical and statistical studies of biological problems, in which one can consider variables as dynamic paths over time and space. Many common problems arise between improving success in computational learning models over performance landscapes, improving evolutionary fitness over adaptive landscapes, and improving statistical fits to data over information landscapes.

BibTeX
@ARTICLE{
         Frank2022Ada,
       author = "Frank, Steven A.",
       title = "Automatic differentiation and the optimization of differential equation models in
         biology",
       journal = "Frontiers in Ecology and Evolution",
       volume = "10",
       year = "2022",
       url =
         "https://www.frontiersin.org/journals/ecology-and-evolution/articles/10.3389/fevo.2022.1010278",
       doi = "10.3389/fevo.2022.1010278",
       issn = "2296-701X",
       abstract = "A computational revolution unleashed the power of artificial neural networks. At
         the heart of that revolution is automatic differentiation, which calculates the derivative of a
         performance measure relative to a large number of parameters. Differentiation enhances the discovery
         of improved performance in large models, an achievement that was previously difficult or impossible.
         Recently, a second computational advance optimizes the temporal trajectories traced by differential
         equations. Optimization requires differentiating a measure of performance over a trajectory, such as
         the closeness of tracking the environment, with respect to the parameters of the differential
         equations. Because model trajectories are usually calculated numerically by multistep algorithms,
         such as Runge-Kutta, the automatic differentiation must be passed through the numerical algorithm.
         This article explains how such automatic differentiation of trajectories is achieved. It also
         discusses why such computational breakthroughs are likely to advance theoretical and statistical
         studies of biological problems, in which one can consider variables as dynamic paths over time and
         space. Many common problems arise between improving success in computational learning models over
         performance landscapes, improving evolutionary fitness over adaptive landscapes, and improving
         statistical fits to data over information landscapes.",
       ad_area = "Ordinary Differential Equations"
}

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