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Re: [Swarm-modeling] Automatic Differentiation of Programs with Discrete

From: Gross, Louis J
Subject: Re: [Swarm-modeling] Automatic Differentiation of Programs with Discrete Randomness
Date: Sat, 22 Oct 2022 21:13:42 +0000

Paul, Glen et al.,

        I recently taught a course on Agent-Based and Hybrid Modeling in Ecology – all the notes and links to references are posted at


so this contains my perspective on the current state of ABMs at least in application to ecology.

    Stay well,




Louis J. Gross (he, him, his)

Chancellor’s Professor Emeritus and Emeritus Distinguished Professor

     of Ecology and Evolutionary Biology and Mathematics

Director Emeritus, National Institute for Mathematical and Biological

     Synthesis (NIMBioS.org)

Director Emeritus The Institute for Environmental Modeling

University of Tennessee - Knoxville

President, 2006-2007, 2021-2022, UTK Faculty Senate

Past-President, 2003-2005, Society for Mathematical Biology




From: Swarm-modeling <swarm-modeling-bounces+gross=tiem.utk.edu@nongnu.org> on behalf of Paul Johnson <pauljohn32@freefaculty.org>
Date: Thursday, October 20, 2022 at 5:40 PM
To: swarm-modeling@nongnu.org <swarm-modeling@nongnu.org>, glen e ropella <gepr@agent-based-modeling.com>
Subject: Re: [Swarm-modeling] Automatic Differentiation of Programs with Discrete Randomness

You don't often get email from pauljohn32@freefaculty.org. Learn why this is important

Neat! More importantly, what else going on with Glen?

I left KU, working in business. But I still get calls from time to time asking for agent based models.

I wondered what is the state of the art?


Paul E. Johnson
Senior Data Scientist, H&R Block Corporate Headquarters
Professor Emeritus, University of Kansas


On October 20, 2022 1:11:50 PM CDT, glen e ropella <gepr@agent-based-modeling.com> wrote:


Automatic differentiation (AD), a technique for constructing new programs which compute the derivative of an original program, has become ubiquitous throughout scientific computing and deep learning due to the improved performance afforded by gradient-based optimization. However, AD systems have been restricted to the subset of programs that have a continuous dependence on parameters. Programs that have discrete stochastic behaviors governed by distribution parameters, such as flipping a coin with probability of being heads, pose a challenge to these systems because the connection between the result (heads vs tails) and the parameters (p) is fundamentally discrete. In this paper we develop a new reparameterization-based methodology that allows for generating programs whose expectation is the derivative of the expectation of the original program. We showcase how this method gives an unbiased and low-variance estimator which is as automated as traditional AD mechanisms. We demonstrate unbiased forward-mode AD of discrete-time Markov chains, agent-based models such as Conway's Game of Life, and unbiased reverse-mode AD of a particle filter. Our code is available at this https URL.


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