Rules to ODEs

[kris-brown]

A potential feature to implement: in section 6 of https://lmcs.episciences.org/6628 (the "voter model") there is an example which uses a combinatorial analysis of rewrite rules and produces continuous time evolution dynamics. This requires the computation of partial overlaps between rewrite rules.

[kris-brown]

with AlgebraicJulia/Catlab.jl#821 this is now possible

[jpfairbanks]

How long do you think it would talk to implement their process?

[kris-brown]

It's definitely a research project with the potential of unknowns to pop up, but I'd guess 1-3 mo if it's something I occasionally work on.

I can already see that AlgebraicJulia/Catlab.jl#860 will be prerequisite since it works with spans up to isomorphism

[jpfairbanks]

Ok so not something we can knock out for a quick demo!

[slwu89]

I used to be really interested in this stuff (limiting behavior of stochastic systems), here's a nice introduction that introduces it generically https://www.sciencedirect.com/science/article/pii/S0166531613000023

Hope it helps somehow. There was some later work that extended it to non-Markovian systems, getting integro-differential systems instead of ODEs.