Direct solutions of the master equation - Githubissues

SciML / ModelingToolkit.jl

An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physics-informed machine learning and automated transformations of differential equations

https://mtk.sciml.ai/dev/

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Direct solutions of the master equation #457

Open ChrisRackauckas opened 6 years ago

ChrisRackauckas commented 6 years ago

Spectral methods:

https://uu.diva-portal.org/smash/get/diva2:117236/FULLTEXT01.pdf http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.142.2891 http://www.it.uu.se/research/publications/lic/2006-007/paperB.pdf https://vtechworks.lib.vt.edu/handle/10919/30018 http://epubs.siam.org/doi/abs/10.1137/070689759 http://ieeexplore.ieee.org/document/6425804/

ChrisRackauckas commented 6 years ago

Additionally, if the maximum number of particles is known (or assumed via truncation), one gets a linear ODE:

https://arxiv.org/abs/1410.1934 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3953644/ https://pdfs.semanticscholar.org/ec67/e296e912f2f1d75534c57e24d758449fb19a.pdf (?) http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7799362

This then harkens back to disccussions with @jagot on https://github.com/JuliaDiffEq/OrdinaryDiffEq.jl/issues/249 https://github.com/JuliaDiffEq/OrdinaryDiffEq.jl/issues/115 and https://github.com/JuliaDiffEq/OrdinaryDiffEq.jl/issues/116

A lazy A could be constructed for the master equation operator to then solve via expmv! algorithms.

ChrisRackauckas commented 6 years ago

Monomolecular reaction constrained case: https://link.springer.com/article/10.1007%2Fs00285-006-0034-x