Alternative ReactionNetwork Lowering

[ChrisRackauckas]

• Linear Noise Approximation (https://tanhevg.github.io/GpABC.jl/latest/overview-lna/, https://arxiv.org/pdf/1509.00612.pdf, https://arxiv.org/pdf/1608.06582.pdf)
• Minimal continuous-time Markov chains (https://www.researchgate.net/publication/317716528_A_Minimal_Continuous-Time_Markov_Pharmacometric_Model)
• Master Equation (as a set of ODEs)
• Master Equation (as a PDESystem)
• Affine noise (ReactionSystem -> Affine Noise? (as well as non parameterized noise) ModelingToolkit.jl#456)
• Full regular jumps

It would be nice to automatically allow for generating this set of ODEs from the ReactionNetwork.

[isaacsas]

Tau-leaping too.

[isaacsas]

What's the master equation as a PDESystem here refer to? Do you mean a PDE for the corresponding generating function, or for spatial particle systems?

[ChrisRackauckas]

For the probability distribution

[isaacsas]

Ahh, ok so you are thinking of it as a differential-difference equation. Could we use some of the infinite dimensional LA tooling for representing the adjoint of the generator in the master equation? (I know next to nothing about whether it would be worthwhile, but that would presumably allow us to "exactly" represent the equation prior to trying to solve it numerically.)

[ChrisRackauckas]

We can represent it via an InfiniteArray of equations, and then find ways to deal with it. Closed systems would be finite of course.

[isaacsas]

Yup, it would just be nice to have a representation that is "exact", so that different methods can truncate / approximate as they see fit.

[vnminin]

@ChrisRackauckas, UCI-MCSB PhD student @yushang-lai is trying to implement LNA inference in Turing. We have run into a problem with the covariance matrix ODE: https://discourse.julialang.org/c/domain/probprog/48

Do you have any advice for us? Thanks!

[ChrisRackauckas]

@vnminin oh, someone just put up a whole library of moment closures: https://github.com/augustinas1/MomentClosure.jl

[vnminin]

Thanks, @ChrisRackauckas. Maybe helpful, but hard to tell, because there is almost no documentation.

Our main problem is with Turing not liking our way of enforcing positive definiteness of the covariance matrix -- ODE returns a nearly positive definite matrix

[ChrisRackauckas]

https://augustinas1.github.io/MomentClosure.jl/dev/

[ChrisRackauckas]

For undocumented libraries, look at their tests: https://github.com/augustinas1/MomentClosure.jl/blob/main/test/moment_convert_tests.jl