Feasibility of optimizing large ODE

[mabuni1998]

Hi,

I am interested in using the framework for doing optimal control on a large ODE. I come from quantum optics, and thus we normally formulate our problems as large matrices (quantum mechanics is a system of linear ODEs). I have recently used Symbolics.jl to instead derive the ODE symbolically and successfully inputed these equations into the OptimalControl.jl framework and begun optimizing!

The problem I considered consisted of 80 ODEs, and I notice already now a long first-time execution time of solve() (like 5min). I assume this is because it is taking a long time to convert all the symbolic equations into executable functions (I know the documentation also says it takes a long time because of the sparsity setup of the Jacobian, but the second time I run solve(), the time it takes is much less).

I am now interested in considering larger systems (maybe more than 1000 ODEs), and I want to hear your thoughts on the feasibility? Of course, this is already a huge system, so it is a difficult problem no matter what, but I am interested in hearing whether you think it is possible to use OptimalControl.jl to convert the equations and subsequently do the optimization or whether this will simply be too large to do symbolically with the parsers you use. Maybe this is helped by MADNLP and ExaModels?

best Matias

[jbcaillau]

hi @mabuni1998, thank you for sharing this. we are about to release the v1.1 of OptimalControl.jl that will add support for solving on CPU and GPU thanks to ExaModels + MadNLP(GPU). let's keep in touch and see if this helps 🤞🏽

PS. if you have some public code to share and illustrate what you've done, we're interested to have a look!

[mabuni1998]

I will definitely check version 1.1 out, thanks! I sent a private message with some code I am working on at the moment that might be public later on.

[ocots]

Here is some documentation to solve on GPU: https://control-toolbox.org/OptimalControl.jl/stable/manual-solve-gpu.html.