How to speed up integration of big ODE system?

Dear all,

My problem relating to chemical reaction field involves an ODE system of [37000 37000]. May I ask if we have any way to make a computational time for ODE integration faster?

I already used 'sparse' to remove zero elements and it reduce computational time 2-3 times, but still takes 2-3 hours for one simulation and 13-15 hours for parameter estimation task.

I have searched for a solution, many suggested to compile my problem to .c and then do simulation (e.g., AMICI toolbox). This approach is a really good idea. I have tried but the compilation took really long time with big ODE system and did not even seem to complete.

I would appreciate all suggestion from you.

Thanks for stopping by.

Best regards,

[Torsten]

You mean you have 37000 equations for 37000 unknowns ?

Best wishes

Torsten.

[Hoang Nguyen]

Hi Torsten,

Yes, it is a 37000-equation ODE system.

In ODE function, I provide, let's say, a Jacob matrix of 37000 rows * 37000 columns (this is a matrix of reaction rate constant).

we have, for example,

function rhs = ODEmodel(t,c,Jacob)
         rhs = Jacob * c(concentration vector)
end

[Torsten]

I guess you already supply the Jacobian matrix for ode15s ?

https://de.mathworks.com/help/matlab/ref/odeset.html

Best wishes

Torsten.

[Hoang Nguyen]

Yes, I did. I set the options = odeset('Jacobian',jacob).

Do you have any suggestion to speed up the ODE integration?

Thanks for still being here :)