How to optimize multiple ODEs at once?

Specific Domains Modelling & Simulations
1

Hello,
I have a set of several ODEs to describe the interaction between six bacteria and six phages (one for bacterium). Collectively, I have 18 equations with 7 parameters.
What is the approach to finding the values of the parameters that generate a “stable environment”? For instance, I can generate a stable environment with two bacteria and two phages, with cyclic but stable values:

initialCondition
initialCondition1920×1440 259 KB

Finding the values that generate such a conditions for 18 ODEs is a bit cumbersome. Is there a procedure to follow? (I am a biologist, not a computer scientist or a mathematician…)
Thank you.

2

Check out how to do parameter estimation for ordinary differential equations here:

https://docs.sciml.ai/SciMLSensitivity/dev/tutorials/parameter_estimation_ode/

What you need to do is then just change the loss function from a loss that calculates the cost of a data fit to a loss that measures how stable the solution is.

1 Like
3

Thank you. I need to let this info sink…