How can we use neural ODE with a limited data set? For example, sometimes, we do not have data for all compartments, so how can we define the NODE problem?
Suppose we have three state variables and real data only for one state. Can we still apply Neural ODE in this case? And if we can, then how?
Thank you in advance for all of you.
You can, but of course the more data the better predictions.
It outputs a time series. Just subset that time series to what matches the data.
Thank you for the response, but my question was not about the time point issue. It was like in the traditional SIR model; when we did not have measurements for all compartments, including S, I, and R, after doing structural identifiability analysis, we could find how many parameters can we estimate with available data. So my question is, do we have the same process in NODE? How can I find examples like this?
I found some examples implemented in Julia, but in most of them, the number of measurements and a number of compartments in the modeling is the same.
A pure neural ODE definitely cannot do predictions on what’s not measured. At best a UDE approach could at least try.