Hi,
I'm loving the idea for this competition but I'd like some clarification regarding the possibility of negative concentrations. It seems to me that for this class of ODEs, and disregarding inputs, when we would simulate a system from an initial condition in the positive orthant (R^15_+) the solution remains in the positive orthant for all t. This makes sense because concentrations cannot become negative I assume.
However, I’m guessing that the way the inputs are modeled is not really physical and that from most initial conditions it would be possible to drive the concentrations to negative values by choosing appropriate inputs… This raises two questions for me:
1. I’m assuming that for all simulations provided as training data the inputs were chosen so that the concentrations don’t become negative and that any negative values we see in the data are simply due to the added measurement noise. Is this the case or are there any additional measures taken to ensure concentrations remain positive at all times in the simulated data?
2. How would negative concentrations work for evaluation? Do we also have to make sure that our inputs don’t result in negative concentrations for any species as that wouldn’t be physically meaningful? Is this penalized in some way?
Best Regards,
João
Hi João,
thank you for your questions. We're glad you're enjoying the competition!
It's important to us that all participants have access to the same information so we cannot answer your questions in full. All details on the data-generating process that are available to participants can be found in the provided materials. These are therefore only partial answers:
1) It is correct that noise may create negative observations.
2) The evaluation criterion is stated explicitly in the white paper and it applies to all inputs and trajectories.
We hope this helps.
Best regards,
Søren
Hi Søren
Thanks for the answers. My main concern was that if additional measures not described in the whitepaper have been used in the process that generated the data (to keep concentrations non-negative) this would potentially undermine the approach of identifying the parameters of the ODE because participants wouldn't be accounting for them. If the data we are provided comes from simply solving an ODE from the class of functions described in the whitepaper (and adding noise) and negative concentrations are simply avoided (or not) by careful choice of the inputs to each simulation then nevermind my questions :p
Best regards,
João