Lots of people seem to already have solved Stage 1 and the organizers seem to think this is trivial (based on their notebook wording), so perhaps I am missing the framing of this problem. My understanding is that our objective is to basically compute the distance function, X, as a function of the potential, Y (basically an inverse function) subject to parameters, i.e.

**X(Y ; Y1, Y2, phi, S1, S2, H, Xm) **

and we are given an example set of curves for choices of parameters and need to find curves for a different choice of parameters. But according to the physical problem Y1 and Y2 are the potentials at the two plates (separated by H), but what is with the weird shift at Y=5? At this point the PBE itself is violated as the curves are non-differentiable. Also assuming that X is non-dimensionalized by H to be between 0 and 1 why are some values larger than 1?
Any clue to what I am missing within the allowed limits would be much appreciated.

The values for 0.0 up to 5.5 is for an alternate set of initial values (i.e., a different 1d problem) - so, of course the PBE behavior might be invalid if trying to plot the solution using the current initial conditions.

Hi @team , Thanks a lot for your reply. I just want to be sure I am interpreting your reply correctly. What I’ve plotted is directly from the starter notebook combining the data in stage1_sample_input_parameterizations.csv and (which has the problem parameters that you refer to as initial conditions) and stage1_sample_submission.csv so my question relates entirely to the sample initial conditions not the current one we are supposed to solve. Are you saying that the Xi’s [i = (1,10)] in the two sample .csv files are not related? I was under the assumption that the curves in stage1_sample_submission.csv were solutions to the conditions in stage1_sample_input_parameterizations.csv subject to the PBE.
Thanks

I agree that it is very confusing. It shouldn’t be this unclear. The jupyter notebook that they provided does not run as is (missing a .csv file). If we use instead the training data from stage1_sample_submission.csv, then we see that non-differentiable behavior for that was not in the plot they had provided initially (or in any other Figure in their explanations). It is not clear if that behavior should be modeled/predicted as well.