Need explanation on data[[i]][[1]]

Question

I am trying to train a physics model and then check its profile. For this model, data for physics model is defined with:

data = Table[{x, physics[20, 20, 2, x]}, {x, 0, 0.5, 0.01}];

I also did something similar with a neural network and define its data with:

NNdata = Table[{data[[i]][[1]]} -> {data[[i]][[2]]}, {i, 1, Length[data]}];

Now for the profiles, I can check model profile with:

Plot[physics[20, 20, 2, x], {x, 0, 1}]

and for NN model,

Plot[trainedNN[[1]][i], {i, 0, 1}]

I wish to modify the models to take extra input such that I could now make plots as follows:

Plot3D[physics[20, y, 2, x], {x, 0, 1},{y, 0, 1}]

Now, my question is this: how do I modify code lines 2 and 4 (shown above) to accommodate y as a variable instead of a constant? Thank you in anticipation of your kind suggestions.

Note:

 physics[C1_, y_, w_, x_] := Module[{B, D, cos, sin, z},
   B = w*x;
   D = w*y;
   cos = Cos[D];
   sin = Sin[B];
   z = (C1)*sin*cos;
   z // N
   ]

Answer 1

Not really sure if this is what you're after, but maybe it'll at least lead to a clarification of the problem.

data2 = Table[{x, y, physics[20, y, 2, x]}, {x, 0, 1, 0.025}, {y, 0, 1, 0.025}];
ListPlot3D[Catenate[data2]]

To get the other structures...

NNdata = Map[Take[#, 2] -> #[[3]] &, data2, {2}]
(* This will have some additional list structure, but you could apply Flatten to it. *)

Or...

NNdata = Map[Take[#, 2] -> #[[3]] &, Catenate[data2]]
(* This one will be "flat". *)

If you want to use Part instead of Take, use this as the function to map:

#[[1 ;; 2]] -> #[[3]] &