algorithm - Determine Mapping Function or Approximation from Massive Amount of Data -

is there good/well known approach flushing out mapping function/approximation having access lots of mapped data?

e.g. situation

let's have domain space of 3d cube (bottom_left: 0,0,0, top_right: 10,10,10). e.g. points: (0,0,1), (1,2,3) etc.

each point maps separate series of 3 values in solution space. not know mapping function guess perhaps heart of problem. have massive amount of mapped data. data these values found range (-30.0 +30.0).e.g. data: [0,0,1] -> (0.1, 0.1, 0.1), [1,2,3]-> (10.2, 3.1, 29.3) etc.

any 2 different keys can mapped same point in solution space these keys positioned far away 1 in domain space.

we have last position , condition searched domain position cannot greater distance given distance e.g (0.1,0.1,0.1) last position. feel can used somehow eliminate condition of identical solution space values?

if have random point (2.3,6.5,2.6) in solution space, how find nearest domain value? since have massive amounts of data there approach flush out mapping function/approximation?