I use software for pollutant propagation on rivers that takes as input a set of parameters ($p_1,p_2,\ldots,p_n$) and creates an output file which is basically a matrix where on each row the concentration of the pollutant in various places along the river at a given timestamp is given.
\begin{array} {|r|r|r|r|r...|r|} \hline \text{TIME} &500\,\text{m}&1000\,\text{m}&1500\,\text{m}&2000\,\text{m}&2500\,\text{m}&...&25000\,\text{m} \\ \hline 2015/12/07 - \text{4:50:00}&0.75&0.71&0.6&0.58&0.55&...&0.12 \\ \hline \hline 2015/12/07- \text{4:55:00}&0.71&0.70&0.58&0.56&0.51&...&0.10 \\ \hline \end{array}
My question is: what models/theories are suitable to be used to predict, based on a set of given INPUT parameters, the OUTPUT that would be closest to what the software will give as a result?
Also how many pairs INPUT/OUTPUT will I need to have in order to minimize the error?