The theoretical structure may vary from information on the smoothness of results, to models that need only parameter values from data or existing literature.
The general case is a non-linear model with a partial theoretical structure and some unknown parts derived from data.
Models with unlike theoretical structures need to be evaluated individually,[1][13][14] possibly using simulated annealing or genetic algorithms.
[5][17] This relation can be specified as q = Ac where A is a matrix of unknown coefficients, and c as in linear regression[6][7] includes a constant term and possibly transformed values of the original operating conditions to obtain non-linear relations[19][20] between the original operating conditions and q.
The model completion becomes an optimization problem to determine the non-zero values in A that minimizes the error terms m(f,p,Ac) over the data.
This can be repeated using multiple selections of the construction set and the resulting models averaged or used to evaluate prediction differences.
[21][22] Residuals that cannot be predicted offer little prospect of improving the model using the current operating conditions.
In this case selection of nonzero terms is not so important and linear prediction can be done using the significant eigenvectors of the regression matrix.