Patent ID: 7330804

Claim:
A computer-implemented method for modeling a non-linear empirical industrial process, said method comprising the steps of: creating an initial model generally corresponding to the non-linear empirical industrial process to be modeled, the initial model having a base non-linear function, an initial input and an initial output; constructing a non-linear network model based on the initial model, the non-linear network model having (a) multiple inputs based on the initial input and (b) a global behavior for the non-linear network model as a whole that conforms generally to the initial output, the global behavior being at least in regions of sparse initial input; and calibrating the non-linear network model based on empirical inputs of the non-linear empirical industrial process by using a hound on an analytical derivative of the base non-linear function that allows global properties including at least a global minimum value and a global maximum value of the analytical derivatives to be calculated directly from model coefficients, the global properties used to produce, via a constrained nonlinear optimization method, an analytically constrained model with global behavior, the constrained model enabling precision control of the non-linear empirical industrial process.