1. A computer-implemented method for managing operations of a system, the method comprising: deriving a nonlinear modeling function from a nonlinear response function, wherein the nonlinear modeling function models an affinity between multiple variables, wherein the multiple variables define one or more characteristics of the operations of the system, and wherein the nonlinear modeling function approximates one or more operations of the system; defining an allowed range for output values of the nonlinear modeling function; determining a range of a first set of input values of the nonlinear modeling function based on the allowed range of the output values, wherein a boundary of the range of the first set of input values is an optimal input value, wherein the optimal input value can be processed through the nonlinear modeling function to produce an optimal output value; deriving a nonlinear probability function from the nonlinear response function; receiving the first set of input values; calculating the output values by processing each input value in the first set of input values through the nonlinear modeling function; determining, using the probability function, a relative probability of performing a first future system operation for each input value of the first set of input values, wherein, for each input value of the first set of input values, the relative probability shows a probability of performing the first future system operation for the corresponding input value relative to a probability of performing the first future system operation for the optimal input value; and displaying, for each input value in the first set of input values, the corresponding output value and the corresponding probability.