1. A computer implemented method for generating parameters for a manufacturing apparatus to produce wafers, the method comprising: identifying one or more input parameters that cause a change in output characteristics of the wafers produced by the manufacturing apparatus; defining at least one cell having one or more extreme values defined by one or more values of the input parameters, wherein the one or more extreme values are characterized by first nodes; estimating output values at the one or more extreme values, wherein an output value numerically represents the output characteristics; assigning at least one first mathematical function to each at least one cell, the at least one first mathematical function based on the estimated output values at the one or more extreme values configured to predict an output value for a set of values of the input parameters within the assigned at least one cell; receiving at least one empirical data point having empirical values for the input parameters and an empirical output value; adjusting the estimated output values at the one or more extreme values based on the empirical output value and a predicted output value calculated using the assigned at least one first mathematical function based on the empirical values for the input parameters, allowing a numerical value for the output characteristics to be calculated using the at least one first mathematical function based on the adjusted estimated output value at the one or more extreme values; generating a second mathematical function, wherein the second mathematical function is based on a difference between the empirical output value for the output characteristics and the predicted output value calculated using the assigned mathematical function based on the adjusted estimated output values of the first nodes; solving the second mathematical function as potential energy of a virtual multidimensional mechanical system to generate optimized output values; and generating a recipe for controlling the manufacturing apparatus to produce the wafers using the optimized output values.