In future, the investigation of property relations in deductive models may ultimately lead to reliable predictions for all desired properties, provided the property relations are well understood and all required experimental data are available. Glass properties and glass behavior during production can be calculated through statistical analysis of glass databases such as GE-SYSTEM SciGlass and Interglad,  sometimes combined with the finite element method. For estimating the melting enthalpy thermodynamic databases are used. If the desired glass property is not related to crystallization (e.g., liquidus temperature) or phase separation, linear regression can be applied using common polynomial functions up to the third degree. Below is an example equation of the second degree. The "C"-values are the glass component concentrations like Na2O or CaO in percent or other fractions, the "b"-values are coefficients, and "n" is the total number of glass components. The glass main component silica (SiO2) is excluded in the equation below because of over-parametrization due to the constraint that all components sum up to 100%. Many terms in the equation below can be neglected based on correlation and significance analysis. Systematic errors such as seen in the picture are quantified by dummy variables. Further details and examples are available in an online tutorial by Fluegel. The liquidus temperature has been modeled by non-linear regression using neural networks and disconnected peak functions. The disconnected peak functions approach is based on the observation that within one primary crystalline phase field linear regression can be applied and at eutectic points sudden changes occur. The glass melting enthalpy reflects the amount of energy needed to convert the mix of raw materials (batch) to a melt glass. It depends on the batch and glass compositions, on the efficiency of the furnace and heat regeneration systems, the average residence time of the glass in the furnace, and many other factors. A pioneering article about the subject was written by Carl Kröger in 1953. For modeling of the glass flow in a glass melting furnace the finite element method is applied commercially, based on data or models for viscosity, density, thermal conductivity, heat capacity, absorption spectra, and other relevant properties of the glass melt. The finite element method may also be applied to glass forming processes. It is often required to optimize several glass properties simultaneously, including production costs. This can be performed, e.g., by simplex search, or in a spreadsheet as follows: It is possible to weight the desired properties differently. Basic information about the principle can be found in an article by Huff "et al."