Maximum Likelihood Estimation Approach: A strategy to automate EOS design.

Using the newly developed POOH code (program d'optimisation heuristique), we propose a systematic statistical approach to producing a multiphase equation of state (EOS). Each phase of the EOS is represented by its Helmholtz free energy which is the sum of the cold curve and the thermal contribution. For every contribution, the POOH code has a large set of models to choose from. Our goal is to automatise the process as far as possible, giving the most likely parameters of the EOS. To do this, the Maximum Likelihood Estimation (MLE) method is applied. The calibration database containing the expected values and their uncertainties is chosen to represent some interesting properties of the material. Here, we apply our procedure to aluminum, emphasizing the versatile aspect of the POOH code. Then, we compare our EOS to a large set of experiments that includes some alloys.