Multi-criteria optimization for parameterization of SAFT-type equations of state for water

Hierarchical Multicriteria Optimization of Molecular Models of Water

Many widely used molecular models of water are built from a single Lennard-Jones site on which three point charges are positioned, one negative and two positive ones. Models from that class, denoted LJ3PC here, are computationally efficient, but it is well known that they cannot represent all relevant properties of water simultaneously with good accuracy. Despite the importance of the LJ3PC water model class, its inherent limitations in simultaneously describing different properties of water have never been studied systematically. This task can only be solved by multicriteria optimization (MCO). However, due to its computational cost, applying MCO to molecular models is a formidable task. We have recently introduced the reduced units method (RUM) to cope with this problem. In the present work, we apply the RUM in a hierarchical scheme to optimize LJ3PC water models taking into account five objectives: the representation of vapor pressure, saturated liquid density, self-diffusion coefficient, shear viscosity, and relative permittivity. Of the six parameters of the LJ3PC models, five were varied; only the H-O-H bond angle, which is usually chosen based on physical arguments, was kept constant. Our hierarchical RUM-based approach yields a Pareto set that contains attractive new water models. Furthermore, the results give an idea of what can be achieved by molecular modeling of water with models from the LJ3PC class.

Parameter Estimation Strategies in Thermodynamics

Many thermodynamic models used in practice are at least partially empirical and thus require the determination of certain parameters using experimental data. However, due to the complexity of the models involved as well as the inhomogeneity of available data, a straightforward application of basic methods often does not yield a satisfactory result. This work compares three different strategies for the numerical solution of parameter estimation problems, including errors both in the input and in the output variables. Additionally, the new idea to apply multi-criteria optimization techniques to parameter estimation problems is presented. Finally, strategies for the estimation and propagation of the model errors are discussed.