Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Multicriteria optimization of molecular force field models Martin Horsch, 1 Katrin Stöbener, 1, 2 Stephan Werth, 1 and Hans Hasse 1 1 Laboratory of Engineering Thermodynamics, University of Kaiserslautern 2 Fraunhofer Institute for Industrial Mathematics, Kaiserslautern Leipzig, 27 th November 2015 Computational NTZ CompPhys15 Workshop Molecular Engineering
Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Computational molecular engineering To Engineering From Physics (quantitative reliability) (qualitative accuracy) • Physically realistic modelling of • No blind fitting, but parameters of intermolecular interactions effective pair potentials are adjusted to experimental data • Separate contributions due to repulsive and dispersive as well as • Physical realism facilitates reliable electrostatic interactions interpolation and extrapolation 27th November 2015 Martin Horsch, Katrin Stöbener, Stephan Werth, and Hans Hasse 2
Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Vapour-liquid equilibria Bulk properties Interfacial properties T ρ vapour pressure, saturated densities, heterogeneous systems composition, enthalpy of vaporization, with finite-size effects and etc., by Grand Equilibrium simulation long-range interactions 27th November 2015 Martin Horsch, Katrin Stöbener, Stephan Werth, and Hans Hasse 3
Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Long-range correction at planar interfaces short range long range For planar interfaces: (explicit) (correction) Long-range correction from the density profile, following Janeček . cutoff radius Full evaluation of all pairwise interactions is too expensive ... ... short-range interactions are evaluated only for neighbours . 27th November 2015 Martin Horsch, Katrin Stöbener, Stephan Werth, and Hans Hasse 4
Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Long-range correction at planar interfaces Two-centre LJ fluid (2CLJ) For planar interfaces: Long-range correction from the surface tension / εσ -2 density profile, following Janeček . T = 0.979 ε 1 nm Janeček-Lustig term no angle averaging no long-range correction Angle-averaging expression for multi-site models, following Lustig . cutoff radius / σ Dipole and dispersion lead to analogous long-range correction expressions. The long-range contribution of the quadrupole can be neglected. 27th November 2015 Martin Horsch, Katrin Stöbener, Stephan Werth, and Hans Hasse 5
Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Validation of molecular force field models temperature simulation density 2CLJQ models: [mol/l] DIPPR correlation • 2 LJ centres • Quadrupole vapour pressure (logarithmic) Fit of parameters σ , ε , L , Q to VLE data of 29 fluids by Stoll et al. No interfacial properties were Deviation: considered for the • δρ ' ≈ 1 % parameterization. • δP sat ≈ 5 % inverse temperature [1/K] 27th November 2015 Martin Horsch, Katrin Stöbener, Stephan Werth, and Hans Hasse 6
Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Validation of molecular force field models Two LJ + quadrupole (2CLJQ) Two LJ + dipole (2CLJD) Fit to bulk properties 10 to 20 % overestimation of vapour-liquid surface tension 27th November 2015 Martin Horsch, Katrin Stöbener, Stephan Werth, and Hans Hasse 7
Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Massively parallel molecular modelling Two LJ + quadrupole (2CLJQ) L * = 0.4 L * = 0.2 surface tension / εσ -2 2CLJQ Q * = 1.41 Q * = 1.41 L * = 0.4 Q * = 0 L * = 0.4 Q * = 2 Model parameters: ● LJ size parameter σ ● LJ energy parameter ε ● Elongation L L * = 0.6 Q * = 1.41 ● Quadrupole moment Q temperature / ε ● Systematic exploration of the four-dimensional model parameter space 27th November 2015 Martin Horsch, Katrin Stöbener, Stephan Werth, and Hans Hasse 8
Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Massively parallel molecular modelling Two LJ + quadrupole (2CLJQ) Two LJ + dipole (2CLJD) L * = 0.4 L * = 0.2 surface tension / εσ -2 Q * = 1.41 Q * = 1.41 L * = 0.4 Q * = 0 L * = 0.4 Q * = 2 L * = 0.6 Q * = 1.41 temperature / ε ● Systematic exploration of the four-dimensional model parameter space ● Correlation of the surface tension by a critical scaling expression 27th November 2015 Martin Horsch, Katrin Stöbener, Stephan Werth, and Hans Hasse 9
Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Multicriteria model optimization Pareto optimality criterion Multiple objectives (2CLJQ for carbon dioxide) Multicriteria optimization requires massively parallel molecular modelling. 27th November 2015 Martin Horsch, Katrin Stöbener, Stephan Werth, and Hans Hasse 10
Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Computation of the Pareto set Multicriteria optimization problem Simultaneously minimized objective functions f ξ with ξ ∊ { ρ ', p s , γ } given by ( 1 − ξ exp ( T ) ) T / T c = 0.55 + 0.4i / N 2 N sim ( T ) 1 N + 1 ∑ 2 〉 0.55 T c f ξ =〈δξ exp = lim (here: N = 9). exp < T < 0.95 T c ξ N →∞ i = 0 Sandwiching Alternating construction of inner (reachable) and outer (unreachable) approximations, assuming local convexity of the Pareto set. Hyperboxing In non-convex regions (“hyperboxes”), Pascoletti-Serafini scalarization is employed to obtain a suitable local single-criterion optimization problem. 27th November 2015 Martin Horsch, Katrin Stöbener, Stephan Werth, and Hans Hasse 11
Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Invariants of Pareto-optimal models criteria: ρ ', p s , γ For obtaining a rough approximation of the Pareto set, the dimension of the parameter space can be reduced from four to three (or even two). 27th November 2015 Martin Horsch, Katrin Stöbener, Stephan Werth, and Hans Hasse 12
Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Pareto sets for 2CLJQ models of real fluids Representation of objective and parameter spaces by patch plots : Pareto-optimal 2CLJQ models of molecular oxygen 27th November 2015 Martin Horsch, Katrin Stöbener, Stephan Werth, and Hans Hasse 13
Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Model tailoring by the end user For each specific application, accuracy requirements can be specified: Restrictions imposed on 2CLJ models of molecular oxygen 27th November 2015 Martin Horsch, Katrin Stöbener, Stephan Werth, and Hans Hasse 14
Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Model tailoring by the end user Intersection of the highlighted areas within all replicas of the patch plot: 2CLJ models of molecular oxygen fulfilling all requirements 27th November 2015 Martin Horsch, Katrin Stöbener, Stephan Werth, and Hans Hasse 15
Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Summary The traditional art of molecular modelling An expert modelling artist designs and publishes • a single optimized model for a particular fluid, • according to his choice of criteria (often unknown to the public), • users are passive, they have to live with the artists' decision. 27th November 2015 Martin Horsch, Katrin Stöbener, Stephan Werth, and Hans Hasse 16
Laboratory of Engineering Thermodynamics (LTD) Prof. Dr.-Ing. H. Hasse Summary The traditional art of molecular modelling An expert modelling artist designs and publishes • a single optimized model for a particular fluid, • according to his choice of criteria (often unknown to the public), • users are passive, they have to live with the artists' decision. Scientific modelling by multicriteria optimization For established model classes and multiple thermodynamic criteria, • the dependence of thermodynamic properties on the model parameters is determined and correlated, • the deviation between model properties and real fluid behaviour is characterized, and the Pareto set is published, • users can design their own tailored model with minimal effort . 27th November 2015 Martin Horsch, Katrin Stöbener, Stephan Werth, and Hans Hasse 17
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