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The paper describes methods for calculating chemical equilibria based on a constrained Gibbs free energy minimization. The methods allow the treatment of multicomponent systems with multiple phases, including gaseous phases, condensed phases, and stoichiometric phases. A special aspect is the detection and treatment of miscibility gaps. The underlying mathematical problem is described in detail together with the algorithmic approach for its solution. Results are presented for some test cases, including the computation of phase diagrams for ternary systems.

GROW: A gradient-based optimization workflow for the automated development of molecular models
(2010)

The Fraunhofer Institute for Algorithms and Scientific Computing (SCAI) has developed a software tool for the automated parameterization of force fields for molecular simulations using efficient gradient-based algorithms. This tool, combined with well-established simulation techniques, can quantitatively determine many physicochemical properties for given compounds.

Automated force field optimisation of small molecules using a gradient-based workflow package
(2010)

In this study, the recently developed gradient-based optimisation workflow for the automated development of molecular models is for the first time applied to the parameterisation of force fields for molecular dynamics simulations. As a proof-of-concept, two small molecules (benzene and phosgene) are considered. In order to optimise the underlying intermolecular force field (described by the (12,6)-Lennard-Jones and the Coulomb potential), the energetic and diameter parameters ε and σ are fitted to experimental physical properties by gradient-based numerical optimisation techniques. Thereby, a quadratic loss function between experimental and simulated target properties is minimised with respect to the force field parameters. In this proof-of-concept, the considered physical target properties are chosen to be diverse: density, enthalpy of vapourisation and self-diffusion coefficient are optimised simultaneously at different temperatures. We found that in both cases, the optimisation could be successfully concluded by fulfillment of a pre-defined stopping criterion. Since a fairly small number of iterations were needed to do so, this study will serve as a good starting point for more complex systems and further improvements of the parametrisation task.

Automated parameterization of intermolecular pair potentials using global optimization techniques
(2014)

In this work, different global optimization techniques are assessed for the automated development of molecular force fields, as used in molecular dynamics and Monte Carlo simulations. The quest of finding suitable force field parameters is treated as a mathematical minimization problem. Intricate problem characteristics such as extremely costly and even abortive simulations, noisy simulation results, and especially multiple local minima naturally lead to the use of sophisticated global optimization algorithms. Five diverse algorithms (pure random search, recursive random search, CMA-ES, differential evolution, and taboo search) are compared to our own tailor-made solution named CoSMoS. CoSMoS is an automated workflow. It models the parameters’ influence on the simulation observables to detect a globally optimal set of parameters. It is shown how and why this approach is superior to other algorithms. Applied to suitable test functions and simulations for phosgene, CoSMoS effectively reduces the number of required simulations and real time for the optimization task.

Liquid–liquid equilibria of dipropylene glycol dimethyl ether and water by molecular dynamics
(2011)

Molecular modeling is an important subdomain in the field of computational modeling, regarding both scientific and industrial applications. This is because computer simulations on a molecular level are a virtuous instrument to study the impact of microscopic on macroscopic phenomena. Accurate molecular models are indispensable for such simulations in order to predict physical target observables, like density, pressure, diffusion coefficients or energetic properties, quantitatively over a wide range of temperatures. Thereby, molecular interactions are described mathematically by force fields. The mathematical description includes parameters for both intramolecular and intermolecular interactions. While intramolecular force field parameters can be determined by quantum mechanics, the parameterization of the intermolecular part is often tedious. Recently, an empirical procedure, based on the minimization of a loss function between simulated and experimental physical properties, was published by the authors. Thereby, efficient gradient-based numerical optimization algorithms were used. However, empirical force field optimization is inhibited by the two following central issues appearing in molecular simulations: firstly, they are extremely time-consuming, even on modern and high-performance computer clusters, and secondly, simulation data is affected by statistical noise. The latter provokes the fact that an accurate computation of gradients or Hessians is nearly impossible close to a local or global minimum, mainly because the loss function is flat. Therefore, the question arises of whether to apply a derivative-free method approximating the loss function by an appropriate model function. In this paper, a new Sparse Grid-based Optimization Workflow (SpaGrOW) is presented, which accomplishes this task robustly and, at the same time, keeps the number of time-consuming simulations relatively small. This is achieved by an efficient sampling procedure for the approximation based on sparse grids, which is described in full detail: in order to counteract the fact that sparse grids are fully occupied on their boundaries, a mathematical transformation is applied to generate homogeneous Dirichlet boundary conditions. As the main drawback of sparse grids methods is the assumption that the function to be modeled exhibits certain smoothness properties, it has to be approximated by smooth functions first. Radial basis functions turned out to be very suitable to solve this task. The smoothing procedure and the subsequent interpolation on sparse grids are performed within sufficiently large compact trust regions of the parameter space. It is shown and explained how the combination of the three ingredients leads to a new efficient derivative-free algorithm, which has the additional advantage that it is capable of reducing the overall number of simulations by a factor of about two in comparison to gradient-based optimization methods. At the same time, the robustness with respect to statistical noise is maintained. This assertion is proven by both theoretical considerations and practical evaluations for molecular simulations on chemical example substances.