Marco Hülsmann

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

Abstract The concept, issues of implementation and file formats of the GRadient-based Optimization Workflow for the Automated Development of Molecular Models ‘GROW’ (version 1.0) software tool are described. It enables users to perform automated optimizations of force field parameters for atomistic molecular simulations by an iterative, gradient-based optimization workflow. The modularly constructed tool consists of a main control script, specific implementations and secondary control scripts for each numerical algorithm, as well as analysis scripts. Taken together, this machinery is able to automatically optimize force fields and it is extensible by developers with regard to further optimization algorithms and simulation tools. Results on nitrogen are briefly reported as a proof of concept.

Assessment of numerical optimization algorithms for the development of molecular models

Abstract In the pursuit to study the parameterization problem of molecular models with a broad perspective, this paper is focused on an isolated aspect: It is investigated, by which algorithms parameters can be best optimized simultaneously to different types of target data (experimental or theoretical) over a range of temperatures with the lowest number of iteration steps. As an example, nitrogen is regarded, where the intermolecular interactions are well described by the quadrupolar two-center Lennard-Jones model that has four state-independent parameters. The target data comprise experimental values for saturated liquid density, enthalpy of vaporization, and vapor pressure. For the purpose of testing algorithms, molecular simulations are entirely replaced by fit functions of vapor–liquid equilibrium (VLE) properties from the literature to assess efficiently the diverse numerical optimization algorithms investigated, being state-of-the-art gradient-based methods with very good convergency qualities. Additionally, artificial noise was superimposed onto the VLE fit results to evaluate the numerical optimization algorithms so that the calculation of molecular simulation data was mimicked. Large differences in the behavior of the individual optimization algorithms are found and some are identified to be capable to handle noisy function values.

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

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.

A Sales Forecast Model for the German Automobile Market Based on Time Series Analysis and Data Mining Methods

In this contribution, various sales forecast models for the German automobile market are developed and tested. Our most important criteria for the assessment of these models are the quality of the prediction as well as an easy explicability. Yearly, quarterly and monthly data for newly registered automobiles from 1992 to 2007 serve as the basis for the tests of these models. The time series model used consists of additive components: trend, seasonal, calendar and error component. The three latter components are estimated univariately while the trend component is estimated multivariately by Multiple Linear Regression as well as by a Support Vector Machine. Possible influences which are considered include macro-economic and market-specific factors. These influences are analysed by a feature selection. We found the non-linear model to be superior. Furthermore, the quarterly data provided the most accurate results.

Automated parameterization of intermolecular pair potentials using global optimization techniques

Abstract 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.

Comparison of a Novel Combined ECOC Strategy with Different Multiclass Algorithms Together with Parameter Optimization Methods

In this paper we consider multiclass learning tasks based on Support Vector Machines (SVMs). In this regard, currently used methods are One-Against-Allor One-Against-One, but there is much need for improvements in the field of multiclass learning. We developed a novel combination algorithm called Comb-ECOC, which is based on posterior class probabilities. It assigns, according to the Bayesian rule, the respective instance to the class with the highest posterior probability. A problem with the usage of a multiclass method is the proper choice of parameters. Many users only take the default parameters of the respective learning algorithms (e.g. the regularization parameter Cand the kernel parameter i¾?). We tested different parameter optimization methods on different learning algorithms and confirmed the better performance of One-Against-Oneversus One-Against-All, which can be explained by the maximum margin approach of SVMs.

Optimizing Molecular Models Through Force-Field Parameterization via the Efficient Combination of Modular Program Packages

A central goal of molecular simulations is to predict physical or chemical properties such that costly and elaborate experiments can be minimized. The reliable generation of molecular models is a critical issue to do so. Hence, striving for semiautomated and fully automated parameterization of entire force fields for molecular simulations, the authors developed several modular program packages in recent years. The programs run with limited user interactions and can be executed in parallel on modern computer clusters. Various interlinked resolutions of molecular modeling are addressed: For intramolecular interactions, a force-field optimization package named Wolf2Pack has been developed that transfers knowledge gained from quantum mechanics to Newtonian-based molecular models. For intermolecular interactions, especially Lennard–Jones parameters, a modular optimization toolkit of programs and scripts has been created combining global and local optimization algorithms. Global optimization is performed by a tool named CoSMoS, while local optimization is done by the gradient-based optimization workflow named GROW or by a derivative-free method called SpaGrOW. The overall goal of all program packages is to realize an easy, efficient, and user-friendly development of reliable force-field parameters in a reasonable time. The various tools are needed and interlinked since different stages of the optimization process demand different courses of action. In this paper, the conception of all programs involved is presented and how they communicate with each other.

Utilization of efficient gradient and Hessian computations in the force field optimization process of molecular simulations

Computer simulations of chemical systems, especially systems of condensed matter, are highly important for both scientific and industrial applications. Thereby, molecular interactions are modeled on a microscopic level in order to study their impact on macroscopic phenomena. To be capable of predicting physical properties quantitatively, accurate molecular models are indispensable. Molecular interactions are described mathematically by force fields, which have to be parameterized. Recently, an automated gradient-based optimization procedure was published by the authors based on the minimization of a loss function between simulated and experimental physical properties. The applicability of gradient-based procedures is not trivial at all because of two reasons: firstly, simulation data are affected by statistical noise, and secondly, the molecular simulations required for the loss function evaluations are extremely time-consuming. Within the optimization process, gradients and Hessians were approximated by finite differences so that additional simulations for the respective modified parameter sets were required. Hence, a more efficient approach to computing gradients and Hessians is presented in this work. The method developed here is based on directional instead of partial derivatives. It is compared with the classical computations with respect to computation time. Firstly, molecular simulations are replaced by fit functions that define a functional dependence between specific physical observables and force field parameters. The goal of these simulated simulations is to assess the new methodology without much computational effort. Secondly, it is applied to real molecular simulations of the three chemical substances phosgene, methanol and ethylene oxide. It is shown that up to 75% of the simulations can be avoided using the new algorithm.

General sales forecast models for automobile markets based on time series analysis and data mining techniques

In this paper, various enhanced sales forecast methodologies and models for the automobile market are presented. The methods used deliver highly accurate predictions while maintaining the ability to explain the underlying model at the same time. The representation of the economic training data is discussed, as well as its effects on the newly registered automobiles to be predicted. The methodology mainly consists of time series analysis and classical Data Mining algorithms, whereas the data is composed of absolute and/or relative market-specific exogenous parameters on a yearly, quarterly, or monthly base. It can be concluded that the monthly forecasts were especially improved by this enhanced methodology using absolute, normalized exogenous parameters. Decision Trees are considered as the most suitable method in this case, being both accurate and explicable. The German and the US-American automobile market are presented for the evaluation of the forecast models.

The perfect fit? Balancing predictive power and computational complexity for an atomistic model as prerequisite for nano-scale simulations

When aiming at quantitative predictions for materials that require huge system sizes in simulation – such as polymers – models at coarse-grained level are the natural choice. However, capturing the chemical identity of beads that are void of any individual structure resembling the original compound is a critical point for achieving meaningful predictions. As the coarse grained model inherits the features from an atomistic precursor, the latter needs to be most predictive. This may be achieved by calibrating the detailed model carefully to experimental data, thereby enhancing the atomistic model structure with most realistic behaviour [1].