Data driven inference for the repulsive exponent of the Lennard-Jones potential in molecular dynamics simulations

The Lennard-Jones (LJ) potential is a cornerstone of Molecular Dynamics (MD) simulations and among the most widely used computational kernels in science. The LJ potential models atomistic attraction and repulsion with century old prescribed parameters (q=6, p=12 respectively), originally related by a factor of two for simplicity of calculations. We propose the infer

ence of the repulsion exponent through Hierarchical Bayesian uncertainty quantification We use experimental data of the radial distribution function and dimer interaction energies from quantum mechanics simulations. We find that the repulsion exponent  p\approx6.5 provides an excellent fit for the experimental data of liquid argon, for a range of thermodynamic conditions, as well as for saturated argon vapour. Calibration using the quantum simulation data did not provide a good fit in these cases.

However, values p\approx12.7 obtained by dimer quantum simulations are preferred for the argon gas while lower values are promoted by experimental data. These results show that the proposed LJ 6-p potential applies to a wider range of thermodynamic conditions, than the classical LJ 6-12 potential. We suggest that calibration of the repulsive exponent in the LJ potential widens the range of applicability and accuracy of MD simulations.

Hierarchical Bayesian inference process: the probability of the parameters conditioned on all the available data is being estimated. The data in this example are experimental measurements of the radial distribution function in argon in different thermodynamic conditions. The parameters are the \epsilon, \sigma parameters of the Lenard-Jones potential and one parameters p that corresponds to the exponent 12.

 

 

Fusing heterogeneous data for the calibration of molecular dynamics force fields using hierarchical Bayesian models

 

We propose a hierarchical Bayesian framework to systematically integrate heterogeneous data for the calibration of force fields in Molecular Dynamics (MD) simulations. Our approach enables the fusion of diverse experimental data sets of the physico-chemical properties of a system at different thermodynamic conditions. We demonstrate the value of this framework for the robust calibration of MD force-fields for water using experimental data of its diffusivity, radial distribution function, and density. In order to address the high computational cost associated with the hierar- chical Bayesian models, we develop a novel surrogate model based on the empirical interpolation method. Further computational savings are achieved by implementing a highly parallel transitional Markov chain Monte Carlo technique. The present method bypasses possible subjective weightings of the experimental data in identifying MD force-field parameters.

 

2017

  • L. Kulakova, G. Arampatzis, P. Angelikopoulos, P. Hadjidoukas, C. Papadimitriou, and P. Koumoutsakos, “Data driven inference for the repulsive exponent of the Lennard-Jones potential in molecular dynamics simulations,” Sci. Rep.-UK, vol. 7, iss. 1, p. 16576, 2017.
    [BibTeX] [Abstract] [PDF] [DOI]

    The Lennard-Jones (LJ) potential is a cornerstone of Molecular Dynamics (MD) simulations and among the most widely used computational kernels in science. The LJ potential models atomistic attraction and repulsion with century old prescribed parameters (q=6, p=12 respectively), originally related by a factor of two for simplicity of calculations. We propose the inference of the repulsion exponent through Hierarchical Bayesian uncertainty quantification We use experimental data of the radial distribution function and dimer interaction energies from quantum mechanics simulations. We find that the repulsion exponent p\approx6.5 provides an excellent fit for the experimental data of liquid argon, for a range of thermodynamic conditions, as well as for saturated argon vapour. Calibration using the quantum simulation data did not provide a good fit in these cases. However, values p\approx12.7 obtained by dimer quantum simulations are preferred for the argon gas while lower values are promoted by experimental data. These results show that the proposed LJ 6-p potential applies to a wider range of thermodynamic conditions, than the classical LJ 6-12 potential. We suggest that calibration of the repulsive exponent in the LJ potential widens the range of applicability and accuracy of MD simulations.

    @article{kulakova2017a,
    author = {Kulakova, Lina and Arampatzis, Georgios and Angelikopoulos, Panagiotis and Hadjidoukas, Panagiotis and Papadimitriou, Costas and Koumoutsakos, Petros},
    doi = {10.1038/s41598-017-16314-4},
    issn = {2045-2322},
    journal = {{Sci. Rep.-UK}},
    number = {1},
    pages = {16576},
    title = {Data driven inference for the repulsive exponent of the {L}ennard-{J}ones potential in molecular dynamics simulations},
    url = {http://www.cse-lab.ethz.ch/wp-content/papercite-data/pdf/kulakova2017a.pdf},
    volume = {7},
    year = {2017}
    }

2016

  • S. Wu, P. Angelikopoulos, G. Tauriello, C. Papadimitriou, and P. Koumoutsakos, “Fusing heterogeneous data for the calibration of molecular dynamics force fields using hierarchical Bayesian models,” J. Chem. Phys., vol. 145, iss. 24, p. 244112, 2016.
    [BibTeX] [PDF] [DOI]
    @article{wu2016a,
    author = {Stephen Wu and Panagiotis Angelikopoulos and Gerardo Tauriello and Costas Papadimitriou and Petros Koumoutsakos},
    doi = {10.1063/1.4967956},
    journal = {{J. Chem. Phys.}},
    month = {dec},
    number = {24},
    pages = {244112},
    publisher = {{AIP} Publishing},
    title = {Fusing heterogeneous data for the calibration of molecular dynamics force fields using hierarchical {B}ayesian models},
    url = {http://www.cse-lab.ethz.ch/wp-content/papercite-data/pdf/wu2016a.pdf},
    volume = {145},
    year = {2016}
    }

2015

  • S. Wu, P. Angelikopoulos, C. Papadimitriou, R. Moser, and P. Koumoutsakos, “A hierarchical Bayesian framework for force field selection in molecular dynamics simulations,” Philos. T. Roy. Soc. A, vol. 374, iss. 2060, p. 20150032, 2015.
    [BibTeX] [Abstract] [PDF] [DOI]

    We present a hierarchical Bayesian framework for the selection of force fields in molecular dynamics (MD) simulations. The framework associates the variability of the optimal parameters of the MD potentials under different environmental conditions with the corresponding variability in experimental data. The high computational cost associated with the hierarchical Bayesian framework is reduced by orders of magnitude through a parallelized Transitional Markov Chain Monte Carlo method combined with the Laplace Asymptotic Approximation. The suitability of the hierarchical approach is demonstrated by performing MD simulations with prescribed parameters to obtain data for transport coefficients under different conditions, which are then used to infer and evaluate the parameters of the MD model. We demonstrate the selection of MD models based on experimental data and verify that the hierarchical model can accurately quantify the uncertainty across experiments; improve the posterior probability density function estimation of the parameters, thus, improve predictions on future experiments; identify the most plausible force field to describe the underlying structure of a given dataset. The framework and associated software are applicable to a wide range of nanoscale simulations associated with experimental data with a hierarchical structure.

    @article{wu2015a,
    author = {S. Wu and P. Angelikopoulos and C. Papadimitriou and R. Moser and P. Koumoutsakos},
    doi = {10.1098/rsta.2015.0032},
    journal = {{Philos. T. Roy. Soc. A}},
    month = {dec},
    number = {2060},
    pages = {20150032},
    publisher = {The Royal Society},
    title = {A hierarchical {B}ayesian framework for force field selection in molecular dynamics simulations},
    url = {http://www.cse-lab.ethz.ch/wp-content/papercite-data/pdf/wu2015a.pdf},
    volume = {374},
    year = {2015}
    }

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