For over five decades, molecular dynamics (MD) simulations have helped to elucidate critical mechanisms in a broad range of physiological systems and technological innovations. MD simulations are synergetic with experiments, relying on measurements to calibrate their parameters and probing “what if scenarios” for systems that are difficult to investigate experimentally. However, in certain systems, such as nanofluidics, the results of experiments and MD simulations differ by several orders of magnitude. This discrepancy may be attributed to the  spatiotemporal scales and structural information accessible by experiments and simulations. Furthermore, MD simulations rely on parameters that are often calibrated semiempirically, while the effects of their computational implementation on their predictive capabilities have only been sporadically probed.  We show that experimental and MD investigations can be consolidated through a rigorous uncertainty quantification framework.

Robust predictions of the water−carbon friction coefficient (red-lower x-axis) and slip length (green-upper x-axis) in a typical nanopore system.
Effect of the cutoff radius on Molecular Dynamics predictions by considering the potential of mean force (PMF) for two C70 fullerenes in aqueous solution. Magenta and green curves correspond respectively to rcut = 0.9 nm and rcut = 1.35 nm, while gray error bars indicate computational uncertainty.
(a) Uncertainty propagation: posterior distribution of the water contact angle predicted from 2 models (magenta and green curve) and PDF quantifying the experimental uncertainty in yellow. (b) Magenta and blue: propagation to the self-diffusion coefficient using experimental data from one temperature (T=298.15K) and three temperatures (T = 298.15, 328, and 358 K), respectively.
Simulation of the “Brazil Nut” effect: (a) Initial resting position of the Brazil nut at t = 0. (b)–(c) Snapshots during the shaking at t = 10.04 and 23.04 s. (d) Final resting position of the nut. Smaller steel particles are depicted white, while the “Brazil” nut is red.
Uncertainty Propagation of the time it takes for the “Brazil nut" to reach a height z for the first time t for initial nut positions zinit. Magenta Lines indicate mean values, whereas the overall uncertainty quantified as 5% and 95% quantiles is denoted with green.

Publications

2014

  • P. E. Hadjidoukas, P. Angelikopoulos, D. Rossinelli, D. Alexeev, C. Papadimitriou, and P. Koumoutsakos, “Bayesian uncertainty quantification and propagation for discrete element simulations of granular materials," Comput. Method. Appl. M., vol. 282, p. 218–238, 2014.
    [BibTeX] [Abstract] [PDF] [DOI]

    Predictions in the behavior of granular materials using Discrete Element Methods (DEM) hinge on the employed interaction potentials. Here we introduce a data driven, Bayesian framework to quantify DEM predictions. Our approach relies on experimentally measured coefficients of restitution for single steel particle{–}wall collisions. The calibration data entail both tangential and normal coefficients of restitution, for varying impact angles and speeds of the bouncing particle. The parametric uncertainty in multiple Force{–}Displacement models is estimated using an enhanced Transitional Markov Chain Monte Carlo implemented efficiently on parallel computer architectures. In turn, the parametric model uncertainties are propagated to predict Quantities of Interest (QoI) for two testbed applications: silo discharge and vibration induced mass-segregation. This work demonstrates that the classical way of calibrating DEM potentials, through parameter optimization, is insufficient and it fails to provide robust predictions. The present Bayesian framework provides robust predictions for the behavior of granular materials using DEM simulations. Most importantly the results demonstrate the importance of including parametric and modeling uncertainties in the potentials employed in Discrete Element Methods.

    @article{hadjidoukas2014c,
author = {P.E. Hadjidoukas and P. Angelikopoulos and D. Rossinelli and D. Alexeev and C. Papadimitriou and P. Koumoutsakos},
doi = {10.1016/j.cma.2014.07.017},
journal = {{Comput. Method. Appl. M.}},
month = {dec},
pages = {218--238},
publisher = {Elsevier {BV}},
title = {{B}ayesian uncertainty quantification and propagation for discrete element simulations of granular materials},
url = {http://www.cse-lab.ethz.ch/wp-content/papercite-data/pdf/hadjidoukas2014c.pdf},
volume = {282},
year = {2014}
}

2013

  • P. Angelikopoulos, C. Papadimitriou, and P. Koumoutsakos, “Data driven, predictive molecular dynamics for nanoscale flow simulations under uncertainty," J. Phys. Chem. B, vol. 117, iss. 47, p. 14808–14816, 2013.
    [BibTeX] [Abstract] [PDF] [DOI]

    For over five decades, molecular dynamics (MD) simulations have helped to elucidate critical mechanisms in a broad range of physiological systems and technological innovations. MD simulations are synergetic with experiments, relying on measurements to calibrate their parameters and probing {\textquotedblleft}what if scenarios{\textquotedblright} for systems that are difficult to investigate experimentally. However, in certain systems, such as nanofluidics, the results of experiments and MD simulations differ by several orders of magnitude. This discrepancy may be attributed to the spatiotemporal scales and structural information accessible by experiments and simulations. Furthermore, MD simulations rely on parameters that are often calibrated semiempirically, while the effects of their computational implementation on their predictive capabilities have only been sporadically probed. In this work, we show that experimental and MD investigations can be consolidated through a rigorous uncertainty quantification framework. We employ a Bayesian probabilistic framework for large scale MD simulations of graphitic nanostructures in aqueous environments. We assess the uncertainties in the MD predictions for quantities of interest regarding wetting behavior and hydrophobicity. We focus on three representative systems: water wetting of graphene, the aggregation of fullerenes in aqueous solution, and the water transport across carbon nanotubes. We demonstrate that the dominant mode of calibrating MD potentials in nanoscale fluid mechanics, through single values of water contact angle on graphene, leads to large uncertainties and fallible quantitative predictions. We demonstrate that the use of additional experimental data reduces uncertainty, improves the predictive accuracy of MD models, and consolidates the results of experiments and simulations.

    @article{angelikopoulos2013a,
author = {Panagiotis Angelikopoulos and Costas Papadimitriou and Petros Koumoutsakos},
doi = {10.1021/jp4084713},
journal = {{J. Phys. Chem. B}},
month = {nov},
number = {47},
pages = {14808--14816},
publisher = {American Chemical Society ({ACS})},
title = {Data Driven, Predictive Molecular Dynamics for Nanoscale Flow Simulations under Uncertainty},
url = {http://www.cse-lab.ethz.ch/wp-content/papercite-data/pdf/angelikopoulos2013a.pdf},
volume = {117},
year = {2013}
}