Error correction in multi-fidelity molecular dynamics simulations using functional uncertainty quantification

Abstract

We use functional, Fréchet, derivatives to quantify how thermodynamic outputs of a molecular dynamics (MD) simulation depend on the potential used to compute atomic interactions. Our approach quantifies the sensitivity of the quantities of interest with respect to the input functions as opposed to its parameters as is done in typical uncertainty quantification methods. We show that the functional sensitivity of the average potential energy and pressure in isothermal, isochoric MD simulations using Lennard-Jones two-body interactions can be used to accurately predict those properties for other interatomic potentials (with different functional forms) without re-running the simulations. This is demonstrated under three different thermodynamic conditions, namely a crystal at room temperature, a liquid at ambient pressure, and a high pressure liquid. The method provides accurate predictions as long as the change in potential does not significantly affect the region in phase space explored by the simulation. The functional uncertainty quantification approach can be used to estimate the uncertainties associated with constitutive models used in the simulation and to correct predictions if a more accurate representation becomes available.

Reliability assessment for large-scale molecular dynamics approximations

“…This reduction in the number of equations to be solved numerically, as well as the reduction in the need to evaluate the complicated expressions that occur on the right side of Eq. (20) considerably reduces the computational cost of implementing the SMA approximation.…”

“…(26) or (27), while the remaining amplitudes are determined numerically by solving Eq. (20). This approach might be appropriate for systems having a few modes with oscillation timescales comparable to the timescales associated with the macroscopic properties of the molecule.…”

“…(17)- (19) for { x CM , v CM , R, Ω}, and simply ignore the exact evolution Eq. (20) for A µ (t). We also test approximations that use angular momentum conservation instead of Eq.…”

“…We assess the reliability of our new large-scale approximation methods by applying the techniques of uncertainty quantification (UQ). [18][19][20][21][22] Here we focus attention on measuring the accuracy of our new large-scale approximation methods by comparing them to standard classical MD, setting aside other important issues such as timestepper integration errors, errors in the molecular interaction potential model, errors that arise from the use of classical rather than a fully quantum description of MD, etc. The MD evolution equations are highly non-linear, as are the equations for our large-scale approximations.…”

Probabilistic calibration of discrete element simulations using the sequential quasi-Monte Carlo filter

“…This "inversemodeling calibration" approach is expedient, because the synergy of the SQMC and SIS algorithms is well-justified for nonlinear and non-Gaussian geomechanical problems, as demonstrated in the applications of these methods to inverse finite element analyses [33,43]. A few innovative calibration methods for DEM or molecular dynamics simulations were recently proposed using Bayesian approaches [3,40,53]. Hadjidoukas et al [16,17] employed the Transitional Markov Chain Monte Carlo algorithm to find optimal parameter values in DEM simulations of silo discharge.…”