Discovering the active subspace for efficient UQ of molecular dynamics simulations of phonon transport in silicon

Abstract

Abstract This paper develops an efficient methodology for both forward and inverse problems in uncertainty quantification with respect to molecular dynamics simulation. Specifically, our objectives are to investigate the impact of uncertainty in the Stillinger-Weber (SW) potential parameters on NEMD-based predictions of bulk thermal conductivity of silicon (forward problem), and perform a Bayesian calibration of these parameters using experimental data (inverse problem). However, both analyses typically require tens of thousands of model evaluations and therefore, relying purely on atomistic simulations would be impractical. The common strategy of building a surrogate model in the space of the uncertain parameters is also unaffordable due to the need for many training evaluations using atomistic simulations. Therefore, computational effort is minimized in this paper by reducing the dimensionality of the input space of the surrogate model by first computing the so-called active subspace. The active subspace is found to be 1-dimensional, indicating enormous scope for dimension reduction and computational savings. A surrogate model is then built in the 1-dimensional subspace to help quantify the variability of the bulk thermal conductivity, and is shown to have reasonable accuracy. The active subspace is also used to perform efficient global sensitivity analysis (GSA) of the SW parameters. Finally, we use the active subspace-based surrogate model for fast calibration of SW parameters in a Bayesian setting.