| This dissertation focuses on uncertainty quantification (UQ) in molecular dynamics (MD) simulations. The application of UQ to molecular dynamics is motivated by the broad uncertainty characterizing MD potential functions and by the complexity of the MD setting, where even small uncertainties can be amplified to yield large uncertainties in the model predictions.;Two fundamental, distinct sources of uncertainty are investigated in this work, namely parametric uncertainty and intrinsic noise. Intrinsic noise is inherently present in the MD setting, due to fluctuations originating from thermal effects. Averaging methods can be exploited to reduce the fluctuations, but due to finite sampling, this effect cannot be completely filtered, thus yielding a residual uncertainty in the MD predictions. Parametric uncertainty, on the contrary, is introduced in the form of uncertain potential parameters, geometry, and/or boundary conditions. We address the UQ problem in both its main components, namely the forward propagation, which aims at characterizing how uncertainty in model parameters affects selected observables, and the inverse problem, which involves the estimation of target model parameters based on a set of observations.;The dissertation highlights the challenges arising when parametric uncertainty and intrinsic noise combine to yield non-deterministic, noisy MD predictions of target macroscale observables. Two key probabilistic UQ methods, namely Polynomial Chaos (PC) expansions and Bayesian inference, are exploited to develop a framework that enables one to isolate the impact of parametric uncertainty on the MD predictions and, at the same time, properly quantify the effect of the intrinsic noise. Systematic applications to a suite of problems of increasing complexity lead to the observation that an uncertain PC representation built via Bayesian regression is the most suitable model for the representation of uncertain MD predictions of target observables in the presence of intrinsic noise and parametric uncertainty.;The dissertation is organized in successive, self-contained problems of increasing complexity aimed at investigating the target UQ challenge in a progressive fashion. |
