Uncertainty quantification for generalized Langevin dynamics

TY - JOUR

T1 - Uncertainty quantification for generalized Langevin dynamics

AU - Hall, Eric J.

AU - Katsoulakis, Markos A.

AU - Rey-Bellet, Luc

PY - 2016/12/14

Y1 - 2016/12/14

N2 - We present efficient finite difference estimators for goal-oriented sensitivity indices with applications to the generalized Langevin equation (GLE). In particular, we apply these estimators to analyze an extended variable formulation of the GLE where other well known sensitivity analysis techniques such as the likelihood ratio method are not applicable to key parameters of interest. These easily implemented estimators are formed by coupling the nominal and perturbed dynamics appearing in the finite difference through a common driving noise or common random path. After developing a general framework for variance reduction via coupling, we demonstrate the optimality of the common random path coupling in the sense that it produces a minimal variance surrogate for the difference estimator relative to sampling dynamics driven by independent paths. In order to build intuition for the common random path coupling, we evaluate the efficiency of the proposed estimators for a comprehensive set of examples of interest in particle dynamics. These reduced variance difference estimators are also a useful tool for performing global sensitivity analysis and for investigating non-local perturbations of parameters, such as increasing the number of Prony modes active in an extended variable GLE.

AB - We present efficient finite difference estimators for goal-oriented sensitivity indices with applications to the generalized Langevin equation (GLE). In particular, we apply these estimators to analyze an extended variable formulation of the GLE where other well known sensitivity analysis techniques such as the likelihood ratio method are not applicable to key parameters of interest. These easily implemented estimators are formed by coupling the nominal and perturbed dynamics appearing in the finite difference through a common driving noise or common random path. After developing a general framework for variance reduction via coupling, we demonstrate the optimality of the common random path coupling in the sense that it produces a minimal variance surrogate for the difference estimator relative to sampling dynamics driven by independent paths. In order to build intuition for the common random path coupling, we evaluate the efficiency of the proposed estimators for a comprehensive set of examples of interest in particle dynamics. These reduced variance difference estimators are also a useful tool for performing global sensitivity analysis and for investigating non-local perturbations of parameters, such as increasing the number of Prony modes active in an extended variable GLE.

KW - Finite difference methods

KW - Anomalous diffusion

KW - Signal processing

KW - Double-well potential

KW - Stochastic processes

KW - Brownian motion

KW - Cognitive science

KW - Optimization

KW - Regression analysis

KW - Langevin dynamics

KW - SDE

UR - https://arxiv.org/abs/1609.02739

U2 - 10.1063/1.4971433

DO - 10.1063/1.4971433

M3 - Article

SN - 0021-9606

VL - 145

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

M1 - 224108

ER -