### Abstract

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.

Original language | English |
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Article number | 224108 |

Journal | Journal of Chemical Physics |

Volume | 145 |

DOIs | |

Publication status | Published - 14 Dec 2016 |

### Keywords

- Finite difference methods
- Anomalous diffusion
- Signal processing
- Double-well potential
- Stochastic processes
- Brownian motion
- Cognitive science
- Optimization
- Regression analysis
- Langevin dynamics
- SDE

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## Cite this

Hall, E. J., Katsoulakis, M. A., & Rey-Bellet, L. (2016). Uncertainty quantification for generalized Langevin dynamics.

*Journal of Chemical Physics*,*145*, [224108 ]. https://doi.org/10.1063/1.4971433