@article{MolkenthinScherbaumGriewanketal.2017,
  author    = {Molkenthin, Christian and Scherbaum, Frank and Griewank, Andreas and Leovey, Hernan and Kucherenko, Sergei and Cotton, Fabrice},
  title     = {Derivative-Based Global Sensitivity Analysis: Upper Bounding of Sensitivities in Seismic-Hazard Assessment Using Automatic Differentiation},
  series = {Bulletin of the Seismological Society of America},
  volume    = {107},
  journal   = {Bulletin of the Seismological Society of America},
  publisher = {Seismological Society of America},
  address   = {Albany},
  issn      = {0037-1106},
  doi       = {10.1785/0120160185},
  pages     = {984 -- 1004},
  year      = {2017},
  abstract  = {Seismic-hazard assessment is of great importance within the field of engineering seismology. Nowadays, it is common practice to define future seismic demands using probabilistic seismic-hazard analysis (PSHA). Often it is neither obvious nor transparent how PSHA responds to changes in its inputs. In addition, PSHA relies on many uncertain inputs. Sensitivity analysis (SA) is concerned with the assessment and quantification of how changes in the model inputs affect the model response and how input uncertainties influence the distribution of the model response. Sensitivity studies are challenging primarily for computational reasons; hence, the development of efficient methods is of major importance. Powerful local (deterministic) methods widely used in other fields can make SA feasible, even for complex models with a large number of inputs; for example, automatic/algorithmic differentiation (AD)-based adjoint methods. Recently developed derivative-based global sensitivity measures can combine the advantages of such local SA methods with efficient sampling strategies facilitating quantitative global sensitivity analysis (GSA) for complex models. In our study, we propose and implement exactly this combination. It allows an upper bounding of the sensitivities involved in PSHA globally and, therefore, an identification of the noninfluential and the most important uncertain inputs. To the best of our knowledge, it is the first time that derivative-based GSA measures are combined with AD in practice. In addition, we show that first-order uncertainty propagation using the delta method can give satisfactory approximations of global sensitivity measures and allow a rough characterization of the model output distribution in the case of PSHA. An illustrative example is shown for the suggested derivative-based GSA of a PSHA that uses stochastic ground-motion simulations.},
  language  = {en}
}
@article{MolkenthinScherbaumGriewanketal.2015,
  author    = {Molkenthin, Christian and Scherbaum, Frank and Griewank, Andreas and K{\"u}hn, Nicolas and Stafford, Peter J. and Leovey, Hernan},
  title     = {Sensitivity of Probabilistic Seismic Hazard Obtained by Algorithmic Differentiation: A Feasibility Study},
  series = {Bulletin of the Seismological Society of America},
  volume    = {105},
  journal   = {Bulletin of the Seismological Society of America},
  number    = {3},
  publisher = {Seismological Society of America},
  address   = {Albany},
  issn      = {0037-1106},
  doi       = {10.1785/0120140294},
  pages     = {1810 -- 1822},
  year      = {2015},
  abstract  = {Probabilistic seismic-hazard analysis (PSHA) is the current tool of the trade used to estimate the future seismic demands at a site of interest. A modern PSHA represents a complex framework that combines different models with numerous inputs. It is important to understand and assess the impact of these inputs on the model output in a quantitative way. Sensitivity analysis is a valuable tool for quantifying changes of a model output as inputs are perturbed, identifying critical input parameters, and obtaining insight about the model behavior. Differential sensitivity analysis relies on calculating first-order partial derivatives of the model output with respect to its inputs; however, obtaining the derivatives of complex models can be challenging. In this study, we show how differential sensitivity analysis of a complex framework such as PSHA can be carried out using algorithmic/automatic differentiation (AD). AD has already been successfully applied for sensitivity analyses in various domains such as oceanography and aerodynamics. First, we demonstrate the feasibility of the AD methodology by comparing AD-derived sensitivities with analytically derived sensitivities for a basic case of PSHA using a simple ground-motion prediction equation. Second, we derive sensitivities via AD for a more complex PSHA study using a stochastic simulation approach for the prediction of ground motions. The presented approach is general enough to accommodate more advanced PSHA studies of greater complexity.},
  language  = {en}
}