@article{1463624,
      recid = {1463624},
      author = {Cacuci, Dan Gabriel, and Fang, Ruixian},
      title = {The nth-order comprehensive adjoint sensitivity analysis  methodology., Volume II,: Overcoming the curse of  dimensionality : large-scale application /},
      pages = {1 online resource (xvii, 463 pages) :},
      abstract = {This text describes a comprehensive adjoint sensitivity  analysis methodology (C-ASAM), developed by the author,  enabling the efficient and exact computation of arbitrarily  high-order functional derivatives of model responses to  model parameters in large-scale systems. The C-ASAM  framework is set in linearly increasing Hilbert spaces,  each of state-function-dimensionality, as opposed to  exponentially increasing parameter-dimensional spaces,  thereby breaking the so-called curse of dimensionality in  sensitivity and uncertainty analysis. The C-ASAM applies to  any model; the larger the number of model parameters, the  more efficient the C-ASAM becomes for computing arbitrarily  high-order response sensitivities. The book will be helpful  to those working in the fields of sensitivity analysis,  uncertainty quantification, model validation, optimization,  data assimilation, model calibration, sensor fusion,  reduced-order modelling, inverse problems and predictive  modelling. This Volume Two, the second of three, presents  the large-scale application of C-ASAM to compute exactly  the first-, second-, third-, and fourth-order sensitivities  of the Polyethylene-Reflected Plutonium (PERP) OECD/NEO  international benchmark which is modeled mathematically by  the Boltzmann particle transport equation. It follows from  the description of the C-ASAM framework applied to linear  systems in Volume One where the PERP benchmark's response  of interest is the leakage of particles through its outer  boundary. The benchmark represents the largest sensitivity  analysis endeavor ever carried out in the field of reactor  physics and the numerical results shown in this book prove,  for the first time ever, that many of the second-order  sensitivities are much larger than the corresponding  first-order ones. Currently, the nth-CASAM is the only  known methodology which enables such large-scale  computations of the exact expressions and values of the  nth-order response sensitivities.},
      url = {http://library.usi.edu/record/1463624},
      doi = {https://doi.org/10.1007/978-3-031-19635-5},
}