TY - JOUR
T1 - Adaptive sampling-based quadrature rules for efficient Bayesian prediction
AU - van den Bos, L. M.M.
AU - Sanderse, B.
AU - Bierbooms, W. A.A.M.
PY - 2020
Y1 - 2020
N2 - A novel method is proposed to infer Bayesian predictions of computationally expensive models. The method is based on the construction of quadrature rules, which are well-suited for approximating the weighted integrals occurring in Bayesian prediction. The novel idea is to construct a sequence of nested quadrature rules with positive weights that converge to a quadrature rule that is weighted with respect to the posterior. The quadrature rules are constructed using a proposal distribution that is determined by means of nearest neighbor interpolation of all available evaluations of the posterior. It is demonstrated both theoretically and numerically that this approach yields accurate estimates of the integrals involved in Bayesian prediction. The applicability of the approach for a fluid dynamics test case is demonstrated by inferring accurate predictions of the transonic flow over the RAE2822 airfoil with a small number of model evaluations. Here, the closure coefficients of the Spalart–Allmaras turbulence model are considered to be uncertain and are calibrated using wind tunnel measurements.
AB - A novel method is proposed to infer Bayesian predictions of computationally expensive models. The method is based on the construction of quadrature rules, which are well-suited for approximating the weighted integrals occurring in Bayesian prediction. The novel idea is to construct a sequence of nested quadrature rules with positive weights that converge to a quadrature rule that is weighted with respect to the posterior. The quadrature rules are constructed using a proposal distribution that is determined by means of nearest neighbor interpolation of all available evaluations of the posterior. It is demonstrated both theoretically and numerically that this approach yields accurate estimates of the integrals involved in Bayesian prediction. The applicability of the approach for a fluid dynamics test case is demonstrated by inferring accurate predictions of the transonic flow over the RAE2822 airfoil with a small number of model evaluations. Here, the closure coefficients of the Spalart–Allmaras turbulence model are considered to be uncertain and are calibrated using wind tunnel measurements.
KW - Adaptivity
KW - Bayesian prediction
KW - Interpolation
KW - Quadrature and cubature formulas
UR - http://www.scopus.com/inward/record.url?scp=85085657402&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2020.109537
DO - 10.1016/j.jcp.2020.109537
M3 - Article
AN - SCOPUS:85085657402
SN - 0021-9991
VL - 417
JO - Journal of Computational Physics
JF - Journal of Computational Physics
M1 - 109537
ER -