Data-Driven Model Reduction for the Bayesian Solution of Inverse Problems

One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo (MCMC) methods for posterior sampling. This paper proposes a data-driven projection-based model reduction technique to reduce this computational cost. The proposed technique has two distinctive features. First, the model reduction strategy is tailored to inverse problems: the snapshots used to construct the reduced-order model are computed adaptively from the posterior distribution. Posterior exploration and model reduction are thus pursued simultaneously. Second, to avoid repeated evaluations of the full-scale numerical model as in a standard MCMC method, we couple the full-scale model and the reduced-order model together in the MCMC algorithm. This maintains accurate inference while reducing its overall computational cost. In numerical experiments considering steady-state flow in a porous medium, the data-driven reduced-order model achieves better accuracy than a reduced-order model constructed using the classical approach. It also improves posterior sampling efficiency by several orders of magnitude compared to a standard MCMC method

Eigenvalue problems for a three-point boundary-value problem on a time scale

Let $\mathbb{T}$ be a time scale such that $0, T \in \mathbb{T}$. We us a cone theoretic fixed point theorem to obtain intervals for $\lambda$ for which the second order dynamic equation on a time scale, \begin{gather*} u^{\Delta\nabla}(t) + \lambda a(t)f(u(t)) = 0, \quad t \in (0,T) \cap \mathbb{T},\\ u(0) = 0, \quad \alpha u(\eta) = u(T), \end{gather*} where $\eta \in (0, \rho(T)) \cap \mathbb{T}$, and $0 < \alpha <T/\eta$, has a positive solution

Flexible body dynamic stability for high performance aircraft

Dynamic equations which include the effects of unsteady aerodynamic forces and a flexible body structure were developed for a free flying high performance fighter aircraft. The linear and angular deformations are assumed to be small in the body reference frame, allowing the equations to be linearized in the deformation variables. Equations for total body dynamics and flexible body dynamics are formulated using the hybrid coordinate method and integrated in a state space format. A detailed finite element model of a generic high performance fighter aircraft is used to generate the mass and stiffness matrices. Unsteady aerodynamics are represented by a rational function approximation of the doublet lattice matrices. The equations simplify for the case of constant angular rate of the body reference frame, allowing the effect of roll rate to be studied by computing the eigenvalues of the system. It is found that the rigid body modes of the aircraft are greatly affected by introducing a constant roll rate, while the effect on the flexible modes is minimal for this configuration

The contingent factors that affect the use of performance measurement systems in the Egyptian medium and large sized manufacturing companies

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Detection of Lead in the Carbon-Rich, Very Metal-Poor Star LP625-44: A Strong Constraint on s-Process Nucleosynthesis at Low Metallicity

We report the detection of the Pb I 4057.8A line in the very metal-poor ([Fe/H]=-2.7), carbon-rich star, LP625-44. We determine the abundance of Pb ([Pb/Fe] = 2.65) and 15 other neutron-capture elements. The abundance pattern between Ba and Pb agrees well with a scaled solar system s-process component, while the lighter elements (Sr-Zr) are less abundant than Ba. The enhancement of s-process elements is interpreted as a result of mass transfer in a binary system from a previous AGB companion, an interpretation strongly supported by radial velocity variations of this system. The detection of Pb makes it possible, for the first time, to compare model predictions of s-process nucleosynthesis in AGB stars with observations of elements between Sr and Pb. The Pb abundance is significantly lower than the prediction of recent models (e.g., Gallino et al. 1998), which succeeded in explaining the metallicity dependence of the abundance ratios of light s-elements (Sr-Zr) to heavy ones (Ba-Dy) found in previously observed s-process-enhanced stars. This suggests that one should either (a) reconsider the underlying assumptions concerning the 13C-rich s-processing site (13C-pocket) in the present models, or (b) investigate alternative sites of s-process nucleosynthesis in very metal-poor AGB stars.Comment: 10 pages, 3 figures, Astrophysical Journal Letters, in pres