Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks

Shrinkage Estimation of the Power Spectrum Covariance Matrix

We seek to improve estimates of the power spectrum covariance matrix from a limited number of simulations by employing a novel statistical technique known as shrinkage estimation. The shrinkage technique optimally combines an empirical estimate of the covariance with a model (the target) to minimize the total mean squared error compared to the true underlying covariance. We test this technique on N-body simulations and evaluate its performance by estimating cosmological parameters. Using a simple diagonal target, we show that the shrinkage estimator significantly outperforms both the empirical covariance and the target individually when using a small number of simulations. We find that reducing noise in the covariance estimate is essential for properly estimating the values of cosmological parameters as well as their confidence intervals. We extend our method to the jackknife covariance estimator and again find significant improvement, though simulations give better results. Even for thousands of simulations we still find evidence that our method improves estimation of the covariance matrix. Because our method is simple, requires negligible additional numerical effort, and produces superior results, we always advocate shrinkage estimation for the covariance of the power spectrum and other large-scale structure measurements when purely theoretical modeling of the covariance is insufficient.Comment: 9 pages, 7 figures (1 new), MNRAS, accepted. Changes to match accepted version, including an additional explanatory section with 1 figur

One-point fluctuation analysis of the high-energy neutrino sky

We perform the first one-point fluctuation analysis of the high-energy neutrino sky. This method reveals itself to be especially suited to contemporary neutrino data, as it allows to study the properties of the astrophysical components of the high-energy flux detected by the IceCube telescope, even with low statistics and in the absence of point source detection. Besides the veto-passing atmospheric foregrounds, we adopt a simple model of the high-energy neutrino background by assuming two main extra-galactic components: star-forming galaxies and blazars. By leveraging multi-wavelength data from Herschel and Fermi, we predict the spectral and anisotropic probability distributions for their expected neutrino counts in IceCube. We find that star-forming galaxies are likely to remain a diffuse background due to the poor angular resolution of IceCube, and we determine an upper limit on the number of shower events that can reasonably be associated to blazars. We also find that upper limits on the contribution of blazars to the measured flux are unfavourably affected by the skewness of the blazar flux distribution. One-point event clustering and likelihood analyses of the IceCube HESE data suggest that this method has the potential to dramatically improve over more conventional model-based analyses, especially for the next generation of neutrino telescopes.Comment: 41 pages, 6 figures, 2 tables; different blazar model than v1 but same result

Screening and metamodeling of computer experiments with functional outputs. Application to thermal-hydraulic computations

To perform uncertainty, sensitivity or optimization analysis on scalar variables calculated by a cpu time expensive computer code, a widely accepted methodology consists in first identifying the most influential uncertain inputs (by screening techniques), and then in replacing the cpu time expensive model by a cpu inexpensive mathematical function, called a metamodel. This paper extends this methodology to the functional output case, for instance when the model output variables are curves. The screening approach is based on the analysis of variance and principal component analysis of output curves. The functional metamodeling consists in a curve classification step, a dimension reduction step, then a classical metamodeling step. An industrial nuclear reactor application (dealing with uncertainties in the pressurized thermal shock analysis) illustrates all these steps