Density Peaks Clustering Based on Feature Reduction and Quasi-Monte Carlo

Density peaks clustering (DPC) is a well-known density-based clustering algorithm that can deal with nonspherical clusters well. However, DPC has high computational complexity and space complexity in calculating local density ρ and distance δ , which makes it suitable only for small-scale data sets. In addition, for clustering high-dimensional data, the performance of DPC still needs to be improved. High-dimensional data not only make the data distribution more complex but also lead to more computational overheads. To address the above issues, we propose an improved density peaks clustering algorithm, which combines feature reduction and data sampling strategy. Specifically, features of the high-dimensional data are automatically extracted by principal component analysis (PCA), auto-encoder (AE), and t-distributed stochastic neighbor embedding (t-SNE). Next, in order to reduce the computational overhead, we propose a novel data sampling method for the low-dimensional feature data. Firstly, the data distribution in the low-dimensional feature space is estimated by the Quasi-Monte Carlo (QMC) sequence with low-discrepancy characteristics. Then, the representative QMC points are selected according to their cell densities. Next, the selected QMC points are used to calculate ρ and δ instead of the original data points. In general, the number of the selected QMC points is much smaller than that of the initial data set. Finally, a two-stage classification strategy based on the QMC points clustering results is proposed to classify the original data set. Compared with current works, our proposed algorithm can reduce the computational complexity from O n 2 to O N n , where N denotes the number of selected QMC points and n is the size of original data set, typically N ≪ n . Experimental results demonstrate that the proposed algorithm can effectively reduce the computational overhead and improve the model performance.

Uncertainty quantification for aerodynamic pressure probes, using adaptive quasi-Monte Carlo

In the present study, an adaptive randomized Quasi Monte Carlo methodology is presented, combining Stein’s two-stage adaptive scheme and Low Discrepancy Sobol sequences. The method is used for the propagation and calculation of uncertainties related to aerodynamic pneumatic probes and high frequency fast response aerodynamic probes (FRAP). The proposed methodology allows the fast and accurate, in a probabilistic sense, calculation of uncertainties, ensuring that the total number of Monte Carlo (MC) trials is kept low based on the desired numerical accuracy. Thus, this method is well-suited for aerodynamic pressure probes, where multiple points are evaluated in their calibration space. Complete and detailed measurement models are presented for both a pneumatic probe and FRAP. The models are segregated in sub-problems allowing the evaluation and inspection of intermediate steps of MC in a transparent manner, also enabling the calculation of the relative contributions of the elemental uncertainties on the measured quantities. Various, commonly used sampling techniques for MC simulation and different adaptive MC schemes are compared, using both theoretical toy distributions and actual examples from aerodynamic probes' measurement models. The robustness of Stein's two-stage scheme is demonstrated even in cases when signiffcant deviation from normality is observed in the underlying distribution of the output of the MC. With regards to FRAP, two issues related to piezo-resistive sensors are addressed, namely temperature dependent pressure hysteresis and temporal sensor drift, and their uncertainties are accounted for in the measurement model. These effects are the most dominant factors, affecting all flow quantities' uncertainties, with signiffcance that varies mainly with Mach and operating temperature. This work highlights the need to construct accurate and detailed measurement models for aerodynamic probes, that otherwise will result in signiffcant underestimation (in most cases in excess of 50%) of the final uncertainties.

Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification

This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice—a setting that, as pointed out by Zeng et al. (Monte Carlo and Quasi-Monte Carlo Methods 2004, Springer, New York, 2006) and Zeng et al. (Constr. Approx. 30: 529–555, 2009), allows fast evaluation by fast Fourier transform, so avoiding the need for a linear solver. The main contribution of the paper is the application to the approximation problem for uncertainty quantification of elliptic partial differential equations, with the diffusion coefficient given by a random field that is periodic in the stochastic variables, in the model proposed recently by Kaarnioja et al. (SIAM J Numer Anal 58(2): 1068–1091, 2020). The paper gives a full error analysis, and full details of the construction of lattices needed to ensure a good (but inevitably not optimal) rate of convergence and an error bound independent of dimension. Numerical experiments support the theory.

Probabilistic Storm Surge Estimation for Landfalling Hurricanes: Advancements in Computational Efficiency Using Quasi-Monte Carlo Techniques

During landfalling tropical storms, predictions of the expected storm surge are critical for guiding evacuation and emergency response/preparedness decisions, both at regional and national levels. Forecast errors related to storm track, intensity, and size impact these predictions and, thus, should be explicitly accounted for. The Probabilistic tropical storm Surge (P-Surge) model is the established approach from the National Weather Service (NWS) to achieve this objective. Historical forecast errors are utilized to specify probability distribution functions for different storm features, quantifying, ultimately, the uncertainty in the National Hurricane Center advisories. Surge statistics are estimated by using the predictions across a storm ensemble generated by sampling features from the aforementioned probability distribution functions. P-Surge relies, currently, on a full factorial sampling scheme to create this storm ensemble, combining representative values for each of the storm features. This work investigates an alternative formulation that can be viewed as a seamless extension to the current NHC framework, adopting a quasi-Monte Carlo (QMC) sampling implementation with ultimate goal to reduce the computational burden and provide surge predictions with the same degree of statistical reliability, while using a smaller number of sample storms. The definition of forecast errors adopted here directly follows published NWS practices, while different uncertainty levels are considered in the examined case studies, in order to offer a comprehensive validation. This validation, considering different historical storms, clearly demonstrates the advantages QMC can offer.

Informing the design of courtyard street blocks using solar energy models: a case study of a university campus in Singapore

This study discusses the interplays between urban form and energy performance using a case study in Singapore. We investigate educational urban quarters in the tropical climate of Singapore using simulation-based parametric geometric modelling. Three input variables of urban form were examined: street network orientation, street canyon width, and building depth. In total, 280 scenarios were generated using a quasi-Monte Carlo Saltelli sampler and Grasshopper. For each scenario, the City Energy Analyst, an open-source urban building energy simulation program, calculated solar energy penetration. To assess the variables’ importance, we applied Sobol’ sensitivity analysis. Results suggest that the street width and building depth were the most influential parameters.