Sparse grid

About: Sparse grid is a research topic. Over the lifetime, 1013 publications have been published within this topic receiving 20664 citations.

Monte Carlo estimation of sparse grid interpolation residual for stochastic collocation of high-order systems with uncertainties

Abstract: In fast sampling-based stochastic numerical techniques, Smolyak-based sparse grids are used to construct interpolation of the system output in random domain. The accuracy and convergence of sparse grid interpolations are evaluated by calculating the residual of the interpolation outputs compared with actual output values at grid nodes of higher levels. The residual is used as a criteria for adaptive refinement, as well as local refinement of sparse grids. In this paper, we propose a Monte Carlo sampling-based method to estimate the residual of sparse grid interpolations.

Heterogeneous Distributed Big Data Clustering on Sparse Grids

Abstract: Clustering is an important task in data mining that has become more challenging due to the ever-increasing size of available datasets. To cope with these big data scenarios, a high-performance clustering approach is required. Sparse grid clustering is a density-based clustering method that uses a sparse grid density estimation as its central building block. The underlying density estimation approach enables the detection of clusters with non-convex shapes and without a predetermined number of clusters. In this work, we introduce a new distributed and performance-portable variant of the sparse grid clustering algorithm that is suited for big data settings. Our computed kernels were implemented in OpenCL to enable portability across a wide range of architectures. For distributed environments, we added a manager–worker scheme that was implemented using MPI. In experiments on two supercomputers, Piz Daint and Hazel Hen, with up to 100 million data points in a ten-dimensional dataset, we show the performance and scalability of our approach. The dataset with 100 million data points was clustered in 1198 s using 128 nodes of Piz Daint. This translates to an overall performance of 352 TFLOPS . On the node-level, we provide results for two GPUs, Nvidia’s Tesla P100 and the AMD FirePro W8100, and one processor-based platform that uses Intel Xeon E5-2680v3 processors. In these experiments, we achieved between 43% and 66% of the peak performance across all computed kernels and devices, demonstrating the performance portability of our approach.

Gradient-Enhanced Kriging

Abstract: Aexible non-intrusive approach to parametric uncertainty quantication problems is developed, aimed at problems with many uncertain parameters, and for applications with a high cost of functional evaluations. It employs a Kriging response surface in the parameter space, augmented with gradients obtained from the adjoint of the deterministic equations. The Kriging correlation parameter optimization problem is solved using the Subplex algorithm, which is robust for noisy functionals, and whose eort typically increases only linearly with problem dimension. Integration over the resulting response surface to obtain statistical moments is performed using sparse grid techniques, which are designed to scale well with dimensionality. The eciency and accuracy of the proposed method is compared with probabilistic collocation, direct application of sparse grid methods, and Monte-Carlo initially for model problems, and nally for a 2d compressible Navier-Stokes problem with a random geometry parameterized by 4 variables.

Vehicle traveling state estimation method based on sparse grid integrating Kalman filtering

Abstract: The invention discloses a vehicle traveling state estimation method based on sparse grid integrating Kalman filtering. Through a selected seven-degree-of-freedom vehicle motion module, on the basis ofan integrating Kalman filtering method combining with a sparse grid theory, multidimensional integration points are selected, time upgrading and measurement upgrading are conducted, and the longitudinal vehicle speed, the lateral vehicle speed and the side slip angle of a vehicle are estimated. The vehicle traveling state parameter estimation method has the characteristic of high precision, and the real-time performance of state parameter estimation can be effectively improved while the state estimation precision is improved.

Sobol Indices for Dimension Adaptivity in Sparse Grids

Abstract: Propagation of random variables through computer codes of many inputs is primarily limited by computational expense. The use of sparse grids mitigates these costs somewhat; here we show how Sobol indices can be used to perform dimension adaptivity to mitigate them further. The method is compared to conventional adaptation schemes on sparse grids (Gerstner and Griebel, Computing 71(1), 65–87, 2003), and seen to perform comparably,without requiring the expense associated with a look-ahead error estimate. It is demonstrated for an expensive computer model of contaminant flow over a barrier.