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A Hybrid Approach to Estimating Error Covariances in Variational Data Assimilation
Get PDFData Assimilation (DA) involves the combination of observational data with the underlying dynamical principles governing the system under observation. In this work we combine the advantages of the two prominent advanced data assimilation systems, the 4D-Var and the ensemble methods. The proposed method consists of identifying the subspace spanned by the major 4D-Var error reduction directions. These directions are then removed from the background covariance through a Galerkin-type projection. This generates an updated error covariance information at both end points of an assimilation window. The error covariance information is updated between assimilation windows to capture the ``error of the day''. Numerical results using our new hybrid approach on a nonlinear model demonstrate how the background covariance matrix leads to an error covariance update that improves the 4D-Var DA results
Continuous Iterative Guided Spectral Class Rejection Classification Algorithm: Part 2
Get PDFThis paper describes in detail the continuous iterative guided spectral class rejection (CIGSCR) classification method based on the iterative guided spectral class rejection (IGSCR) classification method for remotely sensed data. Both CIGSCR and IGSCR use semisupervised clustering to locate clusters that are associated with classes in a classification scheme. In CIGSCR and IGSCR, training data are used to evaluate the strength of the association between a particular cluster and a class, and a statistical hypothesis test is used to determine which clusters should be associated with a class and used for classification and which clusters should be rejected and possibly reï¬ned. Experimental results indicate that the soft classification output by CIGSCR is reasonably accurate (when compared to IGSCR), and the fundamental algorithmic changes in CIGSCR (from IGSCR) result in CIGSCR being less sensitive to input parameters that influence iterations. Furthermore, evidence is presented that the semisupervised clustering in CIGSCR produces more accurate classifications than classification based on clustering without supervision
Continuous Iterative Guided Spectral Class Rejection Classiï¬cation Algorithm: Part 1
Get PDFThis paper outlines the changes necessary to convert the iterative guided spectral class rejection (IGSCR) classification algorithm to a soft classification algorithm. IGSCR uses a hypothesis test to select clusters to use in classification and iteratively reï¬nes clusters not yet selected for classification. Both steps assume that cluster and class memberships are crisp (either zero or one). In order to make soft cluster and class assignments (between zero and one), a new hypothesis test and iterative reï¬nement technique are introduced that are suitable for soft clusters. The new hypothesis test, called the (class) association signiï¬cance test, is based on the normal distribution, and a proof is supplied to show that the assumption of normality is reasonable. Soft clusters are iteratively reï¬ned by creating new clusters using information contained in a targeted soft cluster. Soft cluster evaluation and reï¬nement can then be combined to form a soft classification algorithm, continuous iterative guided spectral class rejection (CIGSCR)
A Library for Pattern-based Sparse Matrix Vector Multiply
Get PDFPattern-based Representation (PBR) is a novel approach to improving the performance of Sparse Matrix-Vector Multiply (SMVM) numerical kernels. Motivated by our observation that many matrices can be divided into blocks that share a small number of distinct patterns, we generate custom multiplication kernels for frequently recurring block patterns.
The resulting reduction in index overhead significantly reduces memory bandwidth requirements and improves performance. Unlike existing methods, PBR requires neither detection of dense blocks nor zero filling, making it particularly advantageous for matrices that lack dense nonzero concentrations. SMVM kernels for PBR can benefit from explicit prefetching and vectorization, and are amenable to parallelization. The analysis and format conversion to PBR is implemented as a library, making it suitable for applications that generate matrices dynamically at runtime. We present sequential and parallel performance results for PBR on two current multicore architectures, which show that PBR outperforms available alternatives for the matrices to which it is applicable,
and that the analysis and conversion overhead is amortized in realistic application scenarios
Algorithm XXX: SHEPPACK: Modiï¬ed Shepard Algorithm for Interpolation of Scattered Multivariate Data
Get PDFScattered data interpolation problems arise in many applications. Shepard’s method for constructing a global interpolant by blending local interpolants using local-support weight functions usually creates reasonable approximations. SHEPPACK is a Fortran 95 package containing ï¬ve versions of the modified Shepard algorithm: quadratic (Fortran 95 translations of Algorithms 660, 661, and 798), cubic (Fortran 95 translation of Algorithm 791), and linear variations of the original Shepard algorithm. An option to the linear Shepard code is a statistically robust ï¬t, intended to be used when the data is known to contain outliers. SHEPPACK also includes a hybrid robust piecewise linear estimation algorithm RIPPLE (residual initiated polynomial-time piecewise linear estimation) intended for data from piecewise linear functions in arbitrary dimension m. The main goal of SHEPPACK is to provide users with a single consistent package containing most existing polynomial variations of Shepard’s algorithm. The algorithms target data of different dimensions. The linear Shepard algorithm, robust linear Shepard algorithm, and RIPPLE are the only algorithms in the package that are applicable to arbitrary dimensional data
The Expected Fitness Cost of a Mutation Fixation under the One-dimensional Fisher Model
Get PDFThis paper employs Fisher’s model of adaptation to understand the expected fitness
effect of ï¬xing a mutation in a natural population. Fisher’s model in one dimension admits
a closed form solution for this expected ï¬tness effect. A combination of different parameters, including the distribution of mutation lengths, population sizes, and the initial state that the population is in, are examined to see how they affect the expected ï¬tness effect of state transitions. The results show that the expected fitness change due to the ï¬xation of a mutation is always positive, regardless of the distributional shapes of mutation lengths, effective population sizes, and the initial state that the population is in. The further away the initial state of a population is from the optimal state, the slower the population returns to the optimal state. Effective population size (except when very small) has little effect on the expected ï¬tness change due to mutation fixation. The always positive expected ï¬tness change suggests that small populations may not necessarily be doomed due to the runaway process of fixation of deleterious mutations
ScALPEL: A Scalable Adaptive Lightweight Performance Evaluation Library for application performance monitoring
Get PDFAs supercomputers continue to grow in scale and capabilities, it is becoming increasingly difficult to isolate processor and system level causes of performance degradation. Over the last several years, a significant number of performance analysis and monitoring tools have been built/proposed. However, these tools suffer from several important shortcomings, particularly in distributed environments. In this paper we present ScALPEL, a Scalable Adaptive Lightweight Performance Evaluation Library for application performance monitoring at the functional level. Our approach provides several distinct advantages. First, ScALPEL is portable across a wide variety of architectures, and its ability to selectively monitor functions presents low run-time overhead, enabling its use for large-scale production applications. Second, it is run-time configurable, enabling both dynamic selection of functions to profile as well as events of interest on a per function basis. Third, our approach is transparent in that it requires no source code modifications. Finally, ScALPEL is implemented as a pluggable unit by reusing existing performance monitoring frameworks such as Perfmon and PAPI and extending them to support both sequential and MPI applications
Clustering constrained by dependencies
Get PDFClustering is the unsupervised method of grouping data samples to form a partition of a given dataset. Such grouping is typically done based on homogeneity assumptions of clusters over an attribute space and hence the precise definition of the similarity metric affects the clusters inferred. In recent years, new formulations of clustering have emerged that posit indirect constraints on clustering, typically in terms of preserving dependencies between data samples and auxiliary variables. These formulations ï¬nd applications in bioinformatics, web mining, social network analysis, and many other domains. The purpose of this survey is to provide a gentle introduction to these formulations, their mathematical assumptions, and the contexts under which they are applicable
Accelerating Electrostatic Surface Potential Calculation with Multiscale Approximation on Graphics Processing Units
Get PDFTools that compute and visualize biomolecular electrostatic surface potential have been used extensively for studying biomolecular function. However, determining the surface potential for large biomolecules on a typical desktop computer can take days or longer using currently available tools and methods. This paper demonstrates how one can take advantage of graphic processing units (GPUs) available in today’s typical desktop computer, together with a multiscale approximation method, to significantly speedup such computations. Specifically, the electrostatic potential computation, using an analytical linearized Poisson Boltzmann (ALPB) method, is implemented on an ATI Radeon 4870 GPU in combination with the hierarchical charge partitioning (HCP) multiscale approximation. This implementation delivers a combined 1800-fold speedup for a 476,040 atom viral capsid
Data Driven Surrogate Based Optimization in the Problem Solving Environment WBCSim
Get PDFLarge scale, multidisciplinary, engineering designs are always difficult due to the complexity and dimensionality of these problems. Direct coupling between the analysis codes and the optimization routines can be prohibitively time consuming due to the complexity of the underlying simulation codes. One way of tackling this problem is by constructing computationally cheap(er) approximations of the expensive simulations, that mimic the behavior of the simulation model as closely as possible. This paper presents a data driven, surrogate based optimization algorithm that uses a trust region based sequential approximate optimization (SAO) framework and a statistical sampling approach based on design of experiment (DOE) arrays. The algorithm is implemented using techniques from two packages—SURFPACK and SHEPPACK that provide a collection of approximation algorithms to build the surrogates and three different DOE techniques—full factorial (FF), Latin hypercube sampling (LHS), and central composite design (CCD)—are used to train the surrogates. The results are compared with the optimization results obtained by directly coupling an optimizer with the simulation code. The biggest concern in using the SAO framework based on statistical sampling is the generation of the required database. As the number of design variables grows, the computational cost of generating the required database grows rapidly. A data driven approach is proposed to tackle this situation, where the trick is to run the expensive simulation if and only if a nearby data point does not exist in the cumulatively growing database. Over time the database matures and is enriched as more and more optimizations are performed. Results show that the proposed methodology dramatically reduces the total number of calls to the expensive simulation runs during the optimization process