Implementing Randomized Matrix Algorithms in Parallel and Distributed Environments

Enriched multi objective optimization model based cloud disaster recovery

Summary In recent years, machine learning methods have been widely used in various fields of science for big data processing. The application of machine learning in the oil industry is also actively expanding. To solve oil recovery problems, it is necessary to use geological models of reservoir fields. With increasing of the reservoir model complexity (size), the computing time also increases. Therefore, it takes longer to predict oil recovery. There are two approaches to solve this problem. The first approach is to develop an effective parallel algorithm taking into account the heterogeneity of computing systems. Many scientists from all over the world are developing parallel algorithms in this field. In particular, we have written many scientific papers. The disadvantage of using this approach is that when you change the initial data for the oil recovery prediction, you need to make calculations on supercomputers every time, which takes a lot of time and resources. The second approach is to use machine learning methods, which is the purpose of this paper. This paper discusses approaches to using effective machine learning methods for oil recovery prediction. To train the system, we used historical data from the oil field and synthetic data obtained from surrogate models based on two wells (injection and production). Synthetic data were generated based on mathematical models (oil displacement models, enhanced oil recovery models) by varying the different geological parameters. This problem belongs to the “supervised learning” - type of machine learning. Supervised learning requires a complete set of marked data for training the model at all stages of its construction. When implementing the algorithm, we considered machine learning methods for solving the regression and classification problems. As a result, it was discovered that compared to traditional computational experiments on a regular grid, calculations using machine learning methods are more productive.

The modeling of physical phenomena in computational fracture mechanics, computational fluid dynamics and other fields is based on solving systems of partial differential equations (PDEs). When PDEs are defined over geometrically complex domains, they often do not admit closed form solutions. In such cases, they are solved approximately using discretizations of domains into simple elements like triangles and quadrilaterals in two dimensions (2D), and tetrahedra and hexahedra in three dimensions (3D). These discretizations are called finite element meshes. Many applications, for example, real-time computer assisted surgery, or crack propagation from fracture mechanics, impose time and/or mesh size constraints that cannot be met on a single sequential machine. As a result, the development of parallel mesh generation algorithms is required. In this dissertation, we describe a complete solution for both sequential and parallel construction of guaranteed quality Delaunay meshes for 2D and 3D geometries. First, we generalize the existing 2D and 3D Delaunay refinement algorithms along with theoretical proofs of mesh quality in terms of element shape and mesh gradation. Existing algorithms are constrained by just one or two specific positions for the insertion of a Steiner point inside a circumscribed disk of a poorly shaped element. We derive an entire 2D or 3D region for the selection of a Steiner point (i.e., infinitely many choices) inside the circumscribed disk. Second, we develop a novel theory which extends both the 2D and the 3D Generalized Delaunay Refinement methods for the concurrent and mathematically guaranteed independent insertion of Steiner points. Previous parallel algorithms are either reactive relying on implementation heuristics to resolve dependencies in parallel mesh generation computations or require the solution of a very difficult geometric optimization problem (the domain decomposition problem) which is still open for general 3D geometries. Our theory solves both of these drawbacks. Third, using our generalization of both the sequential and the parallel algorithms we implemented prototypes of practical and efficient parallel generalized guaranteed quality Delaunay refinement codes for both 2D and 3D geometries using existing state-of-the-art sequential codes for traditional Delaunay refinement methods. On a heterogeneous cluster of more than 100 processors our implementation can generate a uniform mesh with about a billion elements in less than 5 minutes. Even on a workstation with a few cores, we achieve a significant performance improvement over the corresponding state-of-the-art sequential 3D code, for graded meshes.

Random projection algorithm is an iterative gradient method with random projections. Such an algorithm is of interest for constrained optimization when the constraint set is not known in advance or the projection operation on the whole constraint set is computationally prohibitive. This paper presents a distributed random projection (DRP) algorithm for fully distributed constrained convex optimization problems that can be used by multiple agents connected over a time-varying network, where each agent has its own objective function and its own constrained set. With reasonable assumptions, we prove that the iterates of all agents converge to the same point in the optimal set almost surely. In addition, we consider a variant of the method that uses a mini-batch of consecutive random projections and establish its convergence in almost sure sense. Experiments on distributed support vector machines demonstrate fast convergence of the algorithm. It actually shows that the number of iteration required until convergence is much smaller than scanning over all training samples just once.

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An efficient parallel algorithm is presented for computing selected components of $A^{-1}$ where A is a structured symmetric sparse matrix. Calculations of this type are useful for several applications, including electronic structure analysis of materials in which the diagonal elements of the Green's functions are needed. The algorithm proposed here is a direct method based on a block $LDL^T$ factorization. The selected elements of $A^{-1}$ we compute lie in the nonzero positions of $L+L^T$. We use the elimination tree associated with the block $LDL^T$ factorization to organize the parallel algorithm, and reduce the synchronization overhead by passing the data level by level along this tree using the technique of local buffers and relative indices. We demonstrate the efficiency of our parallel implementation by applying it to a discretized two dimensional Hamiltonian matrix. We analyze the performance of the parallel algorithm by examining its load balance and communication overhead, and show that our parallel implementation exhibits an excellent weak scaling on a large-scale high performance distributed-memory parallel machine.

In the last decade, advances in data collection and storage technologies have led to an increased interest in designing and implementing large-scale parallel algorithms for machine learning and data mining (ML-DM). Existing programming paradigms for expressing large-scale parallelism such as MapReduce (MR) and the Message Passing Interface (MPI) have been the de facto choices for implementing these ML-DM algorithms. The MR programming paradigm has been of particular interest as it gracefully handles large datasets and has built-in resilience against failures. However, the existing parallel programming paradigms are too low-level and ill-suited for implementing ML-DM algorithms. To address this deficiency, we present NIMBLE, a portable infrastructure that has been specifically designed to enable the rapid implementation of parallel ML-DM algorithms. The infrastructure allows one to compose parallel ML-DM algorithms using reusable (serial and parallel) building blocks that can be efficiently executed using MR and other parallel programming models; it currently runs on top of Hadoop, which is an open-source MR implementation. We show how NIMBLE can be used to realize scalable implementations of ML-DM algorithms and present a performance evaluation.

Motif finding problems, abstracted as the planted (l, d)-motif finding problem, are a major task in molecular biology--finding functioning units and genes. In 2002, the random projection algorithm was introduced to solve the challenging (15, 4)-motif finding problem by using randomly chosen templates. Two years later, a so-called uniform projection algorithm was developed to improve the random projection algorithm by means of low-dispersion sequences generated by coverings. In this article, we introduce an improved projection algorithm called the low-dispersion projection algorithm, which uses low-dispersion sequences generated by developed almost difference families. Compared with the random projection algorithm, the low-dispersion projection algorithm can solve the (l, d)-motif finding problem with fewer templates without decreasing the success rate.

Submodular maximization has wide applications in machine learning and data mining, where massive datasets have brought the great need for designing efficient and parallelizable algorithms. One measure of the parallelizability of a submodular maximization algorithm is its adaptivity complexity, which indicates the number of sequential rounds where a polynomial number of queries to the objective function can be executed in parallel. In this paper, we study the problem of non-monotone submodular maximization subject to a knapsack constraint, and propose the first combinatorial algorithm achieving an (8+epsilon)-approximation under O(log n) adaptive complexity, which is optimal up to a factor of O(loglog n). Moreover, under slightly larger adaptivity, we also propose approximation algorithms with nearly optimal query complexity of O(n), while achieving better approximation ratios. We show that our algorithms can also be applied to the special case of submodular maximization subject to a cardinality constraint, and achieve performance bounds comparable with those of state-of-the-art algorithms. Finally, the effectiveness of our approach is demonstrated by extensive experiments on real-world applications.

The penetration of Wireless Sensor Networks (WSNs) in various applications poses a high demand on reliable data storage, especially considering sensor networks are usually deployed in harsh environment. In this paper, we introduce Heterogeneous Wireless Sensor Networks where robust storage nodes are deployed in sensor networks and data redundancy is utilized through coding techniques, in order to improve the reliability of data storage. Taking into account the cost of both data delivery and storage, we propose an algorithm to jointly optimize data routing and storage node deployment. This problem is a binary non-linear combinatorial optimization, and it is highly non-trivial to design efficient algorithms due to its NP-hardness. By levering the Markov approximation framework, we elaborately deign a Continuous Time Markov Chain (CTMC) based scheduling algorithm to drive the storage node deployment and the corresponding routing strategy. Extensive simulations are performed to verify the efficacy of our algorithm.

In this paper we study the important problems of message routing, sorting, and selection in a radio network. A radio network consists of stations where each station is a hand-held device. We consider a single-hop radio network. In a single-hop network it is assumed that each station is within the transmission range of every other station. Let RN(p; k) stand for a single-hop network that has p stations and k communication channels. The problems of sorting and selection have been studied on RN(p; k). For these problems it is assumed that there are n/p elements to start with at each station. At the end of sorting, the least n/p elements should be in the first station, the next smallest n/p elements should be in the second station, and so on. The best known prior algorithm for sorting takes 4n/k +o(n/k) broadcast rounds on a RN(p; k). In this paper we present a randomized algorithm that takes only 3n/k +o(n/k) broadcast rounds with high probability. For the selection problem, it is known that the maximum or minimum element can be found in O(log n) rounds on a RN(n; 1), provided broadcast conflicts can be resolved in O(1) time. The problem of general selection has not been addressed. In this paper we present a randomized selection algorithm that takes O(p/k) rounds on a RN(p; k) with high probability. An important message routing problem that is considered in the literature is one where there are n/p packets originating from each station and there are n/p packets destined for each station. The best known routing algorithms take nearly 2n/k times slots. An important open question has been if there exist algorithms that take only close to n/k time slots. Note that a trivial lower bound for routing is n/k. The existence of such algorithms will be highly relevant especially in emergencies and time critical situations. In this paper we answer this question by presenting a randomized algorithm that takes nearly n/k time slots with high probability.

With the rapid development of national economy, our demand for power resources has also increased rapidly. The traditional power grid can not be achieved operational status of equipment for effective monitoring and control, we will not be able to ensure the quality and quality of electricity service. Cloudbased build smart grid information platform enables gathering the parameter of grid operation state, greatly increasing the economic efficiency of power enterprises. Firstly, cloud computing and smart grid briefly described, and then pointed out that cloud computing applications in the smart grid information platform, and specialized of cloud-based smart grid information platform, in order for the power grid enterprises to enhance their level of service and provide effective reference. KEYWORD: cloud computing; smart power grids; information platform; Application 4th International Conference on Mechanical Materials and Manufacturing Engineering (MMME 2016) © 2016. The authors Published by Atlantis Press 202 3 THE MAIN PROBLEM IS STILL THE SMART GRID INFORMATION PLATFORM FACING The transition to a cloud computing data center. Our data center because of the different regions and the degree of information presents different characteristics, some data centers already have a basic cloud computing capabilities, but most data centers still remain in the initial level, to ensure the normal operation of the existing data center power under the premise, gradual transition to cloud computing data center in order to meet future requirements of the development of smart grid. Restricting data transmission problem. State Grid Corporation between provincial branches and there are a lot of data needs to be transmitted, will bring massive data transmission efficiency decreases, taking into account the load balancing device between the cloud node, thus building a wide area network channels to resolve data transmission problem. Security of data transmission. Data Center for Cloud Computing power companies to build internal private cloud, capable of self-maintenance and management, system wide area network data transmission services, according to the third security zone defined security partition, and install proprietary equipment production area and external public network isolation . 4 CLOUD COMPUTING APPLICATIONS IN THE SMART GRID INFORMATION POLICY PLATFORM Integrate and optimize the management of heterogeneous resources. Among the smart grid systems, data resources, information systems between various platforms and mutually dispersed, severe heterogeneity, thus leading to the integration of the quality of information sharing to increase difficulty, unable to effectively improve network management efficiency for the power distribution system electrical work quality management and marketing operations system maintenance upgrade will not be able to effectively meet demand (Jie Yang, 2014). Cloud computing technology enables the power system to effectively integrate the various business data and computing resources on the basis of information for business collaboration platform built on effective, able to satisfy the huge demand for smart grid information resource sharing. Cloud computing network virtualization and application virtualization technology, the server virtualization technology and other resources to achieve each service abstraction, and then realize the difference between the system and the software effectively eliminated by the appropriate method to achieve the effective integration of information resources, and then to optimize the management, greatly improving the efficiency of heterogeneous resources management applications. Distributed storage and management of large volume of data. After application of smart grid information platform construction, customer service requests varied, huge data volume information brought it to the storage and management of data provides a great challenge. Cloud computing technology in general face amount of data each smart grid system and unit collected using forms distributed storage of data to achieve the effective storage, greatly to ensure the security and reliability of data storage. GFS effective use of technology with each node, the master server is responsible for the effective management of the whole file system, the file system and complete the work of the metadata stored in the data block is the main server for data storage block sliced, and by saving three or more redundant backup storage. At the same time, client access and complete access to the main block server information. Fast Power System Parallel Computation and Treatment. Smart grids and information platform for the large volume of data to provide stable operation of the power grid data base, but more critical is the analysis and design of each system operating data, planning and decision-making, and even failures and transient stability, state estimation and intelligent a variety of computing and content analysis and decision-making process, its huge computing needs, general computing system can not reach its goal (Wang, Mengxue, 2015). Cloud computing technology through parallel computing technology has greatly enhanced parallel processing capability of the power system, which provides parallel programming model makes more simple and efficient parallel algorithms. MapReduce as Google made an important parallel programming model, and its role in large data sets in parallel computing plays a very prominent. Parallel processing job results by the client to achieve effective user submitted, via decomposition automated master role, the corresponding task scheduling to working nodes and nodes work completed by the specific calculations and perform the appropriate task. 5 SMART GRID INFORMATION PLATFORM CLOUD COMPUTING ANALYSIS Cloud Computing Smart Grid Information Platform Architecture. Smart grid technology information platform architecture cloud computing include the following several levels and aspects (Yan Cui, 2015): First, that the platform infrastructure layer is the integration of the various hardware resources and related management capabilities of virtualized using virtual technology to achieve the corresponding hardware devices such as computers and network storage devices abstraction, and then complete the automation and optimization of resource data and load management; secondly, the main platform for the integration of the various layers of software

Since computer-aided diagnosis (CAD) schemes of medical images usually computes large number of image features, which creates a challenge of how to identify a small and optimal feature vector to build robust machine learning models, the objective of this study is to investigate feasibility of applying a random projection algorithm (RPA) to build an optimal feature vector from the initially CAD-generated large feature pool and improve performance of machine learning model. We assemble a retrospective dataset involving 1,487 cases of mammograms in which 644 cases have confirmed malignant mass lesions and 843 have benign lesions. A CAD scheme is first applied to segment mass regions and initially compute 181 features. Then, support vector machine (SVM) models embedded with several feature dimensionality reduction methods are built to predict likelihood of lesions being malignant. All SVM models are trained and tested using a leave-one-case-out cross-validation method. SVM generates a likelihood score of each segmented mass region depicting on one-view mammogram. By fusion of two scores of the same mass depicting on two-view mammograms, a case-based likelihood score is also evaluated. Comparing with the principle component analyses, nonnegative matrix factorization, and Chi-squared methods, SVM embedded with RPA yielded a significantly higher case-based lesion classification performance with the area under ROC curve of 0.84 ± 0.01 (p<0.02). The study demonstrates that RPA is a promising method to generate optimal feature vectors and improve SVM performance. This study presents a new method to develop CAD schemes with significantly higher and robust performance.

In the big-data-driven artificial intelligence era, similarity search, as a core operation in machine learning and data mining, demands high speed, energy efficiency, and scenario adaptability. Conventional electronic content-addressable memory (ECAMs) suffer from inherent RC delay bottlenecks, whereas existing optical content-addressable memory (OCAMs) are restricted by fixed bit-widths and limited distance metrics. In this work, we propose a variable bit-width all-optical CAM leveraging multi-segment modulators and phase-change material (PCM) Sb2Se3. The multi-segment memory unit (MSMU) therein compresses N-bit binary data into a single analog photonic unit, supporting direct data writing/loading without digital-to-analog converters (DACs) and flexible trade-offs between precision, storage capacity, noise immunity, and energy while enabling Hamming and nonlinear distance metrics. A six-element three-bit OCAM prototype was fabricated on a silicon nitride silicon-on-insulator (SiN-SOI) platform. Despite the absence of integrated high-speed phase shifters, the device still achieves reliable optical data storage and retrieval. K-nearest neighbor (kNN) simulations based on experimentally derived statistical data—validated on the iris, wine, and breast cancer datasets—show that the three-bit operating mode achieves classification accuracy comparable to Manhattan/Euclidean distances at high signal-to-noise ratios (SNRs), while the one-bit mode exhibits strong noise robustness. Energy consumption is 364 fJ/bit (3-bit) and 890 fJ/bit (1-bit). This work provides a high-speed, energy-efficient, and reconfigurable all-optical similarity search solution with experimentally verified device performance and dataset-validated applicability, showing great potential for widespread deployment in data-intensive machine learning and data-mining applications.

Parallel genetic algorithms for the earliness-tardiness job scheduling problem with general penalty weights