Blind adaptive constrained reduced-rank parameter estimation based on constant modulus design for CDMA interference suppression

This paper proposes a multistage decomposition for blind adaptive parameter estimation in the Krylov subspace with the code-constrained constant modulus (CCM) design criterion. Based on constrained optimization of the constant modulus cost function and utilizing the Lanczos algorithm and Arnoldi-like iterations, a multistage decomposition is developed for blind parameter estimation. A family of computationally efficient blind adaptive reduced-rank stochastic gradient (SG) and recursive least squares (RLS) type algorithms along with an automatic rank selection procedure are also devised and evaluated against existing methods. An analysis of the convergence properties of the method is carried out and convergence conditions for the reduced-rank adaptive algorithms are established. Simulation results consider the application of the proposed techniques to the suppression of multiaccess and intersymbol interference in DS-CDMA systems

Dominant Modes Identification of Linear Systems via Geometrical Search

This paper presents a novel approach, based on the theory of hyperplanes, for mode identification of linear systems. The proposed approach can operate on either a set of ordinary differential equations (converted to diagonal form, if needed) or a set of partial fractions derived from a synthesized transfer function of the system under analysis. For either format, the linear system is structured to have as unknown variable a vector containing the residues. Singular value decomposition is initially used to identify an initial sparsity of the residue vector where the number of nonzero values corresponds to the pre-defined order of the dominant poles (eigenvalues) under search. An algorithm based on geometrical search of hyperplanes is used to optimize the selection of the nonzero residue locations, minimizing the residual of the zero residue hyperplanes. Finally, a recalculation of the residues is carried out by using the obtained optimal sparsity.acceptedVersio

Algorithms for Large Scale Problems in Eigenvalue and Svd Computations and in Big Data Applications

As ”big data” has increasing influence on our daily life and research activities, it poses significant challenges on various research areas. Some applications often demand a fast solution of large, sparse eigenvalue and singular value problems; In other applications, extracting knowledge from large-scale data requires many techniques such as statistical calculations, data mining, and high performance computing. In this dissertation, we develop efficient and robust iterative methods and software for the computation of eigenvalue and singular values. We also develop practical numerical and data mining techniques to estimate the trace of a function of a large, sparse matrix and to detect in real-time blob-filaments in fusion plasma on extremely large parallel computers. In the first work, we propose a hybrid two stage SVD method for efficiently and accurately computing a few extreme singular triplets, especially the ones corresponding to the smallest singular values. The first stage achieves fast convergence while the second achieves the final accuracy. Furthermore, we develop a high-performance preconditioned SVD software based on the proposed method on top of the state-of-the-art eigensolver PRIMME. The method can be used with or without preconditioning, on parallel computers, and is superior to other state-of-the-art SVD methods in both efficiency and robustness. In the second study, we provide insights and develop practical algorithms to accomplish efficient and accurate computation of interior eigenpairs using refined projection techniques in non-Krylov iterative methods. By analyzing different implementations of the refined projection, we propose a new hybrid method to efficiently find interior eigenpairs without compromising accuracy. Our numerical experiments illustrate the efficiency and robustness of the proposed method. In the third work, we present a novel method to estimate the trace of matrix inverse that exploits the pattern correlation between the diagonal of the inverse of the matrix and that of some approximate inverse. We leverage various sampling and fitting techniques to fit the diagonal of the approximation to that of the inverse. Our method may serve as a standalone kernel for providing a fast trace estimate or as a variance reduction method for Monte Carlo in some cases. An extensive set of experiments demonstrate the potential of our method. In the fourth study, we provide first results on applying outlier detection techniques to effectively tackle the fusion blob detection problem on extremely large parallel machines. We present a real-time region outlier detection algorithm to efficiently find and track blobs in fusion experiments and simulations. Our experiments demonstrated we can achieve linear time speedup up to 1024 MPI processes and complete blob detection in two or three milliseconds

Model Order Reduction in Porous Media Flow Simulation and Optimization

Subsurface flow modeling and simulation is ubiquitous in many energy related processes, including oil and gas production. These models are usually large scale and simulating them can be very computationally demanding, particularly in work-flows that require hundreds, if not thousands, runs of a model to achieve the optimal production solution. The primary objective of this study is to reduce the complexity of reservoir simulation, and to accelerate production optimization via model order reduction (MOR) by proposing two novel strategies, Proper Orthogonal Decomposition with Discrete Empirical Interpolation Method (POD-DEIM), and Quadratic Bilinear Formulation (QBLF). While the former is a training-based approach whereby one runs several reservoir models for different input strategies before reducing the model, the latter is a training-free approach. Model order reduction by POD has been shown to be a viable way to reduce the computational cost of flow simulation. However, in the case of porous media flow models, this type of MOR scheme does not immediately yield a computationally efficient reduced system. The main difficulty arises in evaluating nonlinear terms on a reduced subspace. One way to overcome this difficulty is to apply DEIM onto the nonlinear functions (fractional flow, for instance) and to select a small set of grid blocks based on a greedy algorithm. The nonlinear terms are evaluated at these few grid blocks and interpolation based on projection is used for the rest of them. Furthermore, to reduce the number of POD-DEIM basis and the error, a new approach is integrated in this study to update the basis online. In the regular POD-DEIM work flow all the snapshots are used to find one single reduced subspace, whereas in the new technique, namely the localized POD-DEIM, the snapshots are clustered into different groups by means of clustering techniques (k-means), and the reduced subspaces are computed for each cluster in the online (pre-processing) phase. In the online phase, at each time step, the reduced states are used in a classifier to find the most representative basis and to update the reduced subspace. In the second approach in order to overcome the issue of nonlinearity, the QBLF of the original nonlinear porous media flow system is introduced, yielding a system that is linear in the input and linear in the state, but not in both input and state jointly. Primarily, a new set of variables is used to change the problem into QBLF. To highlight the superiority of this approach, the new formulation is compared with a Taylor's series expansion of the system. At this initial phase of development, a POD-based model reduction is integrated with the QBLF in this study in order to reduce the computational costs. This new reduced model has the same form as the original high fidelity model and thus preserves the properties such as stability and passivity. This new form also facilitates the investigation of systematic MOR, where no training or snapshot is required. We test these MOR algorithms on the SPE10 and the results suggest twofold runtime speedups for a case study with more than 60,000 grid blocks. In the case of the QBLF, the results suggests moderate speedups, but more investigation is needed to accommodate an efficient implementation. Finally, MOR is integrated in the optimization work flow for accelerating it. The gradient based optimization framework is used due to its efficiency and fast convergence. This work flow is modified to include the reduced order model and consequently to reduce the computational cost. The water flooding optimization is applied to an offshore reservoir benchmark model, UNISIM-I-D, which has around 38,000 active grid blocks and 25 wells. The numerical solutions demonstrate that the POD-based model order reduction can reproduce accurate optimization results while providing reasonable speedups