Yasunori Futamura

Efficient Parameter Estimation and Implementation of a Contour Integral-Based Eigensolver

We consider an eigensolver for computing eigenvalues in a given domain and the corresponding eigenvectors of large-scale matrix pencils. The Sakurai-Sugiura (SS) method is an eigensolver based on complex moments given by contour integrals of matrix inverses with several shift points. This method has good parallel scalability, and is suitable for massively parallel computing environments. The SS method has several parameters, and the choice of these parameters is crucial for achieving high accuracy and good parallel performance. We discuss some numerical properties of the method, and present efficient parameter estimation techniques. We demonstrate the efficiency of our method with numerical experiments.

Efficient Algorithm for Linear Systems Arising in Solutions of Eigenproblems and Its Application to Electronic-Structure Calculations

We consider an eigenproblem derived from first-principles electronic-structure calculations. Eigensolvers based on a rational filter require solutions of linear systems with multiple shifts and multiple right hand sides for transforming the spectrum. The solutions of the linear systems are the dominant part of the eigensolvers. We derive an efficient algorithm for such linear systems, and develop implementation techniques to reduce time-consuming data copies in the algorithm. Several experiments are performed on the K computer to evaluate the performance of our algorithm.

Numerical Construction of a Low-Energy Effective Hamiltonian in a Self-Consistent Bogoliubov–de Gennes Approach of Superconductivity

We propose a fast and efficient approach for solving the Bogoliubov-de Gennes (BdG) equations in superconductivity, with a numerical matrix-size reduction procedure proposed by Sakurai and Sugiura [J. Comput. Appl. Math. 159, 119 (2003)]. The resultant small-size Hamiltonian contains the information of the original BdG Hamiltonian in a given energy domain. In other words, the present approach leads to a numerical construction of a low-energy effective theory in superconductivity. The combination with the polynomial expansion method allows a self-consistent calculation of the BdG equations. Through numerical calculations of quasi-particle excitations in a vortex lattice, thermal conductivity, and nuclear magnetic relaxation rate, we show that our approach is suitable for evaluating physical quantities in a large-size superconductor and a nano-scale superconducting device, with the mean-field superconducting theory.

Stochastic estimation of nuclear level density in the nuclear shell model: An application to parity-dependent level density in 58Ni

Abstract We introduce a novel method to obtain level densities in large-scale shell-model calculations. Our method is a stochastic estimation of eigenvalue count based on a shifted Krylov-subspace method, which enables us to obtain level densities of huge Hamiltonian matrices. This framework leads to a successful description of both low-lying spectroscopy and the experimentally observed equilibration of J π = 2 + and 2 − states in 58Ni in a unified manner.

Efficient Calculation of Electronic Structure Using O(N) Density Functional Theory

We propose an efficient way to calculate the electronic structure of large systems by combining a large-scale first-principles density functional theory code, Conquest, and an efficient interior eigenproblem solver, the Sakurai-Sugiura method. The electronic Hamiltonian and charge density of large systems are obtained by Conquest, and the eigenstates of the Hamiltonians are then obtained by the Sakurai-Sugiura method. Applications to a hydrated DNA system and adsorbed P2 molecules and Ge hut clusters on large Si substrates demonstrate the applicability of this combination on systems with 10,000+ atoms with high accuracy and efficiency.

Efficient and scalable calculation of complex band structure using Sakurai-Sugiura method

Complex band structures (CBSs) are useful to characterize the static and dynamical electronic properties of materials. Despite the intensive developments, the first-principles calculation of CBS for over several hundred atoms are still computationally demanding. We here propose an efficient and scalable computational method to calculate CBSs. The basic idea is to express the Kohn-Sham equation of the real-space grid scheme as a quadratic eigenvalue problem and compute only the solutions which are necessary to construct the CBS by Sakurai-Sugiura method. The serial performance of the proposed method shows a significant advantage in both run-time and memory usage compared to the conventional method. Furthermore, owing to the hierarchical parallelism in Sakurai-Sugiura method and the domain-decomposition technique for real-space grids, we can achieve an excellent scalability in the CBS calculation of a boron and nitrogen doped carbon nanotube consisting of more than 10,000 atoms using 2,048 nodes (139,264 cores) of Oakforest-PACS.

Highly Parallel Computation of Generalized Eigenvalue Problem in Vibration for Automatic Transmission of Vehicles Using the Sakurai–Sugiura Method and Supercomputers

In this paper, we discuss highly parallel computational approach for solving eigenvalue problems arising from vibration problem in automatic transmission of vehicles. Vibration performance is an important quality measure of vehicles. Typically, vibration performance of automatic transmission strongly ties up to comfortable driving. Therefore, reduction of vibration is one of the key consideration of new automatic transmission design. However, the computational time for solving eigenvalue problems dominates that for the design optimization routine, and it becomes unacceptably long when we use a precise model which has a large number of degrees of freedom. Therefore, efficient approach to solve the large-scale eigenvalue problem is required. Owing to this situation, in this study, we present a performance of a hierarchical parallel eigensolver using state-of-the-art supercomputers such as the K computer and COMA .

Alternating Optimization Method Based on Nonnegative Matrix Factorizations for Deep Neural Networks

The backpropagation algorithm for calculating gradients has been widely used in computation of weights for deep neural networks (DNNs). This method requires derivatives of objective functions and has some difficulties finding appropriate parameters such as learning rate. In this paper, we propose a novel approach for computing weight matrices of fully-connected DNNs by using two types of semi-nonnegative matrix factorizations (semi-NMFs). In this method, optimization processes are performed by calculating weight matrices alternately, and backpropagation (BP) is not used. We also present a method to calculate stacked autoencoder using a NMF. The output results of the autoencoder are used as pre-training data for DNNs. The experimental results show that our method using three types of NMFs attains similar error rates to the conventional DNNs with BP.

Block conjugate gradient type methods for the approximation of bilinear form CHA1B

In this paper, we consider computing the approximation of block bilinear form CHA1B, where square matrix A is large sparse, and B and C are rectangular matrices with the same size. We propose block conjugate gradient (CG) type methods for the approximation of CHA1B, in which approximation Xk of linear systems AX=B does not need to be computed explicitly and only the approximation k of CHA1B, which is mathematically equivalent to CHXk, will be calculated instead. Numerical results show the effectiveness of our proposed methods.

Parallel Implementation of the Nonlinear Semi-NMF Based Alternating Optimization Method for Deep Neural Networks

For computing weights of deep neural networks (DNNs), the backpropagation (BP) method has been widely used as a de-facto standard algorithm. Since the BP method is based on a stochastic gradient descent method using derivatives of objective functions, the BP method has some difficulties finding appropriate parameters such as learning rate. As another approach for computing weight matrices, we recently proposed an alternating optimization method using linear and nonlinear semi-nonnegative matrix factorizations (semi-NMFs). In this paper, we propose a parallel implementation of the nonlinear semi-NMF based method. The experimental results show that our nonlinear semi-NMF based method and its parallel implementation have competitive advantages to the conventional DNNs with the BP method.