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Maho Nakata

Maho Nakata
RIKEN | RIKEN AICS · Advanced Center for Computing and Communication (ACCC)

Dr.

About

44
Publications
5,451
Reads
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1,142
Citations
Introduction
Interested in quantum chemistry (2-RDM, N-representability), linear algebra (http://mplapack.sourceforge.net/), optimization (SDPA project), and opensource projects (Apache OpenOffice, FreeBSD)
Additional affiliations
April 2007 - present
RIKEN
Position
  • technical scientist, researcher

Publications

Publications (44)
Preprint
Full-text available
Graph neural networks are emerging as promising methods for modeling molecular graphs, in which nodes and edges correspond to atoms and chemical bonds, respectively. Recent studies show that when 3D molecular geometries, such as bond lengths and angles, are available, molecular property prediction tasks can be made more accurate. However, computing...
Preprint
Full-text available
Enabling effective and efficient machine learning (ML) over large-scale graph data (e.g., graphs with billions of edges) can have a huge impact on both industrial and scientific applications. However, community efforts to advance large-scale graph ML have been severely limited by the lack of a suitable public benchmark. For KDD Cup 2021, we present...
Article
We report on optimized molecular geometries and electronic properties calculated by the PM6 method for 94.0% of the 91.6 million molecules cataloged in PubChem Compounds retrieved on August 29, 2016. In addition to neutral states, we also calculated those for cationic, anionic, and spin flipped electronic states of 56.2%, 49.7%, and 41.3% of the mo...
Preprint
Full-text available
In numerical computations, precision of floating-point computations is a key factor to determine the performance (speed and energy-efficiency) as well as the reliability (accuracy and reproducibility). However, precision generally plays a contrary role for both. Therefore, the ultimate concept for maximizing both at the same time is the minimal-pre...
Chapter
We implemented pzqd, a high precision arithmetic library for the PEZY-SC2 that is based on Hida et al.’s QD library. PEZY-SC2 is an MIMD (multiple instruction stream, multiple data stream) -type many-core processor. We optimized matrix-matrix multiplication (Rgemm) in double-double precision (DD) on the PEZY-SC2. Porting the CPU code to PEZY-SC2 co...
Chapter
This chapter deals with fundamental theories on the accuracy of numerical calculation and some cases that seems to be important, somewhat different from previous chapters. We must remember that numerical errors are included in the output data of the computer. In particular, do not overlook the important points you need to know when parallelizing co...
Chapter
In this chapter, we explain the basic architecture and use of the linear algebra calculation libraries called BLAS and LAPACK. BLAS and LAPACK libraries are for carrying out vector and matrix operations on computers. They are used by many programs, and their implementations are optimized according to the computer they are run on. These libraries sh...
Preprint
Full-text available
We report on the largest dataset of optimized molecular geometries and electronic properties calculated by the PM6 method for 92.9% of the 91.2 million molecules cataloged in PubChem Compounds retrieved on Aug. 29, 2016. In addition to neutral states, we also calculated those for cationic, anionic, and spin flipped electronic states of 56.2%, 49.7%...
Article
Large-scale molecular databases play an essential role in the investigation of vari- ous subjects such as the development of organic materials, in-silico drug designs, and data-driven studies with machine learning, among others. We developed a large-scale quantum chemistry database based on the first-principles method without performing any experim...
Article
Full-text available
In this research, we have been constructing a large database of molecules by ab initio calculations. Currently, we have over 1.53 million entries of 6-31G* B3LYP optimized geometries and ten excited states by 6-31+G* TDDFT calculations. To calculate molecules, we only refer the InChI (International Chemical Identifier) representation of chemical f...
Article
Full-text available
We observe that in a simple one-dimensional polynomial optimization problem (POP), the ‘optimal’ values of semidefinite programming (SDP) relaxation problems reported by the standard SDP solvers converge to the optimal value of the POP, while the true optimal values of SDP relaxation problems are strictly and significantly less than that value. Som...
Conference Paper
Full-text available
We have implemented a fast double-double precision (has approx. 32 decimal significant digits) version of matrix-matrix multiplication routine called "Rgemm" of MPACK (http://mplapack.sourceforge.net/) on NVIDIA C2050 GPU. This routine is a higher precision version of gdgemmh in the BLAS (Basic Linear Algebra Subprograms) library. Our implementatio...
Conference Paper
Semidefinite programming (SDP) is one of the most important problems among optimization problems at present. It is relevant to a wide range of fields such as combinatorial optimization, structural optimization, control theory, economics, quantum chemistry, sensor network location and data mining. The capability to solve extremely large-scale SDP pr...
Conference Paper
We are interested in the accuracy of linear algebra operations; accuracy of the solution of linear equation, eigenvalue and eigenvectors of some matrices, etc. This is a reason for we have been developing the MPACK. The MPACK consists of MBLAS and MLAPACK, multiple precision version of BLAS and LAPACK, respectively. Features of MPACK are: (i) based...
Article
A SemiDefinite Programming (SDP) problem is one of the most central problems in mathematical optimization. SDP provides an effective computation framework for many research fields. Some applications, however, require solving a large-scale SDP whose size exceeds the capacity of a single processor both in terms of computation time and available memor...
Article
Full-text available
The second-order reduced density matrix method (the RDM method) has performed well in determining energies and properties of atomic and molecular systems, achieving coupled-cluster singles and doubles with perturbative triples (CC SD(T)) accuracy without using the wave-function. One question that arises is how well does the RDM method perform with...
Chapter
The main purpose of this chapter is to introduce the latest developments in SDPA and its family. SDPA is designed to solve large-scale SemiDefinite Programs (SDPs) faster and over the course of 15 years of development, it has been expanded into a high-performance-oriented software package. We hope that this introduction to the latest developments o...
Article
Full-text available
This is an introduction to the RIKEN’s supercomputer RIKEN Integrated Cluster of Clusters (RICC), that has been in operation since August 2009. The basic concept of the RICC is to “provide an environment with high power computational resources to facilitate research and development for RIKEN’s researchers”. Based on this concept, we have been opera...
Conference Paper
Full-text available
This is an introduction to RIKEN's supercomputer RICC (RIKEN Integrated Cluster of Clusters), that has been in operation since August 2009. The basic concept of the RICC is gprovide high power computational resources for research and development for RIKEN's researchersh. Based on this concept, we have been providing for (i) data analysis environm...
Article
Full-text available
Variational calculation of the ground state energy and its properties using the second-order reduced density matrix (2-RDM) is a promising approach for quantum chemistry. A major obstacle with this approach is that the $N$-representability conditions are too difficult in general. Therefore, we usually employ some approximations such as the $P$, $Q$...
Article
Full-text available
The reduced-density-matrix method is an promising candidate for the next generation electronic structure calculation method; it is equivalent to solve the Schr\"odinger equation for the ground state. The number of variables is the same as a four electron system and constant regardless of the electrons in the system. Thus many researchers have been...
Conference Paper
Full-text available
Semidefinite programming (SDP) is an im-portant branch of optimization and has wide range of applications: engineering, industry, chemistry, mathemat-ics, etc. However, obtaining very accurate optimum for a semidefinite programming is difficult in general, es-pecially for ill-posed ones. In this paper, we evaluated numerically highly accurate SDP s...
Article
Full-text available
The SDPA (SemiDefinite Programming Algorithm) Project launched in 1995 has been known to provide high-performance packages for solving large-scale Semidefinite Programs (SDPs). SDPA Ver. 6 solves effi-ciently large-scale dense SDPs, however, it required much computation time compared with other software packages, especially when the Schur complemen...
Article
Full-text available
We propose a new relativistic treatment in the quantum Monte Carlo (QMC) technique using the zeroth-order regular approximation (ZORA) Hamiltonian. The novel ZORA local energy is derived, and its availability is examined with some variational Monte Carlo calculations. We optimize the wave functions variationally and evaluate the relativistic and co...
Article
Full-text available
With the density-matrix variational method, the ground-state energy of a many-electron system is calculated by minimizing the energy expectation value subject to the selected representability conditions for the second-order reduced-density matrix 2-RDM. There is a lack of size extensivity under the P, Q, and G conditions of this method by applying...
Article
Full-text available
The reduced density matrix (RDM) method, which is a variational calculation based on the second-order reduced density matrix, is applied to the ground state energies and the dipole moments for 57 different states of atoms, molecules, and to the ground state energies and the elements of 2-RDM for the Hubbard model. We explore the well-known N-repres...
Chapter
Introduction Formulation as an SDP Problem The Primal-Dual Interior-Point Method Other Methods for SDP Problems Solving SDP Problems in Practice Acknowledgments References
Article
Full-text available
It has been a long-time dream in electronic structure theory in phys- ical chemistry/chemical physics to compute ground state energies of atomic and molecular systems by employing a variational approach in which the two-body reduced density matrix (RDM) is the unknown variable. Realization of the RDM approach has benefited greatly from recent devel...
Article
Full-text available
Calculations on small molecular systems indicate that the variational approach employing the two-particle reduced density matrix (2-RDM) as the basic unknown and applying the P, Q, G, T1, and T2 representability conditions provides an accuracy that is competitive with the best standard ab initio methods of quantum chemistry. However, in this paper...
Article
Full-text available
The valence ionization spectra up to 25–30 eV of the 4π-electron molecules, butadiene, acrolein, glyoxal, methylenecyclopropene and methylenecyclopropane were investigated by the SAC-CI method. Accurate theoretical assignments of the spectra were given and further the natures of the low-lying satellites were examined. Acrolein and glyoxal have the...
Article
For nonrelativistic electrons in an external potential the ground state energy depends only upon the two-body reduced density matrix (2-RDM) and a lower-bound approximation may be obtained by minimizing the energy with respect to the 2-RDM subject to some representability conditions. Work going back to the 1970s and the recent work [1] showed that...
Chapter
Full-text available
We examine the strength of the Weinhold-Wilson (WW) inequalities for calculating the second-order density matrix (2-RDM) by the density matrix variational theory (DMVT) using the P, Q and G conditions as subsidiary conditions as subsidiary conditions. We calculated the 2-RDM of various molecular electronic states and found that some violations of W...
Article
Full-text available
The density matrix variational theory (DMVT) algorithm developed previously [J. Chem. Phys. 114, 8282 (2001)] was utilized for calculations of the potential energy surfaces of molecules, H4, H2O, NH3, BH3, CO, N2, C2, and Be2. The DMVT(PQG), using the P, Q, and G conditions as subsidiary condition, reproduced the full-CI curves very accurately even...
Article
Full-text available
The ground-state fermion second-order reduced density matrix (2-RDM) is determined variationally using itself as a basic variable. As necessary conditions of the N-representability, we used the positive semidefiniteness conditions, P, Q, and G conditions that are described in terms of the 2-RDM. The variational calculations are performed by using r...
Article
Full-text available
We formulated the density equation theory (DET) using the spin-dependent density matrix (SDM) as a basic variable and calculated the density matrices of the open-shell systems and excited states, as well as those of the closed-shell systems, without any use of the wave function. We calculated the open-shell systems, Be(3S), Be-(2S), B+(3S), B(2S),...
Article
The density equation (DE) method was utilized for calculations of the potential energy curves of the molecules HF, CH4, BH3, NH3, and H2O. The equilibrium geometries and the vibrational force constants of these molecules were determined by the DE method without any use of the wavefunction. The calculated values are in close agreement with the resul...
Article
Full-text available
The density equation DE method was utilized for calculations of the potential energy curves of the molecules HF, CH , 4 BH , NH , and H O. The equilibrium geometries and the vibrational force constants of these molecules were determined by 3 3 2 the DE method without any use of the wavefunction. The calculated values are in close agreement with the...
Article
Full-text available
The SDPA (SemiDefinite Programming Algorithm) [5] is a software package for solv-ing semidefinite programs (SDPs). It is based on a Mehrotra-type predictor-corrector infeasible primal-dual interior-point method. The SDPA handles the standard form SDP and its dual. It is implemented in C++ language utilizing the LAPACK [1] for matrix computations. T...
Article
Full-text available
We are interested in realizing the variational calculation with the 2-order Reduced Den- sity Matrix (2-RDM) for fermionic systems. The known necessary N-representability conditions P , Q, G, T 1, and T 20 are im- posed, resulting in an optimization prob- lem called semidenite programming (SDP) problem. The ground state energies for var- ious small...
Article
The Semidefinite Program (SDP) has recently received much attention of researchers in various fields for the following three reasons: (i) It has been intensively studied in both the- oretical and numerical aspects. Especially the primal-dual interior-point method is known as a useful tool for solving large-scale SDPs with accuracy and numerical sta...

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