Zhaojun Bai - US grants

9508543 Perry The Departments of Mathematics and Statistics at the University of Kentucky will purchase high-performance computing equipment which will be dedicated to the support of research in mathematical sciences. This equipment will substantially advance the following research projects: Large-Scale Numerical Linear Algebra Problems. As a part of the continuing LAPACK project, Professor Bai will work on theoretical analysis and implementation of numerical algorithms for large-scale eigenvalue problems. Molecular Conformations from Nuclear Magnetic Resonance (NMR) Data. Finding molecular conformations is a "Grand Challenge" problem in high-performance computing and communications (HPCC). Professor Hayden will develop algorithms to calculate molecular conformations from NMR data and distribute the resulting software through the Quantum Chemistry Program Exchange. Numerical Investigation of Scattering Resonances. Professor Perry will study the distribution of scattering resonances for hyperbolic surfaces in order to elucidate the connection between classical dynamics and quantum scattering. Animated Plots for Robust Regression. Professor Stromberg will study how animated residual plots can be used to assist practitioners in selecting parameters for robust regression estimators as well as how three-dimensional plots of various robust regression parameter estimates can be used to differentiate between the estimates.

The Department of Mathematics and the Institute of Theoretical Dynamics at the University of California will purchase a Servernet-II based Beowulf cluster consisting of 32 Digital 21264 CPUs which will be dedicated to the support of research in the mathematical sciences. The equipment will be used for several research projects, including in particular the following five projects.

Computational Studies of Flow in the Thoracic Aorta - Angela Cheer

Large Scale Numerical Linear Algebra Problems - Zhaojun Bai

Computational Modeling of Micro-scale Jetting Processes with Industrial Applications - Elbridge Gerry Puckett

Object Characterization using Vector-Valued Sensor Data - N. Saito

Constructing conservative and dissipative differential equations - S. Shkoller

The continual and compelling need for accurately and efficiently simulating dynamical behavior of physical systems arising from a wide variety of applications has led to increasingly large and complex models. Reduced-order modeling (ROM), also called model reduction, techniques play an indispensable role in providing efficient computational prototyping tools to replace such large-scale models by approximate smaller models. Such reduced-order models must be capable of capturing critical dynamical behavior and faithfully preserving essential properties of the larger models they approximate. An accurate and effiective reduced-order model can be applied for steady-state analysis, transient analysis, or sensitivity analysis of large-scale models and the physical systems they emulate. Consequently, scientists and engineers can significantly reduce design time and pursue more aggressive design strategies. Designers can try ``what-if" experiments in hours instead of days.

In this proposal, we propose a broad range of synergistic research activities on ROM relating to three interlinking strands: computational theory, reliable algorithms, and high-performance software tools. We will also be actively involved with promoting applications of ROM techniques and testing our methods through existing and new collaborations with researchers in circuit simulation, structural dynamics, control systems, and microelectromechanical systems (MEMS). Specifically, our proposed research activities on computational theory and algorithms include:

Accuracy estimation in both time and frequency domains.

Sensitivity analysis of linear systems using the techniques of ROM and statistical condition estimation.

Development of ROM techniques that directly exploit so-called second-order model structures and generate a reduced-order model in second-order form.

Exploration of a framework of ROM techniques for certain types of large-scale nonlinear systems of technological importance.

This award was made on a 'small' category proposal submitted in response to the ITR solicitation, NSF-02-168. This grant is funded jointly by the Divisions of Materials Research and Mathematical Sciences. It supports interdisciplinary research and education on the optimization of large-scale matrix computations, a long-standing problem in computational science with important applications to computational condensed matter and materials physics and many other fields. The research effort involves computer science, mathematics, and condensed matter physics. While much progress has been made by exploiting special properties of a matrix or the sparsity pattern of its entries, the need remains for more robust and effective methods, including preconditioning techniques to improve iterative solutions. Simulating interacting quantum systems, a powerful approach for understanding many fundamental properties of materials, is an important application of these methods. It provides motivation for this research on developing robust and efficient linear algebra solvers for quadratic form problems and for multi-length scale structured matrices. This research has a potentially high impact on the ability to predict properties of materials, such as lattice structures, magnetic properties, and lattice dynamics, through the application of theory and simulation. This award also supports education of undergraduate and graduate students and advanced training of a postdoctoral researcher.
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Optimization of large scale eigenvalue computations is a long-standing
problem in computational mathematics and scientific computing community.
In this project, the PI and his collaborators will develop novel
structure-preserving algorithms for accurately and efficiently solving
large scale eigenvalue problems. Specifically, they will focus on large
scale eigenvalue problems of structured matrix pencils, quadratic
eigenvalue problems and nonlinear eigenvalue problems. They will study
structure-preserving Rayleight-Ritz subspace projection techniques for
solving these eigenvalue problems, that include the multi-level
orthogonalization process of Krylov subspaces, second-order Arnoldi
(SOAR) method and the nonlinear Arnoldi method.

The goal of the project represents a significant advance in a
frontier area of scientific endeavor and engineering design through
the application of computational mathematics and simulations. The
target applications include these types of eigenvalue problems
arising from simulations of electrical circuits and MEMS devices,
finite element analysis of structure dynamics, acoustics and
electromagnetics. These applications are of great technology importance
for next-generation electronics, automobile efficiency and safety and
energy-efficiency monitoring devices and others. The results of
this project will be both the description of effective computational
simulation strategies for these problems and also software made publicly
available.

TECHNICAL SUMMARY:

This award is made on a proposal submitted to the PetaApps Solicitation. The Office of Cyberinfrastructure, the Computer and Information Science and Engineering Directorate, and the Divisions of Materials Research, Physics, and Chemistry and the Office of Multidisciplinary Activities within the Mathematical and Physical Sciences Directorate contribute funds to this award.

This award supports developing a high-performance software implementation of First-Principles Molecular Dynamics (FPMD) for petascale computers. FPMD is an atomic-scale simulation method that combines molecular dynamics with a quantum mechanical description of electronic structure, thus leading to a very versatile and predictive simulation approach. It is increasingly used in several areas of Materials Science, Physics, Chemistry and Nanotechnology.

Scalability will be achieved by developing i) scalable parallel linear algebra algorithms specialized for the FPMD problem, ii) visualization tools for code performance analysis that will be used to analyze message traffic patterns and optimize the software for specific network architectures, iii) data compression algorithms to handle large datasets resulting from petascale simulations. The capability to compute electronic structure using new hybrid exchange-correlation density functionals will also be included in the implementation in order to improve the accuracy of the simulations.

When deployed on petascale platforms, the new software will considerably enhance the range of FPMD applications in the areas of i) simulation of large samples, ii) long simulation times, and iii) accurate simulations using hybrid density functionals. The resulting software will be made available to the research community and will be ported to major computational facilities including the TeraGrid. A dedicated web server will be setup and maintained for the dissemination of the software and its associated documentation, tutorial material, and reference results. The implementation will build on the expertise acquired with an existing parallel implementation of FPMD, ?Qbox,? that has demonstrated high performance and scalability on up to 128,000 CPUs of a BlueGene/L platform. A modular design using C++ and XML data formats will be adopted in order to facilitate future software development and integration with modern database tools.

The infrastructure developed in this project will provide a powerful atomistic simulation tool to the Materials Science, Physics and Chemistry research communities and will extend the range of applications of first-principles simulations in terms of size, duration and accuracy. By focusing early on issues of scalability at the petascale, this project will ensure that a high-performance implementation of FPMD will be available as soon as petascale platforms are built, which will maximize the efficient utilization of petascale cyberinfrastructure. More generally, this project will help identifying successful strategies for software development and application programming on petascale architectures.
This project also supports training for students in the area of application programming for large-scale parallel computers, and in the area of first principles molecular simulation. The software developed in the project will be used as a tool for teaching first-principles molecular simulation courses. It will also serve as a validation tool for the evaluation of new simulation methods developed by other groups (e.g. linear-scaling algorithms or multiscale methods). Due to the general nature of the simulation method developed, this project will facilitate the creation of electronic databases of validated results for use by other researchers in Chemistry, Physics and Nanoscience. Students from underrepresented groups will be recruited to participate in this project through existing programs at University of California, Davis.


NON-TECHNICAL SUMMARY:

This award is made on a proposal submitted to the PetaApps Solicitation. The Office of Cyberinfrastructure, the Computer and Information Science and Engineering Directorate, and the Divisions of Materials Research, Physics, and Chemistry and the Office of Multidisciplinary Activities within the Mathematical and Physical Sciences Directorate contribute funds to this award.

This award supports the development of software for the most advanced, ?petascale,? high performance supercomputers that will enable high accuracy simulations of the motion of atoms. The resulting software can be used by a broad community of researchers in a variety of disciplinary and multidiscplinary research involving materials research, chemistry, physics, and nanotechnology. The accurate calculation of the forces on atoms requires a lot of computational resources. The resulting code together with the high performance of petascale supercomputers will allow simulations involving larger numbers of atoms and for longer times than in the past. This opens the door to unprecedented quantitative comparison of theoretical calculations with wide range of experiments, including those involving nanoscale structures, solids, liquids and molecules, and biomolecules.

Software developed under this award contributes to the cyberinfrastucture of the science and engineering community and will be broadly distributed and made available at supercomputing facilities.

This project also supports training for students and postdoctoral researchers in the area of high performance computing and in the area of computational nanoscience and technology. The software developed in the project will be used as a tool for teaching. Students from underrepresented groups will be recruited to participate in this project through existing programs at University of California, Davis.

Developing an understanding of, and a predictive capability for, strongly correlated electron systems (SCES), is a rapidly evolving field that relies critically on faster computation for continued progress. SCES form the basis of crucial materials capabilities, including high temperature superconductivity, nuclear fuels, new classes of thermoelectrics, and the exotic and promising behavior seen in cold atomic gases. SCES are difficult materials to model theoretically because of the highly time-dependent fluctuations of their electronic constituents. An important emerging technology is the multicore processor, where an increasingly large number of CPUs ("cores") are juxtaposed on a single chip and thus are extremely closely coupled. The resulting (expected) speedup in computational throughput comprises a promising path to sidestep the well publicized breakdown of Moore's law in semiconductor technology.

This project involves the development of advanced computational physics methods, "Quantum Monte Carlo" and "Density Functional Theory," for studying SCES properties. The capabilities of these new approaches will be greatly enhanced by the formulation of efficient strategies for their implementation on emerging multicore processors. This work crosses the intellectual boundary between condensed matter and atomic physics, and also between physics, applied mathematics, and computer science. The applications will explore effects of interactions on novel quantum states of matter which arise from magnetic, metal-insulator, and superconducting transitions. A particular project focus will be on the effect of spatial inhomogeneities ("defects") on ordered phases of quantum systems. In addition to advancing research in computational physics and materials science, this work has broader impacts to training graduate students and postdoctoral researchers in interdisciplinary
research tools. The Principal Investigators have also a substantial effort in involving undergraduate students and even high school students in research, which they will continue with this project.

TECHNICAL SUMMARY

The UC Davis & Santa Cruz Solar Team will investigate a transformative new paradigm of solar energy conversion: the high efficiency Multiple Exciton Generation (MEG) pathway and the corresponding challenge of charge extraction in all-inorganic nanostructured solar cells. MEG was recently observed in nanoparticles (NPs) and is not subject to the 31% theoretical limit of solar energy conversion. The Solar Team will synthesize pure, doped and alloyed Si and Ge core-shell NPs to analyze their chemistry, quantum states and energetics in a wide range of sizes, dopings, and structures, using PbS NPs as reference. The impact of complex factors such as the relaxation of the NP surface, the various core-shell structures, the exciton-exciton interaction and the NP-NP interaction on the chemistry and spectra of the NPs as well as on the MEG will be analyzed. The tools of the analysis will include photoluminescence and transient absorption studies with femtosecond resolution; and forming fully functional NP based solar cells, complete with embedding charge transport layers. These solar cells will be developed by optimizing the competing design principles of maintaining quantum confinement to preserve the efficiency of the MEG while embedding the NPs into suitably conducting layers for efficient charge extraction and transport. A strong theoretical effort will complement the Team?s experimental work. Density functional theories (DFT) will be used to capture the surface reconstruction and the energetics of NPs; time dependent DFT and Bethe-Salpeter methods to describe the exciton-exciton interaction; and non-equilibrium rate equations to determine the full rate of MEG. Mathematical projects will assist these efforts by developing a Lanczos coefficient extrapolation method, dramatically reducing the computational workload by replacing direct matrix manipulations with matrix by vector products; and by developing global statistical methods to qualitatively improve the analysis and extraction of the hidden dynamics from the noisy, ultra-high dimensional spectrotemporal dataset, obtained by the photoluminescence and transient absorption.

NON-TECHNICAL SUMMARY

Even in theory, the efficiency of solar cells is limited to a disappointing 31%. However, this limit was based on the traditional operation of solar cells, where an incoming solar photon excites only a single electron. A recent breakthrough showed that in nanoparticles one photon may excite several electrons, thus opening a new energy conversion paradigm not constrained by the above limit. The Davis Solar Team will synthesize a wide variety of nanoparticles; perform ultra-fast optical experiments to characterize the energy conversion process in these particles; and construct fully functional solar cells by embedding the nanoparticles into charge transport layers. Path-breaking mathematical work will be performed to accelerate the computational techniques to unprecedented speeds to simulate the energy conversion process with great accuracy. Further, qualitatively new statistical analyses will be developed to uncover the complex factors embedded in the vast amount of data produced by the optical experiments. The improvement of the solar energy conversion efficiency expected to emerge from this project can considerably increase the role solar technologies will play in the US transitioning towards renewable energy sources. The Davis Solar Team will not only develop these new nanoparticle based solar cells, but also plans to chaperon this technology towards the marketplace. This will be pursued through working with the Solar Collaborative of the California Energy Commission (SC-CEC), where the Team played an early leadership role. The Team's industrial collaboration will be developed through one of the PIs who is on the advisory board of a solar company. Besides working toward a wide acceptance of nanoparticle solar technologies, the Team will reach out and serve the solar community at large by analyzing and disseminating the latest academic research to the solar stakeholders: the PV manufacturers, utilities and the regulatory bodies through the SC-CEC. The Team will also develop a "Solarwiki" as a platform for a broad electronic outreach to the interested public. The Team will integrate its work with its activity in the ACS SEED program. Graduate students and postdoctoral fellows will work jointly with the groups of the Solar Team to foster interdisciplinary thinking and to prepare them to join the solar revolution.

This project involves the development of advanced computational methods for solving genuine nonlinear eigenvalue problems. In this project, skillful combination of Kublanovskaya's nonlinear QR algorithm with modern rank-revealing and structure-preserving techniques for small and medium size dense problems enhances the capabilities of new methods. A novel trimmed linearization via Pade rational approximation extends the enhancements for solving large but sparse problems. The investigators seek to develop a systematic and unified treatment of the relevant mathematical theory, and produce numerical methods and software tools for the genuine nonlinear eigenvalue problems. In addition to advancing research in nonlinear eigenvalue problems, the project provides training for graduate students in computational mathematics and interdisciplinary research tools.

Eigenvalue problems are ubiquitous in computational science and engineering, where they arise in the study of dynamics of structures, simulation of nanostructured photovoltaic conversion materials to advance energy science, and many other scenarios. Eigenvalues explain a wide range of physical phenomena such as vibrations and frequencies, (in)stabilities of dynamical systems, and energy excitation states of electrons and molecules. Many eigenvalue problems occur naturally in nonlinear form. In this project, the investigators study the underlying nonlinear problems without relying on linearization approximations. The promise of substantially improved methods for computing solutions of nonlinear eigenvalue problems, brings immediate benefits to a wide range of practical applications.

Society increasingly depends on numerical software, which uses finite precision arithmetic to approximate the reals and necessarily introduces approximation and error. Anti-lock breaks and medical devices such as haptic control systems for remote surgery are two such examples. Numerical errors in these systems can be disastrous. Toyota suspects such errors contributed to its recent, costly unintended acceleration problem, and the Ariane 5 rocket exploded due to an overflow in its inertial reference system. This project explores practical techniques to test and analyze numerical software, which will advance the state-of-the-art in engineering robust numerical software to help avoid costly, dangerous errors.

In particular, the project focuses on the two most fundamental sources of numerical errors: uncaught exceptions and numerical stability and accuracy. The proposed core framework is centered around symbolic execution, and domain insights will be used to develop principles and heuristics to make it practical. This project will complete several preliminary research tasks to validate and demonstrate the promise of the proposed general approach. It will explore new problem modeling strategies for numerical accuracy and stability, examining realistic numerical constraints to build insights into constraint solving strategies and algorithms, and improving the promising Ariadne symbolic analysis infrastructure.

This award provides support for US-based Ph.D. student participation in the Gene Golub SIAM Summer School, which will coincide with the International Summer School on Numerical Linear Algebra (ISSNLA) on July 22 - August 2, 2013 at Fudan University in Shanghai, China. The conference encourages and financially supports participation by members of groups underrepresented in mathematics.

The meeting includes invited lectures on topics of current research interest in computatonal mathematics. The conference brings together workers in a variety of different areas of research in numerical linear algebra, with emphasis on preparing Ph.D. students for useful and engaging research careers. Allocation of the funds will be based on scientific merit, financial need, and diversity, with an emphasis on participation by members of underrepresented groups.

Conference web site: http://g2s3.cs.ucdavis.edu

Large-scale eigenvalue computation is a long-standing problem in computational mathematics and computational science and engineering. It is frequently encountered as a critical kernel in simulations and data analysis. Significant progress has been made both in general-purpose eigensolvers and also in specialized eigensolvers that exploit underlying particular mathematical properties and data structure. However, new needs and challenges continue to emerge from science and engineering applications. This project involves the development of advanced mathematical analysis and robust, efficient algorithms for two emerging classes of eigenvalue problems: sparse plus low rank linear eigenvalue problems and eigenvalue problems with eigenvalue nonlinearity. In addition, this project has broader impacts in training graduate students in interdisciplinary research. While much of the work involves significant technical expertise, other areas can be successfully understood and tackled by advanced undergraduates.

The computational stability, efficiency and reliability of the new solvers for the two classes of eigenvalue problems will be greatly enhanced by skillful exploitation of underlying mathematical properties and matrix structure. In particular, for the eigenvalue problems with eigenvalue nonlinearity, new solver will combine rational approximations of nonlinearity for high accuracy, trimmed linearizations for low dimensionality, and compact representations of the projection subspace bases for memory-saving and communication efficiency. The outcomes of this project will be the publication of new theory and algorithms and open-source software.

Many modern data analysis techniques and applications in machine
learning try to learn what input data has the largest effects on the
outputs. Rayleigh Quotients (RQ), or, more generally, RQ-type
objective functions, are the basis of a mathematical technique that
captures this information. This project conducts in-depth theoretical
and algorithmic studies of three RQ-type optimizations: robust RQ
optimizations that can handle data uncertainty, constrained RQ-type
optimizations that can incorporate prior information from image
segmentation or data clustering, and trace ratio optimizations that
can perform multi-view spectral clustering. This project improves
understanding of this practically important and user-oriented
mathematical theory, creating computational methods that are embodied
in open-source software. It not only advances mathematical theory
and optimization algorithms in data science, but trains computer
science and computational mathematics graduate students in
interdisciplinary knowledge and tools necessary to undertake the
project successfully. The PIs also involve undergraduate students
in all aspects of this research project.

The PIs expect to produce a unified view of RQ-type optimizations,
reformulating them into linear and nonlinear eigenvalue problems for
which new variational principles can characterize the optimal
solutions. These new principles should expose the numerical linear
algebra characteristics of the underlying problems, supporting the
development of fast algorithms that exploit the mathematical
properties and sparse data structure.

Eigenvalue problems are the cornerstones of computational science and engineering. They arise in applications ranging from electronic structure calculations in physics and chemistry, dynamic of supramolecular systems in biology to structural and vibration in civil and mechanical engineering. Emerging applications include the investigation and design of new materials such as Lithium-ion electrolyte and graphene and the study of dynamics of viral capsids of supramolecular systems such as Zika and West Nile viruses. These applications require large number of eigenvalues. The capability of being able to efficiently compute large number of eigenvalues will not just be appealing, but also mandatory for the next generation of eigensolvers. In this project, we will undertake synergistic efforts to develop mathematical theory and numerical methods for large eigenvalue problems. The outcome of this project will provide mathematical theory and computational tools for scientists and engineers to obtain more precise simulation outputs in much less time, and to allow them to pursue more productive simulation strategies. This project will integrate research activities into interdisciplinary teaching, education and training of graduate students in the forefront of computational mathematics. One graduate student will be funded by this award.

To address challenging issues of existing algorithms and software for large linear eigenvalue problems, we will focus on two core techniques. One is an explicit external deflation for reliably moving away the computed eigenpairs to prevent the algorithm from computing over again those quantities. The second technique is a communication-avoiding matrix powers kernel for fast sparse-plus-low-rank matrix-vector products in Krylov subspace solvers with the explicit external deflation. For large nonlinear eigenvalue problems, we develop mathematical theory and algorithm templates for guiding the design and implementation of approximation based nonlinear eigensolvers. In addition, we will explore an emerging formulation of large nonlinear eigenvalue problems where underlying nonlinear matrix-valued functions are not explicitly available.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.