This paper provides an overview of several approaches to formulating and solving optimization under uncertainty (OUU) engineering design problems. In addition, the topic of high-performance computing and OUU is addressed, with a discussion of the coarse- and fine-grained parallel computing opportunities in the various OUU problem formulations. The OUU approaches covered here are: sampling-based OUU, surrogate model-based OUU, analytic reliability-based OUU (also known as reliability-based design optimization), polynomial chaos-based OUU, and stochastic perturbation-based OUU.
This paper is about making reversible logic a reality for supercomputing. Reversible logic offers a way to exceed certain basic limits on the performance of computers, yet a powerful case will have to be made to justify its substantial development expense. This paper explores the limits of current, irreversible logic for supercomputers, thus forming a threshold above which reversible logic is the only solution. Problems above this threshold are discussed, with the science and mitigation of global warming being discussed in detail. To further develop the idea of using reversible logic in supercomputing, a design for a 1 Zettaflops supercomputer as required for addressing global climate warming is presented. However, to create such a design requires deviations from the mainstream of both the software for climate simulation and research directions of reversible logic. These deviations provide direction on how to make reversible logic practical. Copyright 2005 ACM.
We performed molecular dynamics simulations of beta-amyloid (A{beta}) protein and A{beta} fragment(31-42) in bulk water and near hydrated lipids to study the mechanism of neurotoxicity associated with the aggregation of the protein. We constructed full atomistic models using Cerius2 and ran simulations using LAMMPS. MD simulations with different conformations and positions of the protein fragment were performed. Thermodynamic properties were compared with previous literature and the results were analyzed. Longer simulations and data analyses based on the free energy profiles along the distance between the protein and the interface are ongoing.
Our aim is to determine the network of events, or the regulatory network, that defines an immune response to a bio-toxin. As a model system, we are studying T cell regulatory network triggered through tyrosine kinase receptor activation using a combination of pathway stimulation and time-series microarray experiments. Our approach is composed of five steps (1) microarray experiments and data error analysis, (2) data clustering, (3) data smoothing and discretization, (4) network reverse engineering, and (5) network dynamics analysis and fingerprint identification. The technological outcome of this study is a suite of experimental protocols and computational tools that reverse engineer regulatory networks provided gene expression data. The practical biological outcome of this work is an immune response fingerprint in terms of gene expression levels. Inferring regulatory networks from microarray data is a new field of investigation that is no more than five years old. To the best of our knowledge, this work is the first attempt that integrates experiments, error analyses, data clustering, inference, and network analysis to solve a practical problem. Our systematic approach of counting, enumeration, and sampling networks matching experimental data is new to the field of network reverse engineering. The resulting mathematical analyses and computational tools lead to new results on their own and should be useful to others who analyze and infer networks.
The thermal challenge problem has been developed at Sandia National Laboratories as a testbed for demonstrating various types of validation approaches and prediction methods. This report discusses one particular methodology to assess the validity of a computational model given experimental data. This methodology is based on Bayesian Belief Networks (BBNs) and can incorporate uncertainty in experimental measurements, in physical quantities, and model uncertainties. The approach uses the prior and posterior distributions of model output to compute a validation metric based on Bayesian hypothesis testing (a Bayes' factor). This report discusses various aspects of the BBN, specifically in the context of the thermal challenge problem. A BBN is developed for a given set of experimental data in a particular experimental configuration. The development of the BBN and the method for ''solving'' the BBN to develop the posterior distribution of model output through Monte Carlo Markov Chain sampling is discussed in detail. The use of the BBN to compute a Bayes' factor is demonstrated.
The formation and functions of living materials and organisms are fundamentally different from those of synthetic materials and devices. Synthetic materials tend to have static structures, and are not capable of adapting to the functional needs of changing environments. In contrast, living systems utilize energy to create, heal, reconfigure, and dismantle materials in a dynamic, non-equilibrium fashion. The overall goal of the project was to organize and reconfigure functional assemblies of nanoparticles using strategies that mimic those found in living systems. Active assembly of nanostructures was studied using active biomolecules to drive the organization and assembly of nanocomposite materials. In this system, kinesin motor proteins and microtubules were used to direct the transport and interactions of nanoparticles at synthetic interfaces. In addition, the kinesin/microtubule transport system was used to actively assemble nanocomposite materials capable of storing significant elastic energy. Novel biophysical measurement tools were also developed for measuring the collective force generated by kinesin motor proteins, which will provide insight on the mechanical constraints of active assembly processes. Responsive reconfiguration of nanostructures was studied in terms of using active biomolecules to mediate the optical properties of quantum dot (QD) arrays through modulation of inter-particle spacing and associated energy transfer interaction. Design rules for kinesin-based transport of a wide range of nanoscale cargo (e.g., nanocrystal quantum dots, micron-sized polymer spheres) were developed. Three-dimensional microtubule organizing centers were assembled in which the polar orientation of the microtubules was controlled by a multi-staged assembly process. Overall, a number of enabling technologies were developed over the course of this project, and will drive the exploitation of energy-driven processes to regulate the assembly, disassembly, and dynamic reorganization of nanomaterials.
Understanding the properties and behavior of biomembranes is fundamental to many biological processes and technologies. Microdomains in biomembranes or ''lipid rafts'' are now known to be an integral part of cell signaling, vesicle formation, fusion processes, protein trafficking, and viral and toxin infection processes. Understanding how microdomains form, how they depend on membrane constituents, and how they act not only has biological implications, but also will impact Sandia's effort in development of membranes that structurally adapt to their environment in a controlled manner. To provide such understanding, we created physically-based models of biomembranes. Molecular dynamics (MD) simulations and classical density functional theory (DFT) calculations using these models were applied to phenomena such as microdomain formation, membrane fusion, pattern formation, and protein insertion. Because lipid dynamics and self-organization in membranes occur on length and time scales beyond atomistic MD, we used coarse-grained models of double tail lipid molecules that spontaneously self-assemble into bilayers. DFT provided equilibrium information on membrane structure. Experimental work was performed to further help elucidate the fundamental membrane organization principles.
This report documents research to develop robust and efficient solution techniques for solving large-scale systems of nonlinear equations. The most widely used method for solving systems of nonlinear equations is Newton's method. While much research has been devoted to augmenting Newton-based solvers (usually with globalization techniques), little has been devoted to exploring the application of different models. Our research has been directed at evaluating techniques using different models than Newton's method: a lower order model, Broyden's method, and a higher order model, the tensor method. We have developed large-scale versions of each of these models and have demonstrated their use in important applications at Sandia. Broyden's method replaces the Jacobian with an approximation, allowing codes that cannot evaluate a Jacobian or have an inaccurate Jacobian to converge to a solution. Limited-memory methods, which have been successful in optimization, allow us to extend this approach to large-scale problems. We compare the robustness and efficiency of Newton's method, modified Newton's method, Jacobian-free Newton-Krylov method, and our limited-memory Broyden method. Comparisons are carried out for large-scale applications of fluid flow simulations and electronic circuit simulations. Results show that, in cases where the Jacobian was inaccurate or could not be computed, Broyden's method converged in some cases where Newton's method failed to converge. We identify conditions where Broyden's method can be more efficient than Newton's method. We also present modifications to a large-scale tensor method, originally proposed by Bouaricha, for greater efficiency, better robustness, and wider applicability. Tensor methods are an alternative to Newton-based methods and are based on computing a step based on a local quadratic model rather than a linear model. The advantage of Bouaricha's method is that it can use any existing linear solver, which makes it simple to write and easily portable. However, the method usually takes twice as long to solve as Newton-GMRES on general problems because it solves two linear systems at each iteration. In this paper, we discuss modifications to Bouaricha's method for a practical implementation, including a special globalization technique and other modifications for greater efficiency. We present numerical results showing computational advantages over Newton-GMRES on some realistic problems. We further discuss a new approach for dealing with singular (or ill-conditioned) matrices. In particular, we modify an algorithm for identifying a turning point so that an increasingly ill-conditioned Jacobian does not prevent convergence.
This SAND report provides the technical progress through April 2005 of the Sandia-led project, ''Carbon Sequestration in Synechococcus Sp.: From Molecular Machines to Hierarchical Modeling'', funded by the DOE Office of Science GenomicsGTL Program. Understanding, predicting, and perhaps manipulating carbon fixation in the oceans has long been a major focus of biological oceanography and has more recently been of interest to a broader audience of scientists and policy makers. It is clear that the oceanic sinks and sources of CO{sub 2} are important terms in the global environmental response to anthropogenic atmospheric inputs of CO{sub 2} and that oceanic microorganisms play a key role in this response. However, the relationship between this global phenomenon and the biochemical mechanisms of carbon fixation in these microorganisms is poorly understood. In this project, we will investigate the carbon sequestration behavior of Synechococcus Sp., an abundant marine cyanobacteria known to be important to environmental responses to carbon dioxide levels, through experimental and computational methods. This project is a combined experimental and computational effort with emphasis on developing and applying new computational tools and methods. Our experimental effort will provide the biology and data to drive the computational efforts and include significant investment in developing new experimental methods for uncovering protein partners, characterizing protein complexes, identifying new binding domains. We will also develop and apply new data measurement and statistical methods for analyzing microamy experiments. Computational tools will be essential to our efforts to discover and characterize the function of the molecular machines of Synechococcus. To this end, molecular simulation methods will be coupled with knowledge discovery from diverse biological data sets for high-throughput discovery and characterization of protein-protein complexes. In addition, we will develop a set of novel capabilities for inference of regulatory pathways in microbial genomes across multiple sources of information through the integration of computational and experimental technologies. These capabilities will be applied to Synechococcus regulatory pathways to characterize their interaction map and identify component proteins in these pathways. We will also investigate methods for combining experimental and computational results with visualization and natural language tools to accelerate discovery of regulatory pathways. The ultimate goal of this effort is develop and apply new experimental and computational methods needed to generate a new level of understanding of how the Synechococcus genome affects carbon fixation at the global scale. Anticipated experimental and computational methods will provide ever-increasing insight about the individual elements and steps in the carbon fixation process, however relating an organism's genome to its cellular response in the presence of varying environments will require systems biology approaches. Thus a primary goal for this effort is to integrate the genomic data generated from experiments and lower level simulations with data from the existing body of literature into a whole cell model. We plan to accomplish this by developing and applying a set of tools for capturing the carbon fixation behavior of complex of Synechococcus at different levels of resolution. Finally, the explosion of data being produced by high-throughput experiments requires data analysis and models which are more computationally complex, more heterogeneous, and require coupling to ever increasing amounts of experimentally obtained data in varying formats. These challenges are unprecedented in high performance scientific computing and necessitate the development of a companion computational infrastructure to support this effort.
This report describes the test and evaluation methods by which the Teraflops Operating System, or TOS, that resides on Sandia's massively-parallel computer Janus is verified for production release. Also discussed are methods used to build TOS before testing and evaluating, miscellaneous utility scripts, a sample test plan, and a proposed post-test method for quickly examining the large number of test results. The purpose of the report is threefold: (1) to provide a guide to T&E procedures, (2) to aid and guide others who will run T&E procedures on the new ASCI Red Storm machine, and (3) to document some of the history of evaluation and testing of TOS. This report is not intended to serve as an exhaustive manual for testers to conduct T&E procedures.
Damping vibrations is important in the design of some types of inertial sensing devices. One method for adding damping to a device is to use magnetic forces generated by a static magnetic field interacting with eddy currents. In this report, we develop a 2-dimensional finite element model for the analysis of quasistatic eddy currents in a thin sheet of conducting material. The model was used for design and sensitivity analyses of a novel mechanical oscillator that consists of a shuttle mass (thin sheet of conducting material) and a set of folded spring elements. The oscillator is damped through the interaction of a static magnetic field and eddy currents in the shuttle mass. Using a prototype device and Laser Dopler Velocimetry (LDV), measurements were compared to the model in a validation study using simulation based uncertainty analyses. Measurements were found to follow the trends predicted by the model.
Threats to water distribution systems include release of contaminants and Denial of Service (DoS) attacks. A better understanding, and validated computational models, of the flow in water distribution systems would enable determination of sensor placement in real water distribution networks, allow source identification, and guide mitigation/minimization efforts. Validation data are needed to evaluate numerical models of network operations. Some data can be acquired in real-world tests, but these are limited by 1) unknown demand, 2) lack of repeatability, 3) too many sources of uncertainty (demand, friction factors, etc.), and 4) expense. In addition, real-world tests have limited numbers of network access points. A scale-model water distribution system was fabricated, and validation data were acquired over a range of flow (demand) conditions. Standard operating variables included system layout, demand at various nodes in the system, and pressure drop across various pipe sections. In addition, the location of contaminant (salt or dye) introduction was varied. Measurements of pressure, flowrate, and concentration at a large number of points, and overall visualization of dye transport through the flow network were completed. Scale-up issues that that were incorporated in the experiment design include Reynolds number, pressure drop across nodes, and pipe friction and roughness. The scale was chosen to be 20:1, so the 10 inch main was modeled with a 0.5 inch pipe in the physical model. Controlled validation tracer tests were run to provide validation to flow and transport models, especially of the degree of mixing at pipe junctions. Results of the pipe mixing experiments showed large deviations from predicted behavior and these have a large impact on standard network operations models.3
This work focuses on different methods to generate confidence regions for nonlinear parameter identification problems. Three methods for confidence region estimation are considered: a linear approximation method, an F-test method, and a Log-Likelihood method. Each of these methods are applied to three case studies. One case study is a problem with synthetic data, and the other two case studies identify hydraulic parameters in groundwater flow problems based on experimental well-test results. The confidence regions for each case study are analyzed and compared. Although the F-test and Log-Likelihood methods result in similar regions, there are differences between these regions and the regions generated by the linear approximation method for nonlinear problems. The differing results, capabilities, and drawbacks of all three methods are discussed.
Semantic graphs offer one promising avenue for intelligence analysis in homeland security. They provide a mechanism for describing a wide variety of relationships between entities of potential interest. The vertices are nouns of various types, e.g. people, organizations, events, etc. Edges in the graph represent different types of relationships between entities, e.g. 'is friends with', 'belongs-to', etc. Semantic graphs offer a number of potential advantages as a knowledge representation system. They allow information of different kinds, and collected in differing ways, to be combined in a seamless manner. A semantic graph is a very compressed representation of some of relationship information. It has been reported that the semantic graph can be two orders of magnitude smaller than the processed intelligence data. This allows for much larger portions of the data universe to be resident in computer memory. Many intelligence queries that are relevant to the terrorist threat are naturally expressed in the language of semantic graphs. One example is the search for 'interesting' relationships between two individuals or between an individual and an event, which can be phrased as a search for short paths in the graph. Another example is the search for an analyst-specified threat pattern, which can be cast as an instance of subgraph isomorphism. It is important to note than many kinds of analysis are not relationship based, so these are not good candidates for semantic graphs. Thus, a semantic graph should always be used in conjunction with traditional knowledge representation and interface methods. Operations that involve looking for chains of relationships (e.g. friend of a friend) are not efficiently executable in a traditional relational database. However, the semantic graph can be thought of as a pre-join of the database, and it is ideally suited for these kinds of operations. Researchers at Sandia National Laboratories are working to facilitate semantic graph analysis. Since intelligence datasets can be extremely large, the focus of this work is on the use of parallel computers. We have been working to develop scalable parallel algorithms that will be at the core of a semantic graph analysis infrastructure. Our work has involved two different thrusts, corresponding to two different computer architectures. The first architecture of interest is distributed memory, message passing computers. These machines are ubiquitous and affordable, but they are challenging targets for graph algorithms. Much of our distributed-memory work to date has been collaborative with researchers at Lawrence Livermore National Laboratory and has focused on finding short paths on distributed memory parallel machines. Our implementation on 32K processors of BlueGene/Light finds shortest paths between two specified vertices in just over a second for random graphs with 4 billion vertices.
Electromagnetic induction is a classic geophysical exploration method designed for subsurface characterization--in particular, sensing the presence of geologic heterogeneities and fluids such as groundwater and hydrocarbons. Several approaches to the computational problems associated with predicting and interpreting electromagnetic phenomena in and around the earth are addressed herein. Publications resulting from the project include [31]. To obtain accurate and physically meaningful numerical simulations of natural phenomena, computational algorithms should operate in discrete settings that reflect the structure of governing mathematical models. In section 2, the extension of algebraic multigrid methods for the time domain eddy current equations to the frequency domain problem is discussed. Software was developed and is available in Trilinos ML package. In section 3 we consider finite element approximations of De Rham's complex. We describe how to develop a family of finite element spaces that forms an exact sequence on hexahedral grids. The ensuing family of non-affine finite elements is called a van Welij complex, after the work [37] of van Welij who first proposed a general method for developing tangentially and normally continuous vector fields on hexahedral elements. The use of this complex is illustrated for the eddy current equations and a conservation law problem. Software was developed and is available in the Ptenos finite element package. The more popular methods of geophysical inversion seek solutions to an unconstrained optimization problem by imposing stabilizing constraints in the form of smoothing operators on some enormous set of model parameters (i.e. ''over-parametrize and regularize''). In contrast we investigate an alternative approach whereby sharp jumps in material properties are preserved in the solution by choosing as model parameters a modest set of variables which describe an interface between adjacent regions in physical space. While still over-parametrized, this choice of model space contains far fewer parameters than before, thus easing the computational burden, in some cases, of the optimization problem. And most importantly, the associated finite element discretization is aligned with the abrupt changes in material properties associated with lithologic boundaries as well as the interface between buried cultural artifacts and the surrounding Earth. In section 4, algorithms and tools are described that associate a smooth interface surface to a given triangulation. In particular, the tools support surface refinement and coarsening. Section 5 describes some preliminary results on the application of interface identification methods to some model problems in geophysical inversion. Due to time constraints, the results described here use the GNU Triangulated Surface Library for the manipulation of surface meshes and the TetGen software library for the generation of tetrahedral meshes.
The peridynamic model was introduced by Silling in 1998. In this paper, we demonstrate the application of the quasistatic peridynamic model to two-dimensional, linear elastic, plane stress and plane strain problems, with special attention to the modeling of plain and reinforced concrete structures. We consider just one deviation from linearity--that which arises due to the irreversible sudden breaking of bonds between particles. The peridynamic model starts with the assumption that Newton's second law holds true on every infinitesimally small free body (or particle) within the domain of analysis. A specified force density function, called the pairwise force function, (with units of force per unit volume per unit volume) between each pair of infinitesimally small particles is postulated to act if the particles are closer together than some finite distance, called the material horizon. The pairwise force function may be assumed to be a function of the relative position and the relative displacement between the two particles. In this paper, we assume that for two particles closer together than the specified 'material horizon' the pairwise force function increases linearly with respect to the stretch, but at some specified stretch, the pairwise force function is irreversibly reduced to zero.
Due to advances in CMOS fabrication technology, high performance computing capabilities have continually grown. More capable hardware has allowed a range of complex scientific applications to be developed. However, these applications present a bottleneck to future performance. Entrenched 'legacy' codes - 'Dusty Decks' - demand that new hardware must remain compatible with existing software. Additionally, conventional architectures faces increasing challenges. Many of these challenges revolve around the growing disparity between processor and memory speed - the 'Memory Wall' - and difficulties scaling to large numbers of parallel processors. To a large extent, these limitations are inherent to the traditional computer architecture. As data is consumed more quickly, moving that data to the point of computation becomes more difficult. Barring any upward revision in the speed of light, this will continue to be a fundamental limitation on the speed of computation. This work focuses on these solving these problems in the context of Light Weight Processing (LWP). LWP is an innovative technique which combines Processing-In-Memory, short vector computation, multithreading, and extended memory semantics. It applies these techniques to try and answer the questions 'What will a next-generation supercomputer look like?' and 'How will we program it?' To that end, this work presents four contributions: (1) An implementation of MPI which uses features of LWP to substantially improve message processing throughput; (2) A technique leveraging extended memory semantics to improve message passing by overlapping computation and communication; (3) An OpenMP library modified to allow efficient partitioning of threads between a conventional CPU and LWPs - greatly improving cost/performance; and (4) An algorithm to extract very small 'threadlets' which can overcome the inherent disadvantages of a simple processor pipeline.
