Localized and Randomized Linear-Scaling Algorithms for Electronic Structure.
Abstract not provided.
Moussa, Jonathan Edward↗
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Localized and Randomized Algorithms for Electronic Structure.
Abstract not provided.
Moussa, Jonathan Edward↗
Data-driven modeling and control of dynamical systems using Koopman and Perron-Frobenius operators
This dissertation studies the data-driven modeling and control problem of nonlinear systems by exploiting the linear operator theoretic framework involving Koopman and Perro-Frobenius operator. A systematic linear-operator based controller design procedure has been established, which can be used to solve a variety of nonlinear control problems, including feedback stabilization using control Lyapunov functions, optimal quadratic regulation using Koopman eigenfunctions and convex optimization formulation of optimal control problem using P-F and Koopman operator approximation. As the core of data-driven modeling, we first propose a new algorithm for the finite-dimensional approximation of the linear transfer Koopman and Perron-Frobenius operator from time-series data. We argue that the existing approach for the finite-dimensional approximation of these transfer operators such as Dynamic Mode Decomposition (DMD) and Extended Dynamic Mode Decomposition (EDMD) do not capture two important properties of these operators, namely positivity and Markov property. The algorithm we propose preserves these two properties. We call the proposed algorithm as naturally structured DMD (NSDMD) since it retains the inherent properties of these operators. Naturally structured DMD algorithm leads to a better approximation of the steady-state dynamics of the system regarding computing Koopman and Perron- Frobenius operator eigenfunctions and eigenvalues. However, preserving positivity property is critical for capturing the real transient dynamics of the system. This positivity property of the transfer operators and it's finite-dimensional approximation play an important role for controller and estimator design of nonlinear systems. To solve the feedback stabilization problem for nonlinear control systems, we tried to take advantage of the Koopman operator framework. The Koopman operator approach provides a linear representation for a nonlinear dynamical system and a bilinear representation for a nonlinear control system. The problem of feedback stabilization of a nonlinear control system is then transformed to the stabilization of a bilinear control system. We propose a control Lyapunov function (CLF)-based approach for the design of stabilizing feedback controllers for the bilinear system. The search for finding a CLF for the bilinear control system is formulated as a convex optimization problem. This leads to a schematic procedure for designing CLF-based stabilizing feedback controllers for the bilinear system and hence the original nonlinear system. Another advantage of the proposed controller design approach outlined in this dissertation is that it does not require explicit knowledge of system dynamics. In particular, the bilinear representation of a nonlinear control system in the Koopman eigenfunction space can be obtained from time-series data. Next, we study the optimal quadratic regulation problem for nonlinear systems. The linear operator theoretic framework involving the Koopman operator is used to lift the dynamics of nonlinear control system to an infinite-dimensional bilinear system. The optimal quadratic regulation problem for nonlinear system is formulated in terms of the finite-dimensional approximation of the bilinear system. A convex optimization-based approach is proposed for solving the quadratic regulator problem for bilinear system. We applied a variety of examples and compared the simulation results between our framework and conventional LQR control using linearized model. For more general optimal control problems, we provide a density-function based convex formulation for the optimal control problem of the nonlinear system. The convex formulation relies on the duality result in the stability theory of a dynamical system involving density function and Perron-Frobenius operator. The optimal control problem is formulated as an infinite-dimensional convex optimization program. The finite-dimensional approximation of the optimization problem relies on the recent advances made in the data-driven computation of the Koopman operator, which is dual to the Perron-Frobenius operator. Simulation results are presented to demonstrate the application of the developed framework.
Huang, Bowen↗
Optimization of a Lunar Pallet Lander Reinforcement Structure Using a Genetic Algorithm
This paper presents a design automation process using optimization via a genetic algorithm to design the conceptual structure of a Lunar Pallet Lander. The goal is to determine a design that will have the primary natural frequencies at or above a target value as well as minimize the total mass. Several iterations of the process are presented. First, a concept optimization is performed to determine what class of structure would produce suitable candidate designs. From this a stiffened sheet metal approach was selected leading to optimization of beam placement through generating a two-dimensional mesh and varying the physical location of reinforcing beams. Finally, the design space is reformulated as a binary problem using 1-dimensional beam elements to truncate the design space to allow faster convergence and additional mechanical failure criteria to be included in the optimization responses. Results are presented for each design space configuration. The final flight design was derived from these results.
Burt, Adam O.↗
Strain gage selection in loads equations using a genetic algorithm
Traditionally, structural loads are measured using strain gages. A loads calibration test must be done before loads can be accurately measured. In one measurement method, a series of point loads is applied to the structure, and loads equations are derived via the least squares curve fitting algorithm using the strain gage responses to the applied point loads. However, many research structures are highly instrumented with strain gages, and the number and selection of gages used in a loads equation can be problematic. This paper presents an improved technique using a genetic algorithm to choose the strain gages used in the loads equations. Also presented are a comparison of the genetic algorithm performance with the current T-value technique and a variant known as the Best Step-down technique. Examples are shown using aerospace vehicle wings of high and low aspect ratio. In addition, a significant limitation in the current methods is revealed. The genetic algorithm arrived at a comparable or superior set of gages with significantly less human effort, and could be applied in instances when the current methods could not.
Source record↗
Evaluation of improved algorithms for nonlinear transient structural heat transfer
The paper presents the evaluation of algorithms having potential for reducing computer time to integrate large systems of equations governing nonlinear transient heat transfer in complex structures. A series of test problems is being developed to test two algorithms. The Shuttle Orbiter frame model having 190 nodes was the subject of an analytical/experimental study. Plans are to perform calculations for the complete wing model having about 4000 nodes as well as a regional (plug) model having about 200 nodes.
Adelman, H. M.↗
Theoretical search for possible Au-Si crystal structures using a genetic algorithm
Here, we performed a global search for possible Au-Si crystal structures using a genetic algorithm (GA) combined with density functional theory (DFT) calculations. Two Au-Si structures, A u 8 S i 8 and A u 16 S i 8 , were found to be energetically stable and have no imaginary frequencies by phonon calculations. The formation energies of all the studied structures gave a convex hull of the Au-Si system, showing that the most stable composition was Au - Si = 1 : 1 and that the Si-rich structures were much less stable than the Au-rich ones.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Fast Approximate Analysis Of Modified Antenna Structure
Abbreviated algorithms developed for fast approximate analysis of effects of modifications in supporting structures upon root-mean-square (rms) path-length errors of paraboloidal-dish antennas. Involves combination of methods of structural-modification reanalysis with new extensions of correlation analysis to obtain revised rms path-length error. Full finite-element analysis, usually requires computer of substantial capacity, necessary only to obtain responses of unmodified structure to known external loads and to selected self-equilibrating "indicator" loads. Responses used in shortcut calculations, which, although theoretically "exact", simple enough to be performed on hand-held calculator. Useful in design, design-sensitivity analysis, and parametric studies.
Levy, Roy↗
Benchmarking Coordination Number Prediction Algorithms on Inorganic Crystal Structures
Coordination numbers and geometries form a theoretical framework for understanding and predicting materials properties. Algorithms to determine coordination numbers automatically are increasingly used for machine learning and automatic structural analysis. In this work, we introduce MaterialsCoord, a benchmark suite containing 56 experimentally-derived crystal structures (spanning elements, binaries, and ternary compounds) and their corresponding coordination environments as described in the research literature. We also describe CrystalNN, a novel algorithm for determining near neighbors. We compare CrystalNN against 7 existing near-neighbor algorithms on the MaterialsCoord benchmark, finding CrystalNN to perform similarly to several well-established algorithms. For each algorithm, we also assess computational demand and sensitivity towards small perturbations that mimic thermal motion. Finally, we investigate the similarity between bonding algorithms when applied to the Materials Project database. Finally, we expect that this work will aid the development of coordination prediction algorithms as well as improve structural descriptors for machine learning and other applications.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Thermomechanically induced pre- and postbuckling of general structure
An algorithmic solution strategy which enables handling the positive/indefinite stiffness characteristics associated with the pre and postbuckling of structures subject to complex thermomechanical loading fields was developed. The flexibility of the procedure is such that it can be applied to both finite difference and element type simulations. Due to the generality of the algorithmic approach developed, both kinematic and thermal/mechanical type material nonlinearity including inelastic effects can be treated. This includes the possibility of handling completely general thermomechanical boundary conditions. To demonstrate the scheme, the results of several benchmark problems are presented.
Padovan, J.↗
GAtor: A First-Principles Genetic Algorithm for Molecular Crystal Structure Prediction
We present the implementation of GAtor, a massively parallel, first-principles genetic algorithm (GA) for molecular crystal structure prediction. GAtor is written in Python and currently interfaces with the FHI-aims code to perform local optimizations and energy evaluations using dispersion-inclusive density functional theory (DFT). GAtor offers a variety of fitness evaluation, selection, crossover, and mutation schemes. Breeding operators designed specifically for molecular crystals provide a balance between exploration and exploitation. Evolutionary niching is implemented in GAtor by using machine learning to cluster the dynamically updated population by structural similarity and then employing a cluster-based fitness function. Evolutionary niching promotes uniform sampling of the potential energy surface by evolving several subpopulations, which helps overcome initial pool biases and selection biases (genetic drift). The various settings offered by GAtor increase the likelihood of locating numerous low-energy minima, including those located in disconnected, hard to reach regions of the potential energy landscape. The best structures generated are re-relaxed and re ranked using a hierarchy of increasingly accurate DFT functionals and dispersion methods. GAtor is applied to a chemically diverse set of four past blind test targets, characterized by different types of intermolecular interactions. Furthermore, the experimentally observed structures and other low-energy structures are found for all four targets. In particular, for Target II, 5-cyano-3-hydroxythiophene, the top ranked putative crystal structure is a Z' = 2 structure with PT symmetry and a scaffold packing motif, which has not been reported previously.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Vibrio MARTX toxin processing and degradation of cellular Rab GTPases by the cytotoxic effector Makes Caterpillars Floppy
Vibrio vulnificus causes life-threatening wound and gastrointestinal infections, mediated primarily by the production of a Multifunctional-Autoprocessing Repeats-In-Toxin (MARTX) toxin. The most commonly present MARTX effector domain, the Makes Caterpillars Floppy-like (MCF) toxin, is a cysteine protease stimulated by host adenosine diphosphate (ADP) ribosylation factors (ARFs) to autoprocess. Here, we show processed MCF then binds and cleaves host Ra s-related proteins in b rain (Rab) guanosine triphosphatases within their C-terminal tails resulting in Rab degradation. We demonstrate MCF binds Rabs at the same interface occupied by ARFs. Moreover, we show MCF preferentially binds to ARF1 prior to autoprocessing and is active to cleave Rabs only subsequent to autoprocessing. We then use structure prediction algorithms to demonstrate that structural composition, rather than sequence, determines Rab target specificity. We further determine a crystal structure of aMCF as a swapped dimer, revealing an alternative conformation we suggest represents the open, activated state of MCF with reorganized active site residues. The cleavage of Rabs results in Rab1B dispersal within cells and loss of Rab1B density in the intestinal tissue of infected mice. Collectively, our work describes an extracellular bacterial mechanism whereby MCF is activated by ARFs and subsequently induces the degradation of another small host guanosine triphosphatase (GTPase), Rabs, to drive organelle damage, cell death, and promote pathogenesis of these rapidly fatal infections.
Science & Technology - Other Topics↗
Adaptivity and smart algorithms for fluid-structure interaction
This paper reviews new approaches in CFD which have the potential for significantly increasing current capabilities of modeling complex flow phenomena and of treating difficult problems in fluid-structure interaction. These approaches are based on the notions of adaptive methods and smart algorithms, which use instantaneous measures of the quality and other features of the numerical flowfields as a basis for making changes in the structure of the computational grid and of algorithms designed to function on the grid. The application of these new techniques to several problem classes are addressed, including problems with moving boundaries, fluid-structure interaction in high-speed turbine flows, flow in domains with receding boundaries, and related problems.
Oden, J. Tinsley↗
Dynamic effects in thermoviscoplastic structures
An algorithm for three-dimensional thermoviscoplasticity with inertial effects is presented. The algorithm utilizes a unified thermoviscoplastic constitutive model with directional hardening (Bodner-Partom). An example problem is shown in which thermally induced vibrations lead to material yielding at elevated temperatures. Significant dampening caused by inelastic strain is shown to take place in the structure.
Byrom, Ted G.↗
A genetic algorithm for first principles global structure optimization of supported nano structures
We present a newly developed publicly available genetic algorithm (GA) for global structure optimisation within atomic scale modeling. The GA is focused on optimizations using first principles calculations, but it works equally well with empirical potentials. The implementation is described and benchmarked through a detailed statistical analysis employing averages across many independent runs of the GA. This analysis focuses on the practical use of GA’s with a description of optimal parameters to use. New results for the adsorption of M{sub 8} clusters (M = Ru, Rh, Pd, Ag, Pt, Au) on the stoichiometric rutile TiO{sub 2}(110) surface are presented showing the power of automated structure prediction and highlighting the diversity of metal cluster geometries at the atomic scale.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
SMALE: Enhancing Scalability of Machine Learning Algorithms on Extreme-Scale Computing Platforms
Deployment and execution of machine learning tasks on extreme-scale computing platforms face several significant technical challenges: 1) High computing cost incurred by dense networks – The computing workload of deep networks with densely-connected topology increases rapidly with the network size, imposing a non-scalable computing model of extreme-scale computing platforms; 2) Non-optimized workload distribution – Many advanced deep learning algorithms, e.g., sparsification and irregular net-work topology, produce very unbalanced workload distribution on extreme-scale computing platforms. The computation efficiency is greatly hindered by the incurred data and computation redundancies as well as long tails of the node with extensive workload; 3) Constraints in data movement and I/O bottle-neck – Inter-node data movement in extreme-scale computing platforms are associated with high energy and latency costs, and subject to the constraints of I/O bandwidth; and 4) Generalization of algorithm realization and acceleration on computing platforms – The large varieties of machine learning algorithms and structures of extreme-scale computing platforms make the derivation of a generalized algorithm realization and acceleration method very challenging, which, however, is the requirement by domain scientists and interested users. We call the above challenges Smale’s Problems in Machine Learning and Understanding for High-Performance Computing Scientific Discovery. The objective of our three-year research project is to develop a holistic innovation set at structure, assembly, and acceleration layers of machine learning algorithms to address the above challenges in algorithm deployment and execution. Three tasks are particularly performed, including: At the algorithm structure level, we investigate the techniques that can structurally sparsify on the topology of deep networks for computing workload reduction. We also study clustering and pruning techniques that can optimize the workload distributions over the extreme-scale computing platforms; At the algorithm assembly level, we derive a unified learning framework for unsupervised transfer learning and dynamic growing capabilities. Novel training methods are also exploited to enhance the training efficiency of the proposed framework; At the algorithm acceleration level, we will develop a series of techniques that can accelerate the computation of sparse matrix operations, which are one of the core executions in deep learning and optimize memory access of the concerned platforms. Our proposed techniques attack the fundamental problems in machine learning algorithms running on extreme-scale computing platforms by vertically integrating the solutions at three closely entangled layers, paving the long-term scaling path of machine learning applications under DOE context. Three tasks corresponding to the above respective research orientations are performed during the three-year project period with our collaborators at ORNL. The outcome of the proposed project is anticipated to form a holistic solution set of novel algorithms and network topologies, efficient training techniques, and fast acceleration methods to promote the computing scalability of the machine learning applications of particular interest to DOE.
97 MATHEMATICS AND COMPUTING↗
Optimization of a Lunar Pallet Lander Reinforcement Structure Using a Genetic Algorithm
In this paper, a unique system level spacecraft design optimization will be presented. A Genetic Algorithm is used to design the global pattern of the reinforcing structure, while a gradient routine is used to adequately stiffen the sub-structure. The system level structural design includes determining the optimal physical location (and number) of reinforcing beams of a lunar pallet lander deck structure. Design of the substructure includes determining placement of secondary stiffeners and the number of rivets required for assembly.. In this optimization, several considerations are taken into account. The primary objective was to raise the primary natural frequencies of the structure such that the Pallet Lander primary structure does not significantly couple with the launch vehicle. A secondary objective is to determine how to properly stiffen the reinforcing beams so that the beam web resists the shear buckling load imparted by the spacecraft components mounted to the pallet lander deck during launch and landing. A third objective is that the calculated stress does not exceed the allowable strength of the material. These design requirements must be met while, minimizing the overall mass of the spacecraft. The final paper will discuss how the optimization was implemented as well as the results. While driven by optimization algorithms, the primary purpose of this effort was to demonstrate the capability of genetic algorithms to enable design automation in the preliminary design cycle. By developing a routine that can automatically generate designs through the use of Finite Element Analysis, considerable design efficiencies, both in time and overall product, can be obtained over more traditional brute force design methods.
Burt, Adam↗
Validation of deformable image registration algorithms on CT images of ex vivo porcine bladders with fiducial markers
Purpose: The spatial accuracy of deformable image registration (DIR) is important in the implementation of image guided adaptive radiotherapy techniques for cancer in the pelvic region. Validation of algorithms is best performed on phantoms with fiducial markers undergoing controlled large deformations. Excised porcine bladders, exhibiting similar filling and voiding behavior as human bladders, provide such an environment. The aim of this study was to determine the spatial accuracy of different DIR algorithms on CT images ofex vivo porcine bladders with radiopaque fiducial markers applied to the outer surface, for a range of bladder volumes, using various accuracy metrics. Methods: Five excised porcine bladders with a grid of 30–40 radiopaque fiducial markers attached to the outer wall were suspended inside a water-filled phantom. The bladder was filled with a controlled amount of water with added contrast medium for a range of filling volumes (100–400 ml in steps of 50 ml) using a luer lock syringe, and CT scans were acquired at each filling volume. DIR was performed for each data set, with the 100 ml bladder as the reference image. Six intensity-based algorithms (optical flow or demons-based) implemented in theMATLAB platform DIRART, a b-spline algorithm implemented in the commercial software package VelocityAI, and a structure-based algorithm (Symmetric Thin Plate Spline Robust Point Matching) were validated, using adequate parameter settings according to values previously published. The resulting deformation vector field from each registration was applied to the contoured bladder structures and to the marker coordinates for spatial error calculation. The quality of the algorithms was assessed by comparing the different error metrics across the different algorithms, and by comparing the effect of deformation magnitude (bladder volume difference) per algorithm, using the Independent Samples Kruskal-Wallis test. Results: The authors found good structure accuracy without dependency on bladder volume difference for all but one algorithm, and with the best result for the structure-based algorithm. Spatial accuracy as assessed from marker errors was disappointing for all algorithms, especially for large volume differences, implying that the deformations described by the registration did not represent anatomically correct deformations. The structure-based algorithm performed the best in terms of marker error for the large volume difference (100–400 ml). In general, for the small volume difference (100–150 ml) the algorithms performed relatively similarly. The structure-based algorithm exhibited the best balance in performance between small and large volume differences, and among the intensity-based algorithms, the algorithm implemented in VelocityAI exhibited the best balance. Conclusions: Validation of multiple DIR algorithms on a novel physiological bladder phantom revealed that the structure accuracy was good for most algorithms, but that the spatial accuracy as assessed from markers was low for all algorithms, especially for large deformations. Hence, many of the available algorithms exhibit sufficient accuracy for contour propagation purposes, but possibly not for accurate dose accumulation.
60 APPLIED LIFE SCIENCES↗