A New Computational Fluid Dynamics Code I: Fyris Alpha

A new hydrodynamics code aimed at astrophysical applications has been developed. The new code and algorithms are presented along with a comprehensive suite of test problems in one, two, and three dimensions. The new code is shown to be robust and accurate, equalling or improving upon a set of comparison codes. Fyris Alpha will be made freely available to the scientific community.Comment: 59 pages, 27 figures For associated code see http://www.mso.anu.edu.au/fyri

Hardware implementation of non-bonded forces in molecular dynamics simulations

Molecular Dynamics is a computational method based on classical mechanics to describe the behavior of a molecular system. This method is used in biomolecular simulations, which are intended to contribute to the study and advance of nanotechnology, medicine, chemistry and biology. Software implementations of Molecular Dynamics simulations can spend most of time computing the non-bonded interactions. This work presents the design and implementation of an FPGA-based coprocessor that accelerates MD simulations by computing in parallel the non-bonded interactions, specifically, the van der Waals and the electrostatic interactions. These interactions are modeled as the Lennard-Jones 6-12 potential and the direct-space Ewald summation, respectively. In addition, this work introduces a novel variable transformation of the potential energy functions, and a novel interpolation method with pseudo-floating-point representation to compute the short-range forces. Also, it uses a combination of fixed-point and floating-point arithmetic to obtain the best of both representations. The FPGA coprocessor is a memory-mapped system connected to a host by PCI Express, and is provided with interruption capabilities to improve parallelization. Its main block is based on a single functional pipeline, and is connected via Avalon Bus to other peripherals such as the PCIe Hard-IP and the SG-DMA. It is implemented on an Altera¿s EP2AGX125EF35C4 device, can process 16k particles, and is configured to store up to 16 different types of particles. Simulations in a custom C-application for MD that only computes non-bonded forces become up to 12.5x faster using the FPGA coprocessor when considering 12500 atoms.PregradoINGENIERO(A) EN ELECTRÓNIC

Corn yields as a function of specified production factors expressed as variables in quadratic prediction equations

Corn (Zea mays L.) is one of the major crops of American agriculture. It is a dual purpose crop since it is grown both for grain and forage. The grain is consumed directly and in-directly in different forms by human beings. A high quality silage is made from the forage for livestock. Thus the wide uses of corn indicate its importance. In United States the average per acre yield of corn is 61.8 bushels and the total production per year is 3.55 billion bushels. The productivity of land for a given crop is a function of three major influences--the soil, the climate, and the management practices. Each of these three major influences is made up of several components. The soil includes its physical, chemical, and biological conditions. The climate includes rain fall, temperature, light, etc. The management practices include the application of fertilizer, weed control, plant protection measures, tillage, cropping system, etc. Considerable efforts have been made in recent years to study the relationships between corn yields and one or more components. Probably less work has been done to study the relationships between corn yields and all the components together. The need to predict corn yield on various soils with different types and amounts of management inputs under different environmental conditions has been recognized. Since soil types in Tennessee vary greatly in their capacity to produce corn, more precise prediction information is needed for farmers to better utilize their land and other resources by selecting an appropriate cropping system and management level. The objectives of this study were; 1. to interpret rainfall and soil moisture information in terms of drought as one production factor; 2. to develop methodology for fitting appropriate drought values along with varying levels of selected management factors in quadratic prediction equations; 3. to develop a mathematical relationship in terms of a quadratic function between observed yields and varying levels of selected production factors; 4. to develop effective prediction equations for pre-dicting corn yields; and 5. to make an agronomic interpretation of the findings of this study

The use of Delft3D to simulate the deposition of cohesive and non-cohesive sediments in irrigation systems

Sediment deposition threatens the performance of many irrigation systems. Because of the high impact on irrigation performance and crop production, many studies have been done on how to deal with sediment deposition. In this research, the Delft3D model, originally developed for hydro-morphologic modelling of rivers and estuaries, was adapted for the use in irrigation systems simulations and applied to different case studies. This research addresses two shortcomings of previous studies of sediments in irrigation systems. Firstly, while previous studies primarily used 1D models, this research uses a 2D/3D model. The use of 2D/3D models in irrigation systems is significant because the non-uniform flow around structures such as offtakes, weirs and gates, leads to asymmetric sedimentation patterns that are missed by 1D simulations. Secondly, whereas previous studies mostly considered non-cohesive sediments, this research simulates cohesive, non-cohesive and a mix of both sediment types. This is important for irrigation systems that draw water from natural rivers that carry a mix of cohesive and non-cohesive sediments. The findings of this research are important for irrigation system maintenance and gate operation. It is also essential for the development of canal operating plans that meet crop water requirements and at the same time minimizes sediment deposition by alternating gates

Echo state model of non-Markovian reinforcement learning, An

Department Head: Dale H. Grit.2008 Spring.Includes bibliographical references (pages 137-142).There exists a growing need for intelligent, autonomous control strategies that operate in real-world domains. Theoretically the state-action space must exhibit the Markov property in order for reinforcement learning to be applicable. Empirical evidence, however, suggests that reinforcement learning also applies to domains where the state-action space is approximately Markovian, a requirement for the overwhelming majority of real-world domains. These domains, termed non-Markovian reinforcement learning domains, raise a unique set of practical challenges. The reconstruction dimension required to approximate a Markovian state-space is unknown a priori and can potentially be large. Further, spatial complexity of local function approximation of the reinforcement learning domain grows exponentially with the reconstruction dimension. Parameterized dynamic systems alleviate both embedding length and state-space dimensionality concerns by reconstructing an approximate Markovian state-space via a compact, recurrent representation. Yet this representation extracts a cost; modeling reinforcement learning domains via adaptive, parameterized dynamic systems is characterized by instability, slow-convergence, and high computational or spatial training complexity. The objectives of this research are to demonstrate a stable, convergent, accurate, and scalable model of non-Markovian reinforcement learning domains. These objectives are fulfilled via fixed point analysis of the dynamics underlying the reinforcement learning domain and the Echo State Network, a class of parameterized dynamic system. Understanding models of non-Markovian reinforcement learning domains requires understanding the interactions between learning domains and their models. Fixed point analysis of the Mountain Car Problem reinforcement learning domain, for both local and nonlocal function approximations, suggests a close relationship between the locality of the approximation and the number and severity of bifurcations of the fixed point structure. This research suggests the likely cause of this relationship: reinforcement learning domains exist within a dynamic feature space in which trajectories are analogous to states. The fixed point structure maps dynamic space onto state-space. This explanation suggests two testable hypotheses. Reinforcement learning is sensitive to state-space locality because states cluster as trajectories in time rather than space. Second, models using trajectory-based features should exhibit good modeling performance and few changes in fixed point structure. Analysis of performance of lookup table, feedforward neural network, and Echo State Network (ESN) on the Mountain Car Problem reinforcement learning domain confirm these hypotheses. The ESN is a large, sparse, randomly-generated, unadapted recurrent neural network, which adapts a linear projection of the target domain onto the hidden layer. ESN modeling results on reinforcement learning domains show it achieves performance comparable to lookup table and neural network architectures on the Mountain Car Problem with minimal changes to fixed point structure. Also, the ESN achieves lookup table caliber performance when modeling Acrobot, a four-dimensional control problem, but is less successful modeling the lower dimensional Modified Mountain Car Problem. These performance discrepancies are attributed to the ESN’s excellent ability to represent complex short term dynamics, and its inability to consolidate long temporal dependencies into a static memory. Without memory consolidation, reinforcement learning domains exhibiting attractors with multiple dynamic scales are unlikely to be well-modeled via ESN. To mediate this problem, a simple ESN memory consolidation method is presented and tested for stationary dynamic systems. These results indicate the potential to improve modeling performance in reinforcement learning domains via memory consolidation

Decoherence, control, and encoding of coupled solid-state quantum bits

In this thesis the decoherence properties, gate performance, control of solid-state quantum bits (qubits), and novel design proposals for solid-state qubits analogous to quantum optics are investigated. The qubits are realized as superconducting nanocircuits or quantum dot systems. The thesis elucidates both very appealing basic questions, like the generation and detection of deeply nonclassical states of the electromagnetic field, i.e., single photon Fock states, in the solid-state, but also presents a broad range of different strategies to improve the scalability and decoherence properties of solid-state qubit setups

A Fast Matrix-Free Algorithm for Spectral Approximations to High-Dimensional Partial Differential Equations

This thesis is concerned with the computational intractabilities that arise from spectral discretizations of high-dimensional partial differential equations. Using the example of the time-dependent multi-particle Schrödinger equation, we consider a spectral Galerin approximation in space with a tensor product basis of Hermite functions. When propagating the resulting system of ordinary differential equations in time, one typically needs to evaluate matrix-vector products involving a matrix representation of the Hamiltonian operator in each time step. Since the size of this matrix equals the number of equations, which (for an unreduced basis) depends exponentially on the dimension and thus quickly becomes enormously large, this can make computations infeasible - both due to a lack of memory and due to unbearably long computation times. We present a fast algorithm for an efficient computation of these matrix-vector products that scales only linearly with the size of the Galerkin basis - without assembling the matrix itself. Besides being a matrix-free approach, the fast algorithm is compatible with the idea of reducing the index set that underlies the basis. The computational speed-up is achieved using orthogonality of the Hermite functions in combination with their generic three-term recurrence. Briefly, these properties allow to compute the action of the matrix representations of the coordinatewise position operators on vectors in linear time. The basic idea is then to insert these coordinate matrices into a polynomial approximate of the potential. This has originally been proposed by E. Faou, V. Gradinaru, and Ch. Lubich. We modify their approach and turn it into a rigorous algorithm. For an unreduced set of basis functions, we show this tentative proceeding to be equivalent to a suitable entrywise approximation of the potential matrix by Gauß-Hermite quadrature. Reducing the index set for the basis functions yields an additional error. We derive error estimates for all approximation steps involved. In particular, using a binary tree approach, bounds for the errors due to quadrature and index set reduction are deduced. Both errors decay spectrally if the potential is significantly smoother than the exact solution wherever the latter does not essentially vanish. Extensive numerical experiments corroborate these findings. Besides, we show performance tests comparing the fast algorithm to a matrix-free approach from the chemical literature. Apart from the above basic form of the fast algorithm, we present applications of the general methodology to the nonlinear Schrödinger equation and, most prominently, to initial-boundary value problems. As an example, we study the acoustic wave equation with non-constant coefficients and Engquist-Majda boundary conditions, and construct efficient procedures for the different kinds of matrix-vector products together with an error analysis and numerical tests.Das Lösen hochdimensionaler partieller Differentialgleichungen mittels Spektralmethoden stellt in Anbetracht der damit verbundenen enormen Speicherplatz- wie auch Zeitkomplexität eine besondere Herausforderung dar. Wir betrachten das Beispiel der zeitabhäng-igen Vielteilchen-Schrödingergleichung, die mit einem Galerkinansatz im Raum diskretisiert wird. Die zugrundeliegende Basis besteht aus Tensorprodukten von Hermitefunktionen. Bei der Integration des zugehörigen Systems gewöhnlicher Differentialgleichungen sind in jedem Zeitschritt typerischerweise Matrix-Vektor-Produkte mit der Darstellungsmatrix des Hamiltonoperators der Gleichung bezüglich der gewählten Galerkinbasis zu berechnen. Die Größe dieser Matrix hängt im Falle einer nicht ausgedünnten Basis exponentiell von der Dimension des Problems ab. Das explizite Aufstellen der Matrix überschreitet damit leicht den zur Verfügung stehenden Speicherplatz und erfordert unerträglich lange Rechenzeiten. Diese Arbeit stellt einen schnellen Algorithmus zur Berechnung solcher Matrix-Vektor-Produkte vor, dessen Komplexität nur linear von der Größe der Galerkinbasis abhängt und der ohne explizites Aufstellen der Matrix auskommt. Darüber hinaus erlaubt er nahezu beliebiges Ausdünnen der Basis - sofern eine entsprechende Ausdünnung selbst eine gute Approximation an die gesuchte Lösung des Problems liefert. Stellt man die Ortsoperatoren bezüglich der einzelnen Koordinaten in der gewählten Basis dar, so lassen sich mithilfe der wechselseitigen Orthogonalität der Hermitefunktionen sowie der sie definierenden Drei-Term-Rekursion Produkte dieser Koordinatenmatrizen mit Vektoren in linearer Zeit berechnen. Die bereits von E. Faou, V. Gradinaru und Ch. Lubich vorgestellte Kernidee des schnellen Algorithmus besteht nun darin, die Koordinatenmatrizen formal in eine polynomielle Approximation des Potentials einzusetzen. Wir modifizieren diesen Vorschlag und präsentieren einen rigorosen Algorithmus. Für eine nicht ausgedünnte Galerkinbasis erweist sich diese Idee als äquivalent zur Approximation der Integrale in jedem Eintrag der Matrixdarstellung des Potentials mittels einer spezifisch gewählten Gauß-Hermite-Quadratur, wie in der vorliegenden Arbeit gezeigt wird. Ausdünnen der Basis generiert einen zusätzlichen Fehler. Ein wichtiger Bestandteil dieser Arbeit ist die Fehleranalyse. Insbesondere lassen sich die durch Quadratur und ggf. Ausdünnen der Basis verursachten Fehler jeweils durch geschicktes Umschreiben der Hermite-Rekursion als Binärbaum kontrollieren. Unter der Annahme eines im Vergleich zur exakten Lösung hinreichend glatten Potentials fallen diese Fehler spektral ab. Dies wird in numerischen Experimenten bestätigt. Als Vergleichsmaß für die tatsächliche Einsparung an Rechenzeit durch den schnellen Algorithmus dient uns ein matrixfreier Ansatz, der in der chemischen Literatur entwickelt wurde. Darüber hinaus übertragen wir den obigen Ansatz auf eine analoge Behandlung u.a. der nichtlinearen Schrödingergleichung und von Anfangsrandwertproblemen. Als Beispiel für letztere Klasse betrachten wir im zweiten Teil der Arbeit die Wellengleichung mit variablen Koeffizienten und Engquist-Majda-Randbedingungen und konstruieren analoge effiziente Verfahren für die zugehörigen Matrix-Vektor-Produkte. Wir führen ebenfalls eine Fehleranalyse durch und präsentieren numerische Experimente

Semi-Weakly Supervised Learning for Label-efficient Semantic Segmentation in Expert-driven Domains

Unter Zuhilfenahme von Deep Learning haben semantische Segmentierungssysteme beeindruckende Ergebnisse erzielt, allerdings auf der Grundlage von überwachtem Lernen, das durch die Verfügbarkeit kostspieliger, pixelweise annotierter Bilder limitiert ist. Bei der Untersuchung der Performance dieser Segmentierungssysteme in Kontexten, in denen kaum Annotationen vorhanden sind, bleiben sie hinter den hohen Erwartungen, die durch die Performance in annotationsreichen Szenarien geschürt werden, zurück. Dieses Dilemma wiegt besonders schwer, wenn die Annotationen von lange geschultem Personal, z.B. Medizinern, Prozessexperten oder Wissenschaftlern, erstellt werden müssen. Um gut funktionierende Segmentierungsmodelle in diese annotationsarmen, Experten-angetriebenen Domänen zu bringen, sind neue Lösungen nötig. Zu diesem Zweck untersuchen wir zunächst, wie schlecht aktuelle Segmentierungsmodelle mit extrem annotationsarmen Szenarien in Experten-angetriebenen Bildgebungsdomänen zurechtkommen. Daran schließt sich direkt die Frage an, ob die kostspielige pixelweise Annotation, mit der Segmentierungsmodelle in der Regel trainiert werden, gänzlich umgangen werden kann, oder ob sie umgekehrt ein Kosten-effektiver Anstoß sein kann, um die Segmentierung in Gang zu bringen, wenn sie sparsam eingestetzt wird. Danach gehen wir auf die Frage ein, ob verschiedene Arten von Annotationen, schwache- und pixelweise Annotationen mit unterschiedlich hohen Kosten, gemeinsam genutzt werden können, um den Annotationsprozess flexibler zu gestalten. Experten-angetriebene Domänen haben oft nicht nur einen Annotationsmangel, sondern auch völlig andere Bildeigenschaften, beispielsweise volumetrische Bild-Daten. Der Übergang von der 2D- zur 3D-semantischen Segmentierung führt zu voxelweisen Annotationsprozessen, was den nötigen Zeitaufwand für die Annotierung mit der zusätzlichen Dimension multipliziert. Um zu einer handlicheren Annotation zu gelangen, untersuchen wir Trainingsstrategien für Segmentierungsmodelle, die nur preiswertere, partielle Annotationen oder rohe, nicht annotierte Volumina benötigen. Dieser Wechsel in der Art der Überwachung im Training macht die Anwendung der Volumensegmentierung in Experten-angetriebenen Domänen realistischer, da die Annotationskosten drastisch gesenkt werden und die Annotatoren von Volumina-Annotationen befreit werden, welche naturgemäß auch eine Menge visuell redundanter Regionen enthalten würden. Schließlich stellen wir die Frage, ob es möglich ist, die Annotations-Experten von der strikten Anforderung zu befreien, einen einzigen, spezifischen Annotationstyp liefern zu müssen, und eine Trainingsstrategie zu entwickeln, die mit einer breiten Vielfalt semantischer Information funktioniert. Eine solche Methode wurde hierzu entwickelt und in unserer umfangreichen experimentellen Evaluierung kommen interessante Eigenschaften verschiedener Annotationstypen-Mixe in Bezug auf deren Segmentierungsperformance ans Licht. Unsere Untersuchungen führten zu neuen Forschungsrichtungen in der semi-weakly überwachten Segmentierung, zu neuartigen, annotationseffizienteren Methoden und Trainingsstrategien sowie zu experimentellen Erkenntnissen, zur Verbesserung von Annotationsprozessen, indem diese annotationseffizient, expertenzentriert und flexibel gestaltet werden

Simulation of axisymmetric stepped surfaces with a facet

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.Includes bibliographical references (p. 255-266).A crystal lattice with a small miscut from the plane of symmetry has a surface which consists of a series of atomic height steps separated by terraces. If the surface of this crystal is not in equilibrium with the surrounding medium, then its evolution is strongly mediated by the presence of these steps, which act as sites for attachment and detachment of diffusing adsorbed atoms ('adatoms'). In the absence of material deposition and evaporation, steps move in response to two main physical effects: line tension, which is caused by curvature of the step edge, and step-step interactions which can arise because of thermal step fluctuations, or elastic effects. This thesis focuses on axisymmetric crystals, with the result that the position of a step is uniquely described by a single scalar variable, and the step positions obey a coupled system of "step-flow" Ordinary Differential Equations (step flow ODEs). Chapter 2 of this thesis concentrates on the derivation and numerical solution of these equations, and their properties in the limits of slow adatom terrace diffusion and slow adatom attachment-detachment. Chapter 3 focuses on the analysis carried out by Margetis, Aziz and Stone ('MAS') [78] on a Partial Differential Equation (PDE) description of surface evolution.(cont.) Here, the crystal is also axisymmetric and has a single macroscopically flat region, a facet. It is discovered that the boundary condition of Step Chemical Potential Continuity, first suggested by Spohn [109] yields results that are inconsistent with the scalings predicted by the MAS analysis and with results from the step flow ODEs. The 'step drop' condition suggested by Israeli and Kandel [50] is implemented instead, and is shown to give good agreement with the results from the step flow ODEs. Chapters 4 and 5 explore the evolution of algebraic profiles: instead of starting with steps that are equally spaced, the step radii are initialized as a more general algebraic function of the height. In these two chapters, results are presented which involve approximate self-similarity of the profiles, a stability analysis of small perturbations, and quantification of decay rates. Chapter 6 of this thesis details the numerical procedure used to integrate the step flow equations. A 'multi-adaptive' time integrator is used where different time steps are taken for different components of the solution. This procedure has benefits over a standard integrator, because when a few steps cluster tightly together, these steps (and these steps only) become very stiff to integrate.(cont.) Whereas the inner most steps in the structure undergo a rapid motion, the majority of steps which are sufficiently far away from the facet, move relatively slowly and exhibit smooth behaviour in time. Using the same time step for all components in the solution is therefore quite inefficient. This chapter discusses the concept of "local stiffness", and how the motion of the inner most steps is handled.by Pak-Wing Fok.Ph.D