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At least 415 records · Page 23

Generalized master equation for particle transport in binary random media with renewal statistics

Particle transport in binary stochastic mixtures is classically modeled assuming Markovian or exponential mixing statistics but in many applications material memory invalidates the Markov assumption. For non-Markovian mixing characterized by alternating renewal processes, a transport-theoretic framework is presented that provides an exact description of transport in nonscattering random binary media with general non-exponential statistics. Our approach is to Markovianize the problem by augmenting the {material type, particle flux} state space with the age or distance from the last interface. A Chapman-Kolmogorov equation is formulated for the joint probability density of the material type, particle flux, and age, and subsequently reduced to a generalized Master equation (GME) in differential form. This constitutes the primary result of this work. A state-updating Monte Carlo algorithm consistent with the GME is developed and benchmarked against analytical solutions for multiple chord-length laws. For purely absorbing renewal statistical media, the GME reproduces analytical benchmarks for the equilibrium age distribution, interior mean/variance of material-conditioned fluxes, and boundary transmittance. Simulations further demonstrate that a Markov (exponential) approximation of non-exponential statistics can introduce large errors in transmittance and interior flux profiles. Lastly, the reintroduction of memory due to scattering is briefly addressed through heuristic considerations.

Fluctuations & noise↗

Automated Point Cloud Correspondence Detection for Underwater Mapping Using AUVs

An algorithm for automating correspondence detection between point clouds composed of multibeam sonar data is presented. This allows accurate initialization for point cloud alignment techniques even in cases where accurate inertial navigation is not available, such as iceberg profiling or vehicles with low-grade inertial navigation systems. Techniques from computer vision literature are used to extract, label, and match keypoints between "pseudo-images" generated from these point clouds. Image matches are refined using RANSAC and information about the vehicle trajectory. The resulting correspondences can be used to initialize an iterative closest point (ICP) registration algorithm to estimate accumulated navigation error and aid in the creation of accurate, self-consistent maps. The results presented use multibeam sonar data obtained from multiple overlapping passes of an underwater canyon in Monterey Bay, California. Using strict matching criteria, the method detects 23 between-swath correspondence events in a set of 155 pseudo-images with zero false positives. Using less conservative matching criteria doubles the number of matches but introduces several false positive matches as well. Heuristics based on known vehicle trajectory information are used to eliminate these.

Sonar↗

WHAMII - An enumeration and insertion procedure with binomial bounds for the stochastic time-constrained traveling salesman problem

This paper presents an algorithm (WHAMII) designed to solve the Artificial Intelligence Design Challenge at the 1987 AIAA Guidance, Navigation and Control Conference. The problem under consideration is a stochastic generalization of the traveling salesman problem in which travel costs can incur a penalty with a given probability. The variability in travel costs leads to a probability constraint with respect to violating the budget allocation. Given the small size of the problem (eleven cities), an approach is considered that combines partial tour enumeration with a heuristic city insertion procedure. For computational efficiency during both the enumeration and insertion procedures, precalculated binomial probabilities are used to determine an upper bound on the actual probability of violating the budget constraint for each tour. The actual probability is calculated for the final best tour, and additional insertions are attempted until the actual probability exceeds the bound.

Dahl, Roy W.↗

A linguistic geometry for 3D strategic planning

This paper is a new step in the development and application of the Linguistic Geometry. This formal theory is intended to discover the inner properties of human expert heuristics, which have been successful in a certain class of complex control systems, and apply them to different systems. In this paper we investigate heuristics extracted in the form of hierarchical networks of planning paths of autonomous agents. Employing Linguistic Geometry tools the dynamic hierarchy of networks is represented as a hierarchy of formal attribute languages. The main ideas of this methodology are shown in this paper on the new pilot example of the solution of the extremely complex 3D optimization problem of strategic planning for the space combat of autonomous vehicles. This example demonstrates deep and highly selective search in comparison with conventional search algorithms.

Stilman, Boris↗

Theory of Collective Intelligence

In this chapter an analysis of the behavior of an arbitrary (perhaps massive) collective of computational processes in terms of an associated "world" utility function is presented We concentrate on the situation where each process in the collective can be viewed as though it were striving to maximize its own private utility function. For such situations the central design issue is how to initialize/update the collective's structure, and in particular the private utility functions, so as to induce the overall collective to behave in a way that has large values of the world utility. Traditional "team game" approaches to this problem simply set each private utility function equal to the world utility function. The "Collective Intelligence" (COIN) framework is a semi-formal set of heuristics that recently have been used to construct private utility. functions that in many experiments have resulted in world utility values up to orders of magnitude superior to that ensuing from use of the team game utility. In this paper we introduce a formal mathematics for analyzing and designing collectives. We also use this mathematics to suggest new private utilities that should outperform the COIN heuristics in certain kinds of domains. In accompanying work we use that mathematics to explain previous experimental results concerning the superiority of COIN heuristics. In that accompanying work we also use the mathematics to make numerical predictions, some of which we then test. In this way these two papers establish the study of collectives as a proper science, involving theory, explanation of old experiments, prediction concerning new experiments, and engineering insights.

Nash equilibrium↗

Algorithms for high aspect ratio oriented triangulations

Grid generation plays an integral part in the solution of computational fluid dynamics problems for aerodynamics applications. A major difficulty with standard structured grid generation, which produces quadrilateral (or hexahedral) elements with implicit connectivity, has been the requirement for a great deal of human intervention in developing grids around complex configurations. This has led to investigations into unstructured grids with explicit connectivities, which are primarily composed of triangular (or tetrahedral) elements, although other subdivisions of convex cells may be used. The existence of large gradients in the solution of aerodynamic problems may be exploited to reduce the computational effort by using high aspect ratio elements in high gradient regions. However, the heuristic approaches currently in use do not adequately address this need for high aspect ratio unstructured grids. High aspect ratio triangulations very often produce the large angles that are to be avoided. Point generation techniques based on contour or front generation are judged to be the most promising in terms of being able to handle complicated multiple body objects, with this technique lending itself well to adaptivity. The eventual goal encompasses several phases: first, a partitioning phase, in which the Voronoi diagram of a set of points and line segments (the input set) will be generated to partition the input domain; second, a contour generation phase in which body-conforming contours are used to subdivide the partition further as well as introduce the foundation for aspect ratio control, and; third, a Steiner triangulation phase in which points are added to the partition to enable triangulation while controlling angle bounds and aspect ratio. This provides a combination of the advancing front/contour techniques and refinement. By using a front, aspect ratio can be better controlled. By using refinement, bounds on angles can be maintained, while attempting to minimize the number of Steiner points.

Posenau, Mary-Anne K.↗

cuAlign: Scalable Network Alignment on GPU Accelerators

Given two graphs, the objective of network alignment is to find the best one-to-one mapping of vertices in one graph (??) to vertices in the other (??), such that the number of overlaps is maximized. We say that edges(??, ??) ???and(??', ??') ??? are overlapped if ?? is mapped to ??' and ?? is mapped to??'. Network alignment is an important optimization problem with several applications in bioinformatics, computer vision and ontology matching. Since it is an NP-hard problem, efficient heuristics and scalable implementations are necessary. In this work, we introduce a new framework that combines the concepts of intra-network proximity using vertex embedding,Belief Propagation (BP) and approximate weighted matching, and provides qualitative improvements up to22%over state-of-the-art approaches. We also provide scalable implementations on GPU accelerators, demonstrating up to19×speedup for Belief Propagation and 3× speedup for approximate weighted matching relative to previous multithreaded implementation. A combination of combinatorial and algebraic kernels within the network alignment algorithm poses significant hurdles for parallelization. Load imbalance and irregular DRAM traffic limit achievable performance on GPUs. Our novel approach identifies and exploits unique structural proper-ties of the BP-based algorithm and employs code fusion to reduce data movement between different steps of the algorithm. Using a diverse set of inputs, we demonstrate qualitative improvements of our algorithms, and performance gains of our GPU-accelerated implementation. We believe that our work will enable algorithmic improvements and practical applications of network alignment.

Xiang, Lizhi↗

Resource constrained design of artificial neural networks using comparator neural network

We present a systematic design method executed under resource constraints for automating the design of artificial neural networks using the back error propagation algorithm. Our system aims at finding the best possible configuration for solving the given application with proper tradeoff between the training time and the network complexity. The design of such a system is hampered by three related problems. First, there are infinitely many possible network configurations, each may take an exceedingly long time to train; hence, it is impossible to enumerate and train all of them to completion within fixed time, space, and resource constraints. Second, expert knowledge on predicting good network configurations is heuristic in nature and is application dependent, rendering it difficult to characterize fully in the design process. A learning procedure that refines this knowledge based on examples on training neural networks for various applications is, therefore, essential. Third, the objective of the network to be designed is ill-defined, as it is based on a subjective tradeoff between the training time and the network cost. A design process that proposes alternate configurations under different cost-performance tradeoff is important. We have developed a Design System which schedules the available time, divided into quanta, for testing alternative network configurations. Its goal is to select/generate and test alternative network configurations in each quantum, and find the best network when time is expended. Since time is limited, a dynamic schedule that determines the network configuration to be tested in each quantum is developed. The schedule is based on relative comparison of predicted training times of alternative network configurations using comparator network paradigm. The comparator network has been trained to compare training times for a large variety of traces of TSSE-versus-time collected during back-propagation learning of various applications.

Wah, Benjamin W.↗

Fast and robust strategies for large-scale mixed-integer SCOPF

This project develops scalable, computationally efficient algorithms to solve realistic large-scale power system optimization problems, including systems with more than 8,000 buses, as part of a larger series of competitions run by ARPA-E. These problems are critical because the secure and reliable operation of the power grid is becoming increasingly challenging, especially under conditions of increased uncertainty and variability. The economic feasibility of our methods is high, given that they are purely software-based solutions designed to operate power grids more efficiently. The technical effectiveness balances heuristics and approximations to provide a trade-off between speed and accuracy.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Integrated Land Suitability Assessment for Depots Siting in a Sustainable Biomass Supply Chain

A sustainable biomass supply chain would require not only an effective and fluid transportation system with a reduced carbon footprint and costs, but also good soil characteristics ensuring durable biomass feedstock presence. Unlike existing approaches that fail to account for ecological factors, this work integrates ecological as well as economic factors for developing sustainable supply chain development. For feedstock to be sustainably supplied, it necessitates adequate environmental conditions, which need to be captured in supply chain analysis. Using geospatial data and heuristics, we present an integrated framework that models biomass production suitability, capturing the economic aspect via transportation network analysis and the environmental aspect via ecological indicators. Production suitability is estimated using scores, considering both ecological factors and road transportation networks. These factors include land cover/crop rotation, slope, soil properties (productivity, soil texture, and erodibility factor) and water availability. This scoring determines the spatial distribution of depots with priority to fields scoring the highest. Two methods for depot selection are presented using graph theory and a clustering algorithm to benefit from contextualized insights from both and potentially gain a more comprehensive understanding of biomass supply chain designs. Graph theory, via the clustering coefficient, helps determine dense areas in the network and indicate the most appropriate location for a depot. Clustering algorithm, via K-means, helps form clusters and determine the depot location at the center of these clusters. An application of this innovative concept is performed on a case study in the US South Atlantic, in the Piedmont region, determining distance traveled and depot locations, with implications on supply chain design. The findings from this study show that a more decentralized depot-based supply chain design with 3depots, obtained using the graph theory method, can be more economical and environmentally friendly compared to a design obtained from the clustering algorithm method with 2 depots. In the former, the distance from fields to depots totals 801,031,476 miles, while in the latter, it adds up to 1,037,606,072 miles, which represents about 30% more distance covered for feedstock transportation.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Quantification of electron correlation for approximate quantum calculations

State-of-the-art many-body wave function techniques rely on heuristics to achieve high accuracy at an attainable computational cost to solve the many-body Schrödinger equation. By far, the most common property used to assess accuracy has been the total energy; however, total energies do not give a complete picture of electron correlation. In this work, we assess the von Neumann entropy of the one-particle reduced density matrix (1-RDM) to compare selected configuration interaction (CI), coupled cluster, variational Monte Carlo, and fixed-node diffusion Monte Carlo for benchmark hydrogen chains. A new algorithm, the circle reject method, is presented, which improves the efficiency of evaluating the von Neumann entropy using quantum Monte Carlo by several orders of magnitude. The von Neumann entropy of the 1-RDM and the eigenvalues of the 1-RDM are shown to distinguish between the dynamic correlation introduced by the Jastrow and the static correlation introduced by determinants with large weights, confirming some of the lore in the field concerning the difference between the selected CI and Slater–Jastrow wave functions.

Chemistry↗

Intelligent System Partitioning for Agent-Based Security Constrained Optimal Power Flow

This project developed scalable, computationally efficient algorithms to solve realistic large-scale power system optimization problems as part of a larger series of competitions run by ARPA-E. These problems are important because the secure and reliable operation of the power grid, especially under increased uncertainty and variability, is growing increasingly challenging. The economic feasibility of the proposed methods developed by our team is quite low, considering it’s a purely software-based solution to operate power grids more efficiently. The technical effectiveness, as evidenced by our performance in the competition, balances heuristics and approximations to provide a tradeoff between speed and accuracy.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A linguistic geometry for space applications

We develop a formal theory, the so-called Linguistic Geometry, in order to discover the inner properties of human expert heuristics, which were successful in a certain class of complex control systems, and apply them to different systems. This research relies on the formalization of search heuristics of high-skilled human experts which allow for the decomposition of complex system into the hierarchy of subsystems, and thus solve intractable problems reducing the search. The hierarchy of subsystems is represented as a hierarchy of formal attribute languages. This paper includes a formal survey of the Linguistic Geometry, and new example of a solution of optimization problem for the space robotic vehicles. This example includes actual generation of the hierarchy of languages, some details of trajectory generation and demonstrates the drastic reduction of search in comparison with conventional search algorithms.

Stilman, Boris↗

Planning Bias: Planning as a Source of Sampling Bias

Many data-driven planning methods are trained on data generated by planners. It is well known that many statistical learning methods are sensitive to sampling bias, and yet there has been little or no attention to planning as a sampling method and its role in introducing sampling bias into planner-generated training data. Recently, it has been demonstrated that A**,* in the presence of problems with variable heuristic error, prefers some solutions over other equally cost-optimal solutions. But, as we discuss in this paper, mitigation may not be as simple as resolving arbitrary tie-breaking by sampling from ties uniformly at random. In this paper, we formalize an intuition of planning bias. We focus on problems which output a single solution. Diverse planning only complicates the problem by generalizing it to bias in the set of sets; we show how it is subject to bias in the single solution. We make some useful observations about deterministic algorithms in contrast to non-deterministic algorithms. We explain how information entropy may be a good way to measure planning bias, and discuss some issues in evaluating practical approaches to measurement. We address the intuition that uniform random tiebreaking should mitigate bias; and sketch a novel approach to constructing an appropriate random distribution for duplicate detection during forward search for unbiased A*. Finally, we suggest directions for future work.

Planning Scheduling Algorithms↗

Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers

The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.

97 MATHEMATICS AND COMPUTING↗

Deep Space Network Scheduling Using Multi-Objective Optimization with Uncertainty

We have developed a novel technique to incorporate uncertainty modeling within an evolutionary algorithm approach to multi-objective scheduling, with the goal of identifying a Pareto frontier (tradeoff curve) that recognizes the likelihood of events that can impact the schedule outcome. Our approach is particularly applicable to the generation of multiobjective optimized robust schedules, where objectives are assigned a service level, for example that we require an objective value to be greater than or equal to X with Y% confidence. We have demonstrated that such an approach can, for example, minimize scheduling on less reliable resources, based solely on a resource reliability model and not on any ad hoc heuristics. We have also investigated an alternative method of optimizing for robustness, in which we add to the set of objectives a failure risk objective to minimize. We compare the advantages and disadvantages of these two approaches. Future plans for further developing this technology include its application to space-based observatory scheduling problems.

Johnston, Mark D.↗

An advisory system for predicting and resolving airspace violations based on four-dimensional guidance techniques

New heuristics are integrated with four-dimensional guidance techniques developed by NASA in order to automate the prediction and resolution of airspace violations, and three rules are derived to reduce the amount of computation time for conflict detection. Controller experience has been used to establish techniques for resolving potential conflicts including speed control, altitude maneuvers, and horizontal flight maneuvers. Current aircraft states, flight plans, and extrapolation of aircraft trajectories are used to synthesize four-dimensional trajectories, and the state of the air traffic and the interaction between aircraft are projected into the future using the four-dimensional algorithms. The situation is immediately updated to incorporate any new information. Potential conflicts among multiple aircraft are resolved by fast sequential resolution of potential conflicts between aircraft pairs, one at a time.

Lee, Homer Q.↗