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Winograd's algorithm for computing the discrete Fourier transform is extended considerably for certain large transform lengths. This is accomplished by performing the cyclic convolution, required by Winograd's method, by a fast transform over certain complex integer fields. This algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithms.
A simulator investigation of various prediction and quickening algorithms in computer-generated forward-looking displays is presented; the algorithms are used to improve manual aircraft control on curved microwave landing system approaches. The experimental facility consisted of a Link GAT-2 simulator, a PDP 11/40 minicomputer, a high-speed graphic display, a TV camera, and a CRT monitor. Results indicate that second- and third-order predictor displays provide the best lateral performance and that intermediate levels of prediction and quickening provide the best vertical control. Prediction/quickening algorithms of increasing computational order were found to significantly reduce aileron, rudder, and elevator control responses. The conventional crosspointer displays yielded an average 2-sigma lateral error of + or - 200 over all wind conditions at 500 m from touchdown, and was therefore unable to meet FAA requirements (+ or - 22.9 m); the pictorial-preview display yielded much better results: an average 2-sigma lateral error of + or - 27 m. Neither display was able to approach the FAA specified accuracy requirement in the vertical dimension (+ or - 3.7 m).
An approximating algorithm for computing equvalent degrees of freedom of the Modified Allan Variance and its square root, the Modified Allan Deviation (MVAR and MDEV), and the Time Variance and Time Deviation (TVAR and TDEV) is presented, along with an algorithm for approximating the inverse chi-square distribution.
THe Collins-Loos algorithm for computing isolating intervals for the zeros of an integer polynomial requires the evaluation of polynomials at rational points. This implies the use of arbitrary precision integer arithmetic. It is shown how careful use of single precision, floating point arithmetic within the context of a slightly modified algorithm can make the calculation considerably faster and no less exact. Typically, 95% or more of the evaluations can be done without exact arithmetic. The precise speedup depends on the relative costs of the arithmetic in a given implementation. The implementation on DEC KL-10 computer is some 5 to 10 times faster than the original Univac 1110 implementation in SAC-I.
This report compiles the various research activities conducted under the auspices of the NASA Grant NAG3-1026, "Numerical Investigation of Hot Gas Ingestion by STOVL Aircraft" during the period of April 1989 to April 1994. The effort involved the development of multigrid based algorithms and computer programs for the calculation of the flow and temperature fields generated by Short Take-off and Vertical Landing (STOVL) aircraft, while hovering in ground proximity. Of particular importance has been the interaction of the exhaust jets with the head wind which gives rise to the hot gas ingestion process. The objective of new STOVL designs to reduce the temperature of the gases ingested into the engine. The present work describes a solution algorithm for the multi-dimensional elliptic partial-differential equations governing fluid flow and heat transfer in general curvilinear coordinates. The solution algorithm is based on the multigrid technique which obtains rapid convergence of the iterative numerical procedure for the discrete equations. Initial efforts were concerned with the solution of the Cartesian form of the equations. This algorithm was applied to a simulated STOVL configuration in rectangular coordinates. In the next phase of the work, a computer code for general curvilinear coordinates was constructed. This was applied to model STOVL geometries on curvilinear grids. The code was also validated in model problems. In all these efforts, the standard k-Epsilon model was used.
Gaussian processes and other kernel-based methods are used extensively to construct approximations of multivariate data sets. The accuracy of these approximations is dependent on the data used. This paper presents a computationally efficient algorithm to greedily select training samples that minimize the weighted L p error of kernel-based approximations for a given number of data. The method successively generates nested samples, with the goal of minimizing the error in high probability regions of densities specified by users. The algorithm presented is extremely simple and can be implemented using existing pivoted Cholesky factorization methods. Training samples are generated in batches which allows training data to be evaluated (labeled) in parallel. For smooth kernels, the algorithm performs comparably with the greedy integrated variance design but has significantly lower complexity. Numerical experiments demonstrate the efficacy of the approach for bounded, unbounded, multi-modal and non-tensor product densities. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data using Bayesian inference.
This paper tells the story of spatial operators in robot dynamics, emphasizing their physical interpretation, while avoiding lengthly matematical derivations.
This chapter describes ORNL’s (Oak Ridge National Laboratory’s) contributions to imagery preprocessing for geospatial intelligence research and development (R&D) in four sections. First, we discuss challenges involved in building an effective imagery preprocessing workflow and the world-class high-performance computing (HPC) resources at ORNL available to process petabytes of imagery data. Second, we highlight how we developed imagery preprocessing tools over three decades while paving the way for our current cutting-edge machine learning and computer vision algorithms that are impacting humanitarian and disaster response efforts. Third, we discuss how PIPE modules work together to turn raw images into analysis-ready datasets. Fourth, we look toward the future and discuss planned advancements to PIPE and computing trends that will affect geospatial intelligence R&D.
Computer vision algorithms are increasingly leveraged to accelerate geospatial analysis for disaster response and recovery. As the diversity of remote sensing imagery grows with optical, SAR, and other modalities, a perquisite for analytics is cross-modal image registration. There is a high potential to harness computer vision for this pre-processing requirement toward enabling downstream analytics such as heterogeneous change detection, automated feature extraction, and data fusion. Advancement in these areas has the potential to simplify data wrangling tasks and further accelerate disaster response timelines. The SpaceNet 9 challenge (launching in mid-2024) focuses on addressing the cross-modal image registration problem and demonstrating the utility of such modules on earthquake impacted scenarios. This paper describes the motivation for the SpaceNet 9 and provides a first overview of the dataset, the baseline algorithm, and implications for seeking cross-modal image registration in Earth observation. Code is available at https://github.com/SpaceNetChallenge/SpaceNet9.
In this work, we propose a quantum algorithm to compute low-energy expectation values of a quantum Hamiltonian by sampling a partition function associated with the average energy of that Hamiltonian. For any given quantum circuit-Hamiltonian pair, there is an associated average energy. The sampling is done through an accept/reject Metropolis-style algorithm on the quantum gates of the circuit itself. Observables calculated under the canonical ensemble from these samples of circuits are extrapolated from higher energies to the ground state.
Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their implementation remains a major challenge due to, among other things, the need to apply nontrivial stabilization schemes and generate custom quadrature rules. This article introduces the robust and computationally efficient algorithms and data structures comprising an immersed finite element preprocessing framework. The input to the preprocessor consists of a background mesh and one or more geometries defined on its domain. The output is structured into groups of elements with custom quadrature rules formatted such that common finite element assembly routines may be used without or with only minimal modifications. The key to the preprocessing framework is the construction of material topology information, concurrently with the generation of a quadrature rule, which is then used to perform enrichment and generate stabilization rules. While the algorithmic framework applies to a wide range of immersed finite element methods using different types of meshes, integration, and stabilization schemes, the preprocessor is presented within the context of the extended isogeometric analysis. This method utilizes a structured B-spline mesh, a generalized Heaviside enrichment strategy considering the material layout within individual basis functions’ supports, and face-oriented ghost stabilization. Using a set of examples, the effectiveness of the enrichment and stabilization strategies is demonstrated alongside the preprocessor’s robustness in geometric edge cases. Additionally, the performance and parallel scalability of the implementation are evaluated.
Characteristics of the resource structure found in the operating system are considered as a mechanism for classifying distributed computer systems. Since the operating system resources, themselves, are too diversified to provide a consistent classification, the structure upon which resources are built and shared are examined. The location and control character of this indivisibility provides the taxonomy for separating uniprocessors, computer networks, network computers (fully distributed processing systems or decentralized computers) and algorithm and/or data control multiprocessors. The taxonomy is important because it divides machines into a classification that is relevant or important to the client and not the hardware architect. It also defines the character of the kernel O/S structure needed for future computer systems. What constitutes an operating system for a fully distributed processor is discussed in detail.
Focal Area(s): 1) Data acquisition and assimilation enabled by machine learning, AI, and advanced methods including experimental/network design/optimization, unsupervised learning (including deep learning), and hardware-related efforts involving AI (e.g., edge computing). Science Challenge: DOE R&D, including DOE’s Basic Energy Research (BER)’s Environmental Systems Science Division (EESSD) program and DOE’s applied energy research (AER) programs (EERE, FE, and NE) are producers and consumers of Earth systems datasets. This white paper focuses on the first topic area from the call in relation to how crosscutting resources and innovations from DOE’s EESSD and AER can be brought to bear to mutual benefit and more efficient energy-water, Earth system data resources through improved. The overarching challenge posed by this call focuses on how DOE can directly leverage artificial intelligence (AI) to engineer a substantial (paradigm-changing) improvement in Earth System Predictability? While stemming from DOE BER’s EESSD program, this is a challenge that is faced and also being addressed by DOE’s AER programs. Over the past decade plus, FE, EERE, and NE programs have made important strides towards addressing this need. These strides are in many ways highly complementary to EESSD’s MODEX efforts. Energy water systems spanning metocean to groundwater to surface water systems all are data driven whether for basic energy or applied energy. These are remote, multi-variate, complex natural, and in many cases engineered, systems. Key needs and challenges of both EESSD and AER include developing data-focused tools to enhance data search and discovery to fill in knowledge gaps (address sparse data challenge), and rapidly transform datasets, including disparate and multi-source data. Leveraging DOE on-premise computing (HPC, exascale) infrastructure supports the computing-intensive algorithms required to execute these data acquisition and transformation processes to derive enriched knowledge and data, driving AI/ML and big data analytics for these systems. The opportunity lies in combining BER and AER efforts to provide a more robust, advanced, efficient and complete computing data fabric to address energy-water data acquisition and assimilation needs which currently pose significant impediments to AI/ML predictions and research.
Recent advances have demonstrated that 𝒪(log 𝑀) measurements suffice to predict 𝑀 properties of arbitrarily large quantum many-body systems. However, these remarkable findings assume that the properties to be predicted are chosen independently of the data. This assumption can be violated in practice, where scientists adaptively select properties after looking at previous predictions. This work investigates the adaptive setting for three classes of observables: local, Pauli, and bounded-Frobenius-norm observables. We prove that Ω(√𝑀) samples of an arbitrarily large unknown quantum state are necessary to predict expectation values of 𝑀 adaptively chosen local and Pauli observables, where the system size scales exponentially and polynomially in 𝑀, respectively. We also present computationally efficient algorithms that achieve this information-theoretic lower bound. In contrast, for bounded-Frobenius-norm observables, we devise an algorithm requiring only 𝒪(log 𝑀) samples, independent of system size. These results highlight the potential pitfalls of adaptivity in analyzing data from quantum experiments and provide algorithmic tools to safeguard against erroneous predictions in quantum experiments.
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the joint cumulative distribution function (CDF) of a vector-valued quantity of interest in problems with random input parameters and initial conditions. Our approach combines MLMC with stratified sampling of the input sample space by replacing standard Monte Carlo at each level with stratified Monte Carlo initialized with proportionally allocated samples. We show that the resulting stratified MLMC (sMLMC) algorithm is more efficient than its standard MLMC counterpart due to the additional variance reduction provided by the stratification of the random parameter's domain, especially at the coarsest levels. Additional computational cost savings are obtained by smoothing the indicator function with a Gaussian kernel, which proves to be an efficient and robust alternative to recently developed polynomial-based techniques.
The objective was to develop a computerized adaptive pilot model for the computer model of the research aircraft, the Harrier II AV-8B V/STOL with special emphasis on propulsion control. In fact, two versions of the adaptive pilot are given. The first, simply called the Adaptive Control Model (ACM) of a pilot includes a parameter estimation algorithm for the parameters of the aircraft and an adaption scheme based on the root locus of the poles of the pilot controlled aircraft. The second, called the Optimal Control Model of the pilot (OCM), includes an adaption algorithm and an optimal control algorithm. These computer simulations were developed as a part of the ongoing research program in pilot model simulation supported by NASA Lewis from April 1, 1985 to August 30, 1986 under NASA Grant NAG 3-606 and from September 1, 1986 through November 30, 1988 under NASA Grant NAG 3-729. Once installed, these pilot models permitted the computer simulation of the pilot model to close all of the control loops normally closed by a pilot actually manipulating the control variables. The current version of this has permitted a baseline comparison of various qualitative and quantitative performance indices for propulsion control, the control loops and the work load on the pilot. Actual data for an aircraft flown by a human pilot furnished by NASA was compared to the outputs furnished by the computerized pilot and found to be favorable.
An algorithm to compute Markov parameters of an observer or Kalman filter from experimental input and output data is discussed. The Markov parameters can then be used for identification of a state space representation, with associated Kalman gain or observer gain, for the purpose of controller design. The algorithm is a non-recursive matrix version of two recursive algorithms developed in previous works for different purposes. The relationship between these other algorithms is developed. The new matrix formulation here gives insight into the existence and uniqueness of solutions of certain equations and gives bounds on the proper choice of observer order. It is shown that if one uses data containing noise, and seeks the fastest possible deterministic observer, the deadbeat observer, one instead obtains the Kalman filter, which is the fastest possible observer in the stochastic environment. Results are demonstrated in numerical studies and in experiments on an ten-bay truss structure.
An algorithm to compute Markov parameters of an observer or Kalman filter from experimental input and output data is discussed. The Markov parameters can then be used for identification of a state space representation, with associated Kalman gain or observer gain, for the purpose of controller design. The algorithm is a non-recursive matrix version of two recursive algorithms developed in previous works for different purposes. The relationship between these other algorithms is developed. The new matrix formulation here gives insight into the existence and uniqueness of solutions of certain equations and gives bounds on the proper choice of observer order. It is shown that if one uses data containing noise, and seeks the fastest possible deterministic observer, the deadbeat observer, one instead obtains the Kalman filter, which is the fastest possible observer in the stochastic environment. Results are demonstrated in numerical studies and in experiments on a ten-bay truss structure.