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At least 1,135 records · Page 63

Trajectory optimization based on differential inclusion

A method for generating finite-dimensional approximations to the solutions of optimal control problems is introduced. By employing a description of the dynamical system in terms of its attainable sets in favor of using differential equations, the controls are completely eliminated from the system model. Besides reducing the dimensionality of the discretized problem compared to state-of-the-art collocation methods, this approach also alleviates the search for initial guesses from where standard gradient search methods are able to converge. The mechanics of the new method are illustrated on a simple double integrator problem. The performance of the new algorithm is demonstrated on a 1-D rocket ascent problem ('Goddard Problem') in presence of a dynamic pressure constraint.

Seywald, Hans↗

Trajectory optimization based on differential inclusion

A method for generating finite-dimensional approximations to the solutions of optimal control problems is introduced. By employing a description of the dynamical system in terms of its attainable sets in favor of using differential equations, the controls are completely eliminated from the system model. Besides reducing the dimensionality of the discretized problem compared to state-of-the-art collocation methods, this approach also alleviates the search for initial guesses from where standard gradient search methods are able to converge. The mechanics of the new method are illustrated on a simple double integrator problem. The performance of the new algorithm is demonstrated on a I-D rocket ascent problem ('Goddard Problem') in presence of a dynamic pressure constraint.

Seywald, Hans↗

Trajectory optimization based on differential inclusion

A method for generating finite-dimensional approximations to the solutions of optimal control problems is introduced. By employing a description of the dynamical system in terms of its attainable sets in favor of using differential equations, the controls are completely eliminated from the system model. Besides reducing the dimensionality of the discretized problem compared to state-of-the-art collocation methods, this approach also alleviates the search for initial guesses from where standard gradient search methods are able to converge. The mechanics of the new method are illustrated on a simple double integrator problem. The performance of the new algorithm is demonstrated on a 1-D rocket ascent problem (`Goddard Problem') in presence of a dynamic pressure constraint.

Seywald, Hans↗

Enabling computer decisions based on EEG input

Multilayer neural networks were successfully trained to classify segments of 12-channel electroencephalogram (EEG) data into one of five classes corresponding to five cognitive tasks performed by a subject. Independent component analysis (ICA) was used to segregate obvious artifact EEG components from other sources, and a frequency-band representation was used to represent the sources computed by ICA. Examples of results include an 85% accuracy rate on differentiation between two tasks, using a segment of EEG only 0.05 s long and a 95% accuracy rate using a 0.5-s-long segment.

Validation Studies↗

The System for Classification of Low-Pressure Systems (SyCLoPS): An All-In-One Objective Framework for Large-Scale Data Sets

We propose the first unified objective framework (SyCLoPS) for detecting and classifying all types of low-pressure systems (LPSs) in a given data set. We use the state-of-the-art automated feature tracking software TempestExtremes (TE) to detect and track LPS features globally in ERA5 and compute 16 parameters from commonly found atmospheric variables for classification. A Python classifier is implemented to classify all LPSs at once. The framework assigns 16 different labels (classes) to each LPS data point and designates four different types of high-impact LPS tracks, including tracks of tropical cyclone (TC), monsoonal system, subtropical storm and polar low. The classification process involves disentangling high-altitude and drier LPSs, differentiating tropical and non-tropical LPSs using novel criteria, and optimizing for the detection of the four types of high-impact LPS. A comparison of our labels with those in the International Best Track Archive for Climate Stewardship (IBTrACS) revealed an overall accuracy of 95% in distinguishing between tropical systems, extratropical cyclones, and disturbances. SyCLoPS produces a better TC detection skill compared to the previous algorithms, highlighted by an approximately 6% reduction in the false alarm rate compared to the previous TE algorithm. The vertical cross section composite of the four types of high-impact LPS we detect each shows distinct structural characteristics. Finally, we demonstrate that SyCLoPS is valuable for investigating various aspects of LPSs in climate data, such as the evolution of a single LPS track, patterns of LPS frequencies, and precipitation or wind influence associated with a particular LPS class.

54 ENVIRONMENTAL SCIENCES↗

Machine learning for the identification of phase transitions in interacting agent-based systems: A Desai-Zwanzig example

Deriving closed-form analytical expressions for reduced-order models, and judiciously choosing the closures leading to them, has long been the strategy of choice for studying phase- and noise-induced transitions for agent-based models (ABMs). In this paper, we propose a data-driven framework that pinpoints phase transitions for an ABM—the Desai-Zwanzig model—in its mean-field limit, using a smaller number of variables than traditional closed-form models. To this end, we use the manifold learning algorithm Diffusion Maps to identify a parsimonious set of data-driven latent variables, and we show that they are in one-to-one correspondence with the expected theoretical order parameter of the ABM. We then utilize a deep learning framework to obtain a conformal reparametrization of the data-driven coordinates that facilitates, in our example, the identification of a single parameter-dependent ordinary differential equation (ODE) in these coordinates. Additionally, we identify this ODE through a residual neural network inspired by a numerical integration scheme (forward Euler). We then use the identified ODE—enabled through an odd symmetry transformation—to construct the bifurcation diagram exhibiting the phase transition.

97 MATHEMATICS AND COMPUTING↗

A study of the application of differential techniques to the global positioning system for a helicopter precision approach

The results of a simulation study to define the functional characteristics of a airborne and ground reference GPS receiver for use in a Differential GPS system are doumented. The operations of a variety of receiver types (sequential-single channel, continuous multi-channel, etc.) are evaluated for a typical civil helicopter mission scenario. The math model of each receiver type incorporated representative system errors including intentional degradation. The results include the discussion of the receiver relative performance, the spatial correlative properties of individual range error sources, and the navigation algorithm used to smooth the position data.

Mccall, D. L.↗

Partitioning and packing mathematical simulation models for calculation on parallel computers

The development of multiprocessor simulations from a serial set of ordinary differential equations describing a physical system is described. Degrees of parallelism (i.e., coupling between the equations) and their impact on parallel processing are discussed. The problem of identifying computational parallelism within sets of closely coupled equations that require the exchange of current values of variables is described. A technique is presented for identifying this parallelism and for partitioning the equations for parallel solution on a multiprocessor. An algorithm which packs the equations into a minimum number of processors is also described. The results of the packing algorithm when applied to a turbojet engine model are presented in terms of processor utilization.

Arpasi, D. J.↗

A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO

In this work, we provide a new approach for the efficient matrix-free application of the transpose of the Jacobian for the spectral element method for the adjoint-based solution of partial differential equation (PDE) constrained optimization. This results in optimizations of nonlinear PDEs using explicit integrators where the integration of the adjoint problem is not more expensive than the forward simulation. Solving PDE constrained optimization problems entails combining expertise from multiple areas, including simulation, computation of derivatives, and optimization. The Portable, Extensible Toolkit for Scientific computation (PETSc) together with its companion package, the Toolkit for Advanced Optimization (TAO), is an integrated numerical software library that contains an algorithmic/software stack for solving linear systems, nonlinear systems, ordinary differential equations, differential algebraic equations, and large-scale optimization problems and, as such, is an ideal tool for performing PDE-constrained optimization. This paper describes an efficient approach in which the software stack provided by PETSc/TAO can be used for large-scale nonlinear time-dependent problems. Time integration can involve a range of high-order methods, both implicit and explicit. The PDE-constrained optimization algorithm used is gradient-based and seamlessly integrated with the simulation of the physical problem.

97 MATHEMATICS AND COMPUTING↗

Xyce(™) Parallel Electronic Simulator v.7.5

The Xyce Parallel Electronic Simulator simulates electronic circuit behavior in DC, AC, HB, MPDE and transient mode using standard analog (DAE) and/or device (PDE) device models including several age and radiation aware devices. It supports a variety of computing platforms (both serial and parallel) computers. Lastly, it uses a variety of modern solution algorithms dynamic parallel load-balancing and iterative solvers.! ! Xyce is primarily used to simulate the voltage and current behavior of a circuit network (a network of electronic devices connected via a conductive network). As a tool, it is mainly used for the design and analysis of electronic circuits.! ! Kirchoff's conservation laws are enforced over a network using modified nodal analysis. This results in a set of differential algebraic equations (DAEs). The resulting nonlinear problem is solved iteratively using a fully coupled Newton method, which in turn results in a linear system that is solved by either a standard sparse-direct solver or iteratively using Trilinos linear solver packages, also developed at Sandia National Laboratories.

Source record↗

Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schrödinger Equation

We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm that is both insensitive to the rapid changes of the time-dependent Hamiltonian and exhibits commutator scaling. Our method can be used for efficient Hamiltonian simulation in the interaction picture. In particular, we demonstrate that for the simulation of the Schrödinger equation, our method exhibits superconvergence and achieves a surprising second order convergence rate, of which the proof rests on a careful application of pseudo-differential calculus. Numerical results verify the effectiveness and the superconvergence property of our method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Computing Plasma Interactions Of A Spacecraft

NASCAP/LEO (NASA Spacecraft Charging Analyzer Program for Low Earth Orbit) implements collection of mathematical models and algorithms designed to study electrostatic interaction between cold, dense plasma and spacecraft surfaces. Computes variety of electrostatic, plasma, and flow effects. Appropriate for conditions in which temperature of plasma small in comparison with spacecraft-generated potentials and Debye screening length short in comparison with dimensions of spacecraft. Related NASCAP/GEO (LEW-12973) code (NASA Charging Analyzer Program for Geosynchronous Orbit, denoted as NASCAP) appropriate for conditions which spacecraft differential potentials result from interactions with hot plasma and Debye screening length larger than dimensions of spacecraft. Object-definition portion of NASCAP/GEO code provided as part of package. NASCAP/LEO written in FORTRAN 77 and C language.

Mandell, M. J.↗

Constructing LDPC Codes from Loop-Free Encoding Modules

A method of constructing certain low-density parity-check (LDPC) codes by use of relatively simple loop-free coding modules has been developed. The subclasses of LDPC codes to which the method applies includes accumulate-repeat-accumulate (ARA) codes, accumulate-repeat-check-accumulate codes, and the codes described in Accumulate-Repeat-Accumulate-Accumulate Codes (NPO-41305), NASA Tech Briefs, Vol. 31, No. 9 (September 2007), page 90. All of the affected codes can be characterized as serial/parallel (hybrid) concatenations of such relatively simple modules as accumulators, repetition codes, differentiators, and punctured single-parity check codes. These are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. These codes can also be characterized as hybrid turbolike codes that have projected graph or protograph representations (for example see figure); these characteristics make it possible to design high-speed iterative decoders that utilize belief-propagation algorithms. The present method comprises two related submethods for constructing LDPC codes from simple loop-free modules with circulant permutations. The first submethod is an iterative encoding method based on the erasure-decoding algorithm. The computations required by this method are well organized because they involve a parity-check matrix having a block-circulant structure. The second submethod involves the use of block-circulant generator matrices. The encoders of this method are very similar to those of recursive convolutional codes. Some encoders according to this second submethod have been implemented in a small field-programmable gate array that operates at a speed of 100 megasymbols per second. By use of density evolution (a computational- simulation technique for analyzing performances of LDPC codes), it has been shown through some examples that as the block size goes to infinity, low iterative decoding thresholds close to channel capacity limits can be achieved for the codes of the type in question having low maximum variable node degrees. The decoding thresholds in these examples are lower than those of the best-known unstructured irregular LDPC codes constrained to have the same maximum node degrees. Furthermore, the present method enables the construction of codes of any desired rate with thresholds that stay uniformly close to their respective channel capacity thresholds.

Divsalar, Dariush↗

The equation of state for stellar envelopes. II - Algorithm and selected results

A free-energy-minimization method for computing the dissociation and ionization equilibrium of a multicomponent gas is discussed. The adopted free energy includes terms representing the translational free energy of atoms, ions, and molecules; the internal free energy of particles with excited states; the free energy of a partially degenerate electron gas; and the configurational free energy from shielded Coulomb interactions among charged particles. Internal partition functions are truncated using an occupation probability formalism that accounts for perturbations of bound states by both neutral and charged perturbers. The entire theory is analytical and differentiable to all orders, so it is possible to write explicit analytical formulas for all derivatives required in a Newton-Raphson iteration; these are presented to facilitate future work. Some representative results for both Saha and free-energy-minimization equilibria are presented for a hydrogen-helium plasma with N(He)/N(H) = 0.10. These illustrate nicely the phenomena of pressure dissociation and ionization, and also demonstrate vividly the importance of choosing a reliable cutoff procedure for internal partition functions.

Mihalas, Dimitri↗

miss-SNF: a multimodal patient similarity network integration approach to handle completely missing data sources

Abstract Motivation Precision medicine leverages patient-specific multimodal data to improve prevention, diagnosis, prognosis, and treatment of diseases. Advancing precision medicine requires the non-trivial integration of complex, heterogeneous, and potentially high-dimensional data sources, such as multi-omics and clinical data. In the literature, several approaches have been proposed to manage missing data, but are usually limited to the recovery of subsets of features for a subset of patients. A largely overlooked problem is the integration of multiple sources of data when one or more of them are completely missing for a subset of patients, a relatively common condition in clinical practice. Results We propose miss-Similarity Network Fusion (miss-SNF), a novel general-purpose data integration approach designed to manage completely missing data in the context of patient similarity networks. miss-SNF integrates incomplete unimodal patient similarity networks by leveraging a non-linear message-passing strategy borrowed from the SNF algorithm. miss-SNF is able to recover missing patient similarities and is “task agnostic”, in the sense that can integrate partial data for both unsupervised and supervised prediction tasks. Experimental analyses on nine cancer datasets from The Cancer Genome Atlas (TCGA) demonstrate that miss-SNF achieves state-of-the-art results in recovering similarities and in identifying patients subgroups enriched in clinically relevant variables and having differential survival. Moreover, amputation experiments show that miss-SNF supervised prediction of cancer clinical outcomes and Alzheimer’s disease diagnosis with completely missing data achieves results comparable to those obtained when all the data are available. Availability and implementation miss-SNF code, implemented in R, is available at https://github.com/AnacletoLAB/missSNF.

Biochemistry & Molecular Biology↗

Evaluation of SLAR and simulated thematic mapper MSS data for forest cover mapping using computer-aided analysis techniques

Kershaw County, South Carolina was selected as the study site for analyzing simulated thematic mapper MSS data and dual-polarized X-band synthetic aperture radar (SAR) data. The impact of the improved spatial and spectral characteristics of the LANDSAT D thematic mapper data on computer aided analysis for forest cover type mapping was examined as well as the value of synthetic aperture radar data for differentiating forest and other cover types. The utility of pattern recognition techniques for analyzing SAR data was assessed. Topics covered include: (1) collection and of TMS and reference data; (2) reformatting, geometric and radiometric rectification, and spatial resolution degradation of TMS data; (3) development of training statistics and test data sets; (4) evaluation of different numbers and combinations of wavelength bands on classification performance; (5) comparison among three classification algorithms; and (6) the effectiveness of the principal component transformation in data analysis. The collection, digitization, reformatting, and geometric adjustment of SAR data are also discussed. Image interpretation results and classification results are presented.

Hoffer, R. M.↗

Band-Moment Compression of AVIRIS Hyperspectral Data and its Use in the Detection of Vegetation Stress

A remote sensing campaign was conducted over a U.S. Department of Agriculture test farm at Shelton, Nebraska. An experimental field was set off in plots that were differentially treated with anhydrous ammonia. Four replicates of 0-kg/ha to 200-kg/ha plots, in 50-kg/ha increments, were set out in a random block design. Low-altitude (GSD of 3 m) Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) hyperspectral data were collected over the site in 224 bands. Simultaneously, ground data were collected to support the airborne imagery. In an effort to reduce data load while maintaining or enhancing algorithm performance for vegetation stress detection, band-moment compression and analysis was applied to the AVIRIS image cube. The results indicated that band-moment techniques compress the AVIRIS dataset significantly while retaining the capability of detecting environmentally induced vegetation stress.

Estep, L.↗

Scalable Algorithms for Inverse Problems With High-Dimensional Parameter Spaces

Inverse problems, which involve inferring unknown parameters from observed data, present significant computational challenges, especially in large-scale settings with high-dimensional unknown parameters and nonlinear relationships between the unknowns and observations. Bayesian inference provides an approach for addressing these problems, often relying on sequential sampling methods like Markov chain Monte Carlo (MCMC) to approximate the posterior distribution of the parameters. However, MCMC methods become computationally demanding as the dimensionality of the problem increases, particularly in large-scale systems where likelihood evaluations rely on solving partial differential equations (PDEs) on large spatial domains with finely resolved meshes. To overcome these limitations, recent advancements have focused on designing scalable computa tional techniques – for both PDE simulations and sampling strategies – to make Bayesian methods feasible for high-dimensional problems.

97 MATHEMATICS AND COMPUTING↗