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At least 91 records · Page 5

Using MODIS and GLAS Data to Develop Timber Volume Estimates in Central Siberia

The boreal forest is the Earth's largest terrestrial biome, covering some 12 million km2 and accounting for about one third of this planet's total forest area. Mapping of boreal forest's type, structure parameters and biomass are critical for understanding the boreal forest's significance in the carbon cycle, its response to and impact on global climate change. Ground based forest inventories, have much uncertainty in the inventory data, particularly in remote areas of Siberia where sampling is sparse and/or lacking. In addition, many of the forest inventories that do exist for Siberia are now a decade or more old. Thus, available forest inventories fail to capture the current conditions. Changes in forest structure in a particular forest-type and region can change significantly due to changing environment conditions, and natural and anthropogenic disturbance. Remote sensing methods can potentially overcome these problems. Multispectral sensors can be used to provide vegetation cover maps that show a timely and accurate geographic distribution of vegetation types rather than decade old ground based maps. Lidar sensors can be used to directly obtain measurements that can be used to derive critical forest structure information (e.g., height, density, and volume). These in turn can used to estimate biomass components using allometric equations without having to use out dated forest inventory. Finally, remote sensing data is ideally suited to provide a sampling basis for a rigorous statistical estimate of the variance and error bound on forest structure measures. In this study, new remote sensing methods were applied to develop estimates timber volume using NASA's MODerate resolution Imaging Spectroradiometer (MODIS) and unique waveform data of the geoscience laser altimeter system (GLAS) for a 10 deg x 10 deg area in central Siberia. Using MODIS and GLAS data, maps were produced for cover type and timber volume for 2003, and a realistic variance (error bound) for timber volume was calculated for the study area. In this 'study we used only GLAS footprints that had a slope value of less than 10 deg. This was done to avoid large errors due to the effect of slope on the GLAS models. The method requires the integration of new remote sensing methods with available ground studies of forest timber volume conducted in Russian forests. The results were compared to traditional ground forest inventory methods reported in the literature and to ground truth collected in the study area.

Ranson, K. Jon

A General Framework for Error-controlled Unstructured Scientific Data Compression

Data compression plays a key role in reducing storage and I/O costs. Traditional lossy methods primarily target data on rectilinear grids and cannot leverage the spatial coherence in unstructured mesh data, leading to suboptimal compression ratios. We present a multi-component, error-bounded compression framework designed to enhance the compression of floating-point unstructured mesh data, which is common in scientific applications. Our approach involves interpolating mesh data onto a rectilinear grid and then separately compressing the grid interpolation and the interpolation residuals. This method is general, independent of mesh types and typologies, and can be seamlessly integrated with existing lossy compressors for improved performance. We evaluated our framework across twelve variables from two synthetic datasets and two real-world simulation datasets. The results indicate that the multi-component framework consistently outperforms state-of-the-art lossy compressors on unstructured data, achieving, on average, a 2.3 − 3.5× improvement in compression ratios, with error bounds ranging from 1 × 10 the −6 to 1×10−2. We further investigate impact of hyperparameters, such as grid spacing and error allocation, to deliver optimal compression ratios in diverse datasets.

Gong, Qian

Sliding control of pointing and tracking with operator spline estimation

It is shown how a variable structure control technique could be implemented to achieve precise pointing and good tracking of a deformable structure subject to fast slewing maneuvers. The correction torque that has to be applied to the structure is based on estimates of upper bounds on the model errors. For a rapid rotation of the deformable structure, the elastic response can be modeled by oscillators driven by angular acceleration, and where stiffness and damping coefficients are also angular velocity and acceleration dependent. By transforming this slew-driven elastic dynamics into bilinear form (be regarding the vector made up of the angular velocity, squared angular velocity and angular acceleration components, which appear in the coefficients as the input to the deformation dynamics), an operator spline can be constructed, that gives a low order estimate of the induced disturbance. Moreover, a worst case error bound between the estimated deformation and the unknown exact deformation is also generated, which can be used where required in the sliding control correction.

Dwyer, Thomas A. W., III

A Systematic Solution Approach for Neutron Transport Problems in Diffuse Regimes

A systematic solution approach for the neutron transport equation, based on a least-squares finite-element discretization, is presented. This approach includes the theory for the existence and uniqueness of the analytical as well as of the discrete solution, bounds for the discretization error, and guidance for the development of an efficient multigrid solver for the resulting discrete problem. To guarantee the accuracy of the discrete solution for diffusive regimes, a scaling transformation is applied to the transport operator prior to the discretization. The key result is the proof of the V-ellipticity and continuity of the scaled least-squares bilinear form with constants that are independent of the total cross section and the absorption cross section. For a variety of least-squares finite-element discretizations this leads to error bounds that remain valid in diffusive regimes. Moreover, for problems in slab geometry a full multigrid solver is presented with V(1, 1)-cycle convergence rates approximately equal to 0.1, independent of the size of the total cross section and the absorption cross section.

Manteuffel, T. A.

Practical Aspects of the Equation-Error Method for Aircraft Parameter Estimation

Various practical aspects of the equation-error approach to aircraft parameter estimation were examined. The analysis was based on simulated flight data from an F-16 nonlinear simulation, with realistic noise sequences added to the computed aircraft responses. This approach exposes issues related to the parameter estimation techniques and results, because the true parameter values are known for simulation data. The issues studied include differentiating noisy time series, maximum likelihood parameter estimation, biases in equation-error parameter estimates, accurate computation of estimated parameter error bounds, comparisons of equation-error parameter estimates with output-error parameter estimates, analyzing data from multiple maneuvers, data collinearity, and frequency-domain methods.

Morelli, Eugene a.

Deep nonparametric estimation of operators between infinite dimensional spaces

Learning operators between infinitely dimensional spaces is an important learning task arising in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric estimation of Lipschitz operators using deep neural networks. Non-asymptotic upper bounds are derived for the generalization error of the empirical risk minimizer over a properly chosen network class. Under the assumption that the target operator exhibits a low dimensional structure, our error bounds decay as the training sample size increases, with an attractive fast rate depending on the intrinsic dimension in our estimation. Our assumptions cover most scenarios in real applications and our results give rise to fast rates by exploiting low dimensional structures of data in operator estimation. We also investigate the influence of network structures (e.g., network width, depth, and sparsity) on the generalization error of the neural network estimator and propose a general suggestion on the choice of network structures to maximize the learning efficiency quantitatively.

97 MATHEMATICS AND COMPUTING

Control system optimization studies. Volume 2: High frequency cutoff filter analysis

The problem of digital implementation of a cutoff filter is approached with consideration to word length, sampling rate, accuracy requirements, computing time and hardware restrictions. Computing time and hardware requirements for four possible programming forms for the linear portions of the filter are determined. Upper bounds for the steady state system output error due to quantization for digital control systems containing a digital network programmed both in the direct form and in the canonical form are derived. This is accomplished by defining a set of error equations in the z domain and then applying the final value theorem to the solution. Quantization error was found to depend upon the digital word length, sampling rate, and system time constants. The error bound developed may be used to estimate the digital word length and sampling rate required to achieve a given system specification. From the quantization error accumulation, computing time and hardware point of view, and the fact that complex poles and zeros must be realized, the canonical form of programming seems preferable.

Fong, M. H.

Investigation of empirical damping laws for the space shuttle

An analysis of dynamic test data from vibration testing of a number of aerospace vehicles was made to develop an empirical structural damping law. A systematic attempt was made to fit dissipated energy/cycle to combinations of all dynamic variables. The best-fit laws for bending, torsion, and longitudinal motion are given, with error bounds. A discussion and estimate are made of error sources. Programs are developed for predicting equivalent linear structural damping coefficients and finding the response of nonlinearly damped structures.

Bernstein, E. L.

Robust Vision-based Multi-spacecraft Guidance Navigation and Control using CNN-based Pose Estimation

In this paper, we present an end-to-end simulation framework for tracking an uncooperative Target spacecraft in Low Earth Orbit using a CubeSat-class Ego spacecraft outfitted with a camera. Currently, capturing high-fidelity realistic images in space for this scenario is difficult and exorbitantly expensive. Therefore, we developed a framework to simulate the spacecraft orbits in Basilisk software and generate high-fidelity realistic images of spacecraft in Unreal Engine, including the effects from Sun, Earth, Moon and stars. The Ego spacecraft uses cameras to capture images of the uncooperative Target and estimates its position and attitude using a CNN based 6DOF pose estimation pipeline, eliminating need for large SWAP-C(Size, Weight, Power and Cost) sensors like LIDAR or reliance on inter-spacecraft communication, This CNN, which is motivated by ESA’s Pose Estimation challenge of 2019, is trained using simulated data from our end-to-end simulation framework. We compare the performance of two distinct CNNbased algorithms for pose estimation along a nominal trajectory. In presence of non-Gaussian modeling uncertainties, the statedependent estimation error is characterized with a quadratic upper-bound. The quadratically-bounded error can be used by a robust controller to maneuver

Rahmani, Amir

Machine Learning Techniques for Data Reduction of Climate Applications

Scientists conduct large-scale simulations to compute derived quantities-of-interest (QoI) from primary data. Often, QoI are linked to specific features, regions, or time intervals, such that data can be adaptively reduced without compromising the integrity of QoI. For many spatiotemporal applications, these QoI are binary in nature and represent presence or absence of a physical phenomenon. We present a pipelined compression approach that first uses neural-network-based techniques to derive regions where QoI are highly likely to be present. Then, we employ a Guaranteed Autoencoder (GAE) to compress data with differential error bounds. GAE uses QoI information to apply low-error compression to only these regions. This results in overall high compression ratios while still achieving downstream goals of simulation or data collections. Experimental results are presented for climate data generated from the E3SM Simulation model for downstream quantities such as tropical cyclone and atmospheric river detection and tracking. These results show that our approach is superior to comparable methods in the literature.

Li, Xiao [University of Florida]

Scalable Hybrid Learning Techniques for Scientific Data Compression

Data compression is becoming critical for storing scientific data because many scientific applications need to store large amounts of data and post process this data for scientific discovery. Unlike image and video compression algorithms that limit errors to primary data (PD), scientists require compression techniques that accurately preserve derived quantities of interest (QoIs). Here, this article presents a physics-informed compression technique implemented as an end-to-end, scalable, GPU-based pipeline for data compression that addresses this requirement. Our hybrid compression technique combines machine learning techniques and standard compression methods. Specifically, we combine an autoencoder, an error-bounded lossy compressor to provide guarantees on raw data error, and a constraint satisfaction post-processing step to preserve the QoIs within a minimal error (generally less than floating point error). The effectiveness of the data compression pipeline is demonstrated by compressing nuclear fusion simulation data generated by a large-scale fusion code, XGC, which produces hundreds of terabytes of data in a single day. Our approach works within the ADIOS framework and results in compression by a factor of more than 150 while requiring only a few percent of the computational resources necessary for generating the data, making the overall approach highly effective for practical scenarios.

ITER

Altimeter error sources at the 10-cm performance level

Error sources affecting the calibration and operational use of a 10 cm altimeter are examined to determine the magnitudes of current errors and the investigations necessary to reduce them to acceptable bounds. Errors considered include those affecting operational data pre-processing, and those affecting altitude bias determination, with error budgets developed for both. The most significant error sources affecting pre-processing are bias calibration, propagation corrections for the ionosphere, and measurement noise. No ionospheric models are currently validated at the required 10-25% accuracy level. The optimum smoothing to reduce the effects of measurement noise is investigated and found to be on the order of one second, based on the TASC model of geoid undulations. The 10 cm calibrations are found to be feasible only through the use of altimeter passes that are very high elevation for a tracking station which tracks very close to the time of altimeter track, such as a high elevation pass across the island of Bermuda. By far the largest error source, based on the current state-of-the-art, is the location of the island tracking station relative to mean sea level in the surrounding ocean areas.

Martin, C. F.

Determination of Barometric Altimeter Errors for the Orion Exploration Flight Test-1 Entry

The Exploration Flight Test 1 (EFT-1) mission is the unmanned flight test for the upcoming Multi-Purpose Crew Vehicle (MPCV). During entry, the EFT-1 vehicle will trigger several Landing and Recovery System (LRS) events, such as parachute deployment, based on on-board altitude information. The primary altitude source is the filtered navigation solution updated with GPS measurement data. The vehicle also has three barometric altimeters that will be used to measure atmospheric pressure during entry. In the event that GPS data is not available during entry, the altitude derived from the barometric altimeter pressure will be used to trigger chute deployment for the drogues and main parachutes. Therefore it is important to understand the impact of error sources on the pressure measured by the barometric altimeters and on the altitude derived from that pressure. The error sources for the barometric altimeters are not independent, and many error sources result in bias in a specific direction. Therefore conventional error budget methods could not be applied. Instead, high fidelity Monte-Carlo simulation was performed and error bounds were determined based on the results of this analysis. Aerodynamic errors were the largest single contributor to the error budget for the barometric altimeters. The large errors drove a change to the altitude trigger setpoint for FBC jettison deploy.

Brown, Denise L.

Quantum simulation of Lindbladian dynamics via repeated interactions

The Lindblad equation generalizes the Schrödinger equation to quantum systems that undergo dissipative dynamics. The quantum simulation of Lindbladian dynamics is therefore non-unitary, preventing a naive application of state-of-the-art quantum algorithms. Here, we make use of an approximate correspondence between Lindbladian dynamics and evolution based on repeated interaction (RI) CPTP maps to write down a Hamiltonian formulation of the Lindblad dynamics and derive a rigorous error bound on the master equation. Specifically, we show that the number of interactions needed to simulate the Liouvillian within error e scales in most physical scenarios as . This is significant because the error in the Lindbladian approximation to the dynamics is not explicitly bounded in existing quantum algorithms for open system simulations. We then provide quantum algorithms to simulate RI maps using an iterative qubitization approach and Trotter–Suzuki formulas, and specifically show that for iterative qubitization the number of operations needed to simulate the dynamics (for a fixed value of ?) scales as in the limit where a0 (the coefficient 1-norm for the system and bath Hamiltonians) asymptotically dominates over the corresponding factor for the interaction Hamiltonian, which is often the case in weak coupling. This scaling would appear to be optimal if the complexity of ? is not considered, which underscores the importance of considering the error in the Liouvillian that we reveal in this work.

Quantum Computing

Real eigenvalue analysis in NASTRAN by the tridiagonal reduction (FEER) method

Implementation of the tridiagonal reduction method for real eigenvalue extraction in structural vibration and buckling problems is described. The basic concepts underlying the method are summarized and special features, such as the computation of error bounds and default modes of operation are discussed. In addition, the new user information and error messages and optional diagnostic output relating to the tridiagonal reduction method are presented. Some numerical results and initial experiences relating to usage in the NASTRAN environment are provided, including comparisons with other existing NASTRAN eigenvalue methods.

Newman, M.

Response Surface Modeling Using Multivariate Orthogonal Functions

A nonlinear modeling technique was used to characterize response surfaces for non-dimensional longitudinal aerodynamic force and moment coefficients, based on wind tunnel data from a commercial jet transport model. Data were collected using two experimental procedures - one based on modem design of experiments (MDOE), and one using a classical one factor at a time (OFAT) approach. The nonlinear modeling technique used multivariate orthogonal functions generated from the independent variable data as modeling functions in a least squares context to characterize the response surfaces. Model terms were selected automatically using a prediction error metric. Prediction error bounds computed from the modeling data alone were found to be- a good measure of actual prediction error for prediction points within the inference space. Root-mean-square model fit error and prediction error were less than 4 percent of the mean response value in all cases. Efficacy and prediction performance of the response surface models identified from both MDOE and OFAT experiments were investigated.

Morelli, Eugene A.

Complex Correlation Kohn-T Method of Calculating Total and Elastic Cross Sections: Electron-Hydrogen Elastic Scattering - Part 1

We report on the first part of a study of electron-hydrogen scattering, using a method which allows for the ab initio calculation of total and elastic cross sections at higher energies. In its general form the method uses complex 'radial' correlation functions, in a (Kohn) T-matrix formalism. The titled method, abbreviated Complex Correlation Kohn T (CCKT) method, is reviewed, in the context of electron-hydrogen scattering, including the derivation of the equation for the (complex) scattering function, and the extraction of the scattering information from the latter. The calculation reported here is restricted to S-waves in the elastic region, where the correlation functions can be taken, without loss of generality, to be real. Phase shifts are calculated using Hylleraas-type correlation functions with up to 95 terms. Results are rigorous lower bounds; they are in general agreement with those of Schwartz, but they are more accurate and outside his error bounds at a couple of energies,

Bhatia, A. K.

Towards Automated Reasoning Chains for Verification of LLM-Generated Scientific Code

With the rise of Large Language Model (LLM) generated code, including in domains like scientific computing, ensuring not only syntactical, but also mathematical correctness, has become a critical task. Traditional formal methods approaches often struggle with the ambiguity of floating-point code, and full symbolic execution is extremely costly and limited. We propose a chain-of-reasoning approach that iteratively lifts basic semantics from code into the SPIRAL system and then establishes numerical equivalency to the desired mathematical operation. Here, we leverage the ample mathematical knowledge already formalized in SPIRAL to enable the system to recognize not just different implementations of the same algorithm but fully separate approaches to solving the given problem. The chain establishes tight error bounds on the output of given code with respect to the true continuous solution it approximates, quantifying all sources of error. We demonstrate this approach by establishing the correctness of a pseudospectral solver for a simple 1-dimensional Poisson problem.

Oschatz, Quentin [Carnegie Mellon University,Pitts