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At least 1,153 records · Page 64

Model-based VQ for image data archival, retrieval and distribution

An ideal image compression technique for image data archival, retrieval and distribution would be one with the asymmetrical computational requirements of Vector Quantization (VQ), but without the complications arising from VQ codebooks. Codebook generation and maintenance are stumbling blocks which have limited the use of VQ as a practical image compression algorithm. Model-based VQ (MVQ), a variant of VQ described here, has the computational properties of VQ but does not require explicit codebooks. The codebooks are internally generated using mean removed error and Human Visual System (HVS) models. The error model assumed is the Laplacian distribution with mean, lambda-computed from a sample of the input image. A Laplacian distribution with mean, lambda, is generated with uniform random number generator. These random numbers are grouped into vectors. These vectors are further conditioned to make them perceptually meaningful by filtering the DCT coefficients from each vector. The DCT coefficients are filtered by multiplying by a weight matrix that is found to be optimal for human perception. The inverse DCT is performed to produce the conditioned vectors for the codebook. The only image dependent parameter used in the generation of codebook is the mean, lambda, that is included in the coded file to repeat the codebook generation process for decoding.

Manohar, Mareboyana↗

Searching for patterns in remote sensing image databases using neural networks

We have investigated a method, based on a successful neural network multispectral image classification system, of searching for single patterns in remote sensing databases. While defining the pattern to search for and the feature to be used for that search (spectral, spatial, temporal, etc.) is challenging, a more difficult task is selecting competing patterns to train against the desired pattern. Schemes for competing pattern selection, including random selection and human interpreted selection, are discussed in the context of an example detection of dense urban areas in Landsat Thematic Mapper imagery. When applying the search to multiple images, a simple normalization method can alleviate the problem of inconsistent image calibration. Another potential problem, that of highly compressed data, was found to have a minimal effect on the ability to detect the desired pattern. The neural network algorithm has been implemented using the PVM (Parallel Virtual Machine) library and nearly-optimal speedups have been obtained that help alleviate the long process of searching through imagery.

Paola, Justin D.↗

3+2+X: What Is the Most Useful Depolarization Input for Inverting Lidar Measurements of Non-Spherical Particles to Microphysical Properties?

The typical multiwavelength aerosol lidar data set for inversion of optical to microphysical parameters is composed of three backscatter coefficients (β ) at 355, 532, and 1064 nm and two extinction coefficients (α ) at 355 and 532 nm. This data combination is referred to as 3β +2α or 3+2 data set. This set of data is sufficient for retrieving some important microphysical particle parameters if the particles have spherical shape. Here, we investigate the effect of including the particle linear depolarization ratio (δ) as a third input parameter to the inversion of lidar data. The inversion algorithm is generally not used if measurements show values of δ that exceed 0.10 at 532 nm, i.e. in the presence of non-spherical particles such as desert dust, volcanic ash, and under special circumstances biomass-burning smoke.We use experimental data collected with instruments that are capable of measuring δ at all three lidar wavelengths with an inversion routine that uses the theory of light scattering by randomly oriented spheroids to replicate scattering properties of non-spherical particles. This is the first systematic test of the effect of using all theoretically possible combinations of δ taken at 355, 532, and 1064 nm as input in the lidar data inversion. We find that depolarization information at least at one wavelength already provides useful information in the in version of optical data that describe light-scattering by nonspherical particles. However, any choice of δ(λ) will give lower values of the single-scattering albedo than the traditional 3+2 data set. We find that input data sets that include 355 give a non-spherical fraction that closely resembles the dust ratio we obtain from using β(532) and δ(532) in a methodology applied in aerosol-type separation. The use of 355 in data sets of two or three reduces the fraction of non-spherical particles that is retrieved when using δ(532) and δ(1064). Use of the latter two without accounting for 355 generally leads to high fractions of non-spherical particles that we consider not trustworthy. The use of three δ(λ) instead of two δ(λ) including the constraint that one of these is measured at 355 nm does not provide any advantage over using 3+2+δ(355). Because of the technical challenges involved with accurately measuring δ(1064) we conclude that — depending on measurement capability — the future standard input for inversion using spheroid kernels might be 3+2+δ(355) or 3+2+δ(355)+δ(532).

Tesche, M.↗

Bias-Variance Trade-Off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs

Physics-Informed Neural Networks (PINNs) have triggered a paradigm shift in scientific computing, leveraging mesh-free properties and robust approximation capabilities. While proving effective for low-dimensional partial differential equations (PDEs), the computational cost of PINNs remains a hurdle in high-dimensional scenarios. This is particularly pronounced when computing high-order and high-dimensional derivatives in the physics-informed loss. Randomized Smoothing PINN (RS-PINN) introduces Gaussian noise for stochastic smoothing of the original neural net model, enabling the use of Monte Carlo methods for derivative approximation, which eliminates the need for costly automatic differentiation. Despite its computational efficiency, especially in the approximation of high-dimensional derivatives, RS-PINN introduces biases in both loss and gradients, negatively impacting convergence, especially when coupled with stochastic gradient descent (SGD) algorithms. We present a comprehensive analysis of biases in RS-PINN, attributing them to the nonlinearity of the Mean Squared Error (MSE) loss as well as the intrinsic nonlinearity of the PDE itself. We propose tailored bias correction techniques, delineating their application based on the order of PDE nonlinearity. The derivation of an unbiased RS-PINN allows for a detailed examination of its advantages and disadvantages compared to the biased version. Specifically, the biased version has a lower variance and runs faster than the unbiased version, but it is less accurate due to the bias. To optimize the bias-variance trade-off, we combine the two approaches in a hybrid method that balances the rapid convergence of the biased version with the high accuracy of the unbiased version. In addition to methodological contributions, we present an enhanced implementation of RS-PINN. Extensive experiments on diverse high-dimensional PDEs, including Fokker-Planck, Hamilton-Jacobi-Bellman (HJB), viscous Burgers’, Allen-Cahn, and Sine-Gordon equations, illustrate the bias-variance trade-off and highlight the effectiveness of the hybrid RS-PINN. Empirical guidelines are provided for selecting biased, unbiased, or hybrid versions, depending on the dimensionality and nonlinearity of the specific PDE problem.

97 MATHEMATICS AND COMPUTING↗

Adaptive control and noise suppression by a variable-gain gradient algorithm

An adaptive control system based on normalized LMS filters is investigated. The finite impulse response of the nonparametric controller is adaptively estimated using a given reference model. Specifically, the following issues are addressed: The stability of the closed loop system is analyzed and heuristically established. Next, the adaptation process is studied for piecewise constant plant parameters. It is shown that by introducing a variable-gain in the gradient algorithm, a substantial reduction in the LMS adaptation rate can be achieved. Finally, process noise at the plant output generally causes a biased estimate of the controller. By introducing a noise suppression scheme, this bias can be substantially reduced and the response of the adapted system becomes very close to that of the reference model. Extensive computer simulations validate these and demonstrate assertions that the system can rapidly adapt to random jumps in plant parameters.

Merhav, S. J.↗

Discrete random media techniques for microwave modeling of vegetated terrain

Microwave remote sensing models of vegetated terrain are investigated. The problem is to determine canopy characteristics such as biomass, canopy height, and the moisture of the underlying soil. The report describes a discrete scatter model which has been employed to model backscatter in the active (radar) case and to model brightness temperature in the passive (radiometric) case. The acquisition of ground truth data is discussed, as well as the comparison of theory and experiment. The overall conclusion of the work has been that the discrete scatter model in conjunction with efficient scatter algorithms and the distorted Born approximation is a most appropriate methodology to use for modeling purposes in the microwave region.

Lang, Roger H.↗

Single-frame far-field diffractive imaging with randomized illumination

We introduce a single-frame diffractive imaging method called randomized probe imaging (RPI). In RPI, a sample is illuminated by a structured probe field containing speckles smaller than the sample’s typical feature size. Quantitative amplitude and phase images are then reconstructed from the resulting far-field diffraction pattern. The experimental geometry of RPI is straightforward to implement, requires no near-field optics, and is applicable to extended samples. When the resulting data are analyzed with a complimentary algorithm, reliable reconstructions which are robust to missing data are achieved. To realize these benefits, a resolution limit associated with the numerical aperture of the probe-forming optics is imposed. RPI therefore offers an attractive modality for quantitative X-ray phase imaging when temporal resolution and reliability are critical but spatial resolution in the tens of nanometers is sufficient. We discuss the method, introduce a reconstruction algorithm, and present two proof-of-concept experiments: one using visible light, and one using soft X-rays.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Software reliability studies

There are many software reliability models which try to predict future performance of software based on data generated by the debugging process. Our research has shown that by improving the quality of the data one can greatly improve the predictions. We are working on methodologies which control some of the randomness inherent in the standard data generation processes in order to improve the accuracy of predictions. Our contribution is twofold in that we describe an experimental methodology using a data structure called the debugging graph and apply this methodology to assess the robustness of existing models. The debugging graph is used to analyze the effects of various fault recovery orders on the predictive accuracy of several well-known software reliability algorithms. We found that, along a particular debugging path in the graph, the predictive performance of different models can vary greatly. Similarly, just because a model 'fits' a given path's data well does not guarantee that the model would perform well on a different path. Further we observed bug interactions and noted their potential effects on the predictive process. We saw that not only do different faults fail at different rates, but that those rates can be affected by the particular debugging stage at which the rates are evaluated. Based on our experiment, we conjecture that the accuracy of a reliability prediction is affected by the fault recovery order as well as by fault interaction.

Hoppa, Mary Ann↗

Predicting Maximum Temperatures of a Li-ion Battery on a Simulated Flight Profile using a Model-based Prognostics

One of the challenges in using Li-ion packs in aeronautics is their safety, and thermal runaway (TR) is a major concern. The current engineering solutions to prevent a Li-ion pack from a catastrophic TR require additional mass and volume to isolate cells. The excess mass could be reduced by improving detection and, thus, preventing a TR event. One of the possible early warning indicators of a TR is crossing a threshold temperature. We have developed an approach, based on the Unscented Kalman Filter (UKF), to predict the likelihood of reaching the threshold temperature for simulated flight profiles. The current battery prognostics algorithms for aerospace predict state-of-charge (SOC) and end-of-life (EOL) [1]. We extended this two-level algorithm to predict the maximum temperature during discharge. The amount of heat generated in a cell depends on factors such as cell chemistry, cell packaging, total cycles, operating temperature, and abuse history [2]. Our semi-empirical thermal model depends on three phenomenological parameters which account for those factors. In addition, a two-parameter reduced-order model is developed to predict the temperature rise for short bursts of “random-walk” (RW) discharge current sequence, which simulates a flight's current-loading profile. The performance of these models on different datasets and types of current loading will be presented. To predict the maximal temperatures for future cycles we must estimate the evolution of thermal parameters as the batteries age. It is found that the parameters of the 3-parametric thermal model cannot be estimated only from the RW data. To address the issue, we will present two alternative approaches: i) expanding the datasets to include discharge profiles beyond RWs; ii) model reduction to a two-parametric model. The two approaches will be illustrated by an application to the cycling data from a commercial LG 18650 cell. References: 1. M. Daigle, C.S. Kulkarni, End-of-discharge and End-of-life Prediction in Lithium-ion Batteries with Electrochemistry-based Aging Models, in: AIAA Infotech @ Aerospace, American Institute of Aeronautics and Astronautics, San Diego, California, USA, 2016. 2. M. Börner, et. al, Correlation of aging and thermal stability of commercial 18650-type lithium ion batteries, Journal of Power Sources. 342 (2017) 382–392.

Thermal runaway↗

GrainGNN: A dynamic graph neural network for predicting 3D grain microstructure

We propose GrainGNN, a surrogate model for the evolution of polycrystalline grain structure under rapid solidification conditions in metal additive manufacturing. High fidelity simulations of solidification microstructures are typically performed using multicomponent partial differential equations (PDEs) with moving interfaces. The inherent randomness of the PDE initial conditions (grain seeds) necessitates ensemble simulations to predict microstructure statistics, e.g., grain size, aspect ratio, and crystallographic orientation. Here, currently such ensemble simulations are prohibitively expensive and surrogates are necessary.In GrainGNN, we use a dynamic graph to represent interface motion and topological changes due to grain coarsening. We use a reduced representation of the microstructure using hand-crafted features; we combine pattern finding and altering graph algorithms with two neural networks, a classifier (for topological changes) and a regressor (for interface motion). Both networks have an encoder-decoder architecture; the encoder has a multi-layer transformer long-short-term-memory architecture; the decoder is a single layer perceptron.We evaluate GrainGNN by comparing it to high-fidelity phase field simulations for in-distribution and out-of-distribution grain configurations for solidification under laser power bed fusion conditions. GrainGNN results in 80%–90% pointwise accuracy; and nearly identical distributions of scalar quantities of interest (QoI) between phase field and GrainGNN simulations compared using Kolmogorov-Smirnov test. GrainGNN's inference speedup (PyTorch on single x86 CPU) over a high-fidelity phase field simulation (CUDA on a single NVIDIA A100 GPU) is 150×–2000× for 100-initial grain problem. Further, using GrainGNN, we model the formation of 11,600 grains in 220 seconds on a single CPU core.

36 MATERIALS SCIENCE↗

Global Sensitivity Analysis Using the Ultra‐Low Resolution Energy Exascale Earth System Model

Abstract For decades, Arctic temperatures have increased twice as fast as average global temperatures. As a first step toward quantifying parametric uncertainty in Arctic climate, we performed a variance‐based global sensitivity analysis (GSA) using a fully coupled, ultra‐low resolution (ULR) configuration of version 1 of the U.S. Department of Energy's Energy Exascale Earth System Model (E3SMv1). Specifically, we quantified the sensitivity of six quantities of interests (QOIs), which characterize changes in Arctic climate over a 75 year period, to uncertainties in nine model parameters spanning the sea ice, atmosphere, and ocean components of E3SMv1. Sensitivity indices for each QOI were computed with a Gaussian process emulator using 139 random realizations of the random parameters and fixed preindustrial forcing. Uncertainties in the atmospheric parameters in the Cloud Layers Unified by Binormals (CLUBB) scheme were found to have the most impact on sea ice status and the larger Arctic climate. Our results demonstrate the importance of conducting sensitivity analyses with fully coupled climate models. The ULR configuration makes such studies computationally feasible today due to its low computational cost. When advances in computational power and modeling algorithms enable the tractable use of higher‐resolution models, our results will provide a baseline that can quantify the impact of model resolution on the accuracy of sensitivity indices. Moreover, the confidence intervals provided by our study, which we used to quantify the impact of the number of model evaluations on the accuracy of sensitivity estimates, have the potential to inform the computational resources needed for future sensitivity studies.

54 ENVIRONMENTAL SCIENCES↗

Two datasets are better than one: method of double moments for 3D reconstruction in cryo-EM

Cryo-electron microscopy is a powerful imaging technique for reconstructing three-dimensional molecular structures from noisy tomographic projection images of randomly oriented particles. We introduce a new data fusion framework, termed the method of double moments, which reconstructs molecular structures from two instances of the second-order moment of projection images obtained under distinct orientation distributions: one uniform, the other non-uniform and unknown. We prove that these moments generically uniquely determine the underlying structure, up to a global rotation and reflection, and we develop a convex-relaxation-based algorithm that achieves accurate recovery using only second-order statistics. Our results demonstrate the advantage of collecting and modeling multiple datasets under different experimental conditions, illustrating that leveraging dataset diversity can substantially enhance reconstruction quality in computational imaging tasks.

Kam’s method↗

Faster Randomized Dynamical Decoupling

We present a randomized dynamical decoupling (DD) protocol that can substantially improve the performance of any given deterministic DD scheme for suppressing coherent noise by using no more than two additional pulses. Our construction is implemented by probabilistically applying sequences of pulses, which, when combined, effectively eliminate the error terms that scale linearly with the system-environment coupling strength. As a result, we show that a randomized protocol using a few pulses can outperform deterministic DD protocols that require considerably more pulses. Furthermore, we prove that the randomized protocol provides an improvement compared to deterministic DD sequences that aim to reduce the error in the system’s Hilbert space, such as Uhrig DD, which had been previously regarded to be optimal. To rigorously evaluate the performance, we introduce new analytical methods suitable for analyzing higher-order DD protocols that might be of independent interest. Here, we also present numerical simulations confirming the significant advantage of using randomized protocols compared to widely used deterministic protocols.

Quantum algorithms & computation↗

Fokker-Planck Equation Governing the Distribution of Walkers in Auxiliary-Field Quantum Monte Carlo

Auxiliary-field quantum Monte Carlo (AFQMC) is typically formulated as an open-ended random walk in an overcomplete space of Slater determinants, implemented through a Langevin equation. However, the explicit form of the underlying Fokker-Planck equation governing the walker population distribution has remained unknown. Here, in this Letter, we derive the Fokker-Planck equation for AFQMC and propose a novel numerical scheme to solve it. The solution of the Fokker-Planck equation reveals the wave function actually sampled by the AFQMC algorithm. Interestingly, we find that even when the exact ground state is used as a guiding wave function in constrained path AFQMC, contrary to the common assumption, the wave function sampled by AFQMC is not exact. Beyond clarifying several fundamental aspects of AFQMC, the availability of a Fokker-Planck equation formulation opens new avenues for systematically improving its accuracy, which we outline in this Letter.

Monte Carlo methods↗

Modeling of joints for the dynamic analysis of truss structures

An experimentally-based method for determining the stiffness and damping of truss joints is described. The analytical models use springs and both viscous and friction dampers to simulate joint load-deflection behavior. A least-squares algorithm is developed to identify the stiffness and damping coefficients of the analytical joint models from test data. The effects of nonlinear joint stiffness such as joint dead band are also studied. Equations for predicting the sensitivity of beam deformations to changes in joint stiffness are derived and used to show the level of joint stiffness required for nearly rigid joint behavior. Finally, the global frequency sensitivity of a truss structure to random perturbations in joint stiffness is discussed.

Belvin, W. Keith↗

Passive and Active Microwave Remote Sensing of Precipitation and Latent Heating Distributions in the Tropics from TRMM

Passive and active microwave remote sensing data are analyzed to identify signatures of precipitation and vertical motion in tropical convection. A database of cloud/radiative model simulations is used to quantify surface rain rates and latent heating profiles that are consistent with these signatures. At satellite footprint-scale (approximately 10 km), rain rate and latent heating estimates are subject to significant random errors, but by averaging the estimates in space and time, random errors are substantially reduced, Bias errors have been minimized by improving the microphysics in the supporting cloud/radiative model simulations, and by imposing a consistent definition of remotely-sensed and model-simulated convective/stratiform rain coverage. Remotely-sensed precipitation and latent heating distributions in the tropics are derived from Tropical Rainfall Measuring Mission (TRMM) and Special Sensor Microwave/ Imager (SSM/ I) sensor data. The prototype Version 6 TRMM passive microwave algorithm typically yields average heating profiles with maxima between 6 and 7 km altitude for organized mesoscale convective systems. Retrieved heating profiles for individual convective systems are compared to coincident estimates based upon a combination of dual-Doppler radar and rawinsonde data. Also, large-scale latent heating distributions are compared to estimates derived from a simpler technique that utilizes observations of surface rain rate and stratiform rain proportion to infer vertical heating structure. Results of these tests will be presented at the conference.

Olson, William S.↗

Dynamic mode decomposition with core sketch

With the increase in collected data volumes, either from experimental measurements or high fidelity simulations, there is an ever-growing need to develop computationally efficient tools to process, analyze, and interpret these datasets. Modal analysis techniques have gained great interest due to their ability to identify patterns in the data and extract valuable information about the system being considered. Dynamic mode decomposition (DMD) relies on elements of the Koopman approximation theory to compute a set of modes, each associated with a fixed oscillation frequency and a decay/growth rate. Extracting these details from large datasets can be computationally expensive due to the need to implement singular value decomposition of the input data matrix. Sketching algorithms have become popular in numerical linear algebra where statistical theoretic approaches are utilized to reduce the cost of major operations. A sketch of a matrix is another matrix, which is significantly smaller, but still sufficiently approximates the original system. We put forth an efficient DMD framework, SketchyDMD, based on a core sketching algorithm that captures information about the range and corange (their mutual relationship) of input data. The proposed sketching-based framework can accelerate various portions of the DMD routines, compared to classical methods that operate directly on the raw input data. We conduct numerical experiments using the spherical shallow water equations as a prototypical model in the context of geophysical flows. In conclusion, we show that the proposed SketchyDMD is superior to existing randomized DMD methods that are based on capturing only the range of the input data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Hierarchical Gaussian Random Field Sampling for Multilevel Markov Chain Monte Carlo: Coupling Stochastic Partial Differential Equation and the Karhunen–Loève Decomposition

This work introduces structure preserving hierarchical decompositions for sampling Gaussian random fields (GRFs) within the context of multilevel Bayesian inference in high-dimensional space. Existing scalable hierarchical sampling methods, such as those based on stochastic partial differential equations (SPDEs), often reduce the dimensionality of the sample space at the cost of accuracy of inference. Other approaches, such that those based on Karhunen-Loève (KL) expansions, offer sample space dimensionality reduction but sacrifice GRF representation accuracy and ergodicity of the Markov chain Monte Carlo (MCMC) sampler and are computationally expensive for high-dimensional problems. The proposed method integrates the dimensionality reduction capabilities of KL expansions with the scalability of SPDE-based sampling, thereby providing a robust, unified framework for high-dimensional uncertainty quantification (UQ) that is scalable and accurate, preserves ergodicity, and offers dimensionality reduction of the sample space. The hierarchy in our multilevel algorithm is derived from the geometric multigrid hierarchy. By constructing a hierarchical decomposition that maintains the covariance structure across the levels in the hierarchy, the approach enables efficient coarse-to-fine sampling while ensuring that all samples are drawn from the desired distribution. The effectiveness of the proposed method is demonstrated on a benchmark subsurface flow problem, demonstrating its effectiveness in improving computational efficiency and statistical accuracy. Furthermore, our proposed technique is more efficient and accurate and displays better convergence properties than existing methods for high-dimensional Bayesian inference problems.

Gaussian random fields↗