Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “sparsity estimation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A nudged hybrid analysis and modeling approach for realtime wake-vortex transport and decay prediction

Here, we put forth a long short-term memory (LSTM) nudging framework for the enhancement of reduced order models (ROMs) of fluid flows utilizing noisy measurements for air traffic improvements. Toward emerging applications of digital twins in aviation, the proposed approach allows for constructing a realtime predictive tool for wake-vortex transport and decay systems. We build on the fact that in realistic application, there are uncertainties in initial and boundary conditions, model parameters, as well as measurements. Moreover, conventional nonlinear ROMs based on Galerkin projection (GROMs) suffer from imperfection and solution instabilities, especially for advection-dominated flows with slow decay in the Kolmogorov n-width. In the presented LSTM nudging (LSTM-N) approach, we fuse forecasts from a combination of imperfect GROM and uncertain state estimates, with sparse Eulerian sensor measurements to provide more reliable predictions in a dynamical data assimilation framework. We illustrate our concept by solving the two-dimensional vorticity transport equation. We investigate the effects of measurements noise and state estimate uncertainty on the performance of the LSTM-N behavior. We also demonstrate that it can sufficiently handle different levels of temporal and spatial measurement sparsity, and offer a huge potential in developing next-generation digital twin technologies for aerospace applications.

42 ENGINEERING↗
DOE OSTI2016

Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations

We extend the reduced basis (RB) accelerated Bayesian inversion methods for affine-parametric, linear operator equations which are considered in [16,17] to non-affine, nonlinear parametric operator equations. We generalize the analysis of sparsity of parametric forward solution maps in [20] and of Bayesian inversion in [48,49] to the fully discrete setting, including Petrov–Galerkin high-fidelity (“HiFi”) discretization of the forward maps. We develop adaptive, stochastic collocation based reduction methods for the efficient computation of reduced bases on the parametric solution manifold. The nonaffinity and nonlinearity with respect to (w.r.t.) the distributed, uncertain parameters and the unknown solution is collocated; specifically, by the so-called Empirical Interpolation Method (EIM). For the corresponding Bayesian inversion problems, computational efficiency is enhanced in two ways: first, expectations w.r.t. the posterior are computed by adaptive quadratures with dimension-independent convergence rates proposed in [49]; the present work generalizes [49] to account for the impact of the PG discretization in the forward maps on the convergence rates of the Quantities of Interest (QoI for short). Second, we propose to perform the Bayesian estimation only w.r.t. a parsimonious, RB approximation of the posterior density. Based on the approximation results in [49], the infinite-dimensional parametric, deterministic forward map and operator admit N-term RB and EIM approximations which converge at rates which depend only on the sparsity of the parametric forward map. In several numerical experiments, the proposed algorithms exhibit dimension-independent convergence rates which equal, at least, the currently known rate estimates for N-term approximation. We propose to accelerate Bayesian estimation by first offline construction of reduced basis surrogates of the Bayesian posterior density. The parsimonious surrogates can then be employed for online data assimilation and for Bayesian estimation. They also open a perspective for optimal experimental design.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A Markov chain Monte Carlo (MCMC) Bayesian inference approach to analyze apparent activation barriers and reaction orders from microreactor data

Statistical analysis of steady-state catalytic kinetic data is often limited by data sparsity due to the slow pace at which the data is collected. Data sparsity and limitations in statistical analysis make it difficult to differentiate between mechanistic models and catalytic sites. A Bayesian inference tool is reported for catalysis researchers to estimate error in the determination of reaction orders from steady state microreactor data. The benefits of a Bayesian inference approach are discussed, as an alternative to the more common frequentist approach. The approach incorporates prior knowledge of the system and the data collected to form an error estimate on reaction orders. We investigated the effects of three distinct data treatments—individual fitting of trials, pooled analysis, and constrained regression methods—on the precision and uncertainty of reaction order determinations. To assess the robustness of our findings, we conducted sensitivity analyses to evaluate the influence of Bayesian parameters on uncertainty estimation. Additionally, we utilized synthetic data to illustrate how data quality impacts the precision of uncertainty assessments. We show Bayesian analysis can obtain a more precise estimation of error with a sparse data set than a frequentist analysis. Finally, this work provides strong evidence that the adoption of Bayesian analysis of kinetic data may help researchers make more precise arguments as to the strength of their evidence for a particular mechanistic hypothesis, or in comparing across different catalysts.

42 ENGINEERING↗
DOE OSTI2020

Radiation Mapping for an Unmanned Aerial Vehicle: Development and Simulated Testing of Algorithms for Source Mapping and Navigation Path Generation

Image reconstruction algorithms were developed for radiation source mapping and used for generating the search path of a moving radiation detector, such as one onboard an unmanned aerial vehicle. Simulations consisted of first assuming radioactive sources of varying complexity and estimating the radiation fields that would then be produced by that source distribution. Next, the "measurements" that would result from a pair of adjacent spatial locations were computed. A crude estimate of the source distribution likely to have produced such "measurements" was reconstructed based upon the limited measurements. Location of the next "measurement" was then determined as halfway between the location of the estimated source and the current "measurement." With each additional sample, improved source distribution reconstructions were made and used to inform the immediate direction of detector motion. Source reconstruction or mapping was formulated as an inverse problem solved with either maximum a posteriori or least squares (LS) regression deconvolution methods. Different amounts of noise were added to the simulated "measurements," allowing evaluation of the methods' performances as functions of signal-to-noise ratio of the measured map. As expected, methods that promote sparsity were better suited in reconstructing point sources. Reliable prior information of the source distribution also improved the reconstruction results, especially with distributed sources. With a non-negative least square algorithm and the suggested paths it generated, location of sources was successfully estimated to an accuracy of 0.014 m within nine iterations in a single-source scenario and 12 iterations in a two-source scenario, given a 10% error on the integrated counts and a Poisson distribution of the noise associated with the measured counts.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
NASA NTRS1993

A general rough-surface inversion algorithm: Theory and application to SAR data

Rough-surface inversion has significant applications in interpretation of SAR data obtained over bare soil surfaces and agricultural lands. Due to the sparsity of data and the large pixel size in SAR applications, it is not feasible to carry out inversions based on numerical scattering models. The alternative is to use parameter estimation techniques based on approximate analytical or empirical models. Hence, there are two issues to be addressed, namely, what model to choose and what estimation algorithm to apply. Here, a small perturbation model (SPM) is used to express the backscattering coefficients of the rough surface in terms of three surface parameters. The algorithm used to estimate these parameters is based on a nonlinear least-squares criterion. The least-squares optimization methods are widely used in estimation theory, but the distinguishing factor for SAR applications is incorporating the stochastic nature of both the unknown parameters and the data into formulation, which will be discussed in detail. The algorithm is tested with synthetic data, and several Newton-type least-squares minimization methods are discussed to compare their convergence characteristics. Finally, the algorithm is applied to multifrequency polarimetric SAR data obtained over some bare soil and agricultural fields. Results will be shown and compared to ground-truth measurements obtained from these areas. The strength of this general approach to inversion of SAR data is that it can be easily modified for use with any scattering model without changing any of the inversion steps. Note also that, for the same reason it is not limited to inversion of rough surfaces, and can be applied to any parameterized scattering process.

Moghaddam, M.↗
DOE OSTI2017

Adaptive OFDM Waveform Design for Spatio-Temporal-Sparsity Exploited STAP Radar

In this chapter, we describe a sparsity-based space-time adaptive processing (STAP) algorithm to detect a slowly moving target using an orthogonal frequency division multiplexing (OFDM) radar. The motivation of employing an OFDM signal is that it improves the target-detectability from the interfering signals by increasing the frequency diversity of the system. However, due to the addition of one extra dimension in terms of frequency, the adaptive degrees-of-freedom in an OFDM-STAP also increases. Therefore, to avoid the construction a fully adaptive OFDM-STAP, we develop a sparsity-based STAP algorithm. We observe that the interference spectrum is inherently sparse in the spatio-temporal domain, as the clutter responses occupy only a diagonal ridge on the spatio-temporal plane and the jammer signals interfere only from a few spatial directions. Hence, we exploit that sparsity to develop an efficient STAP technique that utilizes considerably lesser number of secondary data compared to the other existing STAP techniques, and produces nearly optimum STAP performance. In addition to designing the STAP filter, we optimally design the transmit OFDM signals by maximizing the output signal-to-interference-plus-noise ratio (SINR) in order to improve the STAP performance. The computation of output SINR depends on the estimated value of the interference covariance matrix, which we obtain by applying the sparse recovery algorithm. Therefore, we analytically assess the effects of the synthesized OFDM coefficients on the sparse recovery of the interference covariance matrix by computing the coherence measure of the sparse measurement matrix. Our numerical examples demonstrate the achieved STAP-performance due to sparsity-based technique and adaptive waveform design.

Sen, Satyabrata↗
DOE OSTI2025

Multi-head physics-informed neural networks for learning functional priors and uncertainty quantification

In numerous applications, the integration of prior knowledge and historical information is essential, particularly for tasks requiring the solution of ordinary or partial differential equations (ODEs/PDEs) in data-sparse or noisy environments. For instance, achieving accurate solutions to time-dependent PDEs with limited initial condition measurements necessitates an effective strategy for embedding prior knowledge. Hard-parameter sharing architectures in neural networks (NNs) have demonstrated success in both traditional and scientific machine learning domains, facilitating the learning of informative representations. Here, in this study, we introduce a novel, yet efficient, method to enhance physics-informed neural networks (PINNs) by incorporating a multi-head structure that enables the learning of functional priors from both empirical data and governing physical laws. This prior information can then be used to address data sparsity and high-level noise in solving ODE/PDE problems with uncertainty quantification (UQ). The approach, termed Multi-Head PINN (MH-PINN), consists of a shared body NN and multiple head NNs, each corresponding to an individual PINN instance. Our framework for functional prior learning is carried out in two stages: (1) training the MH-PINNs to develop a shared body NN alongside multiple head NNs, and (2) employing these trained head NNs to estimate a prior distribution through a normalizing flow-based density estimator. The learned functional prior can then be applied as a regularization mechanism in deterministic contexts or as an informative prior within a Bayesian inference framework, aiding in the resolution of subsequent ODE/PDE tasks. We evaluate the efficacy of MH-PINNs across five benchmark problems, including a high-dimensional parametric PDE, all characterized by data sparsity or substantial noise levels. Our findings reveal that MH-PINNs deliver accurate solutions and robust UQ, demonstrating adaptability across a range of complex and challenging scenarios.

Bayesian inference↗
DOE OSTI2017

A scalable design of experiments framework for optimal sensor placement

Here, we present a scalable design of an experiments framework for sensor placement in systems described by partial differential equations (PDEs). In particular, we aim to compute optimal sensor locations by minimizing the uncertainty of parameters estimated from Bayesian inverse problems and where the system. The resulting problem is a computationally intractable mixed-integer nonlinear program constrained by PDEs. We approach this problem with two heuristics used in compressed sensing and optimal control literature: a sparsity-inducing approach and a sum-up rounding approach. We also investigate metrics to guide the design of experiments (the total flow variance and the A-optimal design criterion) and analyze the effect of different noise structures (white and colored). Using an application in natural gas pipelines, we conclude that the sum-up rounding approach approach gives the best results and produces shrinking gaps with increasing mesh resolution. We also observe that convergence for the white noise measurement error case is slower than for the colored noise case. For A-optimal design, the solution is close to a uniform distribution of sensors along the pipeline while for the flow variance design the distribution is unstructured.

42 ENGINEERING↗
DOE OSTI2024

Exploration with Scalable Gaussian Process Reinforcement Learning

Exploration is a challenging problem in reinforcement learning (RL), especially in environments with sparse rewards. Quantifying and utilizing the parametric uncertainty has been shown to be paramount for successful exploration [Osband et al., 2018]. Bayesian, or approximately Bayesian, methods present a principled means of estimating the parametric uncertainty in RL problems. Gaussian processes, nonparametric Bayesian models, are often impractical due to poor scalability and computational bottlenecks. We introduce a scalable Gaussian process RL (GPRL) method which directly induces sparsity in the covariance matrix to facilitate faster computation. This is a departure from previous GPRL methods which instead rely on data reduction and subsampling. We compare various covariance-based exploration techniques (Thompson sampling, upper confidence bound, and probabilistic maximum variance) which leverage our scalable GP framework in sparse reward environments. Finally, we show favorable comparison against the bootstrapped deep Q-Network.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2021

Weekly Mapping of Sea Ice Freeboard in the Ross Sea from ICESat-2

NASA’s ICESat-2 has been providing sea ice freeboard measurements across the polar regions since October 2018. In spite of the outstanding spatial resolution and precision of ICESat-2, the spatial sparsity of the data can be a critical issue for sea ice monitoring. This study employs a geostatistical approach (i.e., ordinary kriging) to characterize the spatial autocorrelation of the ICESat-2 freeboard measurements (ATL10) to estimate weekly freeboard variations in 2019 for the entire Ross Sea area, including where ICESat-2 tracks are not directly available. Three variogram models (exponential, Gaussian, and spherical) are compared in this study. According to the cross-validation results, the kriging-estimated freeboards show correlation coefficients of 0.56–0.57, root mean square error (RMSE) of ~0.12 m, and mean absolute error (MAE) of ~0.07 m with the actual ATL10 freeboard measurements. In addition, the estimated errors of the kriging interpolation are low in autumn and high in winter to spring, and low in southern regions and high in northern regions of the Ross Sea. The effective ranges of the variograms are 5–10 km and the results from the three variogram models do not show significant differences with each other. The southwest (SW) sector of the Ross Sea shows low and consistent freeboard over the entire year because of the frequent opening of wide polynya areas generating new ice in this sector. However, the southeast (SE) sector shows large variations in freeboard, which demonstrates the advection of thick multiyear ice from the Amundsen Sea into the Ross Sea. Thus, this kriging-based interpolation of ICESat-2 freeboard can be used in the future to estimate accurate sea ice production over the Ross Sea by incorporating other remote sensing data.

Satellite altimeter↗
DOE OSTI2018

Detecting False Data Injection Attacks Against Power System State Estimation With Fast Go-Decomposition Approach

State estimation is a fundamental function in modern energy management system, but its results may be vulnerable to false data injection attacks (FDIAs). FDIA is able to change the estimation results without being detected by the traditional bad data detection algorithms. In this paper, we propose an accurate and computational attractive approach for FDIA detection. In this work, we first rely on the low rank characteristic of the measurement matrix and the sparsity of the attack matrix to reformulate the FDIA detection as a matrix separation problem. Then, four algorithms that solve this problem are presented and compared, including the traditional augmented Lagrange multipliers (ALMs), double-noise-dual-problem (DNDP) ALM, the low rank matrix factorization, and the proposed new “Go Decomposition (GoDec).” Numerical simulation results show that our GoDec algorithm outperforms the other three alternatives and demonstrates a much higher computational efficiency. Furthermore, GoDec is shown to be able to handle measurement noise and applicable for large-scale attacks.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Non-asymptotic analysis of ensemble Kalman updates: effective dimension and localization

Many modern algorithms for inverse problems and data assimilation rely on ensemble Kalman updates to blend prior predictions with observed data. Ensemble Kalman methods often perform well with a small ensemble size, which is essential in applications where generating each particle is costly. This paper develops a non-asymptotic analysis of ensemble Kalman updates, which rigorously explains why a small ensemble size suffices if the prior covariance has moderate effective dimension due to fast spectrum decay or approximate sparsity. Here, we present our theory in a unified framework, comparing everal implementations of ensemble Kalman updates that use perturbed observations, square root filtering and localization. As part of our analysis, we develop new dimension-free covariance estimation bounds for approximately sparse matrices that may be of independent interest.

Mathematics↗
DOE OSTI2017

Bayesian K-SVD Using Fast Variational Inference

Recent work in signal processing in general and image processing in particular deals with sparse representation related problems. Two such problems are of paramount importance: an overriding need for designing a well-suited overcomplete dictionary containing a redundant set of atoms— i.e., basis signals—and how to find a sparse representation of a given signal with respect to the chosen dictionary. Dictionary learning techniques, among which we find the popular K-singular value decomposition algorithm, tackle these problems by adapting a dictionary to a set of training data. A common drawback of such techniques is the need for parameter-tuning. In order to overcome this limitation, we propose a fullyautomated Bayesian method that considers the uncertainty of the estimates and produces a sparse representation of the data without prior information on the number of non-zeros in each representation vector. We follow a Bayesian approach that uses a three-tiered hierarchical prior to enforce sparsity on the representations and develop an efficient variational inference framework that reduces computational complexity. Furthermore, we describe a greedy approach that speeds up the whole process. Lastly, we present experimental results that show superior performance on two different applications with real images: denoising and inpainting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Deconvolving distribution of relaxation times, resistances and inductance from electrochemical impedance spectroscopy via statistical model selection: Exploiting structural-sparsity regularization and data-driven parameter tuning

The distribution of relaxation times (DRT) has drawn increasing attention for interpreting electrochemical impedance spectroscopy (EIS). Deconvolution of DRT from EIS is a challenging ill-posed problem that requires regularization methods. In this work, we formulate DRT reconstruction task as a statistical model selection problem with structural-sparsity penalties. We utilize the Elastic net regularization that simultaneously benefits from Ridge and Lasso regularizations with optimal tuning parameter automatically determined by the information criteria. We benchmark our approach on four synthetic experiments (a ZARC element, ZARC mixtures, a RC circuit and a Fractal element) and two real EIS datasets of a Lithium ion battery and an organic-inorganic halide class of perovskites in oxygen environment at different gas pressures. We demonstrate the superiority of proposed model selection procedure, that is capable of eliminating pseudo peaks and representing asymmetries in DRT as well as precisely estimating resistances. Here, we highlight our approach is robust to reducing and subsampling EIS frequency range, making it a promising tool for timing-resolved, localized and large scale EIS data analysis. For the Lithium ion battery data analysis, we extend the classical DRT model to incorporate the inductive effect and illustrate DRT as a guidance for equivalent circuit modeling to refine impedance reconstruction at low risks of overfitting. Furthermore, the structural-sparsity regularization could be extended for multidimensional and Bayesian EIS data analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

ReLU, Sparseness, and the Encoding of Optic Flow in Neural Networks

Accurate self-motion estimation is critical for various navigational tasks in mobile robotics. Optic flow provides a means to estimate self-motion using a camera sensor and is particularly valuable in GPS- and radio-denied environments. The present study investigates the influence of different activation functions—ReLU, leaky ReLU, GELU, and Mish—on the accuracy, robustness, and encoding properties of convolutional neural networks (CNNs) and multi-layer perceptrons (MLPs) trained to estimate self-motion from optic flow. Our results demonstrate that networks with ReLU and leaky ReLU activation functions not only achieved superior accuracy in self-motion estimation from novel optic flow patterns but also exhibited greater robustness under challenging conditions. The advantages offered by ReLU and leaky ReLU may stem from their ability to induce sparser representations than GELU and Mish do. Our work characterizes the encoding of optic flow in neural networks and highlights how the sparseness induced by ReLU may enhance robust and accurate self-motion estimation from optic flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Expectation propagation for nonlinear inverse problems – with an application to electrical impedance tomography

In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of efficiently delivering reliable estimates of the posterior mean and covariance, thereby providing an inverse solution together with quantified uncertainties. Some theoretical properties of the iterative algorithm are discussed, and the efficient implementation for an important class of problems of projection type is described. The method is illustrated with one typical nonlinear inverse problem, electrical impedance tomography with complete electrode model, under sparsity constraints. Numerical results for real experimental data are presented, and compared with that by Markov chain Monte Carlo. The results indicate that the method is accurate and computationally very efficient.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Cardinality-Regularized Hawkes-Granger Model

We propose a new sparse Granger-causal learning framework for temporal event data. We focus on a specific class of point processes called the Hawkes process. We begin by pointing out that most of the existing sparse causal learning algorithms for the Hawkes process suffer from a singularity in maximum likelihood estimation. As a result, their sparse solutions can appear only as numerical artifacts. In this paper, we propose a mathematically well-defined sparse causal learning framework based on a cardinality-regularized Hawkes process, which remedies the pathological issues of existing approaches. We leverage the proposed algorithm for the task of instance-wise causal event analysis, where sparsity plays a critical role. We validate the proposed framework with two real use-cases, one from the power grid and the other from the cloud data center management domain.

Ide, Tsuyoshi↗