Search NASA⌕ Search

SEARCH · Search NASA

Results for “sparse representations”

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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

CO 2 storage site characterization using ensemble-based approaches with deep generative models

Estimating spatially distributed properties such as permeability from available sparse measurements is a great challenge in efficient subsurface CO 2 storage operations. In this paper, a deep generative model that can accurately capture complex subsurface structure is tested with an ensemble-based inversion method for accurate and accelerated characterization of CO 2 storage sites. We chose Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) for its realistic reservoir property representation and Ensemble Smoother with Multiple Data Assimilation (ES-MDA) for its robust data fitting and uncertainty quantification capability. WGAN-GP are trained to generate high-dimensional permeability fields from a low-dimensional latent space and ES-MDA then updates the latent variables by assimilating available measurements. Several subsurface site characterization examples including Gaussian, channelized, and fractured reservoirs are used to evaluate the accuracy and computational efficiency of the proposed method and the main features of the unknown permeability fields are characterized accurately with reliable uncertainty quantification. Furthermore, the estimation performance is compared with a widely-used variational, i.e., optimization-based, inversion approach, and the proposed approach outperforms the variational inversion method in several benchmark cases. We explain such superior performance by visualizing the objective function in the latent space: because of nonlinear and aggressive dimension reduction via generative modeling, the objective function surface becomes extremely complex while the ensemble approximation can smooth out the multi-modal surface during the minimization. This suggests that the ensemble-based approach works well over the variational approach when combined with deep generative models at the cost of forward model runs unless convergence-ensuring modifications are implemented in the variational inversion.

42 ENGINEERING↗
DOE OSTI2020

Conditional Karhunen-Loève expansion for uncertainty quantification and active learning in partial differential equation models

We use a conditional Karhunen-Lo` eve (KL) model to quantify and reduce uncertainty in a stochastic partial differential equation (SPDE) problem with partially-known space-dependent coefficient, Y (x). We assume that a small number of Y (x) measurements are available and model Y (x) with a KL expansion. We achieve reduction in uncertainty by conditioning the KL expansion coefficients on measurements. We consider two approaches for conditioning the KL expansion: In Approach 1, we condition the KL model first and then truncate it. In Approach 2, we first truncate the KL expansion and then condition it. We employ the conditional KL expansion together with Monte Carlo and sparse grid collocation methods to compute the moments of the solution of the SPDE problem. Uncertainty of the problem is further reduced by adaptively selecting additional observation locations using two active learning methods. Method 1 minimizes the variance of the PDE coefficient, while Method 2 minimizes the variance of the solution of the PDE. We demonstrate that conditioning leads to dimension reduction of the KL representation of Y (x). For a linear diffusion SPDE with uncertain log-normal coefficient, we show that Approach 1 provides a more accurate approximation of the conditional log-normal coefficient and solution of the SPDE than Approach 2 for the same number of random dimensions in a conditional KL expansion. Furthermore, Approach 2 provides a good estimate for the number of terms of the truncated KL expansion of the conditional field of Approach 1. Finally, we demonstrate that active learning based on Method 2 is more efficient for uncertainty reduction in the SPDE’s states (i.e., it leads to a larger reduction of the variance) than active learning using Method 2.

Conditioned Karhunen-Lo` eve expanion, machine lea↗
DOE OSTI2020

Simulating Observations of Southern Ocean Clouds and Implications for Climate

Southern Ocean (S. Ocean) clouds are important for climate prediction. Yet previous global climate models failed to accurately represent cloud phase distributions in this observation-sparse region. In this study, data from the Southern Ocean Clouds, Radiation, Aerosol, Transport Experimental Study (SOCRATES) experiment is compared to constrained simulations from a global climate model (the Community Atmosphere Model, CAM). Nudged versions of CAM are found to reproduce many of the features of detailed in situ observations, such as cloud location, cloud phase, and boundary layer structure. The simulation in CAM6 has improved its representation of S. Ocean clouds with adjustments to the ice nucleation and cloud microphysics schemes that permit more supercooled liquid. Comparisons between modeled and observed hydrometeor size distributions suggest that the modeled hydrometeor size distributions represent the dual peaked shape and form of observed distributions, which is remarkable given the scale difference between model and observations. Comparison to satellite observations of cloud physics is difficult due to model assumptions that do not match retrieval assumptions. Some biases in the model's representation of S. Ocean clouds and aerosols remain, but the detailed cloud physical parameterization provides a basis for process level improvement and direct comparisons to observations. This is crucial because cloud feedbacks and climate sensitivity are sensitive to the representation of S. Ocean clouds.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1989

Some methods of encoding simple visual images for use with a sparse distributed memory, with applications to character recognition

To study the problems of encoding visual images for use with a Sparse Distributed Memory (SDM), I consider a specific class of images- those that consist of several pieces, each of which is a line segment or an arc of a circle. This class includes line drawings of characters such as letters of the alphabet. I give a method of representing a segment of an arc by five numbers in a continuous way; that is, similar arcs have similar representations. I also give methods for encoding these numbers as bit strings in an approximately continuous way. The set of possible segments and arcs may be viewed as a five-dimensional manifold M, whose structure is like a Mobious strip. An image, considered to be an unordered set of segments and arcs, is therefore represented by a set of points in M - one for each piece. I then discuss the problem of constructing a preprocessor to find the segments and arcs in these images, although a preprocessor has not been developed. I also describe a possible extension of the representation.

Jaeckel, Louis A.↗
DOE OSTI2025

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.

Data-driven model reduction↗
DOE OSTI2021

Seasonal Disorder in Urban Traffic Patterns: A Low Rank Analysis

This article proposes several advances to sparse nonnegative matrix factorization (SNMF) as a way to identify large-scale patterns in urban traffic data. The input to our model is traffic counts organized by time and location. Nonnegative matrix factorization additively decomposes this information, organized as a matrix, into a linear sum of temporal signatures. Penalty terms encourage this factorization to concentrate on only a few temporal signatures, with weights which are not too large. Our interest here is to quantify and compare the regularity of traffic behavior, particularly across different broad temporal windows. In addition to the rank and error, we adapt a measure introduced by Hoyer to quantify sparsity in the representation. Combining these, we construct several curves which quantify error as a function of rank (the number of possible signatures) and sparsity; as rank goes up and sparsity goes down, the approximation can be better and the error should decreases. Plots of several such curves corresponding to different time windows leads to a way to compare disorder/order at different time scalewindows. In this paper, we apply our algorithms and procedures to study a taxi traffic dataset from New York City. In this dataset, we find weekly periodicity in the signatures, which allows us an extra framework for identifying outliers as significant deviations from weekly medians. We then apply our seasonal disorder analysis to the New York City traffic data and seasonal (spring, summer, winter, fall) time windows. We do find seasonal differences in traffic order.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Bayesian differential programming for robust systems identification under uncertainty

This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling. This allows an efficient inference of the posterior distributions over plausible models with quantified uncertainty, while the use of sparsity-promoting priors enables the discovery of interpretable and parsimonious representations for the underlying latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed methods, including nonlinear oscillators, predator–prey systems and examples from systems biology. Taken together, our findings put forth a flexible and robust workflow for data-driven model discovery under uncertainty. All codes and data accompanying this article are available at https://bit.ly/34FOJMj .

Science & Technology - Other Topics↗
DOE OSTI2021

Scalable Techniques for Stochastic Power Flow Problems (Final Report)

The proposed research focuses on developing scalable algorithms for two-stage security-constrained OPF problems with AC power flow constraints, a class of problems complicated by (i) scale arising from a scenario representation; and (ii) the presence of nonlinearity, nonconvexity, and possibly second-stage discreteness or complementarity. Unfortunately, most existing solvers cannot contend with both challenges simultaneously; accordingly, the proposed research focuses on developing solution techniques that can both scale with the number of scenarios and contend with nonconvexity and second-stage complementarity. We consider three avenues for addressing such problems: (i) Variable sample-size SQP (VS-SQP) methods that combine sparse Quasi-Newton updates with a scalable variance-reduced stochastic gradient scheme for stochastic QP subproblems, allowing for contending with second-stage complementarity via regularization; (ii) Variable sample-size stochastic Interior-point (VS-sIP) schemes that propose a sampling-based regularized (to allow for contending with complementarity) interior-point schemes in which a Schur-complement technique is employed for decomposing the Newton direction computation step; (iii) Variable sample-size tractable ADMM (VS-tADMM) schemes combine variable sample-sizes with carefully designed techniques for resolving each of the nonconvex updates (by leveraging the QCQP structures). We intend to compare the three schemes using performance profiles in terms of solution quality, scalability, etc. and then select one scheme which will then be developed and further refined in Python for purposes of the GO competition.

42 ENGINEERING↗
DOE OSTI2018

Denoising Poisson phaseless measurements via orthogonal dictionary learning

Phaseless diffraction measurements recorded by CCD detectors are often affected by Poisson noise. In this paper, we propose a dictionary learning model by employing patches based sparsity in order to denoise such Poisson phaseless measurements. The model consists of three terms: (i) A representation term by an orthogonal dictionary, (ii) an L 0 pseudo norm of the coefficient matrix, and (iii) a Kullback-Leibler divergence term to fit phaseless Poisson data. Fast alternating minimization method (AMM) and proximal alternating linearized minimization (PALM) are adopted to solve the proposed model, and especially the theoretical guarantee of the convergence of PALM is provided. The subproblems for these two algorithms both have fast solvers, and indeed, the solutions for the sparse coding and dictionary updating both have closed forms due to the orthogonality of learned dictionaries. Numerical experiments for phase retrieval using coded diffraction and ptychographic patterns are conducted to show the efficiency and robustness of proposed methods, which, by preserving texture features, produce visually and quantitatively improved restored images compared with other phase retrieval algorithms without regularization and local sparsity promoting algorithms.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

The Cortex Transform as an image preprocessor for sparse distributed memory: An initial study

An experiment is described which was designed to evaluate the use of the Cortex Transform as an image processor for Sparse Distributed Memory (SDM). In the experiment, a set of images were injected with Gaussian noise, preprocessed with the Cortex Transform, and then encoded into bit patterns. The various spatial frequency bands of the Cortex Transform were encoded separately so that they could be evaluated based on their ability to properly cluster patterns belonging to the same class. The results of this study indicate that by simply encoding the low pass band of the Cortex Transform, a very suitable input representation for the SDM can be achieved.

Olshausen, Bruno↗
DOE OSTI2021

Leveraging Prior Concept Learning Improves Generalization From Few Examples in Computational Models of Human Object Recognition

Humans quickly and accurately learn new visual concepts from sparse data, sometimes just a single example. The impressive performance of artificial neural networks which hierarchically pool afferents across scales and positions suggests that the hierarchical organization of the human visual system is critical to its accuracy. These approaches, however, require magnitudes of order more examples than human learners. We used a benchmark deep learning model to show that the hierarchy can also be leveraged to vastly improve the speed of learning. We specifically show how previously learned but broadly tuned conceptual representations can be used to learn visual concepts from as few as two positive examples; reusing visual representations from earlier in the visual hierarchy, as in prior approaches, requires significantly more examples to perform comparably. These results suggest techniques for learning even more efficiently and provide a biologically plausible way to learn new visual concepts from few examples.

Rule, Joshua S.↗
DOE OSTI2021

City-Wide Distributed Roof-Top Photovoltaic System Adoption Forecast, Grid Impact Simulation, & Neighborhood Microgrid Contribution Assessment

The adoption of distributed photovoltaic (PV) systems grew significantly in recent years. Market projections anticipate future growth for both residential and commercial installations. To understand grid impacts associated with distributed PV, useful hosting capacity studies require accurate representations of the spatial distribution of PV adoptions. Prediction of PV locations and numbers depends on median income data, building use zoning maps, and permit records to understand existing trends and predict future adoption rates and locations throughout an entire city. Using the PV adoption data, advanced and realistic simulations were performed to capture the distributed PV impacts on the grid. Also, using graph theory community detection hundreds of neighborhood microgrids can be discovered for the entire city by identifying densely connected loads that are sparsely connected to other communities. Then, based on the PV adoption predictions, this work identified the contribution of PV within each of the newly discovered graph theory defined microgrid communities.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2017

A comparative study of discrete fracture network and equivalent continuum models for simulating flow and transport in the far field of a hypothetical nuclear waste repository in crystalline host rock

One of the major challenges of simulating flow and transport in the far field of a geologic repository in crystalline host rock is related to reproducing the properties of the fracture network over the large volume of rock with sparse fracture characterization data. Various approaches have been developed to simulate flow and transport through the fractured rock. The approaches can be broadly divided into Discrete Fracture Network (DFN) and Equivalent Continuum Model (ECM). The DFN explicitly represents individual fractures, while the ECM uses fracture properties to determine equivalent continuum parameters. In this paper, we compare DFN and ECM in terms of upscaled observed transport properties through generic fracture networks. The major effort was directed on making the DFN and ECM approaches similar in their conceptual representations. This allows for separating differences related to the interpretation of the test conditions and parameters from the differences between the DFN and ECM approaches. The two models are compared using a benchmark test problem that is constructed to represent the far field (1 × 1 × 1 km 3 ) of a hypothetical repository in fractured crystalline rock. The test problem setting uses generic fracture properties that can be expected in crystalline rocks. The models are compared in terms of the: 1) effective permeability of the domain, and 2) nonreactive solute breakthrough curves through the domain. The principal differences between the models are mesh size, network connectivity, matrix diffusion and anisotropy. We demonstrate how these differences affect the flow and transport. Finally, we identify the factors that should be taken in consideration when selecting an approach most suitable for the site-specific conditions.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS1990

Discrete integration of continuous Kalman filtering equations for time invariant second-order structural systems

A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.

Park, K. C.↗
DOE OSTI2021

Dynamic global vegetation models underestimate net CO 2 flux mean and inter-annual variability in dryland ecosystems

Despite their sparse vegetation, dryland regions exert a huge influence over global biogeochemical cycles because they cover more than 40% of the world surface (Schimel 2010 Science 327 418–9). It is thought that drylands dominate the inter-annual variability (IAV) and long-term trend in the global carbon (C) cycle (Poulter et al 2014 Nature 509 600–3, Ahlstrom et al 2015 Science 348 895–9, Zhang et al 2018 Glob. Change Biol. 24 3954–68). Projections of the global land C sink therefore rely on accurate representation of dryland C cycle processes; however, the dynamic global vegetation models (DGVMs) used in future projections have rarely been evaluated against dryland C flux data. Here, we carried out an evaluation of 14 DGVMs (TRENDY v7) against net ecosystem exchange (NEE) data from 12 dryland flux sites in the southwestern US encompassing a range of ecosystem types (forests, shrub- and grasslands). We find that all the models underestimate both mean annual C uptake/release as well as the magnitude of NEE IAV, suggesting that improvements in representing dryland regions may improve global C cycle projections. Across all models, the sensitivity and timing of ecosystem C uptake to plant available moisture was at fault. Spring biases in gross primary production (GPP) dominate the underestimate of mean annual NEE, whereas models' lack of GPP response to water availability in both spring and summer monsoon are responsible for inability to capture NEE IAV. Errors in GPP moisture sensitivity at high elevation forested sites were more prominent during the spring, while errors at the low elevation shrub and grass-dominated sites were more important during the monsoon. We propose a range of hypotheses for why model GPP does not respond sufficiently to changing water availability that can serve as a guide for future dryland DGVM developments. Our analysis suggests that improvements in modeling C cycle processes across more than a quarter of the Earth's land surface could be achieved by addressing the moisture sensitivity of dryland C uptake.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Modular hybrid modeling to increase efficiency, explore structural uncertainty, and allow multidimensional complexity scaling in land surface models

Land surface models (LSMs) are indispensable tools for predicting hydrologic extremes, as well as a particularly uncertain component of Earth system models that has stubbornly resisted the convergence in projections over several successive generations of model intercomparisons. This uncertainty in LSMs is poorly quantified and poorly attributed to specific processes, which has hampered efforts to focus research in reducing uncertainty. This has resulted from sparse sampling of the possible uncertainty space—which is high-dimensional and has contributions from parametric, structural, initial, and boundary condition uncertainties—as an artifact of CMIP-type ensembles of opportunity and limitations inherent in observational benchmarks. A new approach is needed to understand and reduce this uncertainty, based around individual LSMs that can represent the breadth of assumptions represented in current CMIP-type efforts, while at the same time exploring that uncertainty in a systematic way, confronting multiple types of observations, and where justified, replacing process representations with ML-driven emulators. We propose an approach of modular hybrid modeling to address these challenges.

58 GEOSCIENCES↗
DOE OSTI2025

Joint state-parameter estimation for the reduced fracture model via the united filter

Here, in this paper, we introduce an effective United Filter method for jointly estimating the solution state and physical parameters in flow and transport problems within fractured porous media. Fluid flow and transport in fractured porous media are critical in subsurface hydrology, geophysics, and reservoir geomechanics. Reduced fracture models, which represent fractures as lower-dimensional interfaces, enable efficient multi-scale simulations. However, reduced fracture models also face accuracy challenges due to modeling errors and uncertainties in physical parameters such as permeability and fracture geometry. To address these challenges, we propose a United Filter method, which integrates the Ensemble Score Filter (EnSF) for state estimation with the Direct Filter for parameter estimation. EnSF, based on a score-based diffusion model framework, produces ensemble representations of the state distribution without deep learning. Meanwhile, the Direct Filter, a recursive Bayesian inference method, estimates parameters directly from state observations. The United Filter combines these methods iteratively: EnSF estimates are used to refine parameter values, which are then fed back to improve state estimation. Numerical experiments demonstrate that the United Filter method surpasses the state-of-the-art Augmented Ensemble Kalman Filter, delivering more accurate state and parameter estimation for reduced fracture models. This framework also provides a robust and efficient solution for PDE-constrained inverse problems with uncertainties and sparse observations.

Bayesian inference↗
DOE OSTI2023

Implementing and Benchmarking the Locally Competitive Algorithm on the Loihi 2 Neuromorphic Processor

Neuromorphic processors have garnered considerable interest in recent years for their potential in enabling energy-efficient and high-speed computing. The Locally Competative Algorithm (LCA) has been utilized for power efficient sparse coding on neuromophic processors, including the first Loihi processor \cite{appletospikes, loihi1}. With the Loihi 2 processor enabling custom neuron models and graded spike communication, more complex implementations of LCA are possible \cite{loihi2}. We present a new implementation of LCA designed for the Loihi 2 processor and perform an initial set of benchmarks comparing it to LCA on CPU and GPU devices. In these experiments LCA on Loihi 2 is faster and orders of magnitude more efficient, while maintaining similar reconstruction quality. We find this performance improvement increases as the LCA parameters are tuned towards greater representation sparsity. Our study highlights the potential of neuromorphic processors, particularly Loihi 2, in enabling intelligent,autonomous, real-time processing on small robots, satellite where there are strict SWaP (small, lightweighr, and low-power) requirement. By demonstrating the superior performance of LCA on Loihi 2 compared to conventional computing device, our study suggests that Loihi 2 could be a valuable tool in advancing these types of applications. Overall, our study highlights the potential of neuromorphic processors for efficient and accurate data processing on resource-constrained devices.

Parpart, Gavin G.↗