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.
A hyper-spherical adaptive sparse-grid method for high-dimensional discontinuity detection
This work proposes and analyzes a hyper-spherical adaptive hierarchical sparse-grid method for detecting jump discontinuities of functions in high-dimensional spaces is proposed. The method is motivated by the theoretical and computational inefficiencies of well-known adaptive sparse-grid methods for discontinuity detection. Our novel approach constructs a function representation of the discontinuity hyper-surface of an N-dimensional dis- continuous quantity of interest, by virtue of a hyper-spherical transformation. Then, a sparse-grid approximation of the transformed function is built in the hyper-spherical coordinate system, whose value at each point is estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hyper-surface, the new technique can identify jump discontinuities with significantly reduced computational cost, compared to existing methods. Moreover, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. Rigorous error estimates and complexity analyses of the new method are provided as are several numerical examples that illustrate the effectiveness of the approach.
DECOVALEX-2019 (Task G Final Report)
The DECOVALEX Project is an on-going international research collaboration, established in 1992, to advance the understanding and modeling of coupled Thermal (T), Hydrological (H), Mechanical (M) and Chemical (C) processes in geological in geological systems. This document is the final report of Task G which was proposed by the Swedish Radiation Safety Authority (SSM) and coordinated by geomecon GmbH, presenting the technical definitions of the problems studied, approaches applied, achievements made and outstanding issues for future research. Task G in DECOVALEX-2019 is primarily concerned with the evolution of transmissivity throughout the lifetime of a repository for radioactive waste, and in particular of spent nuclear fuel, in sparsely fractured and competent crystalline rock masses, and the representation of these processes via numerical simulation. The numerical simulations were to be evaluated for their suitability, and to be validated. Over the course of the work presented here, not only were transmissivity changes and the best approaches to simulate those change examined, but also strategies were to be developed on how to monitor transmissivity change. Guidelines on what a control program and a monitoring system for a repository should include and be able to measure, and how this can be done in practice, was a key objective of the research project.
Prong Segmentation using Point Set Transformers in Multiple View Neutrino Detectors
NOvA is a long-baseline neutrino experiment studying neutrino oscillations by detecting neutrinos from the NuMI beam at Fermilab. Its physics analysis relies on accurate prong segmentation, which involves matching each hit to its source particle and identifying the particle type. This task has commonly been addressed using a combination of traditional clustering algorithms and convolutional neural networks (CNNs). However, NOvA’s detector design presents data as two sparse and decoupled 2D images (XZ and YZ views) rather than a native 3D representation, posing a significant challenge for traditional CNN-based models. In this talk, we propose a novel neural network based on the Point Set Transformer. By treating detector hits as sparse point clouds and implementing a cross-view attention mechanism, our model enables efficient information mixing between both views. Evaluated on NOvA simulated data, our model achieves superior accuracy while requiring significantly fewer computational resources compared to other models. Furthermore, the model demonstrates great performance when applied to Liquid Argon Time Projection Chamber (LArTPC) data, which shows its potential as a universal prong segmentation algorithm for multiple view neutrino detectors.
A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations I: Derivation and algorithms
We propose a dynamically bi-orthogonal method (DyBO) to solve time dependent stochastic partial differential equations (SPDEs). The objective of our method is to exploit some intrinsic sparse structure in the stochastic solution by constructing the sparsest representation of the stochastic solution via a bi-orthogonal basis. It is well-known that the Karhunen–Loeve expansion (KLE) minimizes the total mean squared error and gives the sparsest representation of stochastic solutions. However, the computation of the KL expansion could be quite expensive since we need to form a covariance matrix and solve a large-scale eigenvalue problem. The main contribution of this paper is that we derive an equivalent system that governs the evolution of the spatial and stochastic basis in the KL expansion. Unlike other reduced model methods, our method constructs the reduced basis on-the-fly without the need to form the covariance matrix or to compute its eigendecomposition. In the first part of our paper, we introduce the derivation of the dynamically bi-orthogonal formulation for SPDEs, discuss several theoretical issues, such as the dynamic bi-orthogonality preservation and some preliminary error analysis of the DyBO method. We also give some numerical implementation details of the DyBO methods, including the representation of stochastic basis and techniques to deal with eigenvalue crossing. In the second part of our paper [11], we will present an adaptive strategy to dynamically remove or add modes, perform a detailed complexity analysis, and discuss various generalizations of this approach. An extensive range of numerical experiments will be provided in both parts to demonstrate the effectiveness of the DyBO method.
Bayesian State-Space Modeling Framework for Understanding and Predicting Golden Eagle Movements Using Telemetry Data
Predicting raptor movements through a wind power plant under given atmospheric and topographical conditions is a crucial first step in the overall goal of quantifying the risk of turbine-related collisions and mortalities. Extracting behavioral traits of golden eagles (Aquila chrysaetos) from telemetry data requires the fusion of noisy and sparse movement data (location, heading, velocity) with a stochastic mathematical representation of the eagles' decision-making processes. In this study, we framed this problem in a Bayesian state-space framework where both observations and decision-making are assumed to be stochastic processes connected through hidden states (mode of flight, intent), and the unknown model parameters are assumed to be random variables that are calibrated using the available telemetry data. This framework allowed for rigorous consideration of underlying uncertainties while allowing for both data and prior biological knowledge to contribute to a probabilistic and predictive agent-based movement model. We implemented and applied the Bayesian framework to understand movement behavior of 23 GPS-tagged golden eagles travelling in the western US for years 2019 and 2020. Our preliminary findings show that the Bayesian state-space framework provides a robust inverse modeling apparatus to decode eagle behavioral characteristics from telemetry data. This study was primarily aimed at verifying and validating the framework with selected golden eagle tracks (both long- and short-ranged), with future research aimed at extending the framework to include multi-mode flight, consideration of atmospheric data and uplift mechanisms, eagle-to-eagle interaction, and eagle-to-turbine interaction.
Distributed Stochastic Optimization of a Neural Representation Network for Time-Space Tomography Reconstruction
4D time-space reconstruction of dynamic events or deforming objects using X-ray computed tomography (CT) is an important inverse problem in non-destructive evaluation. Conventional back-projection based reconstruction methods assume that the object remains static for the duration of several tens or hundreds of X-ray projection measurement images (reconstruction of consecutive limited-angle CT scans). However, this is an unrealistic assumption for many in-situ experiments that causes spurious artifacts and inaccurate morphological reconstructions of the object. To solve this problem, we propose to perform a 4D time-space reconstruction using a distributed implicit neural representation (DINR) network that is trained using a novel distributed stochastic training algorithm. Our DINR network learns to reconstruct the object at its output by iterative optimization of its network parameters such that the measured projection images best match the output of the CT forward measurement model. Here, we use a forward measurement model that is a function of the DINR outputs at a sparsely sampled set of continuous valued 4D object coordinates. Unlike previous neural representation architectures that forward and back propagate through dense voxel grids that sample the object's entire time-space coordinates, we only propagate through the DINR at a small subset of object coordinates in each iteration resulting in an order-of-magnitude reduction in memory and compute for training. DINR leverages distributed computation across several compute nodes and GPUs to produce high-fidelity 4D time-space reconstructions. We use both simulated parallel-beam and experimental cone-beam X-ray CT datasets to demonstrate the superior performance of our approach.
Monthly Mean In Situ Surface Flux Observations Paired with Satellite-Derived and Reanalysis-Based Flux Data for the Great Lakes Region, 2001–2020
Surface radiative and turbulent heat fluxes over the Great Lakes strongly influence regional hydrological and meteorological processes, and their accurate representation is critical for numerical weather prediction and coupled atmosphere–lake modeling. However, direct flux observations are spatially sparse across the region, so gridded reanalysis and satellite-derived products are often used for climatological analyses and model evaluation despite differences in their flux representations. This dataset provides processed, quality-controlled, monthly mean surface flux observations from the Great Lakes Evaporation Network (GLEN), AmeriFlux, and the National Data Buoy Center, paired with spatiotemporally matched flux estimates from two reanalysis products, the fifth generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis dataset (ERA5) and the Modern Era Reanalysis for Research and Applications, version 2 (MERRA-2), and two satellite-derived products, the Clouds and Earth's Radiant Energy Systems Energy Balanced and Filled (CERES-EBAF) and the Cloud, Albedo and Surface Radiation dataset from AVHRR data - Edition 3 (CLARA-A3). The dataset includes sixteen observational stations with variable temporal coverage within 2001–2020. For each station, a CSV file contains monthly time series of available flux variables, including surface downwelling shortwave radiation (SW), surface downwelling longwave radiation (LW), sensible heat (SH) flux, and latent heat flux (LH), alongside matched gridded product values where available. Columns in the CSV file correspond to different variables sourced from each dataset, with column titles structured as "{dataset}_{variable}". Columns with relevant metadata are also provided in each CSV file, including station latitude and longitude, monthly timestamps, and the name of the sourced observational data. These files are structured for direct use in common analysis tools, including Microsoft Excel, Python pandas, and Python matplotlib. This dataset supports climatological analysis of the Great Lakes regional surface energy budget, evaluation of satellite-derived and reanalysis-based flux products, and development or validation of flux representations in numerical weather prediction and coupled atmosphere–lake models.
Optimal Network Topology for Node-Breaker Representations With AC Power Flow Constraints
It has been demonstrated that network topology optimization (NTO) may change the topology of power system networks, and consequently, provide additional flexibility to reduce network congestion and violations. Most NTO problems are formulated based on the bus-branch model in which it is challenging to represent a realistic picture of all substation configurations. In this paper, we explore advantages of substation reconfiguration modeling based on node-breaker representations for NTO problem with full nonlinear alternating current power flow. It also proposes a tailored solution algorithm to solve this nonconvex mixed-integer nonlinear programming through the outer approximation method. The proposed solution approach iterates between a mixed-integer linear programming and a nonlinear subproblem. Additional enhancements to further accelerate the iteration process are illustrated. Numerical case studies demonstrate the relative economic and operational impact of optimal network topology with node-breaker representations.
Large-Scale Optimization with Linear Equality Constraints Using Reduced Compact Representation
For optimization problems with linear equality constraints, we prove that the (1,1) block of the inverse KKT matrix remains unchanged when projected onto the nullspace of the constraint matrix. In this work, we develop reduced compact representations of the limited-memory inverse BFGS Hessian to compute search directions efficiently when the constraint Jacobian is sparse. Orthogonal projections are implemented by a sparse QR factorization or a preconditioned LSQR iteration. In numerical experiments two proposed trust-region algorithms improve in computation times, often significantly, compared to previous implementations of related algorithms and compared to IPOPT.
Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanics
Data-driven constitutive modeling with neural networks has received increased interest in recent years due to its ability to easily incorporate physical and mechanistic constraints and to overcome the challenging and time-consuming task of formulating phenomenological constitutive laws that can accurately capture the observed material response. However, even though neural network-based constitutive laws have been shown to generalize proficiently, the generated representations are not easily interpretable due to their high number of trainable parameters. Sparse regression approaches exist that allow for obtaining interpretable expressions, but the user is tasked with creating a library of model forms which by construction limits their expressiveness to the functional forms provided in the libraries. Here, in this work, we propose to train regularized physics-augmented neural network-based constitutive models utilizing a smoothed version of $L^0$-regularization. This aims to maintain the trustworthiness inherited by the physical constraints, but also enables interpretability which has not been possible thus far on any type of machine learning-based constitutive model where model forms were not assumed a priori but were actually discovered. During the training process, the network simultaneously fits the training data and penalizes the number of active parameters, while also ensuring constitutive constraints such as thermodynamic consistency. We show that the method can reliably obtain interpretable and trustworthy constitutive models for compressible and incompressible hyperelasticity, yield functions, and hardening models for elastoplasticity, using synthetic and experimental data. This work aims to set a new paradigm for interpretable machine learning models in the broad area of solid mechanics where low and limited data is available along with prior knowledge of physical constraints that the learned maps need to obey. This paradigm can potentially be extended to a broader spectrum of scientific exploration.
Plant Root Characteristics and Dynamics in Arctic Tundra Ecosystems, 1960-2012
Plant roots play a critical role in ecosystem function in arctic tundra, but root dynamics in these ecosystems are poorly understood. To address this knowledge gap, we synthesized available literature on tundra roots, including their distribution, dynamics, and contribution to ecosystem carbon and nutrient fluxes, and we highlighted key aspects of their representation in terrestrial biosphere models. Across all tundra ecosystems, belowground plant biomass exceeded aboveground biomass, with the exception of polar desert tundra. Roots were shallowly-distributed in the thin layer of soil that thaws annually, and were often found in surface organic soil horizons. Root traits including distribution, chemistry, anatomy, and resource partitioning play an important role in controlling plant species competition, and therefore ecosystem carbon and nutrient fluxes, under changing climatic conditions, but have only been quantified for a small fraction of tundra plants. Further, the annual production and mortality of fine roots are key components of ecosystem processes in tundra, but extant data are sparse. Tundra root traits and dynamics should be the focus of future research efforts. Better representation of the dynamics and characteristics of tundra roots will improve the utility of models for evaluating the responses of tundra ecosystems to changing environmental conditions. Includes a data file in *.csv, and *.xlsx format and a *.pdf. The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research. The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska. Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).
Paradeisos: A perfect hashing algorithm for many-body eigenvalue problems
Here, we describe an essentially perfect hashing algorithm for calculating the position of an element in an ordered list, appropriate for the construction and manipulation of many-body Hamiltonian, sparse matrices. Each element of the list corresponds to an integer value whose binary representation reflects the occupation of single-particle basis states for each element in the many-body Hilbert space. The algorithm replaces conventional methods, such as binary search, for locating the elements of the ordered list, eliminating the need to store the integer representation for each element, without increasing the computational complexity. Combined with the “checkerboard” decomposition of the Hamiltonian matrix for distribution over parallel computing environments, this leads to a substantial savings in aggregate memory. While the algorithm can be applied broadly to many-body, correlated problems, we demonstrate its utility in reducing total memory consumption for a series of fermionic single-band Hubbard model calculations on small clusters with progressively larger Hilbert space dimension.
A multiresolution adaptive wavelet method for nonlinear partial differential equations
We report the multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to solve partial differential equations (PDEs) with features evolving on a wide range of spatial and temporal scales. To meet these challenges, we present a multiresolution wavelet algorithm to solve PDEs with significant data compression and explicit error control. We discretize in space by projecting fields and spatial derivative operators onto wavelet basis functions. We provide error estimates for the wavelet representation of fields and their derivatives. Then, our estimates are used to construct a sparse multiresolution discretization which guarantees the prescribed accuracy. Additionally, we embed a predictor-corrector procedure within the temporal integration to dynamically adapt the computational grid and maintain the accuracy of the solution of the PDE as it evolves. We present examples to highlight the accuracy and adaptivity of our approach.
Object detection approach using generative sparse, hierarchical networks with top-down and lateral connections for combining texture/color detection and shape/contour detection
An approach to detecting objects in an image dataset may combine texture/color detection, shape/contour detection, and/or motion detection using sparse, generative, hierarchical models with lateral and top-down connections. A first independent representation of objects in an image dataset may be produced using a color/texture detection algorithm. A second independent representation of objects in the image dataset may be produced using a shape/contour detection algorithm. A third independent representation of objects in the image dataset may be produced using a motion detection algorithm. The first, second, and third independent representations may then be combined into a single coherent output using a combinatorial algorithm.
Object detection approach using generative sparse, hierarchical networks with top-down and lateral connections for combining texture/color detection and shape/contour detection
An approach to detecting objects in an image dataset may combine texture/color detection, shape/contour detection, and/or motion detection using sparse, generative, hierarchical models with lateral and top-down connections. A first independent representation of objects in an image dataset may be produced using a color/texture detection algorithm. A second independent representation of objects in the image dataset may be produced using a shape/contour detection algorithm. A third independent representation of objects in the image dataset may be produced using a motion detection algorithm. The first, second, and third independent representations may then be combined into a single coherent output using a combinatorial algorithm.
Advanced modeling of $\mathrm{DER}$s and $\mathrm{UPFC}$ devices with Sparse Tableau Formulation for $\mathrm{ACOPF}$
Distributed energy resources (DERs) are projected to be significant contributors in electric power grid modernization efforts. Yet many distribution and transmission system operators are concerned about potential reliability and security impacts of high penetration of DERs, and cite the need of greater visibility and controllability of decision variables associated with these DERs. Tractable modeling of DERs in AC optimal power flow (ACOPF) is one of the barriers to their integration into the existing operation, planning and market paradigm. Similarly, as more intermittent renewable resources are deployed, power flow control becomes more valuable, and accurate representation of Flexible AC Transmission System (FACTS) devices in ACOPF will likely grow in importance. Here this paper focuses on the detailed representation of substations with the high penetration of DERs, and on the Unified Power Flow Controller (UPFC) FACTS devices, in OPF. To this end, a novel Sparse Tableau Formulation (STF) for ACOPF is used to accurately model such features as substation reconfiguration to accommodate DERs, and to represent decision variables appropriate to the voltage source converters within UPFCs. Numerical studies are provided to demonstrate the impacts of detailed DER and UPFC representations on optimal operation, and the computational efficiency.
Graph theory inspired anomaly detection at the LHC
Designing model-independent anomaly detection algorithms for analyzing LHC data remains a central challenge in the search for new physics, due to the high dimensionality of collider events. In this work, we develop a graph autoencoder as an unsupervised, model-agnostic tool for anomaly detection, using the LHC Olympics dataset as a benchmark. By representing jet constituents as a graph, we introduce a method to systematically control the information available to the model through sparse graph constructions that serve as physically motivated inductive biases. Specifically, (1) we construct graph autoencoders based on locally rigid Laman graphs and globally rigid unique graphs, and (2) we explore the clustering of jet constituents into subjets to interpolate between high- and low-level input representations. We obtain the best performance, measured in terms of the Significance Improvement Characteristic curve for an intermediate level of subjet clustering and certain sparse unique graph constructions. We further investigate the role of graph connectivity in jet classification tasks. Our results demonstrate the potential of leveraging graph-theoretic insights to refine and increase the interpretability of machine learning tools for collider experiments.