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DOE OSTI2026

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.

Liu, Jiaxi [UC, Irvine]↗

NASA NTRS1990

Optimal parallel solution of sparse triangular systems

A method for the parallel solution of triangular sets of equations is described that is appropriate when there are many right-handed sides. By preprocessing, the method can reduce the number of parallel steps required to solve Lx = b compared to parallel forward or backsolve. Applications are to iterative solvers with triangular preconditioners, to structural analysis, or to power systems applications, where there may be many right-handed sides (not all available a priori). The inverse of L is represented as a product of sparse triangular factors. The problem is to find a factored representation of this inverse of L with the smallest number of factors (or partitions), subject to the requirement that no new nonzero elements be created in the formation of these inverse factors. A method from an earlier reference is shown to solve this problem. This method is improved upon by constructing a permutation of the rows and columns of L that preserves triangularity and allow for the best possible such partition. A number of practical examples and algorithmic details are presented. The parallelism attainable is illustrated by means of elimination trees and clique trees.

Alvarado, Fernando L.↗

NASA NTRS1991

Eigenvalue calculation procedure for an Euler/Navier-Stokes solver with application to flows over airfoils

A Lanczos procedure is presently applied to a Navier-Stokes (N-S) solver for eigenvalues and eigenvectors associated with the small-perturbation analysis of the N-S equations' finite-difference representation for airfoil flows; the matrix used is very large, sparse, real, and nonsymmetric. The Lanczos procedure is shown to furnish complete spectral information for the eigenvalues, as required for transient-stability analysis of N-S solvers.

Mahajan, Aparajit J.↗

DOE OSTI2022

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.

Bayesian modeling↗

DOE OSTI2025

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.

36 MATERIALS SCIENCE↗

NASA NTRS1993

A path-oriented matrix-based knowledge representation system

Experience has shown that designing a good representation is often the key to turning hard problems into simple ones. Most AI (Artificial Intelligence) search/representation techniques are oriented toward an infinite domain of objects and arbitrary relations among them. In reality much of what needs to be represented in AI can be expressed using a finite domain and unary or binary predicates. Well-known vector- and matrix-based representations can efficiently represent finite domains and unary/binary predicates, and allow effective extraction of path information by generalized transitive closure/path matrix computations. In order to avoid space limitations a set of abstract sparse matrix data types was developed along with a set of operations on them. This representation forms the basis of an intelligent information system for representing and manipulating relational data.

Feyock, Stefan↗

DOE OSTI2026

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.

Great Lakes↗

NASA NTRS2022

Megadroughts in the Common Era and the Anthropocene

Megadroughts, often lasting multiple decades, have caused major ecological and societal disturbances in the past. While most research has focused on megadroughts in North America, the concept has gained increased international attention in recent years. In this Review, we discuss shared causes and features of Common Era and future megadroughts. Paleoclimate reconstructions spanning the last 2,000 years document the occurrence of megadroughts on every continent, save Antarctica. Megadroughts are often linked to decadal variations in sea surface temperatures, with radiative forcing and land-atmosphere interactions acting as secondary factors. Anthropogenic climate change has already contributed to recent megadroughts in southwestern North America and Chile-Argentina and will likely increase future megadrought risk and severity in many regions. Notably, future megadroughts will be differentiated from past events through higher temperatures, which act as the main driver of increased risk, severity, and impacts. Major deficiencies in our understanding of natural and anthropogenic megadrought processes remain, however. These include 1) sparse high-resolution paleoclimate information over some regions, 2) incomplete representations of internal variability and land-surface processes in climate models, and 3) the undetermined capacity of water-resource management systems to manage megadrought impacts. Resolving these key uncertainties will be necessary to increase confidence in projections of future megadrought risk and resiliency planning.

Droughts↗

DOE OSTI2020

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.

42 ENGINEERING↗

DOE OSTI2022

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.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2008

A Data Type for Efficient Representation of Other Data Types

A self-organizing, monomorphic data type denoted a sequence has been conceived to address certain concerns that arise in programming parallel computers. A sequence in the present sense can be regarded abstractly as a vector, set, bag, queue, or other construct. Heretofore, in programming a parallel computer, it has been necessary for the programmer to state explicitly, at the outset, what parts of the program and the underlying data structures must be represented in parallel form. Not only is this requirement not optimal from the perspective of implementation; it entails an additional requirement that the programmer have intimate understanding of the underlying parallel structure. The present sequence data type overcomes both the implementation and parallel structure obstacles. In so doing, the sequence data type provides unified means by which the programmer can represent a data structure for natural and automatic decomposition to a parallel computing architecture. Sequences exhibit the behavioral and structural characteristics of vectors, but the underlying representations are automatically synthesized from combinations of programmers advice and execution use metrics. Sequences can vary bidirectionally between sparseness and density, making them excellent choices for many kinds of algorithms. The novelty and benefit of this behavior lies in the fact that it can relieve programmers of the details of implementations. The creation of a sequence enables decoupling of a conceptual representation from an implementation. The underlying representation of a sequence is a hybrid of representations composed of vectors, linked lists, connected blocks, and hash tables. The internal structure of a sequence can automatically change from time to time on the basis of how it is being used. Those portions of a sequence where elements have not been added or removed can be as efficient as vectors. As elements are inserted and removed in a given portion, then different methods are utilized to provide both an access and memory strategy that is optimized for that portion and the use to which it is put.

James, Mark↗

DOE OSTI2024

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.

Data-driven constitutive models↗

DOE OSTI2021

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.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1993

Vision based obstacle detection and grouping for helicopter guidance

Electro-optical sensors can be used to compute range to objects in the flight path of a helicopter. The computation is based on the optical flow/motion at different points in the image. The motion algorithms provide a sparse set of ranges to discrete features in the image sequence as a function of azimuth and elevation. For obstacle avoidance guidance and display purposes, these discrete set of ranges, varying from a few hundreds to several thousands, need to be grouped into sets which correspond to objects in the real world. This paper presents a new method for object segmentation based on clustering the sparse range information provided by motion algorithms together with the spatial relation provided by the static image. The range values are initially grouped into clusters based on depth. Subsequently, the clusters are modified by using the K-means algorithm in the inertial horizontal plane and the minimum spanning tree algorithms in the image plane. The object grouping allows interpolation within a group and enables the creation of dense range maps. Researchers in robotics have used densely scanned sequence of laser range images to build three-dimensional representation of the outside world. Thus, modeling techniques developed for dense range images can be extended to sparse range images. The paper presents object segmentation results for a sequence of flight images.

Sridhar, Banavar↗

NASA NTRS1991

Total recall in distributive associative memories

Iterative error correction of asymptotically large associative memories is equivalent to a one-step learning rule. This rule is the inverse of the activation function of the memory. Spectral representations of nonlinear activation functions are used to obtain the inverse in closed form for Sparse Distributed Memory, Selected-Coordinate Design, and Radial Basis Functions.

Danforth, Douglas G.↗

DOE OSTI2019

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.

42 ENGINEERING↗

DOE OSTI2026

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.

Automation↗

NASA NTRS2019

Electromagnetic Scattering by Discrete Random Media. III: The Vector Radiative Transfer Equation

A vector radiative transfer equation with an additional source term typical of dense media is obtained. The analysis includes (i) the derivation of an integral equation for the correlation matrix of the exciting field coefficients accounting for the correlation between the particles, (ii) the derivation of an integral representation for the specific coherency dyadicin terms of this matrix, and (iii) the simplification of the integral equation for the correlation matrix and of the integral representation for the specific coherency dyadic by employing a series of approximations which are characteristic of sparse media.

Adrian Doicu↗