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Results for “Subspace Matching”

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.

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9 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Exact solution of the frustrated Potts model with next-nearest-neighbor interactions in one dimension via AI bootstrapping

The one-dimensional (1D) 𝐽 1 −𝐽 2 𝑞-state Potts model is solved exactly for arbitrary 𝑞 by analytically block-diagonalizing the original 𝑞 2 ×𝑞 2 transfer matrix into a simple 2 × 2 maximally symmetric subspace, based on using OpenAI's reasoning model o3-mini-high to exactly solve the 𝑞 = 3 case. Furthermore, by matching relevant subspaces, we map the Potts model onto a simpler effective 1D 𝑞-state Potts model, where 𝐽 2 acts as the nearest-neighbor interaction and 𝐽 1 as an effective magnetic field, nontrivially generalizing a 56-year-old theorem previously limited to the simplest case (𝑞 = 2, the Ising model). Our exact results provide insights to phenomena such as atomic or electronic order stacking in layered materials and the emergence of dome-shaped phases in complex phase diagrams. In conclusion, this work is anticipated to fuel both research in 1D frustrated magnets for recently discovered finite-temperature application potentials and the fast moving topic area of AI in science.

1-dimensional spin chains↗
DOE OSTI2025

Subspace-Driven Learning for Anomaly Detection in Process Transients

Nuclear power plant (NPP) monitoring and diagnostic centers are actively investigating and implementing automated anomaly detection algorithms to help plants catch anomalies sooner, thereby preventing or reducing the duration of unexpected shutdowns. Current machine learning-based anomaly detection methods are expected to be highly effective during stable, full-power operations because NPPs typically operate as baseload power generators, meaning there are extensive operating data available from plant equipment. However, it is expected that anomaly detection methods will face significant challenges during transient conditions (i.e., when power output falls below full power) because plants only occasionally operate at these lower power levels, generating sparse transient operational data, and resulting in false alarms or missed detections. Here, to address this issue, transfer learning is used, which for this problem leverages knowledge (in the form of learned features) from stable, full-power operations to improve detection accuracy during transient conditions, even with limited data. In this effort, a novel subspace approach is developed to transfer a subset of the data features from full power operation to transients. This approach is validated through experiments using synthetic data and was found to outperform two baseline transfer learning approaches in anomaly detection performance across a range of amounts of transient data used in the training process.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗
NASA NTRS1989

Model reduction and control of flexible structures using Krylov subspaces

Krylov vectors and the concept of parameter-matching are combined to develop a model reduction algorithm for a damped structural dynamics system. The reduced-order model obtained matches a certain number of low-frequency moments of the full-order system. The major application of the present method is to the control of flexible structures. It is shown that, in the control of flexible structures, there generally exist three types of control energy spillover, namely, the control spillover, the observation spillover, and dynamic spillover. The formulation based on Krylov subspaces can eliminate the control and the observation spillover, while leaving only the dynamic spillover to be considered. Two examples are used to illustrate the efficacy of the Krylov method.

Craig, Roy R., Jr.↗
NASA NTRS2011

Visual Object Recognition and Tracking of Tools

A method has been created to automatically build an algorithm off-line, using computer-aided design (CAD) models, and to apply this at runtime. The object type is discriminated, and the position and orientation are identified. This system can work with a single image and can provide improved performance using multiple images provided from videos. The spatial processing unit uses three stages: (1) segmentation; (2) initial type, pose, and geometry (ITPG) estimation; and (3) refined type, pose, and geometry (RTPG) calculation. The image segmentation module files all the tools in an image and isolates them from the background. For this, the system uses edge-detection and thresholding to find the pixels that are part of a tool. After the pixels are identified, nearby pixels are grouped into blobs. These blobs represent the potential tools in the image and are the product of the segmentation algorithm. The second module uses matched filtering (or template matching). This approach is used for condensing synthetic images using an image subspace that captures key information. Three degrees of orientation, three degrees of position, and any number of degrees of freedom in geometry change are included. To do this, a template-matching framework is applied. This framework uses an off-line system for calculating template images, measurement images, and the measurements of the template images. These results are used online to match segmented tools against the templates. The final module is the RTPG processor. Its role is to find the exact states of the tools given initial conditions provided by the ITPG module. The requirement that the initial conditions exist allows this module to make use of a local search (whereas the ITPG module had global scope). To perform the local search, 3D model matching is used, where a synthetic image of the object is created and compared to the sensed data. The availability of low-cost PC graphics hardware allows rapid creation of synthetic images. In this approach, a function of orientation, distance, and articulation is defined as a metric on the difference between the captured image and a synthetic image with an object in the given orientation, distance, and articulation. The synthetic image is created using a model that is looked up in an object-model database. A composable software architecture is used for implementation. Video is first preprocessed to remove sensor anomalies (like dead pixels), and then is processed sequentially by a prioritized list of tracker-identifiers.

English, James↗
NASA NTRS2017

Subspace-based Background Subtraction Applied to Aeroacoustic Wind Tunnel Testing

A subspace-based form of background subtraction is presented and applied to aeroacoustic wind tunnel data. A variant of this method has seen use in other fields such as climatology and medical imaging. The technique is based on an eigenvalue decomposition of the background noise cross-spectral matrix. Simulated results indicate similar performance to conventional background subtraction when the subtracted spectra are weaker than the true contaminating background levels. Superior performance is observed when the subtracted spectra are stronger than the true contaminating background levels, and when background data do not match between measurements. Experimental results show limited success in recovering signal behavior for data in which conventional background subtraction fails. The results also demonstrate the subspace subtraction technique's ability to maintain a physical coherence relationship in the modified cross-spectral matrix. Deconvolution results from microphone phased array data indicate that array integration methods are largely insensitive to subtraction type, and that background subtraction with appropriate background data is an effective alternative to diagonal removal.

deconvolution↗
DOE OSTI2025

Datasets for Custom-trained Machine-learning Interatomic Potentials: Nitric Acid Aqueous Solution

This dataset was generated using an iterative active learning strategy with the ArcaNN software package (https://github.com/arcann-chem/arcann_training) to train machine-learning interatomic potentials (MLIPs) for aqueous nitric acid. Each active-learning cycle consisted of three stages: (1) training, (2) exploration, and (3) labeling. The initial training set comprised approximately 800 randomly selected configurations from a previous study by Lewis et al. (https://doi.org/10.1021/jp205510q), which investigated nitric acid solutions at 2, 3, 4, and 5 mol/L. For all configurations, single-point calculations of atomic forces and total energies were performed at the quantum density functional theory BLYP-D2 and PBE-D3 levels of theory using the CP2K Quickstep module. Valence electrons were treated explicitly, while core electrons on all atoms were represented by norm-conserving Goedecker–Teter–Hutter (GTH) pseudopotentials. Long-range dispersion interactions were accounted for using Grimme dispersion corrections. Wave functions were expanded in a mixed Gaussian-and-plane-wave scheme using TZV2P-MOLOPT basis sets for all elements and an 800 Ry auxiliary plane-wave cutoff for the electron density. Self-consistent field convergence was accelerated using orbital transformation and Direct Inversion in the Iterative Subspace, with a convergence threshold of 10^{-6}. All single-point calculations were carried out in periodic orthorhombic cells whose dimensions match those of the molecular configurations sampled from earlier trajectories. The CELL_REF keyword in CP2K was used to define a fixed reference cell, ensuring consistency in the reference data used for MLIP training, particularly when cell fluctuations are present in NpT simulations. The resulting high-fidelity energies and forces constitute the ground-truth labels used to train the MLIPs contained in this dataset.

Dinpajooh, Mohammadhasan [Pacific Northwest Nation↗
NASA NTRS1993

Binary tree eigen solver in finite element analysis

This paper presents a transputer-based binary tree eigensolver for the solution of the generalized eigenproblem in linear elastic finite element analysis. The algorithm is based on the method of recursive doubling, which parallel implementation of a number of associative operations on an arbitrary set having N elements is of the order of o(log2N), compared to (N-1) steps if implemented sequentially. The hardware used in the implementation of the binary tree consists of 32 transputers. The algorithm is written in OCCAM which is a high-level language developed with the transputers to address parallel programming constructs and to provide the communications between processors. The algorithm can be replicated to match the size of the binary tree transputer network. Parallel and sequential finite element analysis programs have been developed to solve for the set of the least-order eigenpairs using the modified subspace method. The speed-up obtained for a typical analysis problem indicates close agreement with the theoretical prediction given by the method of recursive doubling.

Akl, F. A.↗
NASA NTRS1989

Controller reduction by preserving impulse response energy

A model order reduction algorithm based on a Krylov recurrence formulation is developed to reduce order of controllers. The reduced-order controller is obtained by projecting the full-order LQG controller onto a Krylov subspace in which either the controllability or the observability grammian is equal to the identity matrix. The reduced-order controller preserves the impulse response energy of the full-order controller and has a parameter-matching property. Two numerical examples drawn from other controller reduction literature are used to illustrate the efficacy of the proposed reduction algorithm.

Craig, Roy R., Jr.↗
NASA NTRS2017

Color Algebras

A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. We would like it to match the well-defined algebra of spectral functions describing lights and surface reflectances, but an exact correspondence is impossible after the spectra have been projected to a three-dimensional color space, because of metamerism physically different spectra can produce the same color sensation. Metameric spectra are interchangeable for the purposes of addition, but not multiplication, so any color algebra is necessarily an approximation to physical reality. Nevertheless, because the majority of naturally-occurring spectra are well-behaved (e.g., continuous and slowly-varying), color algebras can be formulated that are largely accurate and agree well with human intuition. Here we explore the family of algebras that result from associating each color with a member of a three-dimensional manifold of spectra. This association can be used to construct a color product, defined as the color of the spectrum of the wavelength-wise product of the spectra associated with the two input colors. The choice of the spectral manifold determines the behavior of the resulting system, and certain special subspaces allow computational efficiencies. The resulting systems can be used to improve computer graphic rendering techniques, and to model various perceptual phenomena such as color constancy.

color constancy↗