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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Entanglement Renormalization for Quantum Field Theories with Discrete Wavelet Transforms

We propose an adaptation of Entanglement Renormalization for quantum field theories that, through the use of discrete wavelet transforms, strongly parallels the tensor network architecture of the Multiscale Entanglement Renormalization Ansatz (a.k.a. MERA). Our approach, called wMERA, has several advantages of over previous attempts to adapt MERA to continuum systems. In particular, (i) wMERA is formulated directly in position space, hence preserving the quasi-locality and sparsity of entanglers; and (ii) it enables a built-in RG flow in the implementation of real-time evolution and in computations of correlation functions, which is key for efficient numerical implementations. As examples, we describe in detail two concrete implementations of our wMERA algorithm for free scalar and fermionic theories in (1+1) spacetime dimensions. Possible avenues for constructing wMERAs for interacting field theories are also discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

Confinement effects of solvation on a molecule physisorbed on a polarizable continuum particle

We investigate the effects of solvation on the static properties of a molecule physisorbed on a spherical polarizable continuum particle, with a static dielectric constant. The effective polarizability of the physisorbed molecule is enhanced by a factor of 105 in vacuo and by only 102 when solvated. The electrostatic interaction between molecules and the polarizable continuum particle (PCP) results in a magnified reflected electric field with a magnitude that depends on the PCP-molecule separation. A similar and greater magnification effect in reflected field also results from the PCP-field (external electric field) interaction. The variation of the polarizability of the molecules with respect to the changes in their environment illustrates the importance of electrostatic interaction in the enhancement of the effective polarizability. In the course of the investigation, the solute and the continuous body are represented with the same adaptive multi-wavelet basis functions, thereby, within the user specified precision, eliminating basis set error.

Chemistry↗
DOE OSTI2012

Wavelet Approach for Operational Gamma Spectral Peak Detection - Preliminary Assessment

Gamma spectroscopy for radionuclide identifications typically involves locating spectral peaks and matching the spectral peaks with known nuclides in the knowledge base or database. Wavelet analysis, due to its ability for fitting localized features, offers the potential for automatic detection of spectral peaks. Past studies of wavelet technologies for gamma spectra analysis essentially focused on direct fitting of raw gamma spectra. Although most of those studies demonstrated the potentials of peak detection using wavelets, they often failed to produce new benefits to operational adaptations for radiological surveys. This work presents a different approach with the operational objective being to detect only the nuclides that do not exist in the environment (anomalous nuclides). With this operational objective, the raw-count spectrum collected by a detector is first converted to a count-rate spectrum and is then followed by background subtraction prior to wavelet analysis. The experimental results suggest that this preprocess is independent of detector type and background radiation, and is capable of improving the peak detection rates using wavelets. This process broadens the doors for a practical adaptation of wavelet technologies for gamma spectral surveying devices.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2023

Deep neural operators can predict the real-time response of floating offshore structures under irregular waves

The use of neural operators in a digital twin model of an offshore floating structure holds the potential for a significant shift in the prediction of structural responses and health monitoring, offering valuable real-time control insights. In this work, we investigate the effectiveness of three neural operators, namely the deep operator network (DeepONet), the Fourier neural operator (FNO), and the Wavelet neural operator (WNO), to accurately capture the responses of a floating structure under six different sea state codes (3 − 8) based on the wave characteristics described by the World Meteorological Organization (WMO). To further enhance the accuracy of the vanilla architecture of the neural operators, novel extensions, such as wavelet-DeepONet and self-adaptive WNO, are proposed in this paper. The results demonstrate that these high-precision neural operators can deliver structural responses more efficiently, up to two orders of magnitude faster than a dynamic analysis using conventional numerical solvers. Additionally, compared to gated recurrent units (GRUs), a commonly used recurrent neural network for time-series estimation, neural operators are both more accurate and efficient, especially in situations with limited data availability. Taken together, our study shows that FNO outperforms all other operators for approximating the mapping of one input functional space to the output space as well as for responses that have small bandwidth of the frequency spectrum. Conversely, DeepONet, with historical states, proves most accurate in learning the mapping of multiple input functions to the output space and capturing responses within a broad frequency spectrum.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Exploring metastable states in UO 2 using hybrid functionals and dynamical mean field theory

A detailed exploration of the f-atomic orbital occupancy space for UO2 is performed using a first principles approach based on density functional theory (DFT), employing a full hybrid functional within a systematic basis set. Specifically, the PBE0 functional is combined with an occupancy biasing scheme implemented in a wavelet-based algorithm which is adapted to large supercells. The results are compared with previous DFT + U calculations reported in the literature, while dynamical mean field theory is also performed to provide a further base for comparison. This work shows that the computational complexity of the energy landscape of a correlated f-electron oxide is much richer than has previously been demonstrated. The resulting calculations provide evidence of the existence of multiple previously unexplored metastable electronic states of UO 2 , including those with energies which are lower than previously reported ground states.

36 MATERIALS SCIENCE↗
DOE OSTI2016

SU-F-J-27: Segmentation of Prostate CBCT Images with Implanted Calypso Transponders Using Double Haar Wavelet Transform

Purpose: Segmentation of prostate CBCT images is an essential step towards real-time adaptive radiotherapy. It is challenging For Calypso patients, as more artifacts are generated by the beacon transponders. We herein propose a novel wavelet-based segmentation algorithm for rectum, bladder, and prostate of CBCT images with implanted Calypso transponders. Methods: Five hypofractionated prostate patients with daily CBCT were studied. Each patient had 3 Calypso transponder beacons implanted, and the patients were setup and treated with Calypso tracking system. Two sets of CBCT images from each patient were studied. The structures (i.e. rectum, bladder, and prostate) were contoured by a trained expert, and these served as ground truth. For a given CBCT, the moving window-based Double Haar transformation is applied first to obtain the wavelet coefficients. Based on a user defined point in the object of interest, a cluster algorithm based adaptive thresholding is applied to the low frequency components of the wavelet coefficients, and a Lee filter theory based adaptive thresholding is applied to the high frequency components. For the next step, the wavelet reconstruction is applied to the thresholded wavelet coefficients. A binary/segmented image of the object of interest is therefore obtained. DICE, sensitivity, inclusiveness and ΔV were used to evaluate the segmentation result. Results: Considering all patients, the bladder has the DICE, sensitivity, inclusiveness, and ΔV ranges of [0.81–0.95], [0.76–0.99], [0.83–0.94], [0.02–0.21]. For prostate, the ranges are [0.77–0.93], [0.84–0.97], [0.68–0.92], [0.1–0.46]. For rectum, the ranges are [0.72–0.93], [0.57–0.99], [0.73–0.98], [0.03–0.42]. Conclusion: The proposed algorithm appeared effective segmenting prostate CBCT images with the present of the Calypso artifacts. However, it is not robust in two scenarios: 1) rectum with significant amount of gas; 2) prostate with very low contrast. Model based algorithm might improve the segmentation in these two scenarios.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Efficient Generalized Boundary Detection Using a Sliding Information Distance

In this work, we present a general machine learning algorithm for boundary detection within general signals based on an efficient, accurate, and robust approximation of the universal normalized information distance. Our approach uses an adaptive sliding information distance (SLID) combined with a wavelet-based approach for peak identification to locate the boundaries. Special emphasis is placed on developing an adaptive formulation of SLID to handle general signals with multiple unknown and/or drifting section lengths. Although specialized algorithms may outperform SLID when domain knowledge is available, these algorithms are limited to specific applications and do not generalize. SLID excels in these cases. We demonstrate the versatility and efficacy of SLID on a variety of signal types, including synthetically generated sequences of tokens, binary executables for reverse engineering applications, and time series of seismic events.

42 ENGINEERING↗
DOE OSTI2012

Final Technical Report Recovery Act: Online Nonintrusive Condition Monitoring and Fault Detection for Wind Turbines

The penetration of wind power has increased greatly over the last decade in the United States and across the world. The U.S. wind power industry installed 1,118 MW of new capacity in the first quarter of 2011 alone and entered the second quarter with another 5,600 MW under construction. By 2030, wind energy is expected to provide 20% of the U.S. electricity needs. As the number of wind turbines continues to grow, the need for effective condition monitoring and fault detection (CMFD) systems becomes increasingly important [3]. Online CMFD is an effective means of not only improving the reliability, capacity factor, and lifetime, but it also reduces the downtime, energy loss, and operation and maintenance (O&M) of wind turbines. The goal of this project is to develop novel online nonintrusive CMFD technologies for wind turbines. The proposed technologies use only the current measurements that have been used by the control and protection system of a wind turbine generator (WTG); no additional sensors or data acquisition devices are needed. Current signals are reliable and easily accessible from the ground without intruding on the wind turbine generators (WTGs) that are situated on high towers and installed in remote areas. Therefore, current-based CMFD techniques have great economic benefits and the potential to be adopted by the wind energy industry. Specifically, the following objectives and results have been achieved in this project: (1) Analyzed the effects of faults in a WTG on the generator currents of the WTG operating at variable rotating speed conditions from the perspective of amplitude and frequency modulations of the current measurements; (2) Developed effective amplitude and frequency demodulation methods for appropriate signal conditioning of the current measurements to improve the accuracy and reliability of wind turbine CMFD; (3) Developed a 1P-invariant power spectrum density (PSD) method for effective signature extraction of wind turbine faults with characteristic frequencies in the current or current demodulated signals, where 1P stands for the shaft rotating frequency of a WTG; (4) Developed a wavelet filter for effective signature extraction of wind turbine faults without characteristic frequencies in the current or current demodulated signals; (5) Developed an effective adaptive noise cancellation method as an alternative to the wavelet filter method for signature extraction of wind turbine faults without characteristic frequencies in the current or current demodulated signals; (6) Developed a statistical analysis-based impulse detection method for effective fault signature extraction and evaluation of WTGs based on the 1P-invariant PSD of the current or current demodulated signals; (7) Validated the proposed current-based wind turbine CMFD technologies through extensive computer simulations and experiments for small direct-drive WTGs without gearboxes; and (8) Showed, through extensive experiments for small direct-drive WTGs, that the performance of the proposed current-based wind turbine CMFD technologies is comparable to traditional vibration-based methods. The proposed technologies have been successfully applied for detection of major failures in blades, shafts, bearings, and generators of small direct-drive WTGs. The proposed technologies can be easily integrated into existing wind turbine control, protection, and monitoring systems and can be implemented remotely from the wind turbines being monitored. The proposed technologies provide an alternative to vibration-sensor-based CMFD. This will reduce the cost and hardware complexity of wind turbine CMFD systems. The proposed technologies can also be combined with vibration-sensor-based methods to improve the accuracy and reliability of wind turbine CMFD systems. When there are problems with sensors, the proposed technologies will ensure proper CMFD for the wind turbines, including their sensing systems. In conclusion, the proposed technologies offer an effective means to achieve condition-based smart maintenance for wind turbines and have a great potential to be adopted by the wind energy industry due to their almost no-cost, nonintrusive features. Although only validated for small direct-drive wind turbines without gearboxes, the proposed technologies are also applicable for CMFD of large-size wind turbines with and without gearboxes. However, additional investigations are recommended in order to apply the proposed technologies to those large-size wind turbines.

17 WIND ENERGY↗
DOE OSTI2014

Daubechies wavelets for linear scaling density functional theory

We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10 000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.

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

Lifting MGARD: Construction of (pre)wavelets on the interval using polynomial predictors of arbitrary order

MGARD (MultiGrid Adaptive Reduction of Data) is an algorithm for compressing and refactoring scientific data, based on the theory of multigrid methods. The core algorithm is built around stable multilevel decompositions of conforming piecewise linear $C^0$ finite element spaces, enabling accurate error control in various norms and derived quantities of interest. In this work, we extend this construction to arbitrary order Lagrange finite elements $\mathbb{Q}_p$, $p \geq 0$, and propose a reformulation of the algorithm as a lifting scheme with polynomial predictors of arbitrary order. Additionally, a new formulation using a compactly supported wavelet basis is discussed, and an explicit construction of the proposed wavelet transform for uniform dyadic grids is described.

Reshniak, Viktor [Oak Ridge National Laboratory (O↗
DOE OSTI2015

Fragment approach to constrained density functional theory calculations using Daubechies wavelets

In a recent paper, we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions are optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix of the system can be projected. In this paper, we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e., without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A Novel Fault Diagnosis Approach for Rolling Bearing Based on CWT and Adaptive Sparse Representation

Extraction and enhancement of weak impulse signature is the key of rolling bearing fault prognostics in which case the features are often weak and covered by noise. Tunable Q-factor wavelet transform (TQWT), as an emerging wavelet construction theory developed in a frequency domain explicitly, has the advantages of matching with the specific oscillation behavior of signal components. In this article, an adaptive sparse representation (ASR) method is proposed, which integrates the sparse code shrinkage (SCS) and parameter optimization into TQWT. However, direct application of ASR is difficult to extract fault signatures at the early stage or low-speed operation due to weak fault symptoms and background noise. A novel fault diagnosis strategy based on continuous wavelet transform (CWT) and ASR is investigated. CWT owns significant advantages on multiscale subdivision and weak signal detection. The results of simulated and experimental vibration signal analyses verify the effectiveness of the proposed method in accurately extracting weak impulse features from the noise environment.

Yuan, Xing↗
DOE OSTI2024

Haar-Like Wavelets on Hierarchical Trees

Here, discrete wavelet methods, originally formulated in the setting of regularly sampled signals, can be adapted to data defined on a point cloud if some multiresolution structure is imposed on the cloud. A wide variety of hierarchical clustering algorithms can be used for this purpose, and the multiresolution structure obtained can be encoded by a hierarchical tree of subsets of the cloud. Prior work introduced the use of Haar-like bases defined with respect to such trees for approximation and learning tasks on unstructured data. This paper builds on that work in two directions. First, we present an algorithm for constructing Haar-like bases on general discrete hierarchical trees. Second, with an eye towards data compression, we present thresholding techniques for data defined on a point cloud with error controlled in the $L$ $\infty$ norm and in a Hölder-type norm. In a concluding trio of numerical examples, we apply our methods to compress a point cloud dataset, study the tightness of the $L$ $\infty$ error bound, and use thresholding to identify MNIST classifiers with good generalizability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Automatic detection of small bowel tumors in wireless capsule endoscopy images using ensemble learning

Purpose Wireless Capsule Endoscopy (WCE) is a minimally invasive diagnosis tool for lesion detection in the gastrointestinal tract, reaching places where conventional endoscopy is unable to. However, the significant amount of acquired data leads to difficulties in the diagnosis by the physicians; which can be eased with computer assistance. This paper addresses a method for the automatic detection of tumors in WCE by using a two‐step based procedure: region of interest selection and classification. Methods The first step aims to separate abnormal from normal tissue by using automatic segmentation based on a Gaussian Mixture Model (GMM). A modified version of the Anderson method for convergence acceleration of the expectation–maximization (EM) algorithm is proposed. The proposed features for both segmentation and classification are based on the CIELab color space, as a way of bypassing lightness variations, where the L component is discarded. Tissue variability among subjects, light inhomogeneities and even intensity differences among different devices can be overcome by using simultaneously features from both regions. In the second step, an ensemble system with partition of the training data with a new training scheme is proposed. At this stage, the gating network is trained after the experts have been trained decoupling the joint maximization of both modules. The partition module is also used at the test step, leading the incoming data to the most likely expert allowing incremental adaptation by preserving data diversity. Results This algorithm outperforms others based on texture features selected from Wavelets and Curvelets transforms, classified by a regular support vector machine (SVM) in more than 5%. Conclusions This work shows that simpler features can outperform more elaborate ones if appropriately designed. In the current case, luminance was discarded to cope with saturated tissue, facilitating the color perception. Ensemble systems remain an open research field. In the current case, changes in both topology and training strategy have led to significant performance improvements. A system with this level of performance can be used in current clinical practice.

Vieira, Pedro M.↗
DOE OSTI2013

Diagnosing heterogeneous dynamics in single-molecule/particle trajectories with multiscale wavelets

In this study, we describe a simple automated method to extract and quantify transient heterogeneous dynamical changes from large data sets generated in single-molecule/particle tracking experiments. Based on wavelet transform, the method transforms raw data to locally match dynamics of interest. This is accomplished using statistically adaptive universal thresholding, whose advantage is to avoid a single arbitrary threshold that might conceal individual variability across populations. How to implement this multiscale method is described, focusing on local confined diffusion separated by transient transport periods or hopping events, with three specific examples: in cell biology, biotechnology, and glassy colloid dynamics. The discussion is generalized within the framework of continuous time random walk. This computationally efficient method can run routinely on hundreds of millions of data points analyzed within an hour on a desktop personal computer.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Efficient generalized boundary detection

Fast, efficient, and robust compression-based methods for detecting boundaries in arbitrary datasets, including sequences (1D datasets), are desired. The methods, each employing three simple algorithms, approximate the information distance between two adjacent sliding windows within a dataset. One of the algorithms calculates an initial ordered list of subsequences; while a second algorithm updates the ordered list of subsequences by dropping a first entry and appending a last entry rather than calculating completely new ordered lists with each iteration. Large values in the distance metric are indicative of boundary locations. A smoothed z-score or a wavelet-based algorithm may then be used to locate peaks in the distance metric, thereby identifying boundary locations. An adaptive version of the method employs a collection of window sizes and corresponding weighting functions, making it more amenable to real datasets with unknown, complex, and changing structures.

Ting, Christina↗
DOE OSTI2019

Aperture‐Synthesis Radar Imaging With Compressive Sensing for Ionospheric Research

Abstract Inverse methods involving compressive sensing are tested in the application of two‐dimensional aperture‐synthesis imaging of radar backscatter from field‐aligned plasma density irregularities in the ionosphere. We consider basis pursuit denoising, implemented with the fast iterative shrinkage thresholding algorithm, and orthogonal matching pursuit (OMP) with a wavelet basis in the evaluation. These methods are compared with two more conventional optimization methods rooted in entropy maximization (MaxENT) and adaptive beamforming (linearly constrained minimum variance or often “Capon's Method.”) Synthetic data corresponding to an extended ionospheric radar target are considered. We find that MaxENT outperforms the other methods in terms of its ability to recover imagery of an extended target with broad dynamic range. Fast iterative shrinkage thresholding algorithm performs reasonably well but does not reproduce the full dynamic range of the target. It is also the most computationally expensive of the methods tested. OMP is very fast computationally but prone to a high degree of clutter in this application. We also point out that the formulation of MaxENT used here is very similar to OMP in some respects, the difference being that the former reconstructs the logarithm of the image rather than the image itself from basis vectors extracted from the observation matrix. MaxENT could in that regard be considered a form of compressive sensing.

Hysell, D. L.↗
DOE OSTI2018

Accurate correlation energies in one-dimensional systems from small system-adapted basis functions

We propose a general method for constructing system-dependent basis functions for correlated quantum calculations. Our construction combines features from several traditional approaches: plane waves, localized basis functions, and wavelets. In a one-dimensional mimic of Coulomb systems, it requires only 2–3 basis functions per electron to achieve high accuracy, and reproduces the natural orbitals. We illustrate its effectiveness for molecular energy curves and chains of many one-dimensional atoms. Furthermore, we discuss the promise and challenges for realistic quantum chemical calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗