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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Noise suppression for dual-energy CT via penalized weighted least-square optimization with similarity-based regularization

Purpose: Dual-energy CT (DECT) expands applications of CT imaging in its capability to decompose CT images into material images. However, decomposition via direct matrix inversion leads to large noise amplification and limits quantitative use of DECT. Their group has previously developed a noise suppression algorithm via penalized weighted least-square optimization with edge-preservation regularization (PWLS-EPR). In this paper, the authors improve method performance using the same framework of penalized weighted least-square optimization but with similarity-based regularization (PWLS-SBR), which substantially enhances the quality of decomposed images by retaining a more uniform noise power spectrum (NPS). Methods: The design of PWLS-SBR is based on the fact that averaging pixels of similar materials gives a low-noise image. For each pixel, the authors calculate the similarity to other pixels in its neighborhood by comparing CT values. Using an empirical Gaussian model, the authors assign high/low similarity value to one neighboring pixel if its CT value is close/far to the CT value of the pixel of interest. These similarity values are organized in matrix form, such that multiplication of the similarity matrix to the image vector reduces image noise. The similarity matrices are calculated on both high- and low-energy CT images and averaged. In PWLS-SBR, the authors include a regularization term to minimize the L-2 norm of the difference between the images without and with noise suppression via similarity matrix multiplication. By using all pixel information of the initial CT images rather than just those lying on or near edges, PWLS-SBR is superior to the previously developed PWLS-EPR, as supported by comparison studies on phantoms and a head-and-neck patient. Results: On the line-pair slice of the Catphan{sup ©}600 phantom, PWLS-SBR outperforms PWLS-EPR and retains spatial resolution of 8 lp/cm, comparable to the original CT images, even at 90% reduction in noise standard deviation (STD). Similar performance on spatial resolution is observed on an anthropomorphic head phantom. In addition, results of PWLS-SBR show substantially improved image quality due to preservation of image NPS. On the Catphan{sup ©}600 phantom, NPS using PWLS-SBR has a correlation of 93% with that via direct matrix inversion, while the correlation drops to −52% for PWLS-EPR. Electron density measurement studies indicate high accuracy of PWLS-SBR. On seven different materials, the measured electron densities calculated from the decomposed material images using PWLS-SBR have a root-mean-square error (RMSE) of 1.20%, while the results of PWLS-EPR have a RMSE of 2.21%. In the study on a head-and-neck patient, PWLS-SBR is shown to reduce noise STD by a factor of 3 on material images with image qualities comparable to CT images, whereas fine structures are lost in the PWLS-EPR result. Additionally, PWLS-SBR better preserves low contrast on the tissue image. Conclusions: The authors propose improvements to the regularization term of an optimization framework which performs iterative image-domain decomposition for DECT with noise suppression. The regularization term avoids calculation of image gradient and is based on pixel similarity. The proposed method not only achieves a high decomposition accuracy, but also improves over the previous algorithm on NPS as well as spatial resolution.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

A Regularized Entropy-Based Moment Method for Kinetic Equations

Here, we present a new entropy-based moment method for the velocity discretization of kinetic equations. This method is based on a regularization of the optimization problem defining the original entropy-based moment method, and this gives the new method the advantage that the moment vectors of the solution do not have to take on realizable values. We show that this equation still retains many of the properties of the original equations, including hyperbolicity, an entropy-dissipation law, and rotational invariance. The cost of the regularization is mismatch between the moment vector of the solution and that of the ansatz returned by the regularized optimization problem. However, we show how to control this error using the parameter defining the regularization. This suggests that with proper choice of the regularization parameter, the new method can be used to generate accurate solutions of the original entropy-based moment method, and we confirm this with numerical simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Qubit Regularization of Quantum Field Theories

To study quantum field theories on a quantum computer, we must begin with Hamiltonians defined on a finite-dimensional Hilbert space and then take appropriate limits. This approach can be seen as a new type of regularization for quantum field theories, which we refer to as qubit regularization. A related finite-dimensional regularization, known as the D-theory approach, was proposed long ago as a general framework for all quantum field theories. In this framework, the dimensionality of the local Hilbert space at each spatial point can increase as needed through an additional flavor index. To reproduce asymptotically free QFTs, most studies assume that qubit-regularized theories require extending the local Hilbert space to infinity. However, contrary to this common belief, recent discoveries in (1+1) dimensions have revealed two examples where asymptotic freedom appears to emerge within a strictly finite-dimensional local Hilbert space through a novel renormalization group (RG) flow. These findings motivate further investigation into whether asymptotically free gauge theories could also emerge within a strictly finite-dimensional local Hilbert space. To support these explorations, we propose an orthonormal basis called the monomer-dimer-tensor-network (MDTN) basis and use it to construct new types of qubit-regularized lattice gauge theories.

Chandrasekharan, Shailesh [Duke Univ., Durham, NC ↗
DOE OSTI2016

Do Lower Calorie or Lower Fat Foods Have More Sodium Than Their Regular Counterparts?

The objective of this study was to compare the sodium content of a regular food and its lower calorie/fat counterpart. Four food categories, among the top 20 contributing the most sodium to the US diet, met the criteria of having the most matches between regular foods and their lower calorie/fat counterparts. A protocol was used to search websites to create a list of “matches”, a regular and comparable lower calorie/fat food(s) under each brand. Nutrient information was recorded and analyzed for matches. In total, 283 matches were identified across four food categories: savory snacks (N = 44), cheese (N = 105), salad dressings (N = 90), and soups (N = 44). As expected, foods modified from their regular versions had significantly reduced average fat (total fat and saturated fat) and caloric profiles. Mean sodium content among modified salad dressings and cheeses was on average 8%–12% higher, while sodium content did not change with modification of savory snacks. Modified soups had significantly lower mean sodium content than their regular versions (28%–38%). Consumers trying to maintain a healthy diet should consider that sodium content may vary in foods modified to be lower in calories/fat.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Qubit Regularization and Qubit Embedding Algebras

Qubit regularization is a procedure to regularize the infinite dimensional local Hilbert space of bosonic fields to a finite dimensional one, which is a crucial step when trying to simulate lattice quantum field theories on a quantum computer. When the qubit-regularized lattice quantum fields preserve important symmetries of the original theory, qubit regularization naturally enforces certain algebraic structures on these quantum fields. We introduce the concept of qubit embedding algebras (QEAs) to characterize this algebraic structure associated with a qubit regularization scheme. We show a systematic procedure to derive QEAs for the O(N) lattice spin models and the SU(N) lattice gauge theories. While some of the QEAs we find were discovered earlier in the context of the D-theory approach, our method shows that QEAs are far richer. A more complete understanding of the QEAs could be helpful in recovering the fixed points of the desired quantum field theories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Regularization of soft-X-ray data in a tokamak application

An image inversion scheme for soft X-ray (SXR) diagnostics at the DIII-D tokamak is developed to obtain the local soft X-ray emission at a poloidal cross-section from the spatially line-integrated image taken by either a set of SXR arrays or a tangential camera. The scheme uses the Tikhonov regularization method since the inversion problem is generally ill-posed. The regularization technique uses the generalized singular value decomposition (GSVD) to determine a solution that depends on a free regularization parameter. The latter has to be chosen carefully, and the so called L -curve method to find the optimum regularization parameter is outlined. A representative test image is used to study the properties of the inversion scheme with respect to inversion accuracy, amount/strength of regularization and image resolution. The SXR arrays thereby represent an under-determined case while the tangential camera is an over-determined case of the linear inversion problem. In conclusion, it is found that the under-determined case suffers from lack of information but can still return a coarse, but fair image, while the camera data can be well inverted with high resolution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Effects of input gradient regularization on neural networks time-series forecasting of thermal power systems

This study proposes using neural networks, specifically gated recurrent unit (GRU), long-short-term memory (LSTM), and transformer networks, to improve control strategies in a 450 MW coal-fired power plant. However, neural networks face issues of becoming overly dependent on just a few variables to make predictions, which negatively impacts control decisions that rely on the model to determine the value of all manipulated variables. The paper introduces regularization techniques, including noise injection and input gradient regularization, during the training phase. Here, the work presents novel contributions in adapting neural networks to control industrial systems and applying regularization techniques from computer vision to industrial process control. Results demonstrate the effectiveness of input gradient regularization in reducing model dependence on subsets of variables, emphasizing the balance between fidelity and controllability. Further exploration is recommended, including the development of recurrent transformers, closed-loop control testing, and a sensitivity analysis on computer models to provide further insight.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2025

3D mesh regularization within an ALE code using a weighted line sweeping method

The Lagrangian formalism is widely used to simulate hydrodynamic responses in complex engineering applications, particularly those involving strong shock waves. However, as the mesh moves with the fluid, it can become highly distorted, requiring a regularization step. This involves constructing a new grid and remapping conservative quantities onto it to restore mesh quality. This work introduces a regularization method for block-structured meshes within a 3D ALE (Arbitrary Lagrangian-Eulerian) code. The proposed approach prevents mesh tangling while preserving the anisotropic features of the initial Lagrangian mesh. This regularization technique incorporates aspect ratio-based weights to control mesh smoothing. Unlike uniform rezoning techniques, this weighted approach maintains proximity to the Lagrangian mesh while improving mesh quality. Here, the method effectively handles concave geometries by mitigating the grid attraction phenomenon, which typically leads to mesh concentration along concave edges. Numerical experiments demonstrate its efficiency in regularizing severely deformed meshes, and its integration within the ALE framework is validated on challenging hydrodynamic test cases, including the triple point problem.

42 ENGINEERING↗
DOE OSTI2021

Relaxed Multibang Regularization for the Combinatorial Integral Approximation

Multibang regularization and combinatorial integral approximation decompositions are two actively researched techniques for integer optimal control. In this work, we consider a class of polyhedral functions that arise particularly as convex lower envelopes of multibang regularizers and show that they have beneficial properties with respect to regularization of relaxations of integer optimal control problems. We extend the algorithmic framework of the combinatorial integral approximation such that a subsequence of the computed discrete-valued controls converges to the infimum of the regularized integer control problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Discrete Regularization for Calibration of Geologic Facies Against Dynamic Flow Data

Abstract Subsurface flow model calibration involves many more unknowns than measurements, leading to ill‐posed problems with nonunique solutions. To alleviate nonuniqueness, the problem is regularized by constraining the solution space using prior knowledge. In certain sedimentary environments, such as fluvial systems, the contrast in hydraulic properties of different facies types tends to dominate the flow and transport behavior, making the effect of within facies heterogeneity less significant. Hence, flow model calibration in those formations reduces to delineating the spatial structure and connectivity of different lithofacies types and their boundaries. A major difficulty in calibrating such models is honoring the discrete, or piecewise constant, nature of facies distribution. The problem becomes more challenging when complex spatial connectivity patterns with higher‐order statistics are involved. This paper introduces a novel formulation for calibration of complex geologic facies by imposing appropriate constraints to recover plausible solutions that honor the spatial connectivity and discreteness of facies models. To incorporate prior connectivity patterns, plausible geologic features are learned from available training models. This is achieved by learning spatial patterns from training data, e.g., ‐SVD sparse learning or the traditional Principal Component Analysis. Discrete regularization is introduced as a penalty functions to impose solution discreteness while minimizing the mismatch between observed and predicted data. An efficient gradient‐based alternating directions algorithm is combined with variable splitting to minimize the resulting regularized nonlinear least squares objective function. Numerical results show that imposing learned facies connectivity and discreteness as regularization functions leads to geologically consistent solutions that improve facies calibration quality.

Khaninezhad, Mohammad‐Reza↗
DOE OSTI2018

Spatially dependent regularization parameter selection for total generalized variation-based image denoising

We propose a novel image denoising model based on the total generalized variation (TGV) regularization. In the model, a spatially dependent regularization parameter is utilized to adaptively fit the local image features, resulting in further exploitation of the denoising potential of the TGV regularization. The proposed model is formulated under a joint optimization framework, by which the estimations of the restored image and the regularization parameter are achieved simultaneously. Furthermore, the model is general purpose that can handle various types of noise occurring in image processing. An alternating minimization-based numerical scheme is especially developed, which leads to an efficient algorithmic solution to the nonconvex optimization problem. Numerical experiments are reported to illustrate the effectiveness of our model in terms of both peak signal-to-noise ratio and visual perception.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

The parameter choice rules for weighted Tikhonov regularization scheme

The well-known approach to solve the ill-posed problem is Tikhonov regularization scheme. But, the approximate solution of Tikhonov scheme may not contain all the details of the exact solution. To circumference this problem, weighted Tikhonov regularization has been introduced. In this article, we propose two a posteriori parameter choice rules to choose the regularization parameter for weighted Tikhonov regularization and establish the optimal rate of convergence O(δ{sup ((α+1)/(α+2))}) for the scheme based on these proposed rules. The numerical results are documented to demonstrate the significance of the theoretical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Deconvolving distribution of relaxation times, resistances and inductance from electrochemical impedance spectroscopy via statistical model selection: Exploiting structural-sparsity regularization and data-driven parameter tuning

The distribution of relaxation times (DRT) has drawn increasing attention for interpreting electrochemical impedance spectroscopy (EIS). Deconvolution of DRT from EIS is a challenging ill-posed problem that requires regularization methods. In this work, we formulate DRT reconstruction task as a statistical model selection problem with structural-sparsity penalties. We utilize the Elastic net regularization that simultaneously benefits from Ridge and Lasso regularizations with optimal tuning parameter automatically determined by the information criteria. We benchmark our approach on four synthetic experiments (a ZARC element, ZARC mixtures, a RC circuit and a Fractal element) and two real EIS datasets of a Lithium ion battery and an organic-inorganic halide class of perovskites in oxygen environment at different gas pressures. We demonstrate the superiority of proposed model selection procedure, that is capable of eliminating pseudo peaks and representing asymmetries in DRT as well as precisely estimating resistances. Here, we highlight our approach is robust to reducing and subsampling EIS frequency range, making it a promising tool for timing-resolved, localized and large scale EIS data analysis. For the Lithium ion battery data analysis, we extend the classical DRT model to incorporate the inductive effect and illustrate DRT as a guidance for equivalent circuit modeling to refine impedance reconstruction at low risks of overfitting. Furthermore, the structural-sparsity regularization could be extended for multidimensional and Bayesian EIS data analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

A comparative study of structural similarity and regularization for joint inverse problems governed by PDEs

Joint inversion refers to the simultaneous inference of multiple parameter fields from observations of systems governed by single or multiple forward models. In many cases these parameter fields reflect different attributes of a single medium and are thus spatially correlated or structurally similar. By imposing prior information on their spatial correlations via a joint regularization term, we seek to improve the reconstruction of the parameter fields relative to inversion for each field independently. One of the main challenges is to devise a joint regularization functional that conveys the spatial correlations or structural similarity between the fields while at the same time permitting scalable and efficient solvers for the joint inverse problem. We describe several joint regularizations that are motivated by these goals: a cross-gradient and a normalized cross-gradient structural similarity term, the vectorial total variation, and a joint regularization based on the nuclear norm of the gradients. Based on numerical results from three classes of inverse problems with piecewise-homogeneous parameter fields, we conclude that the vectorial total variation functional is preferable to the other methods considered. Besides resulting in good reconstructions in all experiments, it allows for scalable, efficient solvers for joint inverse problems governed by PDE forward models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

On the regularity of the covariance matrix of a discretized scalar field on the sphere

We present a comprehensive study of the regularity of the covariance matrix of a discretized field on the sphere. In a particular situation, the rank of the matrix depends on the number of pixels, the number of spherical harmonics, the symmetries of the pixelization scheme and the presence of a mask. Taking into account the above mentioned components, we provide analytical expressions that constrain the rank of the matrix. They are obtained by expanding the determinant of the covariance matrix as a sum of determinants of matrices made up of spherical harmonics. We investigate these constraints for five different pixelizations that have been used in the context of Cosmic Microwave Background (CMB) data analysis: Cube, Icosahedron, Igloo, GLESP and HEALPix, finding that, at least in the considered cases, the HEALPix pixelization tends to provide a covariance matrix with a rank closer to the maximum expected theoretical value than the other pixelizations. The effect of the propagation of numerical errors in the regularity of the covariance matrix is also studied for different computational precisions, as well as the effect of adding a certain level of noise in order to regularize the matrix. In addition, we investigate the application of the previous results to a particular example that requires the inversion of the covariance matrix: the estimation of the CMB temperature power spectrum through the Quadratic Maximum Likelihood algorithm. Finally, some general considerations in order to achieve a regular covariance matrix are also presented.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Fixed-angle conjectures for the quantum approximate optimization algorithm on regular MaxCut graphs

The quantum approximate optimization algorithm (QAOA) is a near-term combinatorial optimization algorithm suitable for noisy quantum devices. However, little is known about performance guarantees for p > 2. A recent work computing MaxCut performance guarantees for 3-regular graphs conjectures that any d-regular graph evaluated at particular fixed angles has an approximation ratio greater than some worst-case guarantee. In this work, we provide numerical evidence for this fixed angle conjecture for p < 12. We compute and provide these angles via numerical optimization and tensor networks. These fixed angles serve for an optimization-free version of QAOA and have universally good performance on any 3-regular graph. Heuristic evidence is presented for the fixed angle conjecture on graph ensembles, which suggests that these fixed angles are "close" to global optimum. Under the fixed angle conjecture, QAOA has a larger performance guarantee than the Goemans Williamson algorithm on 3-regular graphs for p >= 11.

Wurtz, Jonathan↗
DOE OSTI2022

An ℓ 0 ℓ 2 -norm regularized regression model for construction of robust cluster expansions in multicomponent systems

In this work we introduce ℓ 0 ℓ 2 -norm regularization and hierarchy constraints into linear regression for the construction of cluster expansions to describe configurational disorder in materials. The approach is implemented through mixed integer quadratic programming (MIQP). The ℓ 2 -norm regularization is used to suppress intrinsic data noise, while the ℓ 0 -norm is used to penalize the number of nonzero elements in the solution. The hierarchy relation between clusters imposes relevant physics and is naturally included by the MIQP paradigm. As such, sparseness and cluster hierarchy can be well optimized to obtain a robust, converged set of effective cluster interactions with improved physical meaning. We demonstrate the effectiveness of ℓ 0 ℓ 2 -norm regularization in two high-component disordered rocksalt cathode material systems, where we compare the cross-validation, convergence speed, and the reproduction of phase diagrams, voltage profiles, and Li-occupancy energies with those of the conventional ℓ 1 -norm regularized cluster expansion models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Convolutional Dictionary Regularizers for Tomographic Inversion

There has been a growing interest in the use of data-driven regularizers to solve inverse problems associated with computational imaging systems. The convolutional sparse representation model has recently gained attention, driven by the development of fast algorithms for solving the dictionary learning and sparse coding problems for sufficiently large images and data sets. Nevertheless, this model has seen very limited application to tomographic reconstruction problems. In this paper, we present a model-based tomographic reconstruction algorithm using a learnt convolutional dictionary as a regularizer. The key contribution is the use of a data-dependent weighting scheme for the l 1 regularization to construct an effective denoising method that is integrated into the inversion using the Plug-and-Play reconstruction framework. Using simulated data sets we demonstrate that our approach can improve performance over traditional regularizers based on a Markov random field model and a patch-based sparse representation model for sparse and limited-view tomographic data sets.

Singanallur Vaidyanathan, Venkatakrishnan↗