Non-negative Least Squares Research Articles

Quantitative myelin water assessment for multiple sclerosis using multi-inversion magnetic resonance fingerprinting.

Multiple sclerosis (MS) is a demyelination disease. Myelin water is a biomarker of myelin and thus myelin water imaging is a vital tool to provide insight into the demyelination process. This study aimed to characterize the multiple compartments including myelin water fraction (MWF), gray matter (GM) cellular water, white matter (WM) cellular water, and cerebrospinal fluid (CSF) using multiple inversion recovery (mIR) magnetic resonance fingerprinting (MRF) on a clinical MS cohort. The Phantom experiment was conducted with tubes containing different WM and GM concentrations extracted from pig brains. For the in-vivo experiment, 23 healthy control (HC) volunteers and 18 MS patients were recruited for this study. The experiments were performed using a clinical 3T MRI. A multi-slice, fast imaging with a steady-state precession (FISP) based mIR MRF protocol was used to obtain the MWF measurements, with 6min of scan time for each volunteer. The quantification was based on the iterative non-negative least squares (NNLS) with reweighting. The brain compartments quantified were myelin water, WM cellular water, GM cellular water, and CSF. A radiologist with 6 years of experience labeled the MS lesions on FLAIR, MPRAGE, and MWF. Statistical analysis was performed by applying unpaired and paired student's t-tests to compare the MWF results in different groups and in normal-appearing white matter (NAWM) and MS lesions. The phantom result demonstrated the ability to detect MWF with various myelin concentrations. The maps derived from mIR MRF, including MWF, WM cellular water, GM cellular water, and CSF were consistent with the anatomical structures observed in FLAIR and MPRAGE. The MWF values in the NAWM of MS patients were significantly different from those in HC, with values of 0.32±0.025 and 0.25±0.036, respectively. Additionally, the MWF values in WM lesions were significantly smaller than in NAWM at 0.034±0.036. The mIR-MRF technique, using multi-compartment analysis, can simultaneously generate maps of MWF, WM cellular water, GM cellular water, and CSF with sufficient brain coverage and in a reasonably short scan time. The MWF map might provide insights into the demyelination associated with MS.

The evolution of flexibility and function in the Fc domains of IgM, IgY, and IgE.

Antibody Fc regions harbour the binding sites for receptors that mediate effector functions following antigen engagement by the Fab regions. An extended "hinge" region in IgG allows flexibility between Fab and Fc, but in both the most primitive antibody, IgM, and in the evolutionarily more recent IgE, the hinge is replaced by an additional domain pair in the homodimeric six-domain Fc region. This permits additional flexibility within the Fc region, which has been exploited by nature to modulate antibody effector functions. Thus, in pentameric or hexameric IgM, the Fc regions appear to adopt a planar conformation in solution until antigen binding causes a conformational change and exposes the complement binding sites. In contrast, IgE-Fc principally adopts an acutely bent conformation in solution, but the binding of different receptors is controlled by the degree of bending, and there is allosteric communication between receptor binding sites. We sought to trace the evolution of Fc conformational diversity from IgM to IgE via the intermediate avian IgY by studying the solution conformations of their Fc regions by small-angle X-ray scattering. We compared four extant proteins: human IgM-Fc homodimer, chicken IgY-Fc, platypus IgE-Fc, and human IgE-Fc. These are examples of proteins that first appeared in the jawed fish [425 million years ago (mya)], tetrapod (310 mya), monotreme (166 mya), and hominid (2.5 mya) clades, respectively. We analysed the scattering curves in terms of contributions from a pool of variously bent models chosen by a non-negative linear least-squares algorithm and found that the four proteins form a series in which the proportion of acutely bent material increases: IgM-Fc < IgY-Fc < plIgE-Fc < huIgE-Fc. This follows their order of appearance in evolution. For the huIgM-Fc homodimer, although none are acutely bent, and a significant fraction of the protein is sufficiently bent to expose the C1q-binding site, it predominantly adopts a fully extended conformation. In contrast, huIgE-Fc is found principally to be acutely bent, as expected from earlier studies. IgY-Fc, in this first structural analysis of the complete Fc region, exhibits an ensemble of conformations from acutely bent to fully extended, reflecting IgY's position as an evolutionary intermediate between IgM and IgE.

Non-negative least-squares variance and covariance component estimation using the positive-valued function for errors-in-variables models

Abstract Although (co)variance component estimation has been widely applied in the errors-in-variables (EIV) model, the occurrence of negative variance components is still a major issue in the estimated variance components. This problem may be due to the following unfavorable factors: 1) unreasonable selection of initial variance values; 2) low redundancy in the EIV functional model; 3) improper design in the EIV stochastic model, and 4) other data quality problems. Many attempts have been made to prevent the appearance of negative variance components. In this contribution, a novel and efficient non-negative least-squares variance component estimation using the PVF (PVF-NLS-VCE) is introduced, which can simultaneously estimate the unknown (co)variance components in the EIV stochastic model and the parameters in the EIV functional model. Its principle is to implicitly impose a non-negative constraint by replacing the variance component with the positive-valued function (PVF) whose range is the set of positive real numbers. Two numerical examples using real and simulated data are presented. The numerical results of linear regression are identical to those obtained based on least-squares variance component estimation (LS-VCE) with positive initial values of variance components. The numerical results of two-dimensional affine transformation are shown to prevent negative variance components and precede those obtained by LS-VCE with a negative initial value of variance component. Both numerical examples verify the effectiveness of the PVF-NLS-VCE method whether the initial values of variance components are positive or negative. The proposed PVF-NLS-VCE is a simple, convenient and flexible method to achieve the non-negative estimates of variance components, which can reduce sensitivity to initial value selection and automatically guarantee a non-negative definite covariance matrix.

Connecting palettes — An integrated spectroscopic analysis and UMAP visualisation of Wu Guanzhong's paint palette and his painting

A paint palette of the 20th-century Chinese modern artist Wu Guanzhong (1919–2010) was studied with an integrated spectroscopic approach, macro-scale non-invasive techniques hyperspectral imaging (HSI) and macro X-ray fluorescence (MA-XRF), complemented with Raman spectroscopy. The palette is revealed to be comprised of synthetic inorganic and organic pigments, typical of the 20th century modern palette that is dominated by azo and phthalocyanine pigments. HSI datasets of the paint palette and those of Wu's oil painting ‘Xidi Village’ (2001) were then processed within one unsupervised Uniform Manifold Approximation and Projection (UMAP) model, in an attempt to identify connections between the artefact and the artwork, so that known pigment results of the palette may provide preliminary pigment assignment for the painting. This study describes the steps taken to establish this automated assisted pigment analysis workflow, which involves processing multiple HSI datasets within one UMAP model, density clustering, non-negative least square (NNLS) fitting to extract endmembers (EM) spectra and to generate distribution maps. The approach to perform micro-sampling pigment analysis on the artist's palette (or artist's materials) is considered less invasive to the integrity than that from artworks, the results of which have demonstrated to serve as a critical resource to support further pigment analysis studies of the artist's paintings via non-invasive analytical techniques.

Non-Exponential Reverberation Modeling Using Dark Velvet Noise

Previous research on late-reverberation modeling has mainly focused on exponentially decaying room impulse responses, whereas methods for accurately modeling non-exponential reverberation remain challenging. This paper extends the previously proposed basic darkvelvet- noise reverberation algorithm and proposes a parametrization scheme for modeling late reverberation with arbitrary temporal energy decay. Each pulse in the velvet-noise sequence is routed to a single dictionary filter that is selected from a set of filters based on weighted probabilities. The probabilities control the spectral evolution of the late-reverberation model and are optimized to fit a target impulse response via non-negative least-squares optimization. In this way, the frequency-dependent energy decay of a target late-reverberation impulse response can be fitted with mean and maximum reverberation-time errors of 4% and 8%, respectively, requiring about 50% less coloration filters than a previously proposed filteredvelvet- noise algorithm. Furthermore, the extended dark-velvet-noise reverberation algorithm allows the modeled impulse response to be gated, the frequency-dependent reverberation time to be modified, and the model’s spectral evolution and broadband decay to be decoupled. The proposed method is suitable for the parametric late-reverberation synthesis of various acoustic environments, especially spaces that exhibit a non-exponential energy decay, motivating its use in musical audio and virtual reality.

PSD estimation and modal parameter identification for random vibrations with blade tip timing measurement

Abstract Blade tip timing (BTT) is a vibration measurement technique for blade health monitoring. Most of the existing BTT analysis methods are suitable for deterministic vibration signals but are ineffective for random vibration signals that often occur in practice. Statistical analysis of BTT data is significant for random vibration analysis and improving blade monitoring efficiency. This study proposes a compressive model for power spectral density (PSD) estimation and modal parameter identification. The efficiencies of three compressive sensing algorithms, including the least absolute shrinkage and selection operator (Lasso), nonnegative least squares (NLS), and nonnegative orthogonal matching pursuit, are compared. The effects of the duration of the signal and the frequency resolution on the quality of the estimated PSD and the identified parameters are discussed. According to the analysis, to obtain accurate damping ratios, it is recommended that the duration of the signal be greater than 3000 revolutions. A Q criterion based on the half-power bandwidth is proposed to determine the set of frequency resolutions. Numerical and field tests were conducted to verify the proposed method. The results indicate that the NLS algorithm is recommended to use. The root-mean-square errors of the identified natural frequencies and damping ratios obtained by the proposed method were 0.065 Hz and 0.023%, respectively. The proposed method was verified at different rotational speeds in a field test, demonstrating the capability of the method over a wide rotational speed range and providing more opportunities to detect blade damage.

Manifold Peaks Nonnegative Matrix Factorization.

Nonnegative matrix factorization (NMF) has attracted increasing interest for its high interpretability in recent years. It is shown that the NMF is closely related to fuzzy k -means clustering, where the basis matrix represents the cluster centroids. However, most of the existing NMF-based clustering algorithms often have their decomposed centroids deviate away from the data manifold, which potentially undermines the clustering results, especially when the datasets lie on complicated geometric structures. In this article, we present a manifold peaks NMF (MPNMF) for data clustering. The proposed approach has the following advantages: 1) it selects a number of MPs to characterize the backbone of the data manifold; 2) it enforces the centroids to lie on the original data manifold, by restricting each centroid to be a conic combination of a small number of nearby MPs; 3) it generalizes the graph smoothness regularization to guide the local graph construction; and 4) it solves a general problem of quadratic regularized nonnegative least squares (NNLSs) with group l0 -norm constraint and further develops an efficient optimization algorithm to solve the objective function of the MPNMF. Extensive experiments on both synthetic and real-world datasets demonstrate the effectiveness of the proposed approach.

An Ultra-Throughput Boost Method for Gamma-Ray Spectrometers

(1) Background: Generally, in nuclear medicine and nuclear power plants, energy spectrum measurements and radioactive nuclide identification are required for evaluation of strong radiation fields to ensure nuclear safety and security; thereby, damage is prevented to nuclear facilities caused by natural disasters or the criminal smuggling of nuclear materials. High count rates can lead to signal accumulation, negatively affecting the performance of gamma spectrometers, and in severe cases, even damaging the detectors. Higher pulse throughput with better energy resolution is the ultimate goal of a gamma-ray spectrometer. Traditionally, pileup pulses, which cause dead time and affect throughput, are rejected to maintain good energy resolution. (2) Method: In this paper, an ultra-throughput boost (UTB) off-line processing method was used to improve the throughput and reduce the pileup effect of the spectrometer. Firstly, by fitting the impulse signal of the detector, the response matrix was built by the functional model of a dual exponential tail convolved with the Gaussian kernel; then, a quadratic programming method based on a non-negative least squares (NNLS) algorithm was adopted to solve the constrained optimization problem for the inversion. (3) Results: Both the simulated and experimental results of the UTB method show that most of the impulses in the pulse sequence from the scintillator detector were restored to δ-like pulses, and the throughput of the UTB method for the NaI(Tl) spectrometer reached 207 kcps with a resolution of 7.71% @661.7 keV. A reduction was also seen in the high energy pileup phenomenon. (4) Conclusions: We conclude that the UTB method can restore individual and piled-up pulses to δ-like sequences, effectively boosting pulse throughput and suppressing high-energy tailing and sum peaks caused by the pileup effect at the cost of a slight loss in energy resolution.

Lithological mapping of charnockites using spectral mixture analysis

Charnockite, an orthopyroxene-bearing granitic rock, is the most dominant rock type of the Southern Granulite Terrain (SGT) of India. This study utilises remote sensing data to map the charnockite lithology in the Kodaikanal region within the SGT. Although remote sensing-based lithological mapping dominantly uses VNIR (Visible-Near Infrared) datasets, in this study, PRISMA (hyperspectral) datasets in the VNIR region and ASTER (multispectral) datasets in the TIR (Thermal Infrared) region were utilised in deriving the mineralogical composition and spectral characteristics of charnockites. In addition, image-derived endmember spectra from PRISMA and ASTER were validated using the laboratory-acquired spectra of charnockites. Linear mixing models (LMM) and the Hapke model were applied to quantitatively study the fractional abundance of charnockite rocks in the Kodaikanal region. Three least square methods, i.e., Fully Constrained Least Squares (FCLS), Non-Negative Least Squares (NNLS), and Unconstrained Least Squares (UCLS), were used to derive the fractional abundance of endmembers. Laboratory-derived charnockite spectra in the VNIR region exhibit spectral features characteristics of pyroxenes and hydrated minerals. In the TIR region, charnockite spectra exhibit characteristic vibrational absorption features of quartz and feldspar known as reststrahlen bands. Image analysis indicates that charnockite rocks exhibit spectral characteristics resembling the mafic rock type in the VNIR region and the felsic rock type in the TIR region. Therefore, the combined analysis of VNIR and TIR datasets allows the accurate delineation of charnockite lithology. However, vegetation in the study area introduces strong nonlinear spectral mixing effects, making it challenging to map the lithological units accurately. This study addresses this challenge using spectral mixture analysis to map charnockites in the Kodaikanal region. The fractional abundance study provides valuable insights into the lithological composition, demonstrating the effectiveness of spectral mixture analysis in mapping charnockites in the Kodaikanal region. Overall, the study demonstrates that the spectral mixture analysis significantly enhances the accuracy of lithology mapping, contributing to a more comprehensive understanding of the study area.

Characterizing Protein Concentration in Cerebrospinal Fluid with T2 Component Analysis.

T2 values are hypothesized to be reduced where protein accumulates in the cerebrospinal fluid (CSF). We aimed to verify the accuracy of Carr-Purcell-Meiboom-Gil (CPMG) pulses and non-negative least squares (NNLS) analysis in visualizing protein concentrations by mapping the T2 values. We first dissolved 1.2g of bovine serum albumin powder in 4 mL of artificial CSF to purify an albumin solution with a concentration of 4.5 mM. Artificial CSF was added thereto, and eight types of albumin solutions, with concentrations of 0.002-4.5 mM, were purified. We acquired this albumin solution with CPMG pulses and NNLS, decomposed the T2 values per pixel, and derived 25 T2 component values of 60-2000 ms. We assessed the change of T2 values by the difference in albumin concentration of a single voxel. Finally, we used the method to assess T2 values from two patients, one with a subdural hematoma and one with a suprasellar cystic tumor. T2 component values were plotted graphically, presented individually, and created in color maps. T2 component values for albumin concentrations ranging from 0.056 to 4.55 mM showed different T2 peaks, whereas, for concentrations 0.002 to 0.019 mM, the peaks were similar heights and overlapped. Peak width was similar for all concentrations. The color maps successfully reflected the changes in T2 values across both RGB color patterns. T2 components for albumin samples with 2.5 mM and 6.1 mM concentrations within a single voxel were represented separately and reflected the ratio of the two samples in nine different regions of interest within one slice. In the clinical cases, the T2 component map imaged differences in albumin concentrations, similar to those observed in the albumin samples. The present method with CPMG sequences and NNLS provide adequate images to differentiate accumulating protein concentrations in the CSF, even at the level of a single pixel.

Feature extraction by orthonormal projective non‐negative matrix factorization and longitudinal association between brain atrophy patterns and Alzheimer’s disease

AbstractBackgroundOrthonormal projective non‐negative matrix factorization (OPNMF) was a recently developed approach for feature extraction techniques of neuroimaging data. However, there has been few studies applying this to brain MRI to better characterize the anatomic changes seen in Alzheimer’s Disease (AD) and correlate these patterns with cognitive changes.MethodWe applied OPNMF with refinement to identify distinct spatial components of voxel‐wise volume loss in the structural MRI (3D T1 MPRAGE images) of subjects with AD (N = 109, mean age = 74.6 (7.9), ADNI2) relative to healthy young controls (N = 104, mean age = 24.0 (2.9), ABIDE1). Non‐negative least squares (NNLS) was then used to extract non‐negative coefficients representing subject‐specific quantitative measures of regional atrophy. This calculation of coefficients was extended to images not used for component discovery which also included Mild Cognitive Impairment (MCI) and controls. To investigate the cross‐sectional and longitudinal associations between cognitive assessments scores and regional atrophy severity in different diagnostic groups, we used multiple linear regression models and liner mixed‐effects models with random intercepts and slopes controlled for age, sex, educational level, APOE ε4 genotypes were utilized. A validation analysis was performed using ADNI3 images.ResultWe derived 6 atrophy components upon the same training set and there was a sharp decrease in the magnitude of the reconstruction error gradient when moving from 5 components to 6 components, and the components have meaningful interpretation. In the whole cohort, atrophy in 5 of the 6 regions was significantly associated with all three cognitive scores. There is evidence of overall positive trends between diagnosis group and atrophy severity changing rate in all 6 regions. The increased atrophy in all 6 regions was associated with decreases in MMSE and MOCA scores and increases in CDRSB scores in the whole cohort as well as in LMCI cohort. From the validation analysis, we showed that our result from OPNMF is stable in atrophy pattern discovery.ConclusionWe developed a robust pipeline for detecting spatially distinct atrophy components in AD and associated these atrophy patterns with cognitive changes which may help us better characterize the underlying pathology of types of AD and other dementias on MRI.

Myelin water imaging at 0.55 T using a multigradient-echo sequence.

To investigate the prospects of a multigradient-echo (mGRE) acquisition for in vivo myelin water imaging at 0.55 T. Scans were performed on the brain of four healthy volunteers at 0.55 and 3 T, using a 3D mGRE sequence. The myelin water fraction (MWF) was calculated for both field strengths using a nonnegative least squares (NNLS) algorithm, implemented in the qMRLab suite. The quality of these maps as well as single-voxel fits were compared visually for 0.55 and 3 T. The obtained MWF values at 0.55 T are consistent with previously reported ones at higher field strengths. The MWF maps are a considerable improvement over the ones at 3 T. Example fits show that 0.55 T data is better described by an exponential model than 3 T data, making the assumed multi-exponential model of the NNLS algorithm more accurate. This first assessment shows that mGRE myelin water imaging at 0.55 T is feasible and has the potential to yield better results than at higher fields.

Hybrid deconvolution separation methods based on matrix completion for multi-motion modes sound sources

Beamforming techniques cannot effectively separate the mixed field of stationary and rotating sound sources. The issue becomes even more challenging when strong out-of-focus sources, e.g., stationary sources with rotating beamforming, are present, leading to a smearing effect and false localization results. The current algorithms for separating multiple moving sound sources have problems such as weak separation ability and complex computation. To more effectively address this challenge, two frequency domain hybrid deconvolution methods based on the virtual rotating array (VRA) and a matrix completion algorithm are proposed in this work. A matrix completion algorithm is used to establish the completed cross point spread function (C-PSF) matrix. Afterward, a linear equation system is constructed to separate the sound sources of different motion modes. Finally, the sound source separation localization problem is solved by Non-Negative Least-Squares (NNLS) and sparsity constraints deconvolution, respectively. The simulation and experimental results demonstrate that the proposed method can accurately locate and separate stationary and moving sound sources.

Retrieval of leaf-level fluorescence quantum efficiency and NPQ-related xanthophyll absorption through spectral unmixing strategies for future VIS-NIR imaging spectroscopy

Current and future vegetation imaging spectroscopy satellites will bring a new data stream of information, of high scientific value to refine existing remote sensing products, and develop new ones. The sensors on board ESA's Fluorescence Explorer (FLEX) will cover the entire 500–780 nm range, designed to track the photosynthetic energy partitioning based on the key pigment players in the light reactions. To quantify the actual photosynthetic efficiency unambiguously, the dynamic pigment absorption behavior is crucial to complement the fluorescence information. An important role is given by the xanthophylls, regulating the non-photosynthetic quenching (NPQ) behavior which affects the 500–600 nm range. Therefore, this work focused on the development of a non-negative least squares (NNLS) spectral unmixing algorithm for reflectance (500–780 nm) retrieving the effective absorbance of individual pigments, i.e., Chlorophyll (Chl) a and b, beta-Carotene and xanthophylls. The NNLS fitting was applied to fit the total effective absorbance at leaf level, linearly composed of pigment and background absorption coefficient spectra. The model succeeded to obtain spectral fitting errors generally below 20% across the 500–780 nm range. Further, we focused on the further use of the effective absorbance by Chlorophyll a to calculate the absorbed photosynthetically active radiation or APAR Chl a. This product was combined with the total emitted fluorescence flux (670–780 nm), expressed in photon flux units, to obtain the fluorescence quantum efficiency (FQE), capturing the stress-related fluorescence quenching in the light reactions. Finally, we applied the leaf-based algorithm to foreseen FLEX image products simulated by the FLEX End-to-End Scene Generator. We were able to retrieve APAR Chl a with a RMSE of 85.5 μmol m−2 s−1 (NNLS with additional upper fitting constraints) and 158.2 μmol m−2 s−1 (regular NNLS), and FQE retrievals could be obtained with an R2 of 0.93 and 0.90, respectively. While the subtle xanthophyll absorption could be meaningfully fitted at the leaf scale, further improvements to the algorithms and an understanding of the physiological mechanisms are needed to deal with the complexity at larger scales. Given several challenges to be overcome, the proposed bottom-up strategy using specific pigment absorbance unmixing for (imaging) spectroscopy demonstrates the ongoing developments to complement the fluorescence product, with the aim to provide an unambiguous estimate on the actual carbon sequestration of vegetation.

Comparison of semiquantitative methodologies using Raman mapping for corrosion products on iron artifacts

The quantitative determination of corrosion products is essential for evaluating the corrosion state of archeological iron artifacts. This study explored two semiquantitative approaches using Raman mapping technique combined with chemometrics to quantify a binary mixture of magnetite and goethite. The first approach involved establishing quantification models using Raman spectra treated with Principal Components Regression (PCR) and Partial Least Squares (PLS) algorithms. Both the PCR and PLS model showed good predictive ability as indicated by correlation coefficients and root mean square errors (PLS: Rc2=0.9979, Rp2=0.9970, RMSEC=1.93, RMSEP =2.68, RMSECV=3.25). The second approach was based on spectral fitting using non-negative least squares (NNLS) algorithm. This method demonstrated a fair accuracy between the calculated and actual compositions. The absolute value of relative errors was 0.99%∼10.08% for Fe3O4 and 0.81%∼9.71% for α-FeOOH respectively, for compositions greater than 20%. These methods were then applied to quantify the corrosion products on an iron bar excavated from the Nanhai (South China Sea) No. I shipwreck. Compared with XRD quantitative results, Raman results showed that the spectral fitting method was superior to the established PCA and PLS quantification models in both qualitative determination and quantitative accuracy. Compositional maps depicting the distribution of different phases were also generated using spectral fitting method. It was concluded that Raman mapping has significant potential as an accurate quantitative method for the detection of iron corrosion products, and that the spectral fitting method is more suitable for determining iron corrosion compared to the PCR and PLS quantification models in this study.

A ReLU-based hard-thresholding algorithm for non-negative sparse signal recovery

In numerous applications, such as DNA microarrays, face recognition, and spectral unmixing, we need to acquire a non-negative K-sparse signal x from an underdetermined linear model y=Ax+v, where A is a sensing matrix and v is a noise vector. In this paper, we first propose a ReLU-based hard-thresholding algorithm (RHT) to recover x by taking advantage of its non-negative sparsity. Two sufficient conditions for stable recovery with RHT are then developed, which are respectively based on the restricted isometry property (RIP) and mutual coherence of the sensing matrix A. As far as we know, these two sufficient conditions are the best for hard-thresholding-type algorithms. Numerical experiments show that RHT has better overall recovery performance in the recovery non-negative sparse signals than the non-negative least squares (NNLS) algorithm, some hard-thresholding-type algorithms including the iterative hard-thresholding (IHT) algorithm, hard-thresholding pursuit (HTP), Newton-step-based iterative hard-thresholding algorithm (NSIHT), and Newton-step-based hard-thresholding pursuit (NSHTP), several non-negative sparse recovery approaches including non-negative orthogonal matching pursuit (NNOMP), fast NNOMP (FNNOMP), non-negative orthogonal least squares (NNOLS), and non-negative regularization (NNREG) method. In terms of efficiency, RHT has a similar performance to IHT, and is much more efficient than other tested algorithms.

Physics-Informed Machine Learning for Surrogate Modeling of Heat Transfer Phenomena

Abstract In this paper, we propose a sparse modeling method for automatically creating a surrogate model for nonlinear time-variant systems from a very small number of time series data with nonconstant time steps. We developed three machine learning methods, namely, (1) a data preprocessing method for considering the correlation between errors, (2) a sequential thresholded non-negative least-squares method based on term size criteria, and (3) a solution space search method involving similarity model classification—to apply sparse identification of nonlinear dynamical systems, as first proposed in 2016, to temperature prediction simulations. The proposed method has the potential for wide application to fields where the concept of equivalent circuits can be applied. The effectiveness of the proposed method was verified using time series data obtained by thermofluid analysis of a power module. Two types of cooling systems were verified: forced air cooling and natural air cooling. The model created from the thermofluid analysis results with fewer than the number of input parameters, predicted multiple test data, including extrapolation, with a mean error of less than 1 K. Because the proposed method can be applied using a very small number of data, has a high extrapolation accuracy, and is easy to interpret, it is expected not only that design parameter can be fine-tuned and actual loads can be taken into account, but also that condition-based maintenance can be realized through real-time simulation.

TetraFreeQ: Tetrahedra-free quadrature on polyhedral elements

In this paper we provide a tetrahedra-free algorithm to compute low-cardinality quadrature rules with a given degree of polynomial exactness, positive weights and interior nodes on a polyhedral element with arbitrary shape. The key tools are the notion of Tchakaloff discretization set and the solution of moment-matching equations by Lawson-Hanson iterations for NonNegative Least-Squares. Several numerical tests are presented. The method is implemented in Matlab as open-source software.

Applications of the non-negative least-squares deconvolution method to analyze energy-dispersive x-ray fluorescence spectra.

We used the Monte Carlo simulation method to establish a detector response matrix and the non-negative least-squares method to deconvolute x-ray spectra. The simulation and experimental data verified the effectiveness of this method, and the influence of full-width at the half of the maximum calibration accuracy on the deconvolution results was investigated. The non-negative least-squares method had high accuracy and efficiency compared with others. The results showed that, except for Zn, the relative errors between the inversion and the standard values were less than 0.1% for the simulated spectra. For the experimental data, the relative errors were within 0.2%. The peaks with similar characteristic energies can be better distinguished in the deconvolution spectra, reducing the errors caused by overlapping peaks in subsequent analysis.

Resolution enhancement of 2D controlled-source electromagnetic images by use of point-spread function inversion

The marine controlled-source electromagnetic technique is employed both in large-scale geophysical applications as well as within the exploration of hydrocarbons and gas hydrates. Because of the diffusive character of the EM field, only very low frequencies are used, leading to inversion results with low resolution. In this paper, we calculated the resolution matrix associated with the inversion and derived the corresponding point-spread functions. The PSFs provided information about how much the actual inversion was blurred. Using a space-varying deconvolution can thus further improve the inversion result. The actual deblurring was carried out using the nonnegative flexible conjugate gradient least-squares (NN-FCGLS) algorithm, which is a fast iterative restoration technique. To attain completeness, we also introduced the results obtained using a blind deconvolution algorithm based on the maximum likelihood estimation with unknown PSFs. The potential of the proposed approach has been demonstrated using both complex synthetic data and field data acquired at the Wisting oil field in the Barents Sea. In both cases, the resolution of the final inversion result was improved and showed greater agreement with the known target area.