Broyden-Fletcher-Goldfarb-Shanno Research Articles

GLAD-M35: A joint P and S global tomographic model with uncertainty quantification

Summary We present our third and final generation joint P and S global adjoint tomography (GLAD) model, GLAD-M35, and quantify its uncertainty based on a low-rank approximation of the inverse Hessian. Starting from our second-generation model, GLAD-M25, we added 680 new earthquakes to the database for a total of 2,160 events. New P-wave categories are included to compensate for the imbalance between P- and S-wave measurements, and we enhanced the window selection algorithm to include more major-arc phases, providing better constraints on the structure of the deep mantle and more than doubling the number of measurement windows to 40 million. Two stages of a Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton inversion were performed, each comprising five iterations. With this BFGS update history, we determine the model’s standard deviation and resolution length through randomized singular value decomposition.

Artificial Neural Network (ANN)-Based Water Quality Index (WQI) for Assessing Spatiotemporal Trends in Surface Water Quality—A Case Study of South African River Basins

Artificial neural networks (ANNs) are powerful data-oriented “black-box” algorithms capable of assessing and delineating linear and multifaceted non-linear correlations between the dependent and explanatory variables. Through the years, neural networks have proven to be effective and robust analytical techniques for establishing artificial intelligence-based tools for modelling, estimating, and projecting spatial and temporal variations in water bodies. Accordingly, ANN-based algorithms gained increased attention and have emerged as practical alternatives to traditional approaches for hydro-chemical analysis. ANNs are among the widely used computer systems for modelling surface water quality. Considering their wide recognition, resilience, flexibility, and accuracy, the current study employs a neural network-based methodology to construct a novel water quality index (WQI) model suitable for analysing South African rivers. The feed-forward, back-propagated multilayered perceptron model has three parallel-distributed neuron layers interconnected with seventy weighted links orientated laterally from left to right. First, the input layer includes thirteen neuro-nodes symbolising thirteen explanatory variables, including NH3, Ca, Cl, Chl-a, EC, F, CaCO3, Mg, Mn, NO3, pH, SO4, and turbidity (NTU). Second, the hidden layer consists of eleven neuro-nodes accountable for computational tasks. Lastly, the output layer features one neuron responsible for conveying network outcomes using a single-digit WQI rating extending from zero to one hundred, where zero represents substandard water quality and one hundred denotes exceptional water quality. The AI-based model was developed using water quality data obtained from six monitoring locations within four drainage basins under the management of the Umgeni Water Board in the KwaZulu-Natal Province of South Africa. The dataset comprises 416 samples randomly divided into training, testing, and validation sets using a proportional split of 70:15:15%. The Broyden–Fletcher–Goldfarb–Shanno (BFGS) technique was utilised to conduct backpropagation training and adjust synapse weights. The dependent variables are the WQI scores from the universal water quality index (UWQI) model developed specifically for South African river basins. The ANN demonstrated enhanced efficiency through an overall correlation coefficient (R) of 0.985. Furthermore, the neural network attained R-values of 0.987, 0.992, and 0.977 for the training, testing, and validation intervals. The ANN model achieved a Nash–Sutcliffe efficiency (NSE) value of 0.974 and coefficient of determination (R2) of 0.970. Sensitivity analysis provided additional validation of the preparedness and computational competence of the ANN model. The typical target-to-output error tolerance for the ANN model is 0.242, demonstrating an adequate predictive ability to deliver results comparable with the target UWQI, having the lowest and highest index ratings of 75.995 and 94.420, respectively. Accordingly, the three-layer neural network is scientifically sound, with index values and water quality evaluations corresponding to the UWQI results. The current research project seeks to document the processes used and the outcomes obtained.

Inverse Scheme to Locally Determine Nonlinear Magnetic Material Properties: Numerical Case Study

We are interested in the determination of the local nonlinear magnetic material behaviour in electrical steel sheets due to cutting and punching effects. For this purpose, the inverse problem has to be solved, where the objective function, which penalises the difference between the measured and the simulated magnetic flux density, has to be minimised under a constraint defined according to the corresponding partial differential equation model. We use the adjoint method to efficiently obtain the gradients of the objective function with respect to the material parameters. The optimisation algorithm is low-memory Broyden–Fletcher–Goldfarb–Shanno (BFGS), the forward and adjoint formulations are solved using the finite element (FE) method and the ill-posedness is handled via Tikhonov regularisation, in combination with the discrepancy principle. Realistic numerical case studies show promising results.

Determination of boundary conditions from the solution of the inverse heat conduction problem in the gas nitriding process

Two non-linear unsteady methods for solving the inverse heat conduction problem are discussed and compared in this paper. The first method is based on the finite element method, uses the variational calculus and the BFGS (Broyden-Fletcher–Goldfarb–Shanno) optimization algorithm. The second is an analytical and numerical method based on the approximation of the solution in the form of a linear combination of Chebyshev polynomials. In numerical tests, the stability of the temperature, heat flux density, and heat transfer coefficient obtained from both methods was analyzed. On the basis of experimental data, oscillations of the measured gas temperature and temperature in the component were analyzed. Oscillations of the gas temperature obtained from the experiment were taken into consideration during tests. The first method to solve the inverse problem was used to determine the boundary conditions for the entire gas nitriding process. As a result, stable values of temperature, heat flux density, and the heat transfer coefficient on the surface of the component under treatment in a real gas nitriding process, so far unpublished, were obtained.

DFT insight into structural, mechanical, electronic, optical and thermal properties of eco-friendly perovskites CuXO3 (X= Al, In)

This report aims to investigate the structural, mechanical, optical, thermal, and electronic properties along with hardness of CuXO3 (X = Al, In) perovskites for the first time by using first-principles calculations within the density functional theory (DFT). The geometry of the both structures have been optimized by using Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimization technique and confirmed as the cubic structure with the space group of P m‾ 3 m (No. 221). The studied lattice parameters of CuXO3 (X = Al, In) closely resemble with previous theoretical and experimental results. Both the compounds of CuXO3 (X = Al, In) under investigation are mechanically stable as the calculated elastic constants satisfy the Born stability criteria. The calculated value of Pugh's ratio, Poisson's ratio and Cauchy pressure confirm strong ductility behavior in contrast to brittleness of these compounds. The elastic anisotropy calculations confirm the anisotropic nature in CuAlO3 in contrast to isotropic nature as observed in CuInO3. CuAlO3 is predicted to be harder than that of CuInO3. CuInO3 shows the highest machinability index among studied compounds. The electronic band-structure and density of states ensure semiconducting nature in CuAlO3 whereas, CuInO3 reveals metallic nature. The investigation of optical properties reveals the prospective application of the entitled substances in a wide range of electronic and optoelectronic device uses. The title compounds could be used as thermal barrier coating materials (TBC) for exhibiting low thermal conductivity.

Capturing Valuation Study Sampling Uncertainty in the Estimation of Health State Utility Values Using the EQ-5D-3L.

Utility scores associated with preference-based health-related quality-of-life instruments such as the EQ-5D-3L are reported as point estimates. In this study, we develop methods for capturing the uncertainty associated with the valuation study of the UK EQ-5D-3L that arises from the variability inherent in the underlying data, which is tacitly ignored by point estimates. We derive a new tariff that properly accounts for this and assigns a specific closed-form distribution to the utility of each of the 243 health states of the EQ-5D-3L. Using the UK EQ-5D-3L valuation study, we used a Bayesian approach to obtain the posterior distributions of the derived utility scores. We constructed a hierarchical model that accounts for model misspecification and the responses of the survey participants to obtain Markov chain Monte Carlo (MCMC) samples from the posteriors. The posterior distributions were approximated by mixtures of normal distributions under the Kullback-Leibler (KL) divergence as the criterion for the assessment of the approximation. We considered the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm to estimate the parameters of the mixture distributions. We derived an MCMC sample of total size 4,000 × 243. No evidence of nonconvergence was found. Our model was robust to changes in priors and starting values. The posterior utility distributions of the EQ-5D-3L states were summarized as 3-component mixtures of normal distributions, and the corresponding KL divergence values were low. Our method accounts for layers of uncertainty in valuation studies, which are otherwise ignored. Our techniques can be applied to other instruments and countries' populations. Guidelines for health technology assessments typically require that uncertainty be accounted for in economic evaluations, but the parameter uncertainty of the regression model used in the valuation study of the health instrument is often tacitly ignored.We consider the UK valuation study of the EQ-5D-3L and construct a Bayesian model that accounts for layers of uncertainty that would otherwise be disregarded, and we derive closed-form utility distributions.The derived tariff can be used by researchers in economic evaluations, as it allows analysts to directly sample a utility value from its corresponding distribution, which reflects the associated uncertainty of the utility score.

Periodic DFT study of structural transformations of cocrystal CL-20/MMI under high pressure.

The crystal and molecular structure, electronic properties, optical parameters, and elastic properties of a 1:2 hexanitrohexaazaisowurtzitane (CL-20)/2-mercapto-1-methylimidazole (MMI) cocrystal under 0 ~ 100 GPa hydrostatic pressure were calculated. The results show that the cocrystal CL-20/MMI undergoes three structural transitions at 72 GPa, 95 GPa, and 97 GPa, respectively, and the structural transition occurs in the part of the MMI compound. Structural mutations formed new bonds S1-S2, C2-C7, and N1C5 at 72GPa, 95 GPa, and 97 GPa, respectively. Similarly, the formation of new bonds is confirmed on the basis of an analysis of the changes in lattice constants, cell volumes, and partial densities of states (PDOS) for S1, S2, C2, C7, N1, and C3 at the corresponding pressures. The optical parameters show that the pressure makes the peaks of various optical parameters of CL-20/MMI larger, and the optical activity is enhanced. The optical parameters also confirm the structural mutation of CL-20/MMI under the corresponding pressure. CL-20/MMI was calculated by using the first-principles norm-conservative pseudopotential based on density functional theory (DFT) in the CASTEP software package. For the optimization results, the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is selected to optimize the geometry of the cocrystal in the range of 0-100 GPa. GGA/PBE (Perdew-Burke-Ernzerhof) was selected to relax the cocrystal CL-20/MMI fully without constraints at atmospheric pressure. The sampling scheme in the Brillouin zone [10] is the Monkhorst-Pack scheme, and the number of k-point grids was 2 × 2 × 2. By contrast, this study will use the LDA method to calculate.

Machine Learning in Quasi-Newton Methods

In this article, we consider the correction of metric matrices in quasi-Newton methods (QNM) from the perspective of machine learning theory. Based on training information for estimating the matrix of the second derivatives of a function, we formulate a quality functional and minimize it by using gradient machine learning algorithms. We demonstrate that this approach leads us to the well-known ways of updating metric matrices used in QNM. The learning algorithm for finding metric matrices performs minimization along a system of directions, the orthogonality of which determines the convergence rate of the learning process. The degree of learning vectors’ orthogonality can be increased both by choosing a QNM and by using additional orthogonalization methods. It has been shown theoretically that the orthogonality degree of learning vectors in the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method is higher than in the Davidon–Fletcher–Powell (DFP) method, which determines the advantage of the BFGS method. In our paper, we discuss some orthogonalization techniques. One of them is to include iterations with orthogonalization or an exact one-dimensional descent. As a result, it is theoretically possible to detect the cumulative effect of reducing the optimization space on quadratic functions. Another way to increase the orthogonality degree of learning vectors at the initial stages of the QNM is a special choice of initial metric matrices. Our computational experiments on problems with a high degree of conditionality have confirmed the stated theoretical assumptions.

Photospheric Stereoscopy: Direct Estimation of Solar Surface-Height Variations

The orbit of the Solar Orbiter mission carries it and the Polarimetric and Helioseismic Imager (PHI), which is onboard, away from the Sun–Earth line, opening up the first ever possibility of doing stereoscopy of solar photospheric structures. We present a method for a stereoscopic analysis of the height variations in the solar photosphere. This method enables the estimation of relevant quantities, such as the Wilson depression of sunspots and pores. We demonstrate the feasibility of the method using simulated Stokes-I\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$I$\\end{document} continuum observations of an MHD simulation of the solar-surface layers. Our method estimates the large-scale variations in the solar surface by shifting and correlating two virtual images, mapped from the same surface feature observed from two different vantage points. The resulting vector is then introduced as an initial height estimate in the least-squares Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimization algorithm to reproduce smaller scale structures. The height estimates from the simulated images reproduce well the overall height variations of the MHD simulation. We studied which viewing angles give the best results and found the optimal separation of the view points to be between 10∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$10^{\\circ }$\\end{document} and 40∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$40^{\\circ }$\\end{document}; but neither viewing direction should be inclined by more than 30∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$30^{\\circ }$\\end{document} from the vertical to the solar surface. The method yields reliable results if the data have a signal-to-noise ratio of 50 or higher. The influence of the spatial resolution of the observed images is considered and discussed.

A New Hybrid Three-Term LS-CD Conjugate Gradient In Solving Unconstrained Optimization Problems

The Conjugate Gradient (CG) method is renowned for its rapid convergence in optimization applications. Over the years, several modifications to CG methods have emerged to improve computational efficiency and tackle practical challenges. This paper presents a new three-term hybrid CG method for solving unconstrained optimization problems. This algorithm utilizes a search direction that combines Liu-Storey (LS) and Conjugate Descent (CD) CG coefficients and standardizes it using a spectral which acts as a scheme for the choices of the conjugate parameters. This resultant direction closely approximates the memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton direction, known for its bounded nature and compliance with the sufficient descent condition. The paper establishes the global convergence under standard Wolfe conditions and some appropriate assumptions. Additionally, the numerical experiments were conducted to emphasize the robustness and superior efficiency of this hybrid algorithm in comparison to existing approaches.

Formic acid stability in different solvents by DFT calculations.

New technologies have been developed toward the use of green energies. The production of formic acid (FA) from carbon dioxide (CO[Formula: see text]) hydrogenation with H[Formula: see text] is a sustainable process for H[Formula: see text] storage. However, the FA adduct stabilization is thermodynamically dependent on the type of solvent and thermodynamic conditions. The results suggest a wide range of dielectric permittivity values between the dimethyl sulfoxide (DMSO) and water solvents to stabilize the FA in the absence of base. The thermodynamics analysis and the infrared and charge density difference results show that the formation of the FA complex with H[Formula: see text]O is temperature dependent and has a major influence on aqueous solvents compared to the FA adduct with amine, in good agreement with the experiment. In these conditions, the stability thermodynamic of the FA molecule may be favorable at non-organic solvents and dielectric permittivity values closer to water. Therefore, a mixture of aqueous solvents with possible ionic composition could be used to increase the thermodynamic stability of H[Formula: see text] storage in CO[Formula: see text] conversion processes. Using the Quantum ESPRESSO package, density functional theory (DFT) calculations were performed with periodic boundary conditions, and the electronic wave functions were expanded in plane waves. For the exchange-correlation functional, we use the vdW-DF functional with the inclusion of van der Waals (vdW) forces. Electron-ion interactions are treated by the projector augmented wave (PAW) method with pseudopotentials available in the PSlibrary repository. The wave functions and the electronic densities were expanded employing accurate cut-off energies of 6.80[Formula: see text]10[Formula: see text] and 5.44[Formula: see text]10[Formula: see text] eV, respectively. The electronic density was computed from the wave functions calculated at the [Formula: see text]-point in the first Brillouin-zone. Each structural optimization was minimized according to the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, with force and energy convergence criteria of 25 meV[Formula: see text]Å[Formula: see text] and 1.36 meV, respectively. The electrostatic solvation effects were performed by the [Formula: see text] package with the Self-Consistent Continuum Solvation (SCCS) approach.

Penerapan Model Regresi Hurdle Binomial Negatif Menggunakan Algoritma Broyden-Fletcher-Goldfarb-Shanno pada Data Jumlah Kematian Bayi di Kota Makassar Tahun 2017

Poisson regression is a nonlinear regression method used to analyse the relationship between discrete response variables. Equidispersion is the assumption that must be met in the Poisson regression. Furthermore, there are cases in which the equidispersion assumption is invalidated when using the Poisson regression model to analyze data. One such case is overdispersion, which occurs when there is an excess of zero. As a result, the Negative Hurdle Binomial (HBN) regression is implemented to solve the overdispersion issue. Maximum Likelihood Estimation (MLE) with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm was applied in this study to perform parameter estimation. In addition, the HBN regression model was used to analyze the data on the number of infant mortality cases in Makassar in 2017 with the variables assumed to be significant with infant mortality. The percentage of infants who were exclusively breastfed was the variable that had a significant impact on the outcome of HBN regression on the data on the number of infant mortality that experienced overdispersion.

A convergence‐enhanced Timoshenko beam element for the stochastic nonlinear analysis of reinforced concrete components

AbstractAn effective and precise physical model is generally required for the performance assessment of reinforced concrete (RC) components. In this study, a convergence‐enhanced Timoshenko beam element considering finite deformation is proposed for the stochastic nonlinear analysis of RC components. The unified framework of the rank 2 correction matrix is obtained by approximating the iterative matrix through the linearly independent basis vectors, and two types of Broyden–Fletcher–Goldfarb–Shanno (BFGS) operators are constructed. Then, a consistent solution scheme with superior numerical stability and efficiency is proposed based on the second kind of BFGS operator and improved quasi‐Newton method. Accurate discretization of the displacement fields and description of nonlinear sectional behavior are achieved by the high‐order Lagrangian interpolation functions, concrete damage‐plasticity model and J2 plasticity model. In an updated Lagrangian formulation, these shape functions and constitutive relationships are used to develop a complete secant stiffness with higher‐order terms in the strain tensor and residual force vector. To validate the proposed Timoshenko beam element, numerical applications involving material nonlinearity and geometrical nonlinearity are conducted. The numerical stability and efficiency of the solution scheme, the shear‐locking free technique, and the oscillation of axial force are thoroughly examined and discussed by solution of RC columns, cantilever beam and progressive collapse of planar RC frame. Finally, the parametric study considering the geometric and material randomness indicates that the RC column designed for flexural failure mode suffered considerable degradation of loading capacity and a larger scatter of residual load.

A data analysis system for thermal energy loss in electrical automation management

In order to achieve data analysis of thermal energy loss for electrical automation management, the author proposes a Broyden Fletcher Goldfarb Shanno (BFGS) trust region algorithm based thermal energy loss calculation method for the integrated energy system of electricity and gas, the BFGS trust region algorithm is utilized to obtain the thermal energy loss distribution of natural gas system, which is not highly dependent on the initial value, this solves the problem of non-convergence in power flow calculation when using the Newton method for calculation. The experimental results show that the relative errors of natural gas system node pressure, pipe-line flow and power system node voltage and phase angle calculated by Newton?s method and BFGS trust region algorithm are within 1 ? 10-4, within the allowable range, which verifies the correctness of the calculation results of the method described by the author. It has been proven that the BFGS trust region algorithm can achieve data analysis of thermal energy loss for electrical automation management.

Robust Prediction of Healthcare Inflation Rate With Statistical and AI Methods in Iran

The expected healthcare (HC) inflation rate (IR) (HCIR) is an important variable for all economic agents within HC systems. In recent years, during the COVID‐19 pandemic, Iran has experienced a high HCIR in its health system. In this context, a robust approximation of HCIR will be a helpful tool for health authorities and other decision makers. Using monthly time series data of HCIR in Iran, we developed various forecasting techniques based on classical smoothing methods, decomposition ETS (error, trend, and seasonality) approaches, autoregressive (AR) integrated moving average (ARIMA), seasonal ARIMA (SARIMA), and a multilayer nonlinear AR artificial neural network (NARANN) with several training algorithms including Bayesian regularization (BR), Levenberg–Marquardt (LM), scaled conjugate gradient (SCG), Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi‐Newton, conjugate gradient with Powell–Beale restarts (CGB), conjugate gradient with Fletcher–Reeves updates (CGF), and resilient propagation (RPROP) algorithms. Initially, based upon various criteria and possible combinations, we selected the superior model for each method separately. After that, the best model in each category is involved in 6‐ and 12‐multi‐step‐ahead prediction. In this stage, several error criteria are calculated. According to our findings, in a six‐step forecasting window, the Holt–Winters with a multiplicative seasonal pattern and SARIMA showed less bias, though compared to other alternatives like NARANN‐lm/br, the difference was relatively small. In the next process, by doubling the forecasting window, it is observed that artificial neural network (ANN) (i.e., Bayesian NARANN) strictly outperformed other models. As a result, in shorter steps, the Holt–Winters method can provide a better prediction, while in longer windows, Bayesian NARANN can be implemented vigorously for the prediction. Finally, we used 10 models to predict the future trend of HCIR in Iran till the end of July 2024.

An accelerated structured quasi-Newton method with a diagonal second-order Hessian approximation for nonlinear least squares problems

Our study focuses on exploring new variants of the structured quasi-Newton (SQN) method with a secant-like diagonal approximation (SLDA) of the second-order term of Hessian for solving nonlinear least squares (NLS) problems. In addition, an accelerated version of SQN-SLDA referred to as ASQN-SLDA, is also considered. In ASQN-SLDA, we rescale the search direction after the first backtracking linesearch procedure to produce a more aggressive step to increase the objective function value reduction. The concept of the proposed methods is simple and easy to implement. We prove the proposed methods are globally convergent under some appropriate assumptions and report several numerical experiments based on a suite of benchmark problems for NLS. The numerical results show that ASQN-SLDA is more robust than some baseline methods, including SQN-SLDA, the generalized Gauss–Newton (GN), Levenberg–Marquardt update, and the hybrid GN with Broyden–Fletcher–Goldfarb–Shanno (BFGS) method, also called H-GN-BFGS. For computing time, AQN-SLDA outperforms H-GN-BFGS for most test problems, and the speedup is more significant as the problem size increases. Furthermore, due to the trade-off between the number of iterations for convergence and the overhead needed in ASQN-SLDA, the benefit of the acceleration step is more evident for the largest-sized problems.

Investigating the effect of textural properties on CO2 adsorption in porous carbons via deep neural networks using various training algorithms

The adsorption of carbon dioxide (CO2) on porous carbon materials offers a promising avenue for cost-effective CO2 emissions mitigation. This study investigates the impact of textural properties, particularly micropores, on CO2 adsorption capacity. Multilayer perceptron (MLP) neural networks were employed and trained with various algorithms to simulate CO2 adsorption. Study findings reveal that the Levenberg–Marquardt (LM) algorithm excels with a remarkable mean squared error (MSE) of 2.6293E−5, indicating its superior accuracy. Efficiency analysis demonstrates that the scaled conjugate gradient (SCG) algorithm boasts the shortest runtime, while the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm requires the longest. The LM algorithm also converges with the fewest epochs, highlighting its efficiency. Furthermore, optimization identifies an optimal radial basis function (RBF) network configuration with nine neurons in the hidden layer and an MSE of 9.840E−5. Evaluation with new data points shows that the MLP network using the LM and bayesian regularization (BR) algorithms achieves the highest accuracy. This research underscores the potential of MLP deep neural networks with the LM and BR training algorithms for process simulation and provides insights into the pressure-dependent behavior of CO2 adsorption. These findings contribute to our understanding of CO2 adsorption processes and offer valuable insights for predicting gas adsorption behavior, especially in scenarios where micropores dominate at lower pressures and mesopores at higher pressures.

A Novel Method to Design Multirate Filter Banks Using BroydenFletcher-Goldfarb-Shanno (BFGS) Optimization

A Novel Method to Design Multirate Filter Banks Using BroydenFletcher-Goldfarb-Shanno (BFGS) Optimization

A novel spaceborne ISAR imaging approach for space target with high-order translational motion compensation and spatial variant MTRC correction

ABSTRACT For spaceborne ISAR imaging of space targets, due to the high-speed relative motion between the radar and targets, both the translational and rotational motion exhibit the high-order characteristics. Conventional translational motion compensation (TMC) methods are ineffective in handling such high-order translational motion. Moreover, the migration through resolution cell (MTRC) stems from the presence of the high-order spatial variant phase of the echo signal, resulting in severe defocusing of ISAR images. In this paper, a novel spaceborne ISAR imaging approach for space targets is proposed, which incorporates the high-order TMC and the high-order MTRC correction. First, the slant range model for spaceborne ISAR imaging is derived as a third-order polynomial form. Based on this model, a modified high-order TMC method is proposed, which utilizes the minimum entropy method combined with the Broyden – Fletcher – Goldfarb – Shanno (BFGS) algorithm. The proposed method leverages orbital model information to obtain the initial TMC coefficients, enabling TMC to be completed more accurately and effectively. Then, a modified polynomial keystone transform (PKT) is proposed to correct the high-order MTRC. The PKT-based method effectively addresses both the high-order and first-order MTRC corrections simultaneously. Finally, a spaceborne ISAR imaging approach is proposed to obtain well-focused ISAR images. Simulated and real data results validate the analysis of the spaceborne ISAR imaging model and demonstrate the effectiveness of the spaceborne imaging approach for space targets proposed in this paper.

Deep Neural Networks Training by Stochastic Quasi-Newton Trust-Region Methods

While first-order methods are popular for solving optimization problems arising in deep learning, they come with some acute deficiencies. To overcome these shortcomings, there has been recent interest in introducing second-order information through quasi-Newton methods that are able to construct Hessian approximations using only gradient information. In this work, we study the performance of stochastic quasi-Newton algorithms for training deep neural networks. We consider two well-known quasi-Newton updates, the limited-memory Broyden–Fletcher–Goldfarb–Shanno (BFGS) and the symmetric rank one (SR1). This study fills a gap concerning the real performance of both updates in the minibatch setting and analyzes whether more efficient training can be obtained when using the more robust BFGS update or the cheaper SR1 formula, which—allowing for indefinite Hessian approximations—can potentially help to better navigate the pathological saddle points present in the non-convex loss functions found in deep learning. We present and discuss the results of an extensive experimental study that includes many aspects affecting performance, like batch normalization, the network architecture, the limited memory parameter or the batch size. Our results show that stochastic quasi-Newton algorithms are efficient and, in some instances, able to outperform the well-known first-order Adam optimizer, run with the optimal combination of its numerous hyperparameters, and the stochastic second-order trust-region STORM algorithm.