Regularization Approach Research Articles

The modified fractional‐order quasi‐reversibility method for a class of direct and inverse problems governed by time‐fractional heat equations with involution perturbation

This study aims to explore two classes of ill‐posed problems governed by a nonclassical fractional heat equation with an involution perturbation. To achieve a stable solution, we introduce a modified pseudo‐parabolic regularization method that involves a correction term through a mixed fractional derivation operator, resulting in a sequence of well‐posed problems that depend on a regularization parameter . We rigorously demonstrate that the resulting approximate problems are well‐posed and present convergence results for this regularization approach.

Classification of Alzheimer’s Disease Detecting Using Deep Learning

There are a wide range of reasons for dementia, yet Alzheimer's Infection is the most normal structure. As the condition advances, it restricts one's capacity to play out any errand without help, and the analysis timetable and maturing populace are supposed to make its commonness increment. The regular approaches to distinguishing Alzheimer's is tiring for the two patients, specialists where it includes recovering the previous clinical records and having Attractive Reverberation Imaging sweeps and even neuro actual testing which can be awkward for patients. An early determination of cerebrum infections has a major effect with regards to endeavouring to fix them. Our work has utilized profound learning (brain organizations) to identify Alzheimer's sickness sooner than expected by joining it with profound learning. As the got dataset from UCI Storehouse is vigorously imbalanced, we equitably conveyed the information between the classifications utilizing Destroyed. Then the model is prepared and tried with the ordered X-ray information for example extremely gentle, gentle, moderate and serious Promotion lastly remove elements to look at the outcomes. The outcomes we accomplished are contrasted and the past endeavours on recognition of Alzheimer's and emerged to be fundamentally more noteworthy with regards to accuracy and exactness.

Optimized dual-gas co-production from hydrate reservoirs with underlying gas through depressurization & well closure cycling: An experimental evaluation

The regular depressurization method for the exploitation of natural gas hydrate, while effective in gas production, carries a high risk of hydrate regeneration and significant reservoir shrinkage. In this study, the hydrate reservoirs containing underlying gas were synthesized by controlling the initial water distribution, and confining pressure was applied to replicate sub-seafloor conditions. An innovative cyclic depressurization (DP) + well closure (WC) cycling scheme was implemented to facilitate the joint production of hydrate and underlying gas. The heat transfer, gas production, and sediment deformation characteristics during dual-gas co-production were compared and examined considering different DP and WC duration. The findings clearly indicate that the DP + WC cycling method yielded significantly superior results compared to the regular DP approach. Specifically, it achieved effective CH4 recovery rates 1.83–2.33 times higher, temperature recovery rates 1.2–1.3 times greater, and a reduced the duration of reservoir contraction. More importantly, the extent of influence on these factors could be controlled by adjusting DP or WC duration. A discovery like this offers diverse gas production approaches tailored to various hydrate reservoir requirements. Overall, this study provides preliminary evidence that the DP + WC cycling method allows for the simultaneous attainment of efficient production and reservoir security, highlighting its potential significance for gas production from hydrate reservoirs containing underlying gas.

Existence of entropy solutions to nonlinear degenerate weighted elliptic p(.)-Laplacian problem and L1-data

Our aim in this paper is to study the existence result of entropy solution for a specific type of nonlinear degenerate weighted elliptic  p(.)-Laplacian problems with Dirichlet-type boundary condition and  L1 data. In the framework of the theory of weighted Sobolev spaces with variable exponents, we use the regularization approach combined with a priori estimates. 

Compositional Inversion for Stable Diffusion Models

Inversion methods, such as Textual Inversion, generate personalized images by incorporating concepts of interest provided by user images. However, existing methods often suffer from overfitting issues, where the dominant presence of inverted concepts leads to the absence of other desired concepts. It stems from the fact that during inversion, the irrelevant semantics in the user images are also encoded, forcing the inverted concepts to occupy locations far from the core distribution in the embedding space. To address this issue, we propose a method that guides the inversion process towards the core distribution for compositional embeddings. Additionally, we introduce a spatial regularization approach to balance the attention on the concepts being composed. Our method is designed as a post-training approach and can be seamlessly integrated with other inversion methods. Experimental results demonstrate the effectiveness of our proposed approach in mitigating the overfitting problem and generating more diverse and balanced compositions of concepts in the synthesized images. The source code is available at https://github.com/zhangxulu1996/Compositional-Inversion.

Multi-task learning regression via convex clustering

Multi-task learning (MTL) is a methodology that aims to improve the general performance of estimation and prediction by sharing common information among related tasks. In the MTL, there are several assumptions for the relationships and methods to incorporate them. One of the natural assumptions in the practical situation is that tasks are classified into some clusters with their characteristics. For this assumption, the group fused regularization approach performs clustering of the tasks by shrinking the difference among tasks. This enables the transfer of common information within the same cluster. However, this approach also transfers the information between different clusters, which worsens the estimation and prediction. To overcome this problem, an MTL method is proposed with a centroid parameter representing a cluster center of the task. Because this model separates parameters into the parameters for regression and the parameters for clustering, estimation and prediction accuracy for regression coefficient vectors are improved. The effectiveness of the proposed method is shown through Monte Carlo simulations and applications to real data.

Can neural networks benefit from objectives that encourage iterative convergent computations? A case study of ResNets and object classification.

Recent work has suggested that feedforward residual neural networks (ResNets) approximate iterative recurrent computations. Iterative computations are useful in many domains, so they might provide good solutions for neural networks to learn. However, principled methods for measuring and manipulating iterative convergence in neural networks remain lacking. Here we address this gap by 1) quantifying the degree to which ResNets learn iterative solutions and 2) introducing a regularization approach that encourages the learning of iterative solutions. Iterative methods are characterized by two properties: iteration and convergence. To quantify these properties, we define three indices of iterative convergence. Consistent with previous work, we show that, even though ResNets can express iterative solutions, they do not learn them when trained conventionally on computer-vision tasks. We then introduce regularizations to encourage iterative convergent computation and test whether this provides a useful inductive bias. To make the networks more iterative, we manipulate the degree of weight sharing across layers using soft gradient coupling. This new method provides a form of recurrence regularization and can interpolate smoothly between an ordinary ResNet and a "recurrent" ResNet (i.e., one that uses identical weights across layers and thus could be physically implemented with a recurrent network computing the successive stages iteratively across time). To make the networks more convergent we impose a Lipschitz constraint on the residual functions using spectral normalization. The three indices of iterative convergence reveal that the gradient coupling and the Lipschitz constraint succeed at making the networks iterative and convergent, respectively. To showcase the practicality of our approach, we study how iterative convergence impacts generalization on standard visual recognition tasks (MNIST, CIFAR-10, CIFAR-100) or challenging recognition tasks with partial occlusions (Digitclutter). We find that iterative convergent computation, in these tasks, does not provide a useful inductive bias for ResNets. Importantly, our approach may be useful for investigating other network architectures and tasks as well and we hope that our study provides a useful starting point for investigating the broader question of whether iterative convergence can help neural networks in their generalization.

Numerical investigation of a fractional order Wolbachia invasive model using stochastic Bayesian neural network

The major goal of this research study is to solve the fractional order Wolbachia invasive model (FWIM) by developing a computational framework based on the Bayesian regularization backpropagation neural network (BRB-NN) approach. The population of mosquitoes is categorized into two classes, Wolbachia-infected mosquitoes and Wolbachia-uninfected mosquitoes. We also incorporate incomplete cytoplasmic incompatibility and imperfect maternal transmission. We investigate the effects of the fractional order derivative (α) and reproduction rate of Wolbachia-infected mosquitoes ϕw on the dynamics of mosquitoes. The proposed Bayesian regularization backpropagation scheme is applied to three distinct cases using 80% and 20% of the created dataset for training and testing, respectively, with 15 hidden neurons. Comparisons of the results are presented to verify the validity of the proposed technique for solving the model. The Bayesian regularization approach is used to lower the mean square error (MSE) for the fractional order Wolbachia invasive model. The achieved results are based on MSE, correlation, state transitions, error histograms, and regression analysis to confirm the effectiveness of the suggested approach. Additionally, the absolute error value modifies the designed approach’s accuracy.

A conditional and regularized approach for large-scale spatiotemporal wind power forecasting

Large-scale wind power forecasting at intraday horizons of minutes-ahead up to hours-ahead is essential to secure important operations in transmission systems. It is clear that recent information collected about neighboring sites improve the predictive performance of autoregressive models. At the scale of a region or of a country, regularization or feature selection are needed to mitigate the high dimensionality of the autoregressive model. Unconditional approaches of regularization have shown limited added value compared to benchmark models in the context of wind power forecasting. This work proposes an intraday wind power forecasting method that predicts the production of any wind farm in the control area of a Transmission System Operator (TSO), taking into account the information collected from other wind farms. The method combines feature selection, regularization and local-learning via conditioning on recent production levels or on expected weather conditions. Improvements in Root Mean Squared Error (RMSE) with respect to other models, evaluated on a dataset with a large number of wind farms are comprised between 4% (10-min horizon) and 11% (3-h horizon). Interpretability of the forecasting model is demonstrated via an analysis of the model coefficients and a discussion of the performance in a challenging situation, namely a wind front.

Improved collaborative filtering for cross-store demand forecasting

Accurate and reliable demand forecasting is crucial for decision-making in assortment planning, store location, and various operational aspects. This study proposes a hybrid TS-SimPMF framework for multi-store multi-product demand forecasting, employing probabilistic matrix factorization (PMF) with time-series similarity measures to capture product and store heterogeneity. The heterogeneity enables the framework to achieve multi-step demand forecasting under unknown item-store combinations through an adaptive integration strategy. We first employ a hybrid dynamic regularization approach to measure the similarity of product sales simultaneously, and then the PMF framework is applied to generate latent vectors of products and stores. The performance of the proposed framework is verified by the real-world retail data, in which the dataset includes all sales records with 50 SKUs in 10 locations, totaling over 180,000 sales records. These experimental results demonstrate the superior performance of the proposed hybrid model compared to state-of-the-art methods.

Regularization of the Boundary Equilibrium Bifurcation in Filippov System with Rich Discontinuity Boundaries

This paper studies a particular type of planar Filippov system that consists of two discontinuity boundaries separating the phase plane into three disjoint regions with different dynamics. This type of system has wide applications in various subjects. As an illustration, a plant disease model and an avian-only model are presented, and their bifurcation scenarios are investigated. By means of the regularization approach, the blowing up method, and the singular perturbation theory, we provide a different way to analyze the dynamics of this type of Filippov system. In particular, the boundary equilibrium bifurcations of such systems are studied. As a consequence, the nonsmooth fold bifurcation becomes a saddle-node bifurcation, while the persistence bifurcation disappears after regularization.

Regularization Effects in Deep Learning Architecture

This research examines the impact of three widely utilized regularization approaches -- data augmentation, weight decay, and dropout --on mitigating overfitting, as well as various amalgamations of these methods. Employing a Convolutional Neural Network (CNN), the study assesses the performance of these strategies using two distinct datasets: a flower dataset and the CIFAR-10 dataset. The findings reveal that dropout outperforms weight decay and augmentation on both datasets. Additionally, a hybrid of dropout and augmentation surpasses other method combinations in effectiveness. Significantly, integrating weight decay with dropout and augmentation yields the best performance among all tested method blends. Analyses were conducted in relation to dataset size and convergence time (measured in epochs). Dropout consistently showed superior performance across all dataset sizes, while the combination of dropout and augmentation was the most effective across all sizes, and the triad of weight decay, dropout, and augmentation excelled over other combinations. The epoch-based analysis indicated that the effectiveness of certain techniques scaled with dataset size, with varying results.

Conjugate gradient method with regularization in estimating mold surface heat flux during continuous casting

The reconstruction of the boundary heat flux between solidifying steel and water-cooled mold wall using measured temperature data is recognized as an inverse heat conduction problem (IHCP). A Tikhonov spatial regularization approach to enhance the smoothness of the Conjugate Gradient Method (CGMr) was proposed which incorporates three different orders of spatial regularization: zeroth, first, and second order. The optimal regularization parameter was selected using a modified L-curve method. The accuracy of the CGMr is investigated with Case 1: a triangular time-spatial variation heat flux, and Case 2: a step change in the form of rectangular variation heat flux. The effects of measurement noise, grid points and time-step size are investigated. The results show that the minimum relative error (eRMS) of the predicted Case 1 heat flux is 1.98%, 7.64%, and 8.02% for zeroth-, first-, and second-order spatial regularization, respectively. The corresponding values for the predicted Case 2 heat flux are 3.82%, 13.42%, and 14.91%. Subsequently, CGMr algorithm is applied to calculate the heat flux in a mold simulator experiment. By comparing the relationship between heat fluxes reconstructed by CGMr after different iteration numbers, it is observed that the recovered heat flux of 2.14 MW/m2 with zeroth regularization remains highly stable.

Three-dimensional magnetotelluric modeling with nontrivial anisotropy by a regularization approach

The regularization approach has been successfully applied to remove spurious solutions in the magnetotelluric (MT) forward problems of isotropic Earth media. However, spurious modes are more likely to occur in numerical solutions of anisotropic media, as electrical anisotropy introduces many more complications to electromagnetic (EM) induction in such media. This study focuses on developing the regularization approach to 3D MT forward problems of anisotropic media, especially those of nontrivial anisotropy. The governing equation is now derived with a conductivity tensor, and an accordingly adapted form of a scaled grad-div term is augmented to regularize the solutions and constrain the divergence-free condition. A new scaling scheme is proposed to cope with the complicated distribution of current densities in nontrivial anisotropy media, and an effective conductivity is approximated by the diagonal elements of the conductivity tensor to formulate the scaling factor. Numerical tests show that, for various models of electrical anisotropy, the regularization approach can effectively enforce the divergence condition and successfully suppress spurious solutions. Therefore, for nontrivial anisotropy media, this approach can also improve the efficiency of the iterative solvers while retaining the accuracy of the solutions. The derivation of the governing equation is based on the MT method. However, this strategy should be generally applicable to other frequency-domain EM methods.

Analytical Investigation of Arrhenius Kinetics with Heat Source/Sink Impacts along a Heated Superhydrophobic Microchannel

Exothermic Arrhenius-controlled chemical reactions are widely employed for heating applications, such as combustion in heating systems and fuel-burning motors.  These effects are critical for manufacturing high thermal systems required for high thermal performances.  Therefore, this paper presents the analytical investigation into the Arrhenius-controlled heat-generating/absorbing fluid of a hydromagnetic flow along a heated upstanding plate in a microchannel.  One wall had a superhydrophobic surface and temperature jump conditions, but the other was unaltered.  The regular perturbation approach investigated the nonlinear, coupled governing equations.  With the help of graphical plots, the impacts of crucial and relevant parameters embedded in the flow are described.  This investigation concludes that chemically reacting parameters' impact significantly elevates the micro-channel's thermal and hydromagnetic flow.  However, applying the heat generation parameter increases fluid velocity, whereas the heat absorption parameter produces the contrary effect.  The outcomes of this study can be relevant to the field of biomedical sciences and devices for improving heat transfer efficiency, chemical synthesis, enhancing the performances of micro-electro-mechanical systems (MEMS) and mini-devices, heating and energy generation, designing efficient energy conversion processes, and so on.

Predicting proximal tubule failed repair drivers through regularized regression analysis of single cell multiomic sequencing

Renal proximal tubule epithelial cells have considerable intrinsic repair capacity following injury. However, a fraction of injured proximal tubule cells fails to undergo normal repair and assumes a proinflammatory and profibrotic phenotype that may promote fibrosis and chronic kidney disease. The healthy to failed repair change is marked by cell state-specific transcriptomic and epigenomic changes. Single nucleus joint RNA- and ATAC-seq sequencing offers an opportunity to study the gene regulatory networks underpinning these changes in order to identify key regulatory drivers. We develop a regularized regression approach to construct genome-wide parametric gene regulatory networks using multiomic datasets. We generate a single nucleus multiomic dataset from seven adult human kidney samples and apply our method to study drivers of a failed injury response associated with kidney disease. We demonstrate that our approach is a highly effective tool for predicting key cis- and trans-regulatory elements underpinning the healthy to failed repair transition and use it to identify NFAT5 as a driver of the maladaptive proximal tubule state.

Strain‐controlled dynamics of transverse domain walls in hybrid piezoelectric–magnetostrictive heterostructures: An asymptotic approach

AbstractThe present work deals with an analytical study of the statical and dynamical behavior of transverse magnetic domain walls in hybrid bilayer piezoelectric/magnetostrictive heterostructures under the combined influence of spin‐polarized electric currents, transverse, and axial applied magnetic fields. The magnetostrictive material is considered to be isotropic and linearly elastic. We perform the investigation within the framework of the one‐dimensional Landau–Lifshitz–Gilbert equation. By employing the regular perturbation asymptotic expansion approach, we derive the explicit analytical expression of the most significant dynamic features, namely, traveling wave profile, DW velocity, and displacement under the influence of small and moderate transverse magnetic fields. Finally, we illustrate numerically the analytical results and delineate the domain wall motion for metallic and semiconductor ferromagnets.

Iterative Pseudo-Sparse Partial Least Square and Its Higher Order Variant: Application to Inference From High-Dimensional Biosignals

Partial Least Square (PLS) regression and its (L1 or L2 norm) regularized versions have been proposed to handle the high-dimensionality aspects of the problem at hand and select relevant features. Addressing these issues improves the generalizability of decoding the unseen data, with the severe challenge of high computational complexity. In order to avoid directly solving the L1 norm optimization problem or performing matrix inversion, this paper proposes two PLS-based algorithms, Pseudo-Sparse PLS (PS-PLS) and iterative Pseudo-Sparse Higher-Order PLS (iPS-HOPLS). In these proposed methods, we add the Pseudo-Sparsity term to reduce the L1 norm of the regression coefficient vector in a selective scheme for better importance interpretation while keeping the algorithm as simple as possible. Regarding the evaluation of the proposed methods, we investigate three critical high-dimensionality regression problems of 1) the prediction of 3D trajectory from Electrocorticography (ECoG) recordings, 2) decoding continuous fluctuation of the Electromyography (EMG) powers from recorded Magnetoencephalography (MEG) signals, and 3) continuous decoding of the finger forces from the High-Density surface Electromyogram (HD-sEMG) signals. As well as providing cognitive-relevant interpretations, the experimental results show significant improvements over the generic methods and competitive performance compared to the state-of-the-art regularized PLS approaches.

Optimizing E-waste management: Deep learning classifiers for effective planning

E-waste demands urgent attention to devise effective and sustainable waste management solutions. In response to this challenge, the integration of deep learning classifiers emerges as a promising avenue to optimize the planning of e-waste collection. By harnessing the capabilities of deep learning, these classifiers yield enriched navigational insights, facilitating more informed asset allocation and strategic interventions. This synthesis of technology-driven planning holds the potential to address the intricate intricacies of e-waste in a sustainable environmental landscape. Furthermore, the identification of important parts in e-waste helps in improving recycling processes, adding to a more maintainable and harmless ecosystem. To improve the potential efficiency and accuracy in waste collection the proposed methodology of Adaptive V3 and Federated Learning (Adaptive V3 and FL) are proposed to optimize e-waste collecting planning. The Inception V3 structure can enhance the classification of the e-waste, also the L2 regularization is utilized to overcome the overfitting issues. Also, federated learning is employed to improve the performance of the Inception V3 with the L2 Regularization approach. The datasets like the Starter e-waste dataset and the Compressed E-waste dataset are employed for the e-waste classification. The performance metrics like accuracy, precision, recall, specificity, and f1-score are utilized for the classification. The overall performance achieved by the proposed method is 98.9 % and this maximized the performance than existing approaches such as DCNN, DLRNN, LSTM as well as BSFC which attained 78.4 %, 78.1 %, 58.6 %, and 39.4 % respectively. This research overcomes the proposed strategy in revolutionizing e-waste collecting, planning, and advancing a technology-driven approach to e-waste management. Further, it is performed to perform the effective e-waste classification with multiple wastes using large equipment.

Tikhonov Regularization for the Fully Coupled Integral Method of Incremental Hole-Drilling

BackgroundThe unit pulse integral method is used extensively with the incremental hole-drilling residual stress measurement technique. The ASTM E837 standard, which applies only to isotropic materials, recommends the use of Tikhonov regularization to reduce instability when many depth increments are used. In its current formulation, Tikhonov regularization requires the decoupling of stress, as is possible for isotropic materials. The fully coupled integral method is needed for residual stress determination in layered composite laminates and is currently employed without Tikhonov regularization. This causes greater sensitivity to measurement errors and consequently large stress uncertainties. An approximate method of applying Tikhonov regularization exists for biaxial composites, but is not applicable to more complex laminates.ObjectiveExtend Tikhonov regularization to the fully coupled integral method to improve residual stress determination in composite laminates.MethodsThis work investigates the use of the approximate and fully coupled regularization approaches in an angle ply composite laminate of [+45/-45/0/90]s construction. Experimental validation in a [0/+45/90/-45]s laminate is also presented where the regularized fully coupled integral method is compared to the series expansion method that includes all in-plane stress and strain directions simultaneously in a least-squares solution.ResultsThe regularized integral method produces comparable results to those of series expansion while requiring twelve times less FE computation to calculate the compliances. The optimal degree of regularization is also more convenient to determine than the optimal combination of series order required by series expansion.ConclusionsThe new method is easily applied and should find wide application in the measurement of residual stresses in composite laminates.