Nonlinear Mapping Research Articles

Modeling and signal integrity analysis of silicon interposer channels based on MTL and KBNN

In this paper, the equivalent circuit model of interconnect channels in silicon interposer is developed for three-dimensional integrated circuit (3-D IC) based on the theory of multi-conductor transmission line (MTL). The deep neural network (DNN) is employed to learn the nonlinear mapping relationship between the geometric parameters and the distributed parameters, and it is demonstrated that the DNN has a high prediction accuracy. In the implementation, a coarse model is firstly developed by solving the scattering parameters of the model using the chain parameter matrix. The model is optimized using a knowledge-based neural network (KBNN), and a fine model is then established. The numerical examples demonstrate that the optimized model can achieve high accuracy. Finally, the inner contour of the worst-case eye diagrams of the channel is generated using the peak distortion algorithm (PDA), with the worst eye width and height obtained.

Some Remarks on Smooth Mappings of Hilbert and Banach Spaces and Their Local Convexity Property

We analyze smooth nonlinear mappings for Hilbert and Banach spaces that carry small balls to convex sets, provided that the radii of the balls are small enough. We focus on the study of new and mildly sufficient conditions for the nonlinear mapping of Hilbert and Banach spaces to be locally convex, and address a suitably reformulated local convexity problem analyzed within the Leray–Schauder homotopy method approach for Hilbert spaces, and within the Lipschitz smoothness condition for both Hilbert and Banach spaces. Some of the results presented in this work prove to be interesting and novel, even for finite-dimensional problems. Open problems related to the local convexity property for nonlinear mappings of Banach spaces are also formulated.

An Artificial Neural Network Method for Forecasting the Stability of Soil Slopes

Artificial neural network (ANN) methods, based on sophisticated models, have been developed recently that can predict slope stability. In this study, we have developed a genetic algorithm (GA) based on ANN to assess the stability of soil slope. Firstly, an ANN-based genetic algorithm was trained for nonlinear input-output mapping of the slope. A total of 190 soil slopes with unique values of shear strength properties (friction angle, cohesion, and unit weight), geometric parameters (slope angle and slope height), and corresponding factor of safety (FS) have been collected to give a neural network training dataset. Then, a three-layer neural network model is established based on GA. The prediction and performance ability of the established model is assessed using the correlation coefficient (R2). By the outcomes, the trained ANN model with the R2 value of 0.98 is reliable, valid, and simple for evaluating the soil slope stability and estimating the FS. Additionally, the proposed neural network model is applied to a case of soil slope from prior studies. Findings show that the developed ANN model can be versatile in studying the stability of soil slopes.

Scaling properties of the action in the Riemann-Liouville fractional standard map.

The Riemann-Liouville fractional standard map (RL-fSM) is a two-dimensional nonlinear map with memory given in action-angle variables (I,θ). The RL-fSM is parameterized by K and α∈(1,2], which control the strength of nonlinearity and the fractional order of the Riemann-Liouville derivative, respectively. In this work we present a scaling study of the average squared action 〈I^{2}〉 of the RL-fSM along strongly chaotic orbits, i.e., for K≫1. We observe two scenarios depending on the initial action I_{0}, I_{0}≪K or I_{0}≫K. However, we can show that 〈I^{2}〉/I_{0}^{2} is a universal function of the scaled discrete time nK^{2}/I_{0}^{2} (n being the nth iteration of the RL-fSM). In addition, we note that 〈I^{2}〉 is independent of α for K≫1. Analytical estimations support our numerical results.

A lightweight improved residual neural network for bearing fault diagnosis

Timely and accurate fault diagnosis is essential for modern industrial system reliability and safety. However, traditional bearing fault diagnosis using the residual neural network (ResNet) is limited by high parameters, computational costs, and low accuracy. To address this, a lightweight improved residual network (LIResNet) is proposed to enhance the ResNet structure. LIResNet introduces a parallel layer (PL) merging the discrete cosine transform convolutional layer (DCTConv) and the standard convolutional layer (Conv). This reduces trainable parameters, aiding feature extraction from input signals, with spectrograms preprocessed by CWT fed into the PL. Furthermore, integrating a self-attention mechanism enhances fault feature comprehension. The residual structure is refined using low-rank decomposition, reducing model complexity. This refinement, combined with a max-pooling layer and single convolutional layer, forms the downsampling residual module (DAM). The proposed batch-free normalization (BFN) and improved hard-swish activation function constitute the normalized activation module (NAM), ensuring model stability and nonlinear mapping in low-batch data situations. Experiments across bearing datasets reveal that the proposed method achieves a diagnostic accuracy of 99.8%, surpassing ResNet18′s 98.7%. Moreover, while ResNet comprises 11.18M parameters and 753.07M Flops, the proposed method uses 0.06M parameters and 49.49M Flops. These findings underscore the improved lightweight performance and diagnostic capability of our approach.

Generalized latent multi-view clustering with tensorized bipartite graph

Tensor-based multi-view spectral clustering algorithms use tensors to model the structure of multi-dimensional data to take advantage of the complementary information and high-order correlations embedded in the graph, thus achieving impressive clustering performance. However, these algorithms use linear models to obtain consensus, which prevents the learned consensus from adequately representing the nonlinear structure of complex data. In order to address this issue, we propose a method called Generalized Latent Multi-View Clustering with Tensorized Bipartite Graph (GLMC-TBG). Specifically, in this paper we introduce neural networks to learn highly nonlinear mappings that encode nonlinear structures in graphs into latent representations. In addition, multiple views share the same latent consensus through nonlinear interactions. In this way, a more comprehensive common representation from multiple views can be achieved. An Augmented Lagrangian Multiplier with Alternating Direction Minimization (ALM-ADM) framework is designed to optimize the model. Experiments on seven real-world data sets verify that the proposed algorithm is superior to state-of-the-art algorithms.

Integrated passive design method optimized for carbon emissions, economics, and thermal comfort of zero-carbon buildings

Improving passive design methods are important for achieving zero-carbon building (ZCB) targets. Data-driven design approaches are more accurate than conventional methods for multiple-objective optimization (MOO) targets such as carbon emissions (CE), economics, and thermal comfort. In this study, a comprehensive data-driven-based PSO-SVM-NSGA-III method that assists in optimizing passive design parameters are proposed. First, the simulation results for the objectives of CE, incremental cost (IC), and time not comfort (TNC) are performed for an office building in a cold region in China using EnergyPlus and jEPlus software. Then, key influencing factors are chosen via a sensitivity analysis. Second, nonlinear mapping relationships between the passive design parameters and objectives are established with the PSO-SVM model. Compared to the BPNN, SVM, and PSO-BPNN algorithms, the PSO-SVM model exhibits superior prediction performance, with R2 values of 0.977, 0.925, and 0.903 for CE, IC, and TNC, respectively. Third, the nonlinear mapping relationships are used in the established objective functions of NSGA-II and NSGA-III. NSGA-III performed 100 iterations within 21 min and exhibited robust diversity within its population, with a hypervolume value of 0.738. Finally, the Pareto-optimal solution set is formed with the PSO-SVM-NSGA-III framework. This data-driven method offers an efficient approach for improving building performance.

SuperJunction: Learning-Based Junction Detection for Retinal Image Registration

Keypoints-based approaches have shown to be promising for retinal image registration, which superimpose two or more images from different views based on keypoint detection and description. However, existing approaches suffer from ineffective keypoint detector and descriptor training. Meanwhile, the non-linear mapping from 3D retinal structure to 2D images is often neglected. In this paper, we propose a novel learning-based junction detection approach for retinal image registration, which enhances both the keypoint detector and descriptor training. To improve the keypoint detection, it uses a multi-task vessel detection to regularize the model training, which helps to learn more representative features and reduce the risk of over-fitting. To achieve effective training for keypoints description, a new constrained negative sampling approach is proposed to compute the descriptor loss. Moreover, we also consider the non-linearity between retinal images from different views during matching. Experimental results on FIRE dataset show that our method achieves mean area under curve of 0.850, which is 12.6% higher than 0.755 by the state-of-the-art method. All the codes are available at https://github.com/samjcheng/SuperJunction.

High-Dimensional Analysis for Generalized Nonlinear Regression: From Asymptotics to Algorithm

Overparameterization often leads to benign overfitting, where deep neural networks can be trained to overfit the training data but still generalize well on unseen data. However, it lacks a generalized asymptotic framework for nonlinear regressions and connections to conventional complexity notions. In this paper, we propose a generalized high-dimensional analysis for nonlinear regression models, including various nonlinear feature mapping methods and subsampling. Specifically, we first provide an implicit regularization parameter and asymptotic equivalents related to a classical complexity notion, i.e., effective dimension. We then present a high-dimensional analysis for nonlinear ridge regression and extend it to ridgeless regression in the under-parameterized and over-parameterized regimes, respectively. We find that the limiting risks decrease with the effective dimension. Motivated by these theoretical findings, we propose an algorithm, namely RFRed, to improve generalization ability. Finally, we validate our theoretical findings and the proposed algorithm through several experiments.

OENet: An overexposure correction network fused with residual block and transformer

With the wide application of vision in the fields of autonomous driving and medical imaging, the demand for overexposure image correction algorithms is becoming increasingly urgent. However, existing overexposure image correction algorithms can lead to problems such as blurring, color bias, and over-enhancement of the generated images. Optimizing overexposure image quality has a significant impact on improving system performance, accuracy, and safety. In this paper, we propose an overexposure image correction network. First, we built the Detail Enhancement Module (DEM). It adopts global average pooling on each channel of the input feature map. After pooling, an activation function is used for nonlinear mapping to generate a channel attention weight vector. And it is multiplied with the original input feature map to achieve the purpose of enhancing the details of the overexposed image. Second, we construct a context-aware backbone (CAB) to extract features such as color and texture. The linear attention gating mechanism replaces the multi-head attention module in Transformer, and reduces the computational complexity in high-resolution images while maintaining performance by learning linear transformation and attention gating. Finally, we design an attention-guided feature fusion (AGFF) to fuse shallow and deep features. It computes weight vectors for shallow features through an attention module. The calculated result is converted to the same dimension as the input feature by bilinear interpolation, so as to enrich the semantic information and detailed information of the generated image. In addition to designing the network structure, we design a hybrid loss function to improve the quality of the generated image from the spatial and structural aspects, and the exposure function can correct the exposure degree of the generated image. Experiments are conducted on two public datasets and the dataset in this paper. Specifically, the PSNR and SSIM of images generated on the dataset MSEC increased by 1.3813% and 5.56%. The PSNR and SSIM of images generated on the dataset SICE increased by 1.545% and 4.64%. The proposed method can effectively generate clear and high-fidelity images.

Microwave photonics frequency measurement with improved accuracy based on an artificial neural network.

Photonics-assisted techniques for microwave frequency measurement (MFM) show great potential for overcoming electronic bottlenecks, with wild applications in radar and communication. The MFM system based on the stimulated Brillouin scattering (SBS) effect can measure the frequency of multiple high-frequency and wide-band signals. However, the accuracy of the MFM system in multi-tone frequency measurement is constrained by the SBS bandwidth and the nonlinearity of the system. To resolve this problem, a method based on an artificial neural network (ANN) is suggested, which can establish a nonlinear mapping between the measured two-tone signal spectra and the theoretical frequencies. Through simulation verification, the ANN optimized frequencies within the range of (0.5, 27) GHz of the MFM system show 79%, 76%, 70%, 44% reduction in errors separately under four spectral signal-to-noise ratios (SNR) conditions, 20dB, 15dB, 10dB, 0dB, and the frequency resolution is improved from 30MHz to 10MHz.

Short-term power load forecasting method based on Bagging-stochastic configuration networks.

Accurate short-term load forecasting is of great significance in improving the dispatching efficiency of power grids, ensuring the safe and reliable operation of power grids, and guiding power systems to formulate reasonable production plans and reduce waste of resources. However, the traditional short-term load forecasting method has limited nonlinear mapping ability and weak generalization ability to unknown data, and it is prone to the loss of time series information, further suggesting that its forecasting accuracy can still be improved. This study presents a short-term power load forecasting method based on Bagging-stochastic configuration networks (SCNs). First, the missing values in the original data are filled with the average values. Second, the influencing factors, such as the weather- and week-type data, are coded. Then, combined with the data of influencing factors after coding, the Bagging-SCNs integration algorithm is used to predict the short-term load. Finally, by taking the daily load data of Quanzhou City, Zhejiang Province as an example, the program of the abovementioned method is compiled in Python language and then compared with the long short-term memory neural network algorithm and the single-SCNs algorithm. Simulation results show that the proposed method for medium- and short-term load forecasting has a high forecasting accuracy and a significant effect on improving the accuracy of load forecasting.

Zero‐sum game for nonlinear multiagent systems with full‐state constraints

AbstractThis paper addresses the zero‐sum game problem for strict‐feedback nonlinear multiagent systems with full‐state constraints. Specifically, this paper focuses on the zero‐sum game scenario, wherein multiple agents aim to optimize the control strategies while considering the conflicting objectives of their opponents. To handle the full‐state constraints, a one‐to‐one nonlinear mapping technique is employed to convert the original strict‐feedback system into a more manageable pure‐feedback system without state constraints. In order to find a Nash equilibrium for virtual control signals and external disturbances, a simplified reinforcement learning algorithm is proposed, which tackles the challenges posed by solving the Hamilton–Jacobi–Isaacs equation. Unlike the existing optimal control strategies that deal with matching conditions, the optimal control strategy for strict‐feedback nonlinear systems needs to address the computational complexity issue arising from the repeated derivation of the virtual controller. To overcome the high‐order virtual controller problem, an approach based on the dynamic surface technique is introduced. By incorporating an approximation term of the high‐order virtual controller into the value function, the computational complexity challenge is effectively resolved. Based on the Lyapunov stability theorem, it is proved that all signals of the closed‐loop systems are semi‐global uniformly ultimately bounded and the tracking control performance can be guaranteed. Finally, simulation results are given to verify the effectiveness of the proposed control strategy.

Out-of-focus artifact removal for Fresnel incoherent correlation holography by deep learning

Fresnel incoherent correlation holography (FINCH) is a promising three-dimensional (3D) imaging method due to its incoherent illumination and inline optical configuration. However, due to information crosstalk, especially out-of-focus artifacts, the axial resolution of FINCH 3D imaging is limited, and the relationship between the artifacts and the reconstructed image is complex and nonlinear, which is difficult to obtain by traditional optical measurement methods. Here, inspired by the superiority of deep learning in nonlinear mapping over traditional physical methods, we propose and demonstrate a deep learning based out-of-focus artifact removal method for FINCH reconstruction, in which a out-of-focus segmentation convolutional neural network (CNN) is designed for obtaining accurate nonlinear relationship between the artifacts and the reconstructed image by training dataset and optimizing parameters, thereby eliminating information crosstalk in the reconstructed image. Both optical experiment and performance analysis demonstrate the effectiveness and superiority of the designed CNN in realizing out-of-focus artifacts removal. Importantly, this deep learning-based out-of-focus artifacts removal method will provide a useful strategy for realizing high quality 3D imaging of FINCH.

Research on adaptive practical prescribed-time consensus of multiple mechanical systems with full-state constraints

In this paper, an adaptive practical prescribed-time consensus (PPTC) for multiple mechanical systems with full-state constraints is discussed. We first propose a new nonlinear mapping (NM). By transforming the full state–constrained system with the NM, we can obtain an unconstrained system. Then combined with neural networks, graph theory, and practical prescribed-time control theory, a distributed adaptive PPTC protocol is proposed for the unconstrained system, which can ensure that position errors and speed errors reach a certain region within a prescribed-time and full-state constraints are satisfied. Finally, an example is given to demonstrate that this method can be implemented.

Novel high-safety aeroengine performance predictive control method based on adaptive tracking weight

Increasing attention has been attracted to the dynamic performance and safety of advanced performance predictive control systems of the next-generation aeroengine. The latest research demonstrates that Subspace-based Improved Model Predictive Control (SIMPC) can overcome the difficulty in solving the predictive model in MPC/NMPC applications. However, applying constant design parameters cannot maintain consistent control effects in all states. Meanwhile, the designed system relies too much on sensor-measured data, and thus it is difficult to thoroughly validate the safety of the system because of its high complexity. This means that any potential hardware/software faults will endanger the engine. Therefore, this paper first presents a novel nonlinear mapping relationship to adaptively tune the tracking weight online with the change of Power Lever Angle (PLA) and real-time relative tracking error. Thus, without introducing additional design parameters, an Adaptive Tracking Weight-based SIMPC (ATW-SIMPC) controller is designed to improve the control performance in all operating states effectively. Then, a Primary/Backup Hybrid Control (PBHC) strategy with the ATW-SIMPC controller as the primary system and the traditional speed (Nf) controller as the backup system is proposed to ensure safety. The designed affiliated switching controller and the real-time monitor therein can be used to realize reasonable and smooth switching between primary/backup systems, so as to avoid bump transition. The PBHC system switches to the Nf controller when the ATW-SIMPC controller is wrong because of potential hardware/software faults; otherwise, the ATW-SIMPC controller keeps acting on the engine. The main results prove that the ATW-SIMPC controller with the optimal nonlinear mapping relationship, compared with the existing SIMPC controller, uplifts the dynamic control performance by 32% and reduces overshoots to an allowable limit, resulting in a better control effect in full state. The comparison results consistently indicate that the PBHC can guarantee engine safety in occurrence of hardware/software faults, such as sensor/onboard adaptive model faults. The approach proposed is applicable to the design of a model-based engine intelligent control system.

Minimization of the norm of a nonlinear mapping

Minimization of the norm of a nonlinear mapping

Enhancing brain tumor diagnosis: an optimized CNN hyperparameter model for improved accuracy and reliability.

Hyperparameter tuning plays a pivotal role in the accuracy and reliability of convolutional neural network (CNN) models used in brain tumor diagnosis. These hyperparameters exert control over various aspects of the neural network, encompassing feature extraction, spatial resolution, non-linear mapping, convergence speed, and model complexity. We propose a meticulously refined CNN hyperparameter model designed to optimize critical parameters, including filter number and size, stride padding, pooling techniques, activation functions, learning rate, batch size, and the number of layers. Our approach leverages two publicly available brain tumor MRI datasets for research purposes. The first dataset comprises a total of 7,023 human brain images, categorized into four classes: glioma, meningioma, no tumor, and pituitary. The second dataset contains 253 images classified as "yes" and "no." Our approach delivers exceptional results, demonstrating an average 94.25% precision, recall, and F1-score with 96% accuracy for dataset 1, while an average 87.5% precision, recall, and F1-score, with accuracy of 88% for dataset 2. To affirm the robustness of our findings, we perform a comprehensive comparison with existing techniques, revealing that our method consistently outperforms these approaches. By systematically fine-tuning these critical hyperparameters, our model not only enhances its performance but also bolsters its generalization capabilities. This optimized CNN model provides medical experts with a more precise and efficient tool for supporting their decision-making processes in brain tumor diagnosis.

Speech Enhancement Using Machine Learning

The incorporation of machine learning, specifically deep learning, into speech enhancement algorithms represents an advanced methodology aimed at restoring original speech signals from distorted counterparts. This innovative approach incorporates the use of Charlier polynomials-based discrete transform, particularly the discrete Charlier transform (DCHT), to extract spectra from noisy signals employing a fully connected neural network. Leveraging the capabilities of deep learning, particularly in handling nonlinear mapping challenges, the system acquires contextual information from speech signals, resulting in enhanced speech characterized by improved quality and intelligibility. The proposed algorithm undergoes rigorous empirical testing through self-comparison, fine-tuning the DCHT parameter to optimize the performance of speech enhancement models. The experimentation entails the variation of DCHT parameter values, with evaluation conducted using the TIMIT database. Diverse speech measures are employed for comprehensive assessment, revealing the effectiveness of the DCHT-based trained model in enhancing speech signals within specific conditions.

Synchronization transitions in coupled q-deformed logistic maps

The concept of q-deformation has been expanded in a variety of situations including q-deformed nonlinear maps. Coupled q-deformed logistic maps with positive and negative q-diffusive coupling are investigated. The transition to state of synchronized fixed point in the thermodynamic limit for random initial conditions is studied as dynamic phase transitions. Though rare for one-dimensional maps, q-deformed maps show multistability. For weak coupling, the synchronized state may not be observed in the thermodynamic limit with random initial conditions even if it is linearly stable. Thus multistability persists. However, for large lattices with random initial conditions, five well-defined critical points are observed where the transition to a synchronized state occurs. Two of these show continuous phase transition. One of them is in the directed percolation universality class. In another case, the order parameter shows power-law decay superposed with oscillations on a logarithmic scale at the critical point and does not match with known universality classes.