Nonlinear Mapping Research Articles

Multi-Module Echo State Network with Variable Skip Length for Chaotic Time Series Prediction

Echo state networks (ESNs) have been extensively applied in time series prediction problems. However, the memory-nonlinearity trade-off problem severely limits the ability of ESNs to deal with chaotic time series prediction problems. In this study, a multi-module echo state network with variable skip length (MESN-VSL) is proposed to address this problem. First, the reservoir is divided into a nonlinear mapping module and multiple linear memory modules based on the idea of memory and nonlinearity separation. This idea can effectively balance the memory-nonlinearity trade-off problems. Second, a multi-module mechanism with skip length is put forward to model the characteristics of chaotic time series. The skip length and the number of linear memory modules of the MESN-VSL model are automatically determined based on the idea of phase-space reconstruction. Finally, the experimental results further demonstrate that the MESN-VSL model is superior to some existing models in chaotic time series prediction.

Adaptive practical prescribed-time control for uncertain nonlinear systems with time-varying parameters

In this paper, adaptive practical prescribed-time (PPT) control is proposed for a class of uncertain nonlinear systems with time-varying parameters and unmodeled dynamics. By constructing a novel time-varying scaling function and utilizing nonlinear mapping, the PPT control is successfully resolved. The dynamical uncertainties resulting from unmodeled dynamics are estimated by employing an auxiliary available signal, and the unknown continuous terms are handled by the aid of radial basis function neural networks (RBFNNs). A novel adaptive control method is developed by introducing the compensating signals and dynamic surface control as well as practical prescribed-time control. All the signals involved are proved to be semi-globally uniformly ultimately bounded, and the tracking error could enter the pre-specified convergence region within a pre-specified time. The robotic manipulator system is used to demonstrate the effectiveness of the proposed control approach.

Rotating machinery flow field prediction based on hybrid neural network

ABSTRACT The flow phenomena in fluid machinery such as pumps, wind turbines and turbines are complex. For large-scale engineering problems, the computational resources required to solve the Navier-Stokes(N-S) equation are large. In order to solve this problem, a fast and accurate solution method based on hybrid neural network (Convolutional Neural Network – Long Short-Term Memory) is proposed. The nonlinear mapping relationship between the flow field characteristics of rotating machinery and the eddy viscosity coefficient is constructed. The deep learning model is used to replace the RANS standard k-ϵ model, and the eddy viscosity coefficient distribution cloud diagram of rotating machinery is obtained. The results show that the predicted value of the eddy viscosity coefficient of the hybrid neural network model on different slices is in good agreement with the original value and the error is small. Compared with traditional machine learning models such as random forest model, hybrid neural network model takes up only 11.4% of memory, and the accuracy is much better than the random forest model. The hybrid neural network model proposed in this paper has great potential in the prediction of the flow field of rotating machinery.

No-reference image quality assessment based on visual explanation images and deep transfer learning

Quantifying image quality in the absence of a reference image continues to be a challenge despite the introduction of numerous no-reference image quality assessments (NR-IQA) in recent years. Unlike most existing NRIQA methods, this paper proposes an efficient NR-IQA method based on deep visual interpretations. Specifically, the main components of the proposed method are: i) generating a pseudo-reference image (PRI) for the input distorted images, ii) employing a pretrained convolutional network to extract feature maps from the distorted image and the corresponding PRI, iii) producing visual explanation images (VEIs) by using the feature maps of the distorted image and the corresponding PRI, iv) measuring the similarity between the two VEIs using an image similarity metric, and v) employing a non-linear mapping function for quality score alignment. In our experiments, we evaluated the efficacy of the proposed method across various forms of distortion using four benchmark datasets (LIVE, SIQAD, CSIQ, and TID2013). The proposed approach demonstrates parity with the latest methods, as evidenced by comparisons with both hand-crafted NR-IQA and deep learning-based approaches.

Integrating deep learning and discrete cosine transform for surface waves full waveform inversion

Summary Accurate estimations of near-surface S-wave velocity (Vs) models hold particular significance in geological and engineering investigations. On the one hand, the popular Multichannel Analysis of Surface Waves (MASW) is limited to the 1D and the plane wave assumptions. On the other hand, the more advanced and computationally expensive full-waveform inversion (FWI) approach is often solved within a deterministic framework that hampers an accurate uncertainty assessment and makes the final predictions heavily reliant on the starting model. Here we combine deep learning with Discrete Cosine Transforms (DCT) to solve the FWI of surface waves and to efficiently estimate the inversion uncertainties. Our neural network approach effectively learns the inverse non-linear mapping between DCT-compressed seismograms and DCT-compressed S-velocity models. The incorporation of DCT into the deep learning framework provides several advantages: it notably reduces parameter space dimensionality and alleviates the ill-conditioning of the problem. Additionally, it decreases the complexity of the network architecture and the computational cost for the training phase compared to training in the full domain. A Monte Carlo simulation is also used to propagate the uncertainties from the data to the model space. We first test the implemented inversion method on synthetic data to showcase the generalization capabilities of the trained network and to explore the implications of incorrect noise assumptions in the recorded seismograms and inaccurate wavelet estimations. Further, we demonstrate the applicability of the implemented method to field data. In this case, available borehole information is used to validate our predictions. In both the synthetic and field applications, the predictions provided by the proposed method are compared with those of a deterministic FWI and the outcomes of a network trained in the full data and model spaces. Our experiments confirm that the implemented deep-learning inversion efficiently and successfully solves the FWI problem and yields more accurate and stable results than a network trained without the DCT compression. This opens the possibility to efficiently train a neural network that provides accurate instantaneous predictions of Vs near-surface models and related uncertainties.

Development of a machine learning-based risk assessment model for loneliness among elderly Chinese: a cross-sectional study based on Chinese longitudinal healthy longevity survey.

Loneliness is prevalent among the elderly and has intensified due to global aging trends. It adversely affects both mental and physical health. Traditional scales for measuring loneliness may yield biased results due to varying definitions. The advancements in machine learning offer new opportunities for improving the measurement and assessment of loneliness through the development of risk assessment models. Data from the 2018 Chinese Longitudinal Healthy Longevity Survey, involving about 16,000 participants aged ≥ 65 years, were used. The study examined the relationships between loneliness and factors such as functional limitations, living conditions, environmental influences, age-related health issues, and health behaviors. Using R 4.4.1, seven assessment models were developed: logistic regression, ridge regression, support vector machines, K-nearest neighbors, decision trees, random forests, and multi-layer perceptron. Models were evaluated based on ROC curves, accuracy, precision, recall, F1 scores, and AUC. Loneliness prevalence among elderly Chinese was 23.4%. Analysis identified 15 evaluative factors and evaluated seven models. Multi-layer perceptron stands out for its strong nonlinear mapping capability and adaptability to complex data, making it one of the most effective models for assessing loneliness risk. The study found a 23.4% prevalence of loneliness among elderly individuals in China. SHAP values indicated that marital status has the strongest evaluative value across all forecasting periods. Specifically, elderly individuals who are never married, widowed, divorced, or separated are more likely to experience loneliness compared to their married counterparts.

Towards harmonization of SO(3)-equivariance and expressiveness: a hybrid deep learning framework for electronic-structure Hamiltonian prediction

Abstract Deep learning for predicting the electronic-structure Hamiltonian of quantum systems necessitates satisfying the covariance laws, among which achieving SO(3)-equivariance without sacrificing the non-linear expressive capability of networks remains unsolved. To navigate the harmonization between SO(3)-equivariance and expressiveness, we propose HarmoSE, a deep learning method synergizing two distinct categories of neural mechanisms as a two-stage encoding and regression framework. The first stage corresponds to group theory-based neural mechanisms with inherent SO(3)-equivariant properties prior to the parameter learning process, while the second stage is characterized by a non-linear 3D graph Transformer network we propose, featuring high capability on non-linear expressiveness. Their combination lies in the point that, the first stage predicts baseline Hamiltonians with abundant SO(3)-equivariant features extracted, assisting the second stage in empirical learning of equivariance; and in turn, the second stage refines the first stage’s output as a fine-grained prediction of Hamiltonians using powerful non-linear neural mappings, compensating for the intrinsic weakness on non-linear expressiveness capability of mechanisms in the first stage. Our method enables precise, generalizable predictions while capturing SO(3)-equivariance under rotational transformations, and achieves state-of-the-art performance in Hamiltonian prediction tasks under multiple mean absolute error (MAE) metrics, such as the average MAE across all samples and matrix elements, the MAE for challenging samples, the MAE for different Hamiltonian blocks, and the MAE for the challenging blocks. It also demonstrates significant improvements in accuracy for downstream quantities, such as occupied orbital energy and the electronic wavefunction, as measured by MAE and cosine similarity, respectively.

Predicting Water Flowing Fracture Zone Height Using GRA and Optimized Neural Networks

As coal mining depths continue to rise, consideration of WFFZ elevations is becoming increasingly important to mine safety. The goal was to accurately predict the height of the WFFZ to effectively prevent and manage possible roof water catastrophes and ensure the ongoing safety of the mine. To achieve this goal, we combined the particle swarm optimisation (PSO) algorithm with a backpropagation neural network (BPNN) in order to enhance the accuracy of the forecast. The present study draws upon the capacity of the PSO algorithm to conduct global searches and the nonlinear mapping capability of the BPNN. Through grey relational analysis (GRA), the order of the correlation degree was as follows: mining thickness > mining depth > overburden structure > mining width > mining dip. GRA has identified the degree of correlation between five influencing factors and the height of the WFFZ, among these, mining thickness, mining depth, overburden structure and mining width all show strong correlations, and the mining dip of the coal seam shows a good correlation. The weight ranking obtained by the PSO-BPNN method was the same as that obtained by the GRA method. Based on two actual cases, the relative errors of the obtained prediction results after PSO implementation were 2.97% and 3.47%, while the relative errors of the BPNN before optimisation were 18.46% and 4.34%, respectively, indicating that the PSO-BPNN method provides satisfactory prediction results and demonstrating that the PSO-optimised BPNN is easy to use and yields reliable results. In this paper, the height of the WFFZ model under the influence of five factors is only established for the Northwest Mining Area. With the continuous progress of technology and research, the neural network can consider more factors affecting the height of hydraulic fracturing development zones in the future to improve the comprehensiveness and accuracy of prediction.

M-IPISincNet: An explainable multi-source physics-informed neural network based on improved SincNet for rolling bearings fault diagnosis

Timely and accurate diagnosis of bearing faults can effectively reduce the chance of accidents in equipment. However, deep learning methods are mostly completely dependent on data and lack interpretability. It is difficult to deal with the differences between real-time data and training data under changing working conditions and noisy environments. In this study, we proposed M-IPISincNet, an explainability multi-source physics-informed convolutional network based on improved SincNet. Rolling bearing fault diagnosis is realized by extracting fault features from vibration and current signals. Firstly, a physics-informed convolutional layer is designed based on inverse Fourier transform and bandpass filters. Fault features are extracted by multi-scale convolution and multi-layer nonlinear mapping. A DBN network is applied extract unsupervised hidden fusion features in the vibration and current signals. The proposed method is validated under the datasets of Paderborn University (PU) and Case Western Reserve University (CWRU), which proves that the proposed method has explainability, robustness and great accuracy under multiple working conditions and noises.

A Class of φ-Contractions in Orthogonal Metric Spaces with an Application

This article deals with certain outcomes on fixed points of an orthogonal nonlinear contraction map in the framework of O-complete metric spaces. The findings investigated herein enhance and sharpen a few outcomes on fixed points. In order to demonstrate our outcomes, we provide a number of illustrative examples. Finally, via our findings, we discuss the existence and uniqueness of solutions to a periodic boundary value problem.

TRUST-DART: Land Surfaces Temperature and Emissivity Nonlinear Mapping from Nonisothermal Mixed Pixels of Satellite Images with the DART 3D Radiative Transfer Model

Abstract. Coarse spatial resolution of Thermal Infrared (TIR) satellites hampers measuring the temperature and emissivity of scene elements from space that improves our understanding of land surfaces' thermal behavior. The stringent conditions of current TIR unmixing methods hinder the production of extensive component temperature and emissivity products. To address this, we designed a gradient-based multi-pixel physical model, TRUST-DART, to derive the temperature and emissivity of urban features from non-isothermal mixed pixels of satellite images using the DART 3D radiative transfer model. Unlike traditional TIR unmixing methods, TRUSTDART is not constrained by issues related to spatial, spectral, temporal resolution, angular, scene, field measurement requirements, or manual operations. Its inputs include an at-surface radiance image, downwelling sky irradiance, a 3D urban mock-up with feature information, and DART input parameters such as spatial resolution. It generates maps of emissivity and temperature per urban feature. Its accuracy is validated for two vegetation and urban scenes and two types of images (DART simulated pseudo satellite and ASTER observed images). The accuracy of the TRUST-DART depends heavily on the fraction of components. TRUST-DART proves robust for high-fraction components. However, its accuracy decreases with decreasing fractions. TRUST-DART is distributed with DART and is available for education and research via Toulouse III University (https://dart.omp.eu).

Partial state-constrained integrated guidance and control for an STT missile with self-adjusting prescribed performance via non-barrier Lyapunov function method

A state-constrained guidance and control law is vital to the flight safety of an aerial interceptor against a maneuvering target. Taking the flight angle limitations, manipulation saturation, and terminal constraints into consideration, a novel integrated guidance and control (IGC) schema with a self-adjusting prescribed performance is proposed. To avoid the feasibility condition via the conventional barrier Lyapunov function-based method, a new state-dependent nonlinear mapping function is designed, based on which the state-constrained IGC system is converted into a constrained-free model. A novel prescribed performance with a self-tuning mechanism is proposed to guarantee satisfied transit and steady guidance performances. The backstepping technique combined with super-twisting integral sliding modes and newly defined predefined-time disturbance observers is implemented to generate state-constrained virtual command signals. All the signals in the closed-loop system are strictly proven to be bounded by Lyapunov stability theory. The simulation results show the effectiveness of the proposed IGC schema.

Research on high-quality factor sensing characteristics of all-dielectric nanopore array metasurface based on POA-DELM

Abstract Based on the optical properties of symmetric structures independent of each other in the orthogonal direction, an all-dielectric nano-square hole array metasurface which is symmetric along the diagonal is proposed. By changing the size of square nanopores, the symmetry of the periodic unit structure is broken and the double Fano resonance can be excited. The influence of each structural parameter on the sensing performance of the metasurface is analyzed respectively. As the main structural parameters and performance index, the metasurface height and the lengths of the main and sub-diagonal square nanoholes are selected as the input parameters, and the figure of merit (FOM) value is used as the output value. Then the nonlinear mapping relationship between the input and the output is established through deep extreme learning machine (DELM). Different optimization algorithms are used to optimize the weighted FOM values globally. The four evaluation indicators including root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and model fit (R-squared, R2) are used to assess the training effectiveness of the model. It is shown that the indexes are 0.9986, 0.9725, 3.1612 and 0.9733 respectively, and the FOM values of the dual Fano resonance after pelican optimization algorithm ( POA ) optimization are as high as 9.88 × 103 and 1.28 × 105, which demonstrate the effectiveness of POA-DELM proposed in this paper.

Research on the application of a hybrid intelligent algorithm in reducing the negative response of shield tunneling construction

Traditional shield project control relies on manual monitoring and management, which suffers from poor reliability, lag, and other defects. In this paper, a hybrid algorithm based on Bayesian optimization (BO), light gradient enhancer (LGBM), and nondominated sorting genetic algorithm-III (NSGA-III) is proposed to realize intelligent control of shield construction safety. The BO-LGBM-NSGA-III is a multiobjective optimization algorithm that takes cutterhead wear and shield energy consumption as objective functions and the nonlinear mapping function of surface settlement and construction parameters as fitness functions. Based on the Pareto distribution of the optimized backing structure construction parameters, reasonable limits of the control parameters of the shield tunneling machine are obtained. The conclusions are as follows. (1) The R2 of the test set for surface subsidence prediction is 0.916, and the RMSE is 2.655. (2) The proposed method can achieve multiobjective optimization, and the surface settlement, cutter head wear, and shield energy consumption are optimized by 49.92%, 24.38%, and 41.88%, respectively. (3) By using this method, both prediction and optimization can be realized, and the optimal control scheme can be obtained. The negative impact of shield tunneling construction has been significantly reduced.

Research on BP neural network model-based data mining technique in KOL identification

Abstract. Accompanied by the development of artificial intelligence industry, to play the data value of web crawler technology has been the focus of research in the field of computer network and data science, and the data mining technology based on artificial neural network intelligent algorithm is widely used. In view of this, this paper takes the BP neural network data mining technology, which has excellent nonlinear mapping capability, parallel processing capability and fault tolerance and is widely used, as the basis, and integrates the methods and ideas of data mining into the mining of data laws in the field of KOL identification of key opinion leaders, with a view to finding valuable intrinsic laws and relationships between the mining of web crawler technology and the identification of KOL features. The research content of this paper mainly includes two aspects of research work, the design of high-performance data mining technology and the actual work in the field of KOL recognition. On the one hand, this paper comprehensively describes the basic theory and methods of data mining, and focuses on the in-depth analysis and elaboration of BP neural network-based data mining technology on the basis of understanding and analyzing a variety of data mining technologies. On the other hand, this paper aims to solve the problem of bias in the prediction of traditional KOL model and design the experimental method of KOL recognition by BP neural network algorithm.

A convolutional neural network based method for fork type wing fuselage docking

The fork-ear connection attachment method is a widely used technique for attaching the fuselage to the wing. During the fork-ear wing-fuselage docking process, it is essential to ensure that the fork-ear holes in the fuselage and wing are precisely aligned before inserting the mounting pins to complete the final connection. Thus, the alignment accuracy of the fork-ear holes is crucial during the assembly process. When employing conventional visual servo methods to determine the pose adjustment for fork-type wing-fuselage docking, it is necessary to establish a conversion relationship between the image, camera, and posture adjustment mechanism. However, this process can introduce various nonlinear errors that are challenging to compensate for through mathematical modeling. To address this issue, this paper proposes a method for nonlinear mapping estimation of the pose adjustment amounts and develops a pose adjustment estimation convolutional neural network (PAAECNN) with superior performance validated through experiments and discussions. PAAECNN achieves end-to-end mapping from the fork-ear intersection hole images to the pose adjustment amounts for fork-ear wing-fuselage docking. The experimental results demonstrate that the proposed method for estimating the pose adjustment amounts in fork-ear wing-fuselage docking is highly accurate and suitable for visually guided docking tasks.

A review of load forecasting technology based on artificial intelligence

Abstract. Driven by the "dual carbon" goals and the construction of new-type power systems, the importance of power load forecasting technology has become increasingly prominent. Accurate power load forecasting can not only ensure the safe and stable operation of the power system, but also promote the efficient use of clean energy and reduce carbon emissions. Traditional power load forecasting methods have become insufficient in dealing with the complexity and nonlinear growth of power systems, and the development of artificial intelligence technology has brought new possibilities for power load forecasting. Power load forecasting methods based on machine learning and deep learning have gradually become a hot topic of research due to their powerful nonlinear mapping capabilities and advantages in processing big data. These methods not only perform well in short-term forecasting, but also show potential in medium- and long-term forecasting. This paper discusses the application of different artificial intelligence technologies in power load forecasting by sorting out the development status of related technologies, and provides a reference direction for future research.

MKAN-MMI: empowering traditional medicine-microbe interaction prediction with masked graph autoencoders and KANs.

The growing microbial resistance to traditional medicines necessitates in-depth analysis of medicine-microbe interactions (MMIs) to develop new therapeutic strategies. Widely used artificial intelligence models are limited by sparse observational data and prevalent noise, leading to over-reliance on specific data for feature extraction and reduced generalization ability. To address these limitations, we integrate Kolmogorov-Arnold Networks (KANs), independent subspaces, and collaborative decoding techniques into the masked graph autoencoder (Mask GAE) framework, creating an innovative MMI prediction model with enhanced accuracy, generalization, and interpretability. First, we apply Bernoulli distribution to randomly mask parts of the medicine-microbe graph, advancing self-supervised training and reducing noise impact. Additionally, the independent subspace technique enables graph neural networks (GNNs) to learn weights independently across different feature subspaces, enhancing feature expression. Fusing the multi-layer outputs of GNNs effectively reduces information loss caused by masking. Moreover, using KANs for advanced nonlinear mapping enhances the learnability and interpretability of weights, deepening the understanding of complex MMIs. These measures significantly enhanced the accuracy, generalization, and interpretability of our model in MMI prediction tasks. We validated our model on three public datasets with results showing that our model outperformed existing leading models. The relevant data and code are publicly accessible at: https://github.com/zhuoninnin1992/MKAN-MMI.

Performance degradation assessment of rolling bearings for electrostatic monitoring based on IDDAE and ADPC

Abstract To improve the early degradation detection capability of the electrostatic monitoring system for rolling bearings, a performance degradation evaluation method based on improved deep denoising autoencoder (IDDAE) and adaptive density peak clustering (ADPC) is proposed in this paper. Firstly, the fusion of electrostatic charge signal features with conventional time-domain, frequency-domain and time-frequency-domain features constitutes the characteristic parameter set of the electrostatic monitoring system indicating the status of the bearings. Then, in order to improve the feature extraction ability of DAE, the deep network DDAE is constructed, and L1 regularisation and Dropout mechanism are applied to avoid overfitting in the deep network, so as to achieve non-linear mapping dimensionality reduction of high-dimensional features. Moreover, to eliminate the error caused by manually selecting the clustering centre, the parameters are adaptively determined by entropy value method and comprehensive optimisation search on the basis of DPC, thus avoiding the "chain effect" that occurs in traditional DPC when data are incorrectly aggregated due to incorrect assignment of clustering centres. Consequently, an improved ADPC algorithm is used to establish a model to measure the health status of bearings, calculate the Mahalanobis distance (MD) be-tween the test set and the cluster centre, and quantitatively characterize the degree of performance degradation of rolling bearings. Finally, combining the 3σ principle, a repair method that can satisfy online monitoring and adapt to spurious fluctuations in different situations is established on a sliding window to obtain an improved index IMD that can accurately characterise the rolling bearing degradation process. The experimental results show that the proposed method can identify early bearing degradation earlier and has better monotonicity, robustness and tendency than other performance degradation assessment methods.

Between-area communication through the lens of within-area neuronal dynamics.

A core problem in systems and circuits neuroscience is deciphering the origin of shared dynamics in neuronal activity: Do they emerge through local network interactions, or are they inherited from external sources? We explore this question with large-scale networks of spatially ordered spiking neuron models where a downstream network receives input from an upstream sender network. We show that linear measures of the communication between the sender and receiver networks can discriminate between emergent or inherited population dynamics. A match in the dimensionality of the sender and receiver population activities promotes faithful communication. In contrast, a nonlinear mapping between the sender to receiver activity, for example, through downstream emergent population-wide fluctuations, can impair linear communication. Our work exposes the benefits and limitations of linear measures when analyzing between-area communication in circuits with rich population-wide neuronal dynamics.