Nonlinear Mapping Research Articles

Reservoir computing with logistic map.

Recent studies on reservoir computing essentially involve a high-dimensional dynamical system as the reservoir, which transforms and stores the input as a higher-dimensional state for temporal and nontemporal data processing. We demonstrate here a method to predict temporal and nontemporal tasks by constructing virtual nodes as constituting a reservoir in reservoir computing using a nonlinear map, namely, the logistic map, and a simple finite trigonometric series. We predict three nonlinear systems, namely, Lorenz, Rössler, and Hindmarsh-Rose, for temporal tasks and a seventh-order polynomial for nontemporal tasks with great accuracy. Also, the prediction is made in the presence of noise and found to closely agree with the target. Remarkably, the logistic map performs well and predicts close to the actual or target values. The low values of the root mean square error confirm the accuracy of this method in terms of efficiency. Our approach removes the necessity of continuous dynamical systems for constructing the reservoir in reservoir computing. Moreover, the accurate prediction for the three different nonlinear systems suggests that this method can be considered a general one and can be applied to predict many systems. Finally, we show that the method also accurately anticipates the time series of the all the three variable of Rössler system for the future (self-prediction).

Sub-sampling graph neural networks for genomic prediction of quantitative phenotypes.

In genomics, use of deep learning (DL) is rapidly growing and DL has successfully demonstrated its ability to uncover complex relationships in large biological and biomedical data sets. With the development of high-throughput sequencing techniques, genomic markers can now be allocated to large sections of a genome. By analysing allele sharing between individuals, one may calculate realized genomic relationships from single nucleotide polymorphisms (SNPs) data rather than relying on known pedigree relationships under polygenic model. The traditional approaches in genome-wide prediction (GWP) of quantitative phenotypes utilise genomic relationships in fixed global covariance modelling, possibly with some non-linear kernel mapping (for example Gaussian processes). On the other hand, the DL approaches proposed so far for GWP fail to take into account the non-Euclidean graph structure of relationships between individuals over several generations. In this paper, we propose one global convolutional neural network (GCN) and one local sub-sampling architecture (GCN-RS) that are specifically designed to perform regression analysis based on genomic relationship information. A GCN is tailored to non-Euclidean spaces and consists of several layers of graph convolutions. The GCN-RS architecture is designed to further improve the GCN's performance by sub-sampling the graph to reduce the dimensionality of the input data. Through these graph convolutional layers, the GCN maps input genomic markers to their quantitative phenotype values. The graphs are constructed using an iterative nearest neighbour approach. Comparisons show that the GCN-RS outperforms the popular Genomic Best Linear Unbiased Predictor (GBLUP) method on one simulated and three real data sets from wheat, mice and pig with a predictive improvement of 4.4% to 49.4% in terms of test mean squared error (MSE). This indicates that GCN-RS is a promising tool for genomic predictions in plants and animals. Furthermore, GCN-RS is computationally efficient, making it a viable option for large-scale applications.

Interior sound quality evaluation and forecasting of passenger vehicles based on hybrid optimization neural networks

The interior noise of vehicles directly affects the comfort of the occupants, necessitating precise evaluation and control. Existing research has focused on constructing mappings between objective parameters and subjective perceptions of noise, where back propagation neural networks (BPNNs) are widely used due to their strong nonlinear mapping capabilities. However, the selection of initial weights and thresholds can affect the predictive accuracy of BPNN. This study developed a BPNN model optimized by an intelligent algorithm for predicting the level of subjective annoyance of passengers during the movement. Initially, objective parameters of interior noise were obtained through acoustic signal processing techniques, and five parameters were selected for studying subjective annoyance through correlation analysis and two-tailed tests. Meanwhile, the actual subjective ratings of passengers on interior noise were captured for subsequent training of the model and testing of the results. Finally, the established sparrow search algorithm (SSA) and genetic algorithm (GA) optimized BPNN were used to predict subjective evaluations. The predictive accuracy and efficiency of the model were significantly improved upon validation, providing a viable alternative to traditional passenger vehicle noise assessment experiments and valuable references for future noise control and optimization efforts. The experimental results are consistent with the view that the neural network model optimized with a mixture of intelligent algorithms is closer to the passenger’s subjective annoyance level having higher accuracy and efficiency.

Generalized Choi–Davis–Jensen’s Operator Inequalities and Their Applications

The original Choi–Davis–Jensen’s inequality, known for its extensive applications in various scientific and engineering fields, has inspired researchers to pursue its generalizations. In this study, we extend the Choi–Davis–Jensen’s inequality by introducing a nonlinear map instead of a normalized linear map and generalize the concept of operator convex functions to include any continuous function defined within a compact region. Notably, operators can be matrices with structural symmetry, enhancing the scope and applicability of our results. The Stone–Weierstrass theorem and the Kantorovich function play crucial roles in the formulation and proof of these generalized Choi–Davis–Jensen’s inequalities. Furthermore, we demonstrate an application of this generalized inequality in the context of statistical physics.

Prescribed Performance Formation Tracking Control for Underactuated AUVs under Time-Varying Communication Delays

Achieving formation tracking control of underactuated autonomous underwater vehicles (AUVs) under communication delays presents a significant challenge. To address this challenge, a distributed prescribed performance control protocol based on a real-time state information online predictor (RSIOP) is proposed in this paper. First, we innovatively designed an RSIOP to achieve active compensation for the delayed state information of neighboring AUVs. Next, considering formation performance and safety, a low-complexity and practical nonlinear mapping function was used to implement prescribed performance tracking control for the AUV formation. Additionally, the adverse effects of external disturbance uncertainties and input saturation are also considered. Finally, the simulation tests demonstrated that the proposed formation control protocol can successfully achieve the predetermined formation tracking tasks in the presence of time-varying communication delays and external disturbances, while also enabling real-time changes in formation configuration during the process. Throughout, the protocol maintains input saturation limits, and the actual control inputs remain smooth, with no significant oscillations. Furthermore, comparative simulation tests verified the necessity of the RSIOP developed in this study and quantitatively demonstrated that the proposed control method exhibits superior performance in terms of formation control accuracy, error convergence speed, and transient-state constraints.

Hyperspectral Image Denoising and Compression Using Optimized Bidirectional Gated Recurrent Unit

The availability of a higher resolution fine spectral bandwidth in hyperspectral images (HSI) makes it easier to identify objects of interest in them. The inclusion of noise into the resulting collection of images is a limitation of HSI and has an adverse effect on post-processing and data interpretation. Denoising HSI data is thus necessary for the effective execution of post-processing activities like image categorization and spectral unmixing. Most of the existing models cannot handle many forms of noise simultaneously. When it comes to compression, available compression models face the problems of increased processing time and lower accuracy. To overcome the existing limitations, an image denoising model using an adaptive fusion network is proposed. The denoised output is then processed through a compression model which uses an optimized deep learning technique called "chaotic Chebyshev artificial hummingbird optimization algorithm-based bidirectional gated recurrent unit" (CCAO-BiGRU). All the proposed models were tested in Python and evaluated using the Indian Pines, Washington DC Mall and CAVE datasets. The proposed model underwent qualitative and quantitative analysis and showed a PSNR value of 82 in the case of Indian Pines and 78.4 for the Washington DC Mall dataset at a compression rate of 10. The study proved that the proposed model provides the knowledge about complex nonlinear mapping between noise-free and noisy HSI for obtaining the denoised images and also results in high-quality compressed output.

Preassigned Time Adaptive Neural Tracking Control for Stochastic Nonlinear Multiagent Systems With Deferred Constraints.

This article studies a preassigned time adaptive tracking control problem for stochastic multiagent systems (MASs) with deferred full state constraints and deferred prescribed performance. A modified nonlinear mapping is designed, which incorporates a class of shift functions, to eliminate the constraints on the initial value conditions. By virtue of this nonlinear mapping, the feasibility conditions of the full state constraints for stochastic MASs can also be circumvented. In addition, the Lyapunov function codesigned by the shift function and the fixed-time prescribed performance function is constructed. The unknown nonlinear terms of the converted systems are handled based on the approximation property of the neural networks. Furthermore, a preassigned time adaptive tracking controller is established, which can achieve deferred prescribed performance for stochastic MASs that provide only local information. Finally, a numerical example is given to demonstrate the effectiveness of the proposed scheme.

Assessing gait in neurological disorders during body weight support: Nonlinear registration and statistical parametric mapping for amplitude and temporal effects

Assessing gait in neurological disorders during body weight support: Nonlinear registration and statistical parametric mapping for amplitude and temporal effects

Intelligent seismic AVO inversion method for brittleness index of shale oil reservoirs

The brittleness index (BI) is crucial for predicting engineering sweet spots and designing fracturing operations in shale oil reservoir exploration and development. Seismic amplitude variation with offset (AVO) inversion is commonly used to obtain the BI. Traditionally, velocity, density, and other parameters are firstly inverted, and the BI is then calculated, which often leads to accumulated errors. Moreover, due to the limited of well-log data in field work areas, AVO inversion typically faces the challenge of limited information, resulting in not high accuracy of BI derived by existing AVO inversion methods. To address these issues, we first derive an AVO forward approximation equation that directly characterizes the BI in P-wave reflection coefficients. Based on this, an intelligent AVO inversion method, which combines the advantages of traditional and intelligent approaches, for directly obtaining the BI is proposed. A TransU-net model is constructed to establish the strong nonlinear mapping relationship between seismic data and the BI. By incorporating a combined objective function that is constrained by both low-frequency parameters and training samples, the challenge of limited samples is effectively addressed, and the direct inversion of the BI is stably achieved. Tests on model data and applications on field data demonstrate the feasibility, advancement, and practicality of the proposed method.

Hybrid Modeling and Management of Lodging in Subtropical Fiber Flax: Optimizing Plant Nutrition for Sustainable Cultivation

ABSTRACT Subtropical fiber flax faces significant challenges due to crop lodging, exacerbated by the high N regimes needed for increased fiber production. This study examines impact of balanced P and K applications under varied N regimes on lodging resistance, fiber yield, and quality of flax. Field experiments with 12 NPK treatments revealed that while 120:19:38 kg N, P, K ha−1 achieved highest plant height, stem-diameter, and fresh-weight while increased lodging percentage and reduced fiber quality when P and K were not balanced. Conversely, balanced P and K applications mitigated negative effects of high N, significantly reducing lodging and enhancing fiber yield, quality. Optimal fiber quality, including fiber length and bundle tenacity, was observed with 90:19:38 kg N, P, K ha−1. The novelty of this study lies in integration of stochastic and ML approaches to develop hybrid models for lodging. By combining LASSO with ANN, NLSVR, and RF techniques, hybrid models outperformed individual models in lodging prediction. Specifically, LASSO-NLSVR provided most accurate predictions due to its nonlinear mapping capabilities. Key predictive factors included fiber content, linear density, and tensile strength at 60 days post-sowing, offering valuable insights for breeders and agronomists to improve flax lodging resistance and fiber quality in subtropical climates.

Neural Adaptive Intermittent Output Feedback Control for Autonomous Underwater Vehicles With Full-State Quantitative Designs.

In this article, a neural adaptive intermittent output feedback control is investigated for autonomous underwater vehicles (AUVs) with full-state quantitative designs (FSQDs). To achieve the prespecified tracking performance determined by quantitative indices (e.g., overshoot, convergence time, steady-state accuracy, and maximum deviation) at both kinematic and kinetic levels, FSQDs are designed by transforming constrained AUV model into an unconstrained model via one-sided hyperbolic cosecant boundaries and nonlinear mapping functions. An intermittent sampling-based neural estimator (ISNE) is devised to reconstruct the matched and mismatched lumped disturbances as well as immeasurable velocity states of transformed AUV model, where only system outputs after intermittent sampling are required. Using the estimations of ISNE and the system outputs after triggering, an intermittent output feedback control law incorporated with hybrid threshold event-triggered mechanism (HTETM) is designed to achieve ultimately uniformly bounded (UUB) results. Simulation results are provided and analyzed to validate the effectiveness of the studied control strategy with application to an omnidirectional intelligent navigator (ODIN).

Reduced-order model-inspired experimental identification of damped nonlinear structures

In this work, we address Nonlinear System Identification (NSI) of geometrically nonlinear structures using experimental response data. Specifically we consider nonlinear structures with large inertia effects. A laboratory scale cantilever-type beam structure is considered, which is chosen for its large inertial effects. Free decay data is gathered from the experimental cantilever-type beam system using an image-based measurement technique. A general mathematical model is derived for nonlinear systems with large inertia, by taking inspiration from model reduction methods. Specifically, a reduced-order modelling method, which accounts for the kinetic energy of the modes not included in the reduction basis, is utilised for experimental NSI. Experimental system identification using the ROM-inspired model shows superior accuracy compared to standard stiffness nonlinear models typically used for modelling such systems. We also identify the damping of the structure by projecting the effect of unmodelled modes onto non-conservative dissipative forces in the ROM-inspired model. We show that this addresses issues of poor fit associated with using a linear damping model. This results in a nonlinear damping force in the ROM-inspired model which accounts for the damping effect of the unmodelled modes. These nonconservative effects of unmodelled modes are often neglected, which results in an incorrect damping estimation. A crude Finite-Element (FE) model of the cantilever-type beam is used to generate the nonlinear mapping of nonlinear damping force. The free decay response of the identified nonconservative ROM-inspired model closely matches the measurement decay response. This further validates the accuracy of the ROM-inspired model in NSI.

Electromagnetic Fields Calculation and Optimization of Structural Parameters for Axial and Radial Helical Air-Core Inductors

To improve the current density distribution and electromagnetic performance of air-core inductors, a structural optimization method combining back-propagation(BP) neural network and genetic algorithm(GA) is proposed for the study of axial and radial spiral multi-winding inductors. The Monte Carlo method was used to extract the structural size samples of the inductors, and the training dataset was obtained through the finite element calculation of electromagnetic fields. Based on BP neural networks, nonlinear mapping models between the inductance value, volumetric inductance density, current distribution non-uniformity coefficient, and inductor structural parameters were constructed. A sensitivity analysis of the inductor inductance value affected by the structural parameters was conducted using the Sobol index calculation. Using the current distribution non-uniformity coefficient as the fitness function and the volumetric inductance density as the constraint condition, a genetic algorithm was applied to globally optimize the structural parameters of the inductor. The optimization results were verified through a finite element comparison. The results show that, under the requirement of satisfying the volumetric inductance density, the current distribution non-uniformity coefficient of the Axial Helical Inductor (AHI)-type inductor was reduced by 4.57% compared with the best sample in the sampling, while that of the Radial Helical Inductor (RHI)-type inductor was reduced by 5.33%, demonstrating the practicality of the BP-GA joint algorithm in the structural optimization design of inductors.

Dual and Multi-Target Cone-Beam X-ray Luminescence Computed Tomography Based on the DeepCB-XLCT Network.

Emerging as a hybrid imaging modality, cone-beam X-ray luminescence computed tomography (CB-XLCT) has been developed using X-ray-excitable nanoparticles. In contrast to conventional bio-optical imaging techniques like bioluminescence tomography (BLT) and fluorescence molecular tomography (FMT), CB-XLCT offers the advantage of greater imaging depth while significantly reducing interference from autofluorescence and background fluorescence, owing to its utilization of X-ray-excited nanoparticles. However, due to the intricate excitation process and extensive light scattering within biological tissues, the inverse problem of CB-XLCT is fundamentally ill-conditioned. An end-to-end three-dimensional deep encoder-decoder network, termed DeepCB-XLCT, is introduced to improve the quality of CB-XLCT reconstructions. This network directly establishes a nonlinear mapping between the distribution of internal X-ray-excitable nanoparticles and the corresponding boundary fluorescent signals. To improve the fidelity of target shape restoration, the structural similarity loss (SSIM) was incorporated into the objective function of the DeepCB-XLCT network. Additionally, a loss term specifically for target regions was introduced to improve the network's emphasis on the areas of interest. As a result, the inaccuracies in reconstruction caused by the simplified linear model used in conventional methods can be effectively minimized by the proposed DeepCB-XLCT method. Numerical simulations, phantom experiments, and in vivo experiments with two targets were performed, revealing that the DeepCB-XLCT network enhances reconstruction accuracy regarding contrast-to-noise ratio and shape similarity when compared to traditional methods. In addition, the findings from the XLCT tomographic images involving three targets demonstrate its potential for multi-target CB-XLCT imaging.

Recursive identification of kernel-based hammerstein model for online energy efficiency estimation of large-scale chemical plants

Accurate energy efficiency prediction is crucial for decision-making in large-scale chemical production, especially considering energy management and environmental concerns. The complexity of chemical processes, characterized by strong nonlinearities, dynamics, and uncertainties, challenges traditional prediction methods. This paper introduces KHSM (Kernel-based Hammerstein Subspace Model), which models nonlinear static and linear dynamic processes in series by embedding kernel function-based nonlinear mapping into subspace modeling for energy efficiency estimation. KHSM identifies nonlinear process models without explicit nonlinear mapping functions, constructing dynamic models that encompass both energy input and product output variables. An adaptive KHSM variant dynamically updates the energy efficiency model, improving accuracy by iteratively selecting and excluding samples. Comparative analysis shows KHSM outperforms existing methods, achieving a coefficient of determination (R2) closest to 1 and reducing the root-mean-square error (RMSE) by up to an order of magnitude, with the smallest mean and standard deviation. Additionally, modeling efficiency increases by an order of magnitude. The developed model enables ongoing energy efficiency estimation and proactive identification of efficiency trends. Validation through mathematical and real-world ethylene process cases demonstrates KHSM's efficacy and applicability. These estimates facilitate informed adjustments to energy management strategies and optimization of production approaches in energy-intensive chemical processes.

Machine learning-based input-augmented Koopman modeling and predictive control of nonlinear processes

Koopman-based modeling and model predictive control have been a promising alternative for optimal control of nonlinear processes. Good Koopman modeling performance significantly depends on an appropriate nonlinear mapping from the original state-space to a lifted state space. In this work, we propose an input-augmented Koopman modeling and model predictive control approach. Both the states and the known inputs are lifted using two deep neural networks (DNNs), and a Koopman model with nonlinearity in inputs is trained within the higher-dimensional state space. A Koopman-based model predictive control problem is formulated. To bypass non-convex optimization induced by the nonlinearity in the Koopman model, we further present an iterative implementation algorithm, which approximates the optimal control input via solving a convex optimization problem iteratively. The proposed method is applied to a chemical process and a biological water treatment process via simulations. The efficacy and advantages of the proposed modeling and control approach are demonstrated.

Fixed Point Results for New Classes of k-Strictly Asymptotically Demicontractive and Hemicontractive Type Multivalued Mappings in Symmetric Spaces

Fixed point theory is a significant area of mathematical analysis with applications across various fields such as differential equations, optimization, and dynamical systems. Recently, multivalued mappings have gained attention due to their ability to model more complex and realistic problems. ln this work, novel classes of nonlinear mappings called k-strictly asymptotically demicontractive-type and asymptotically hemicontractive-type multivalued mappings are introduced in real Hilbert spaces that are symmetric spaces. In addition, we discuss the weak and strong convergence results by considered modified algorithms, and a demiclosedness property, for these classes of mappings are proved. Several non-trivial examples are demonstrated to validate the newly defined mappings. Consequently, the results and iterative methods obtained in this study improve and extend several known outcomes in the literature.

Optimization of Agricultural Tractor Engine Hood Forming Quality Based on Neural Network Genetic Algorithm Function

To improve the forming quality of agricultural tractor engine hood and effectively solve the problems of wrinkling and cracking during the drawing forming process, DYNAFORM 5.9 finite element software was used for numerical simulation of the part. Based on a comprehensive scoring method of orthogonal experiments and grey relational analysis, the critical process parameters affecting the “maximum thickening rate” and “maximum thinning rate” were determined. Latin hypercube sampling was used to randomly sample the key process parameters, and the sampled samples served as the data basis for the optimization stage of the neural network genetic algorithm function; an optimization model of the neural network genetic algorithm function was established, with the key process parameters, and the “maximum thickening rate” and “maximum thinning rate” as inputs and outputs respectively, to construct a nonlinear mapping relationship and optimize the process parameters. The study showed that the blank holder force and die clearance had the greatest impact on the “maximum thickening rate” and “maximum thinning rate”, identifying them as key process parameters; the optimal process parameter combination was the blank holder force of 462.71 kN, the die clearance of 1.09 mm, and corresponding “maximum thickening rate” and “maximum thinning rate” of 3.97% and 25.96%, respectively. Overall, this research provides a practical optimization strategy to solve the quality issues of the engine hood, offering a theoretical basis for its actual production and processing with significant practical application value.

Bayesian learning of feature spaces for multitask regression

This paper introduces a novel approach to learn multi-task regression models with constrained architecture complexity. The proposed model, named RFF-BLR, consists of a randomised feedforward neural network with two fundamental characteristics: a single hidden layer whose units implement the random Fourier features that approximate an RBF kernel, and a Bayesian formulation that optimises the weights connecting the hidden and output layers. The RFF-based hidden layer inherits the robustness of kernel methods. The Bayesian formulation enables promoting multioutput sparsity: all tasks interplay during the optimisation to select a compact subset of the hidden layer units that serve as common non-linear mapping for every tasks. The experimental results show that the RFF-BLR framework can lead to significant performance improvements compared to the state-of-the-art methods in multitask nonlinear regression, especially in small-sized training dataset scenarios.

Neodymium oxide concentration state recognition model in neodymium molten salt electrolysis process based on flame image features

Accurate recognition of the concentration state of neodymium-oxide (Nd2O3) in the neodymium (Nd) molten salt electrolysis process provides crucial feedback information for online adjustment of process parameters during Nd metal batch production. This paper proposes a Nd2O3 concentration state recognition model based on flame image features. The model employs the lightweight flame segmentation algorithm (FEC-Net) to accurately segment the flame regions in the collected Nd electrolysis cell flame images. Then, using image processing techniques, geometric and color features of the flame regions are extracted. Finally, a Support Vector Machine (SVM) is used to establish a nonlinear mapping model between the flame features and Nd2O3 concentration states. This model classifies the collected flame image dataset to verify the Nd2O3 concentration state during a certain period of Nd molten salt electrolysis. Experiments demonstrate that the recognition accuracy of SVM reaches 96.09%, meeting the monitoring requirements of the Nd molten salt electrolysis process.