Nonlinear Mapping Research Articles

Fast reconstruction of EEG signal compression sensing based on deep learning

When traditional EEG signals are collected based on the Nyquist theorem, long-time recordings of EEG signals will produce a large amount of data. At the same time, limited bandwidth, end-to-end delay, and memory space will bring great pressure on the effective transmission of data. The birth of compressed sensing alleviates this transmission pressure. However, using an iterative compressed sensing reconstruction algorithm for EEG signal reconstruction faces complex calculation problems and slow data processing speed, limiting the application of compressed sensing in EEG signal rapid monitoring systems. As such, this paper presents a non-iterative and fast algorithm for reconstructing EEG signals using compressed sensing and deep learning techniques. This algorithm uses the improved residual network model, extracts the feature information of the EEG signal by one-dimensional dilated convolution, directly learns the nonlinear mapping relationship between the measured value and the original signal, and can quickly and accurately reconstruct the EEG signal. The method proposed in this paper has been verified by simulation on the open BCI contest dataset. Overall, it is proved that the proposed method has higher reconstruction accuracy and faster reconstruction speed than the traditional CS reconstruction algorithm and the existing deep learning reconstruction algorithm. In addition, it can realize the rapid reconstruction of EEG signals.

Deep learning-based state prediction of the Lorenz system with control parameters.

Nonlinear dynamical systems with control parameters may not be well modeled by shallow neural networks. In this paper, the stable fixed-point solutions, periodic and chaotic solutions of the parameter-dependent Lorenz system are learned simultaneously via a very deep neural network. The proposed deep learning model consists of a large number of identical linear layers, which provide excellent nonlinear mapping capability. Residual connections are applied to ease the flow of information and a large training dataset is further utilized. Extensive numerical results show that the chaotic solutions can be accurately forecasted for several Lyapunov times and long-term predictions are achieved for periodic solutions. Additionally, the dynamical characteristics such as bifurcation diagrams and largest Lyapunov exponents can be well recovered from the learned solutions. Finally, the principal factors contributing to the high prediction accuracy are discussed.

Physics-Informed Graphical Learning and Bayesian Averaging for Robust Distribution State Estimation

This paper proposes a robust topology change-aware distribution system state estimation (DSSE) method based on a physics-informed graph neural network and Bayesian Probability Weighted Averaging (BPWA). A general state estimator is first built utilizing a graph attention network to learn the nonlinear mapping functions under different distribution network topologies. During this stage, the topology information is embedded in the neural network and the attention mechanism is employed to capture collaborative signals and discriminate the importance of neighboring buses. Then, the BPWA method allows assigning proper weights for the state estimation results under different topologies, which finally yields a single consensus solution via the sparse training samples under the new topology. The physics-informed mechanism enables the proposed method to embed the topology knowledge in the neural network while fully exploiting the value of historical data. Robustness to anomalous measurements is achieved through the embedding of physics knowledge. The application of the BPWA method further allows the proposed method to achieve faster adaptation to topology change and quantification of the estimation uncertainties by measurement errors. MATLAB and Python are used to carry out the comparative tests to evaluate the performance of the proposed method.

Extended scene deep-phase-retrieval Shack-Hartmann wavefront sensors

Context. Strong atmospheric turbulence has been a challenge for high-resolution imaging of solar telescopes. Adaptive optics (AO) systems are capable of improving the quality of imaging by correcting partial aberrations. Thus, the performance of Shack-Hartmann sensors in measuring aberrations generally determines the upper performance bound of AO systems. In solar AO, classic correlation Shack-Hartmann sensors only correct a small number of modal aberrations. Moreover, strong aberrations are difficult to measure stably by correlation Shack-Hartmann. In this context, the improvement in the performance of Shark-Hartmann sensors promises to enable higher-resolution imaging of extended objects for ground-based telescopes or Earth observation. Aims. We propose a new extended scene deep-phase-retrieval Shack-Hartmann wavefront sensing approach to improve the image quality of solar telescopes. It is capable of achieving high-accuracy measurements of high-spatial-resolution wavefronts on extended scene wavefront sensing. Moreover, it has great generalization when observing unknown objects from different fields of view of the telescope. Methods. Our proposed approach can extract features resembling the sub-aperture point spread function (PSF) from a Shack-Hartmann sensor image without any prior information. Then a convolutional neural network is used to establish a nonlinear mapping between the feature image and the wavefront modal coefficients. The extracted feature greatly eliminates the shape information of the extended object while maintaining more information related to aberrations. We verified the performance of the proposed method through simulations and experiments. Results. In the indoor experiment on the ground layer adaptive optics (GLAO) of the 1 m New Vacuum Solar Telescope, compared to the Shack-Hartmann correlation method, the proposed method reduces the correction errors by more than one third. When observing objects from different fields of view in the GLAO that differ from the object in the training data, the relative errors fluctuate within the range of 20% to 26%. The AO system with the proposed wavefront measurement method can obtain higher-resolution focal images of the simulated solar granulation after a round of offline correction. The average latency of the proposed method is about 0.6 ms.

Two-dimensional temperature field inversion of turbine blade based on physics-informed neural networks

Correct evaluation of the blades' surface temperature field is crucial to the structural design and operational safety of aero-engine turbine blades. Current high-temperature measurement technology can only measure the limited discrete points temperature of the hot-end turbine blades. If the boundary conditions are completely unknown, it is still difficult to solve equations through traditional computational fluid dynamics methods. It is an inverse problem to predict the temperature field of the turbine engine blade with unknown boundary conditions. This paper proposes a two-dimensional temperature field inversion of turbine blades based on physics-informed neural networks (PINN) and finite discrete temperature measurement points. The PINN is used to model the nonlinear mapping of input variables and output variables. Only a small amount of data is used to train the neural network. It can be found that adding the loss term of the physical governing equation during training can make the neural network better predict the temperature field of the turbine blade, which can also avoid anomalies such as large temperature errors in some areas that may occur when training with only a small amount of data. When the boundary conditions are completely unknown, the average relative error of PINN trained with only 62 points of temperature data on the test set is below 2%, and the R2−Score is above 0.95. When the training data reaches 122 points of temperature data, the average relative error of PINN on the test set is less than 1%, and the R2−Score reaches 0.99.

InVAErt networks: A data-driven framework for model synthesis and identifiability analysis

Use of generative models and deep learning for physics-based systems is currently dominated by the task of emulation. However, the remarkable flexibility offered by data-driven architectures would suggest to extend this representation to other aspects of system analysis including model inversion and identifiability. We introduce InVAErt (pronounced invert) networks, a comprehensive framework for data-driven analysis and synthesis of parametric physical systems which uses a deterministic encoder and decoder to represent the forward and inverse solution maps, a normalizing flow to capture the probabilistic distribution of system outputs, and a variational encoder designed to learn a compact latent representation for the lack of bijectivity between inputs and outputs. We formally analyze how changes in the penalty coefficients affect the stationarity condition of the loss function, the phenomenon of posterior collapse, and propose strategies for latent space sampling, since we find that all these aspects significantly affect both training and testing performance. We verify our framework through extensive numerical examples, including simple linear, nonlinear, and periodic maps, dynamical systems, and spatio-temporal PDEs.

Estimation of the Born data in inverse scattering of layered media

The first term in the Born series, as we call the Born data, is linear with the scatterers. Here we present a scheme to map the total field data to the Born data in layered media using only the single-input single-output (SISO) setup. This nonlinear mapping is based on the reduced order model (ROM) approach, which constructs ROMs of the original wave operator. Normally, the construction of ROMs requires multi-input multi-output data. By introducing fictitious sensors, we estimate the Born data with SISO data in layered media. We give a simple way of using the time-domain Green’s function to estimate the received data for other fictitious sensors without calculating the complicated Sommerfeld integral. The resulting Born data contains only the single-scattering component, which can be helpful for many imaging applications. A numerical example is given incorporating the direct imaging back-propagation method. It validates the linearity of the Born data by providing an artifact-free image without the optimization process.

CGAN-ECT: Reconstruction of Electrical Capacitance Tomography images from capacitance measurements using Conditional Generative Adversarial Networks

Due to the rapid growth of applications of Electrical Capacitance Tomography (ECT) across diverse industrial sectors, there is a pressing demand for swift and high-fidelity methodologies for image reconstruction from raw capacitance measurements. Deep learning, as an effective non-linear mapping tool for complicated functions, has been going viral in many fields including electrical tomography. This paper introduces a pioneering contribution by proposing a Conditional Generative Adversarial Network (CGAN) model explicitly tailored for the purpose of reconstructing ECT images from capacitance measurements. We propose a novel modulator to transform the raw input capacitance measurements into a 2D image. To the best of our knowledge, this is the first time to represent the capacitance measurements in an image form. We have created a new massive ECT dataset of synthetic image-measurements pairs for training and testing purposes of the proposed model. This extensive ECT dataset comprises 320,000 synthetic image-measurement pairs. It forms the basis for evaluating the feasibility and generalizability of the CGAN-ECT model, with assessments conducted on testing data, contaminated data, and flow patterns which are intentionally excluded from the model’s training phase. The evaluation results prove the efficacy of the proposed CGAN model in generating ECT images with heightened accuracy compared to traditional methods and alternative deep learning-based image reconstruction algorithms. The CGAN-ECT model has succeeded in a achieving an average image correlation coefficient exceeding 99.3%, coupled with an average relative image error of approximately 0.07.

A reduced order modeling-based machine learning approach for wind turbine wake flow estimation from sparse sensor measurements

A comprehensive understanding of wind turbine wake characteristics is vital, particularly in the context of expanding large offshore wind farms. Existing wake measurement techniques provide only spatially sparse wake measurement data, limiting their utility in precise wind turbine design and control. This paper introduces a data-driven approach that combines proper orthogonal decomposition (POD) with machine learning (ML) techniques, designing a Reduced Order Modeling-based Wake Flow Estimation (ROM-WFE) framework. This framework establishes a nonlinear mapping between sensor measurements and low-dimensional POD coefficients. Two distinct sensor placements, wall-mounted and wake-mounted, are investigated for real measurement scenarios. The results highlight the effectiveness of the proposed wake flow estimation method in reconstructing a complete flow field from exceptionally sparse sensor data, with both wall-mounted and wake-mounted strategies, exhibiting promising results with maximum relative errors of 6.37% and 4.51%, respectively. From the reliability assessments considering various configurations of POD modes and sensor numbers, the ROM-WFE framework demonstrates its capability to estimate wake flow effectively, offering a cost-effective tool for practical applications. Furthermore, the framework maintains accuracy even with high-noise and low-frequency data, demonstrating robustness and generalization. This method significantly contributes to wind turbine wake prediction controller design, promising accurate and robust wake flow field estimation, potentially revolutionizing active wake control and enhancing wind farm operational efficiency.

Recognition of Fiber Optic Vibration Signals Based on Laplace Wavelet Transform and Deep Learning

AbstractConvolutional neural networks possess the capability of feature learning and nonlinear mapping, which has significant advantages in classifying and recognizing optical fiber vibration signals. In order to further enhance the recognition rate of vibration signals, this paper combines wavelet transform with convolutional neural networks and designs a convolutional layer based on parameterized wavelets. In this layer, the initial signal is convolved with parameterized Laplace wavelet dictionaries to complete the wavelet transform. Such customized filters make more sense than filters with randomly initialized parameters for traditional CNNs. Simultaneously, we introduce the channel attention mechanism to enhance the features of the filtered signals. Subsequently, standard CNNs are employed to extract and process signal features, ultimately utilizing a multi‐layer perceptron for recognition and classification. The experimental results show that the network model possesses better recognition refinement. © 2024 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

MT2DInv-Unet: A 2D magnetotelluric inversion method based on deep-learning technology

Traditional gradient-based inversion methods usually suffer from the problems of falling into local minima and relying heavily on initial guesses. Deep-learning methods have received increasing attention due to their excellent nonlinear fitting ability. However, given the recent application of deep-learning methods in the field of magnetotelluric (MT) inversion, there are currently challenges associated with achieving high inversion resolution and extracting sufficient features. We develop a neural network model (called MT2DInv-Unet) based on the deformable convolution for 2D MT inversion to approximate the nonlinear mapping from the MT response data to the resistivity model. The deformable convolution is achieved by adding an offset to each sample point of the conventional convolution operation, which extracts hidden relationships and allows the flexible adjustment of the size and shape of the feature region. Meanwhile, we design the network structure with multiscale residual blocks, which effectively extract the multiscale features of the MT response data. This design not only enhances the network performance but also alleviates issues such as vanishing gradients and network degradation. The results of synthetic models indicate that our network inversion method has stable convergence, good robustness, and generalization performance, and it performs better than the fully convolutional neural network and U-Net network. Finally, the inversion results of field data show that MT2DInv-Unet can effectively obtain a reliable underground resistivity structure and has a good application prospect in MT inversion.

Empirically informed convolutional neural network model for logging curve calibration

Environmental calibration of logging curves is critical for petrophysical interpretation and sweet spot characterization. Wellbore failure frequently occurs in clay-rich shale rocks during drilling, leading to biased logging interpretation and uncertainty. To reduce the biased correction or erroneous decision making in the interpreter-dominated logging curve calibration process, we develop an empirically informed convolutional neural network (EiCNN) logging curve correction strategy to calibrate the borehole failure-induced logging curve abnormity more accurately. The EiCNN method, together with high-quality logging curves as labeled samples, provides a nonlinear mapping between input logging curves and calibrations for the distorted curves. The EiCNN method completely alleviates biased correction or decision making by the interpreter-dominated method. It has a strong generalization ability, using many empirically interpreted high-quality data as input samples. The field validation wells demonstrate that the EiCNN model can precisely correct the distorted logging curves of mudstone segments with a correlation coefficient of >0.95. Moreover, the validation and test wells illustrate that the EiCNN method is capable of precisely correcting logging curves of interlayer mudstone, implying that the EiCNN method, to a certain degree, can also accurately perform environmental correction of logging curves from thin mudstone layers.

A Comparative Study of Vehicle Velocity Prediction for Hybrid Electric Vehicles Based on a Neural Network

Vehicle velocity prediction (VVP) plays a pivotal role in determining the power demand of hybrid electric vehicles, which is crucial for establishing effective energy management strategies and, subsequently, improving the fuel economy. Neural networks (NNs) have emerged as a powerful tool for VVP, due to their robustness and non-linear mapping capabilities. This paper describes a comprehensive exploration of NN-based VVP methods employing both qualitative theory analysis and quantitative numerical simulations. The used methodology involved the extraction of key feature parameters for model inputs through the utilization of Pearson correlation coefficients and the random forest (RF) method. Subsequently, three distinct NN-based VVP models were constructed comprising the following: a backpropagation neural network (BPNN) model, a long short-term memory (LSTM) model, and a generative pre-training (GPT) model. Simulation experiments were conducted to investigate various factors, such as the feature parameters, sliding window length, and prediction horizon, and the prediction accuracy and computation time were identified as key performance metrics for VVP. Finally, the relationship between the model inputs and velocity prediction performance was revealed through various comparative analyses. This study not only facilitated the identification of an optimal NN model configuration to balance prediction accuracy and computation time, but also serves as a foundational step toward enhancing the energy efficiency of hybrid electric vehicles.

Approximation of Almost Diagonal Non-linear Maps by Lattice Lipschitz Operators

Lattice Lipschitz operators define a new class of nonlinear Banach-lattice-valued maps that can be written as diagonal functions with respect to a certain basis. In the n-dimensional case, such a map can be represented as a vector of size n of real-valued functions of one variable. In this paper we develop a method to approximate almost diagonal maps by means of lattice Lipschitz operators. The proposed technique is based on the approximation properties and error bounds obtained for these operators, together with a pointwise version of the interpolation of McShane and Whitney extension maps that can be applied to almost diagonal functions. In order to get the desired approximation, it is necessary to previously obtain an approximation to the set of eigenvectors of the original function. We focus on the explicit computation of error formulas and on illustrative examples to present our construction.

Fixed-time adaptive event-triggered control for multiagent systems with full-state constraints

This paper investigates the fixed-time adaptive event-triggered control problem for a class of nonlinear multiagent systems with full-state constraints. The problem of full-state constraints is solved for multiagent systems by utilising a one-to-one nonlinear mapping. The design conditions of the controllers are more easily satisfied than the existing barrier Lyapunov functions strategy. A fixed-time adaptive control scheme is proposed for unconstrained systems that are converted from constrained systems. In contract with the existing finite-time control schemes that rely on the initial states, this restriction condition can be removed in this paper. An improved event-triggered mechanism with an adaptable switching threshold is designed to provide flexible switching between fixed threshold and variable threshold policies, resulting in reduced execution and sampling. It is proved via the Lyapunov stability method that all signals of the closed-loop systems are semi-global practical fixed-time stable. Finally, the effectiveness of the proposed control strategy is verified by some simulation results.

Entropy Error-based Convolutional Neural Network Sparse Optimization and Application

Convolutional Neural Networks (CNNs), as quintessential representatives of deep neural networks, have found widespread applications in numerous domains such as image recognition, object detection, and image generation, owing to their robust nonlinear mapping capabilities. However, the practical deployment of CNNs faces challenges such as low learning efficiency and subpar accuracy due to the intricacies in the network structure. This paper introduces the smoothing L1 regularization term atop the conventional entropy loss function, effectively enhancing both the learning efficiency and algorithmic precision of Convolutional Neural Networks. The efficacy of the improved algorithm is substantiated through numerical simulations.

Vehicle Driving Safety of Underground Interchanges Using a Driving Simulator and Data Mining Analysis

In the process of driving in an underground interchange, drivers are faced with many challenges, such as being in a closed space, visual changes alternating between light and dark conditions, complex road conditions in the confluence section, and dense signage, which directly affect the safety and comfort of drivers in an underground interchange. Thus, driving simulation, building information modeling (BIM), and data mining were used to analyze the impact of underground interchange safety facilities on driving safety and comfort. Acceleration disturbance and steering wheel comfort loss values were used to assist the comfort analysis. The CART algorithm, classification decision trees, and neural networks were used for data mining, which uses a dichotomous recursive partitioning technique where multiple layers of neurons are superimposed to fit and replace very complex nonlinear mapping relationships. Ten different scenarios were designed for comparison. Multiple linear regression combined with ANOVA was used to calculate the significance of the control variables for each scenario on the evaluation index. The results show that appropriately reducing the length of the deceleration section can improve driving comfort, setting reasonable reminder signs at the merge junction can improve driving safety, and an appropriate wall color can reduce speed oscillation. This study indicates that the placement of traffic safety facilities significantly influences the safety and comfort of driving in underground interchanges. This study may provide support for the optimization of the design of underground interchange construction and internal traffic safety facilities.

Tchebichef Transform Domain-Based Deep Learning Architecture for Image Super-Resolution.

Recent advances in the area of artificial intelligence and deep learning have motivated researchers to apply this knowledge to solve multipurpose applications in the area of computer vision and image processing. Super-resolution (SR), in the past few years, has produced remarkable results using deep learning methods. The ability of deep learning methods to learn the nonlinear mapping from low-resolution (LR) images to their corresponding high-resolution (HR) images leads to compelling results for SR in diverse areas of research. In this article, we propose a deep learning-based image SR architecture in the Tchebichef transform domain. This is achieved by integrating a transform layer into the proposed architecture through a customized Tchebichef convolutional layer (TCL). The role of TCL is to convert the LR image from the spatial domain to the orthogonal transform domain using Tchebichef basis functions. The inversion of the transform mentioned earlier is achieved using another layer known as the inverse TCL (ITCL), which converts back the LR images from the transform domain to the spatial domain. It has been observed that using the Tchebichef transform domain for the task of SR takes the advantage of high and low- frequency representation of images that makes the task of SR simplified. Furthermore, a transfer learning-based approach is adopted to enhance the quality of images by considering Covid19 medical images as an additional experiment. It is shown that our architecture enhances the quality of X-ray and CT images of COVID-19, providing a better image quality that may help in clinical diagnosis. Experimental results obtained using the proposed Tchebichef transform domain SR (TTDSR) architecture provides competitive results when compared with most of the deep learning methods employed using a fewer number of trainable parameters.

Composite Learning Adaptive Tracking Control for Full-State Constrained Multiagent Systems Without Using the Feasibility Condition.

This article proposes a distributed consensus tracking controller for a class of nonlinear multiagent systems under a directed graph, in which all agents are subject to time-varying asymmetric full-state constraints, internal uncertainties, and external disturbances. The feasibility condition generally required in the existing constrained control is removed by using the proposed nonlinear mapping function (NMF)-based state reconstruction technology, and the Lipschitz condition usually needed in the consensus tracking is also canceled based on the adaptive command-filtered backstepping framework. The composite learning of the neural network-based function approximator (NN-FAP) and the finite-time smooth disturbance observer (DOB) provides a novel scheme for handling internal and external uncertainties simultaneously. One advantage of this scheme is that the use of online historical data of the closed-loop system strengthens the excitation of NN's learning. Another advantage is that the DOB with NN-FAP embedding realizes that the finite-time observation for external disturbance in the case of the system dynamics is unknown. A complete controller design, sufficient stability analysis, and numerical simulation are provided.

A hybrid Decoder-DeepONet operator regression framework for unaligned observation data

Deep neural operators (DNOs) have been utilized to approximate nonlinear mappings between function spaces. However, DNOs are confronted with challenges stemming from expanded dimensionality and computational costs tied to unaligned observation data, which ultimately compromise the accuracy of predictions. In this study, we present a hybrid Decoder-DeepONet framework to effectively handle unaligned data. This framework is advanced through its extension to the Multi-Decoder-DeepONet, which leverages an average field to enhance input augmentation. Furthermore, on the basis of the universal approximation theorem, we demonstrate that these frameworks preserve consistencies with operator approximation theory despite the substitution of the product with a decoder net. Two numerical experiments, Darcy problem and flow-field around an airfoil, are conducted to demonstrate the advantages of the proposed methods over conventional DeepONet approaches. The results reveal that both Decoder-DeepONet and Multi-Decoder-DeepONet utilize more compact training data dimensions and occupy less space, markedly enhancing prediction accuracy in the context of unaligned data.