Complex-Valued Neural Networks:A Comprehensive Survey

Complex-valued neural networks(CVNNs)have shown their excellent efficiency compared to their real counterparts in speech enhancement,image and signal processing.Researchers throughout the years have made many efforts to improve the learning algorithms and activation functions of CVNNs.Since CVNNs have proven to have better performance in handling the naturally complex-valued data and signals,this area of study will grow and expect the arrival of some effective improvements in the future.Therefore,there exists an obvious reason to provide a comprehensive survey paper that systematically collects and categorizes the advancement of CVNNs.In this paper,we discuss and summarize the recent advances based on their learning algorithms,activation functions,which is the most challenging part of building a CVNN,and applications.Besides,we outline the structure and applications of complex-valued convolutional,residual and recurrent neural networks.Finally,we also present some challenges and future research directions to facilitate the exploration of the ability of CVNNs.

Synthesization of high-capacity auto-associative memories using complex-valued neural networks

In this paper, a novel design procedure is proposed for synthesizing high-capacity auto-associative memories based on complex-valued neural networks with real-imaginary-type activation functions and constant delays. Stability criteria dependent on external inputs of neural networks are derived. The designed networks can retrieve the stored patterns by external inputs rather than initial conditions. The derivation can memorize the desired patterns with lower-dimensional neural networks than real-valued neural networks, and eliminate spurious equilibria of complex-valued neural networks. One numerical example is provided to show the effectiveness and superiority of the presented results.

Pluggable multitask diffractive neural networks based on cascaded metasurfaces

Optical neural networks have significant advantages in terms of power consumption,parallelism,and high computing speed,which has intrigued extensive attention in both academic and engineering communities.It has been considered as one of the powerful tools in promoting the fields of imaging processing and object recognition.However,the existing optical system architecture cannot be reconstructed to the realization of multi-functional artificial intelligence systems simultaneously.To push the development of this issue,we propose the pluggable diffractive neural networks(P-DNN),a general paradigm resorting to the cascaded metasurfaces,which can be applied to recognize various tasks by switching internal plug-ins.As the proof-of-principle,the recognition functions of six types of handwritten digits and six types of fashions are numerical simulated and experimental demonstrated at near-infrared regimes.Encouragingly,the proposed paradigm not only improves the flexibility of the optical neural networks but paves the new route for achieving high-speed,low-power and versatile artificial intelligence systems.

Activation Redistribution Based Hybrid Asymmetric Quantization Method of Neural Networks

The demand for adopting neural networks in resource-constrained embedded devices is continuously increasing.Quantization is one of the most promising solutions to reduce computational cost and memory storage on embedded devices.In order to reduce the complexity and overhead of deploying neural networks on Integeronly hardware,most current quantization methods use a symmetric quantization mapping strategy to quantize a floating-point neural network into an integer network.However,although symmetric quantization has the advantage of easier implementation,it is sub-optimal for cases where the range could be skewed and not symmetric.This often comes at the cost of lower accuracy.This paper proposed an activation redistribution-based hybrid asymmetric quantizationmethod for neural networks.The proposedmethod takes data distribution into consideration and can resolve the contradiction between the quantization accuracy and the ease of implementation,balance the trade-off between clipping range and quantization resolution,and thus improve the accuracy of the quantized neural network.The experimental results indicate that the accuracy of the proposed method is 2.02%and 5.52%higher than the traditional symmetric quantization method for classification and detection tasks,respectively.The proposed method paves the way for computationally intensive neural network models to be deployed on devices with limited computing resources.Codes will be available on https://github.com/ycjcy/Hybrid-Asymmetric-Quantization.

A data-driven model of drop size prediction based on artificial neural networks using small-scale data sets

An artificial neural network(ANN)method is introduced to predict drop size in two kinds of pulsed columns with small-scale data sets.After training,the deviation between calculate and experimental results are 3.8%and 9.3%,respectively.Through ANN model,the influence of interfacial tension and pulsation intensity on the droplet diameter has been developed.Droplet size gradually increases with the increase of interfacial tension,and decreases with the increase of pulse intensity.It can be seen that the accuracy of ANN model in predicting droplet size outside the training set range is reach the same level as the accuracy of correlation obtained based on experiments within this range.For two kinds of columns,the drop size prediction deviations of ANN model are 9.6%and 18.5%and the deviations in correlations are 11%and 15%.

A Review of Computing with Spiking Neural Networks

Artificial neural networks(ANNs)have led to landmark changes in many fields,but they still differ significantly fromthemechanisms of real biological neural networks and face problems such as high computing costs,excessive computing power,and so on.Spiking neural networks(SNNs)provide a new approach combined with brain-like science to improve the computational energy efficiency,computational architecture,and biological credibility of current deep learning applications.In the early stage of development,its poor performance hindered the application of SNNs in real-world scenarios.In recent years,SNNs have made great progress in computational performance and practicability compared with the earlier research results,and are continuously producing significant results.Although there are already many pieces of literature on SNNs,there is still a lack of comprehensive review on SNNs from the perspective of improving performance and practicality as well as incorporating the latest research results.Starting from this issue,this paper elaborates on SNNs along the complete usage process of SNNs including network construction,data processing,model training,development,and deployment,aiming to provide more comprehensive and practical guidance to promote the development of SNNs.Therefore,the connotation and development status of SNNcomputing is reviewed systematically and comprehensively from four aspects:composition structure,data set,learning algorithm,software/hardware development platform.Then the development characteristics of SNNs in intelligent computing are summarized,the current challenges of SNNs are discussed and the future development directions are also prospected.Our research shows that in the fields of machine learning and intelligent computing,SNNs have comparable network scale and performance to ANNs and the ability to challenge large datasets and a variety of tasks.The advantages of SNNs over ANNs in terms of energy efficiency and spatial-temporal data processing have been more fully exploited.And the development of programming and deployment tools has lowered the threshold for the use of SNNs.SNNs show a broad development prospect for brain-like computing.

Prediction of Porous Media Fluid Flow with Spatial Heterogeneity Using Criss-Cross Physics-Informed Convolutional Neural Networks

Recent advances in deep neural networks have shed new light on physics,engineering,and scientific computing.Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots.The physicsinformedneural network(PINN)is currently the most general framework,which is more popular due to theconvenience of constructing NNs and excellent generalization ability.The automatic differentiation(AD)-basedPINN model is suitable for the homogeneous scientific problem;however,it is unclear how AD can enforce fluxcontinuity across boundaries between cells of different properties where spatial heterogeneity is represented bygrid cells with different physical properties.In this work,we propose a criss-cross physics-informed convolutionalneural network(CC-PINN)learning architecture,aiming to learn the solution of parametric PDEs with spatialheterogeneity of physical properties.To achieve the seamless enforcement of flux continuity and integration ofphysicalmeaning into CNN,a predefined 2D convolutional layer is proposed to accurately express transmissibilitybetween adjacent cells.The efficacy of the proposedmethodwas evaluated through predictions of several petroleumreservoir problems with spatial heterogeneity and compared against state-of-the-art(PINN)through numericalanalysis as a benchmark,which demonstrated the superiority of the proposed method over the PINN.

Application of Convolutional Neural Networks in Classification of GBM for Enhanced Prognosis

The lethal brain tumor “Glioblastoma” has the propensity to grow over time. To improve patient outcomes, it is essential to classify GBM accurately and promptly in order to provide a focused and individualized treatment plan. Despite this, deep learning methods, particularly Convolutional Neural Networks (CNNs), have demonstrated a high level of accuracy in a myriad of medical image analysis applications as a result of recent technical breakthroughs. The overall aim of the research is to investigate how CNNs can be used to classify GBMs using data from medical imaging, to improve prognosis precision and effectiveness. This research study will demonstrate a suggested methodology that makes use of the CNN architecture and is trained using a database of MRI pictures with this tumor. The constructed model will be assessed based on its overall performance. Extensive experiments and comparisons with conventional machine learning techniques and existing classification methods will also be made. It will be crucial to emphasize the possibility of early and accurate prediction in a clinical workflow because it can have a big impact on treatment planning and patient outcomes. The paramount objective is to not only address the classification challenge but also to outline a clear pathway towards enhancing prognosis precision and treatment effectiveness.

Channel-Feedback-Free Transmission for Downlink FD-RAN:A Radio Map Based Complex-Valued Precoding Network Approach

As the demand for high-quality services proliferates,an innovative network architecture,the fully-decoupled RAN(FD-RAN),has emerged for more flexible spectrum resource utilization and lower network costs.However,with the decoupling of uplink base stations and downlink base stations in FDRAN,the traditional transmission mechanism,which relies on real-time channel feedback,is not suitable as the receiver is not able to feedback accurate and timely channel state information to the transmitter.This paper proposes a novel transmission scheme without relying on physical layer channel feedback.Specifically,we design a radio map based complex-valued precoding network(RMCPNet)model,which outputs the base station precoding based on user location.RMCPNet comprises multiple subnets,with each subnet responsible for extracting unique modal features from diverse input modalities.Furthermore,the multimodal embeddings derived from these distinct subnets are integrated within the information fusion layer,culminating in a unified representation.We also develop a specific RMCPNet training algorithm that employs the negative spectral efficiency as the loss function.We evaluate the performance of the proposed scheme on the public DeepMIMO dataset and show that RMCPNet can achieve 16%and 76%performance improvements over the conventional real-valued neural network and statistical codebook approach,respectively.

Predicting microseismic,acoustic emission and electromagnetic radiation data using neural networks

Microseism,acoustic emission and electromagnetic radiation(M-A-E)data are usually used for predicting rockburst hazards.However,it is a great challenge to realize the prediction of M-A-E data.In this study,with the aid of a deep learning algorithm,a new method for the prediction of M-A-E data is proposed.In this method,an M-A-E data prediction model is built based on a variety of neural networks after analyzing numerous M-A-E data,and then the M-A-E data can be predicted.The predicted results are highly correlated with the real data collected in the field.Through field verification,the deep learning-based prediction method of M-A-E data provides quantitative prediction data for rockburst monitoring.

A Pooling Method Developed for Use in Convolutional Neural Networks

In convolutional neural networks,pooling methods are used to reduce both the size of the data and the number of parameters after the convolution of the models.These methods reduce the computational amount of convolutional neural networks,making the neural network more efficient.Maximum pooling,average pooling,and minimum pooling methods are generally used in convolutional neural networks.However,these pooling methods are not suitable for all datasets used in neural network applications.In this study,a new pooling approach to the literature is proposed to increase the efficiency and success rates of convolutional neural networks.This method,which we call MAM(Maximum Average Minimum)pooling,is more interactive than other traditional maximum pooling,average pooling,and minimum pooling methods and reduces data loss by calculating the more appropriate pixel value.The proposed MAM pooling method increases the performance of the neural network by calculating the optimal value during the training of convolutional neural networks.To determine the success accuracy of the proposed MAM pooling method and compare it with other traditional pooling methods,training was carried out on the LeNet-5 model using CIFAR-10,CIFAR-100,and MNIST datasets.According to the results obtained,the proposed MAM pooling method performed better than the maximum pooling,average pooling,and minimum pooling methods in all pool sizes on three different datasets.

Event-based nonfragile state estimation for memristive recurrent neural networks with stochastic cyber-attacks and sensor saturations

This paper addresses the issue of nonfragile state estimation for memristive recurrent neural networks with proportional delay and sensor saturations. In practical engineering, numerous unnecessary signals are transmitted to the estimator through the networks, which increases the burden of communication bandwidth. A dynamic event-triggered mechanism,instead of a static event-triggered mechanism, is employed to select useful data. By constructing a meaningful Lyapunov–Krasovskii functional, a delay-dependent criterion is derived in terms of linear matrix inequalities for ensuring the global asymptotic stability of the augmented system. In the end, two numerical simulations are employed to illustrate the feasibility and validity of the proposed theoretical results.

MetaPINNs:Predicting soliton and rogue wave of nonlinear PDEs via the improved physics-informed neural networks based on meta-learned optimization

Efficiently solving partial differential equations(PDEs)is a long-standing challenge in mathematics and physics research.In recent years,the rapid development of artificial intelligence technology has brought deep learning-based methods to the forefront of research on numerical methods for partial differential equations.Among them,physics-informed neural networks(PINNs)are a new class of deep learning methods that show great potential in solving PDEs and predicting complex physical phenomena.In the field of nonlinear science,solitary waves and rogue waves have been important research topics.In this paper,we propose an improved PINN that enhances the physical constraints of the neural network model by adding gradient information constraints.In addition,we employ meta-learning optimization to speed up the training process.We apply the improved PINNs to the numerical simulation and prediction of solitary and rogue waves.We evaluate the accuracy of the prediction results by error analysis.The experimental results show that the improved PINNs can make more accurate predictions in less time than that of the original PINNs.

Multi-Scale-Matching neural networks for thin plate bending problem

Physics-informed neural networks are a useful machine learning method for solving differential equations,but encounter challenges in effectively learning thin boundary layers within singular perturbation problems.To resolve this issue,multi-scale-matching neural networks are proposed to solve the singular perturbation problems.Inspired by matched asymptotic expansions,the solution is decomposed into inner solutions for small scales and outer solutions for large scales,corresponding to boundary layers and outer regions,respectively.Moreover,to conform neural networks,we introduce exponential stretched variables in the boundary layers to avoid semiinfinite region problems.Numerical results for the thin plate problem validate the proposed method.

Multi-Material Topology Optimization of 2D Structures Using Convolutional Neural Networks

In recent years,there has been significant research on the application of deep learning(DL)in topology optimization(TO)to accelerate structural design.However,these methods have primarily focused on solving binary TO problems,and effective solutions for multi-material topology optimization(MMTO)which requires a lot of computing resources are still lacking.Therefore,this paper proposes the framework of multiphase topology optimization using deep learning to accelerate MMTO design.The framework employs convolutional neural network(CNN)to construct a surrogate model for solving MMTO,and the obtained surrogate model can rapidly generate multi-material structure topologies in negligible time without any iterations.The performance evaluation results show that the proposed method not only outputs multi-material topologies with clear material boundary but also reduces the calculation cost with high prediction accuracy.Additionally,in order to find a more reasonable modeling method for MMTO,this paper studies the characteristics of surrogate modeling as regression task and classification task.Through the training of 297 models,our findings show that the regression task yields slightly better results than the classification task in most cases.Furthermore,The results indicate that the prediction accuracy is primarily influenced by factors such as the TO problem,material category,and data scale.Conversely,factors such as the domain size and the material property have minimal impact on the accuracy.

TCAS-PINN:Physics-informed neural networks with a novel temporal causality-based adaptive sampling method

Physics-informed neural networks(PINNs)have become an attractive machine learning framework for obtaining solutions to partial differential equations(PDEs).PINNs embed initial,boundary,and PDE constraints into the loss function.The performance of PINNs is generally affected by both training and sampling.Specifically,training methods focus on how to overcome the training difficulties caused by the special PDE residual loss of PINNs,and sampling methods are concerned with the location and distribution of the sampling points upon which evaluations of PDE residual loss are accomplished.However,a common problem among these original PINNs is that they omit special temporal information utilization during the training or sampling stages when dealing with an important PDE category,namely,time-dependent PDEs,where temporal information plays a key role in the algorithms used.There is one method,called Causal PINN,that considers temporal causality at the training level but not special temporal utilization at the sampling level.Incorporating temporal knowledge into sampling remains to be studied.To fill this gap,we propose a novel temporal causality-based adaptive sampling method that dynamically determines the sampling ratio according to both PDE residual and temporal causality.By designing a sampling ratio determined by both residual loss and temporal causality to control the number and location of sampled points in each temporal sub-domain,we provide a practical solution by incorporating temporal information into sampling.Numerical experiments of several nonlinear time-dependent PDEs,including the Cahn–Hilliard,Korteweg–de Vries,Allen–Cahn and wave equations,show that our proposed sampling method can improve the performance.We demonstrate that using such a relatively simple sampling method can improve prediction performance by up to two orders of magnitude compared with the results from other methods,especially when points are limited.

Downscaling Seasonal Precipitation Forecasts over East Africa with Deep Convolutional Neural Networks

This study assesses the suitability of convolutional neural networks(CNNs) for downscaling precipitation over East Africa in the context of seasonal forecasting. To achieve this, we design a set of experiments that compare different CNN configurations and deployed the best-performing architecture to downscale one-month lead seasonal forecasts of June–July–August–September(JJAS) precipitation from the Nanjing University of Information Science and Technology Climate Forecast System version 1.0(NUIST-CFS1.0) for 1982–2020. We also perform hyper-parameter optimization and introduce predictors over a larger area to include information about the main large-scale circulations that drive precipitation over the East Africa region, which improves the downscaling results. Finally, we validate the raw model and downscaled forecasts in terms of both deterministic and probabilistic verification metrics, as well as their ability to reproduce the observed precipitation extreme and spell indicator indices. The results show that the CNN-based downscaling consistently improves the raw model forecasts, with lower bias and more accurate representations of the observed mean and extreme precipitation spatial patterns. Besides, CNN-based downscaling yields a much more accurate forecast of extreme and spell indicators and reduces the significant relative biases exhibited by the raw model predictions. Moreover, our results show that CNN-based downscaling yields better skill scores than the raw model forecasts over most portions of East Africa. The results demonstrate the potential usefulness of CNN in downscaling seasonal precipitation predictions over East Africa,particularly in providing improved forecast products which are essential for end users.

Multi-scale physics-informed neural networks for solving high Reynolds number boundary layer flows based on matched asymptotic expansions

Multi-scale system remains a classical scientific problem in fluid dynamics,biology,etc.In the present study,a scheme of multi-scale Physics-informed neural networks is proposed to solve the boundary layer flow at high Reynolds numbers without any data.The flow is divided into several regions with different scales based on Prandtl's boundary theory.Different regions are solved with governing equations in different scales.The method of matched asymptotic expansions is used to make the flow field continuously.A flow on a semi infinite flat plate at a high Reynolds number is considered a multi-scale problem because the boundary layer scale is much smaller than the outer flow scale.The results are compared with the reference numerical solutions,which show that the msPINNs can solve the multi-scale problem of the boundary layer in high Reynolds number flows.This scheme can be developed for more multi-scale problems in the future.

Graph neural network-based scheduling for multi-UAV-enabled communications in D2D networks

In this paper,we jointly design the power control and position dispatch for Multi-Unmanned Aerial Vehicle(UAV)-enabled communication in Device-to-Device(D2D)networks.Our objective is to maximize the total transmission rate of Downlink Users(DUs).Meanwhile,the Quality of Service(QoS)of all D2D users must be satisfied.We comprehensively considered the interference among D2D communications and downlink transmissions.The original problem is strongly non-convex,which requires high computational complexity for traditional optimization methods.And to make matters worse,the results are not necessarily globally optimal.In this paper,we propose a novel Graph Neural Networks(GNN)based approach that can map the considered system into a specific graph structure and achieve the optimal solution in a low complexity manner.Particularly,we first construct a GNN-based model for the proposed network,in which the transmission links and interference links are formulated as vertexes and edges,respectively.Then,by taking the channel state information and the coordinates of ground users as the inputs,as well as the location of UAVs and the transmission power of all transmitters as outputs,we obtain the mapping from inputs to outputs through training the parameters of GNN.Simulation results verified that the way to maximize the total transmission rate of DUs can be extracted effectively via the training on samples.Moreover,it also shows that the performance of proposed GNN-based method is better than that of traditional means.

Multi-head neural networks for simulating particle breakage dynamics

The breakage of brittle particulate materials into smaller particles under compressive or impact loads can be modelled as an instantiation of the population balance integro-differential equation.In this paper,the emerging computational science paradigm of physics-informed neural networks is studied for the first time for solving both linear and nonlinear variants of the governing dynamics.Unlike conventional methods,the proposed neural network provides rapid simulations of arbitrarily high resolution in particle size,predicting values on arbitrarily fine grids without the need for model retraining.The network is assigned a simple multi-head architecture tailored to uphold monotonicity of the modelled cumulative distribution function over particle sizes.The method is theoretically analyzed and validated against analytical results before being applied to real-world data of a batch grinding mill.The agreement between laboratory data and numerical simulation encourages the use of physics-informed neural nets for optimal planning and control of industrial comminution processes.