The short-range property of interactions between scales in incompressible turbulent flow was examined. Some formulae for the short-range eddy stress were given. A concept of resonant-range interactions between extreme...The short-range property of interactions between scales in incompressible turbulent flow was examined. Some formulae for the short-range eddy stress were given. A concept of resonant-range interactions between extremely contiguous scales was introduced and some formulae for the resonant-range eddy stress were also derived. Multi-scale equations for the incompressible turbulent flows were proposed. Key words turbulence - incompressible flow - interactions between scales - multi-scale equations MSC 2000 76F70展开更多
The short-range property of interactions between scales in the compressible turbulent flow was examined. An estimation of the short-range scale scope and some formulae for the short-range eddy stress and heat transfe...The short-range property of interactions between scales in the compressible turbulent flow was examined. An estimation of the short-range scale scope and some formulae for the short-range eddy stress and heat transfer etc. were given. A concept of resonant-range interactions between extremely contiguous scales was introduced and some formulae for the resonant-range eddy stress and heat transfer etc. were also given. Multi-scale equations for the compressible turbulent flows were presented. The multi-scale equations are approximately closed and do not contain any empirical constants. The compressibility effects on turbulence are determined by the Farve averaged variables and the nonlinear relationships between the Farve- and physical-averaged variables.展开更多
This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic diff...This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.展开更多
Images taken in dim environments frequently exhibit issues like insufficient brightness,noise,color shifts,and loss of detail.These problems pose significant challenges to dark image enhancement tasks.Current approach...Images taken in dim environments frequently exhibit issues like insufficient brightness,noise,color shifts,and loss of detail.These problems pose significant challenges to dark image enhancement tasks.Current approaches,while effective in global illumination modeling,often struggle to simultaneously suppress noise and preserve structural details,especially under heterogeneous lighting.Furthermore,misalignment between luminance and color channels introduces additional challenges to accurate enhancement.In response to the aforementioned difficulties,we introduce a single-stage framework,M2ATNet,using the multi-scale multi-attention and Transformer architecture.First,to address the problems of texture blurring and residual noise,we design a multi-scale multi-attention denoising module(MMAD),which is applied separately to the luminance and color channels to enhance the structural and texture modeling capabilities.Secondly,to solve the non-alignment problem of the luminance and color channels,we introduce the multi-channel feature fusion Transformer(CFFT)module,which effectively recovers the dark details and corrects the color shifts through cross-channel alignment and deep feature interaction.To guide the model to learn more stably and efficiently,we also fuse multiple types of loss functions to form a hybrid loss term.We extensively evaluate the proposed method on various standard datasets,including LOL-v1,LOL-v2,DICM,LIME,and NPE.Evaluation in terms of numerical metrics and visual quality demonstrate that M2ATNet consistently outperforms existing advanced approaches.Ablation studies further confirm the critical roles played by the MMAD and CFFT modules to detail preservation and visual fidelity under challenging illumination-deficient environments.展开更多
Camouflaged Object Detection(COD)aims to identify objects that share highly similar patterns—such as texture,intensity,and color—with their surrounding environment.Due to their intrinsic resemblance to the backgroun...Camouflaged Object Detection(COD)aims to identify objects that share highly similar patterns—such as texture,intensity,and color—with their surrounding environment.Due to their intrinsic resemblance to the background,camouflaged objects often exhibit vague boundaries and varying scales,making it challenging to accurately locate targets and delineate their indistinct edges.To address this,we propose a novel camouflaged object detection network called Edge-Guided and Multi-scale Fusion Network(EGMFNet),which leverages edge-guided multi-scale integration for enhanced performance.The model incorporates two innovative components:a Multi-scale Fusion Module(MSFM)and an Edge-Guided Attention Module(EGA).These designs exploit multi-scale features to uncover subtle cues between candidate objects and the background while emphasizing camouflaged object boundaries.Moreover,recognizing the rich contextual information in fused features,we introduce a Dual-Branch Global Context Module(DGCM)to refine features using extensive global context,thereby generatingmore informative representations.Experimental results on four benchmark datasets demonstrate that EGMFNet outperforms state-of-the-art methods across five evaluation metrics.Specifically,on COD10K,our EGMFNet-P improves F_(β)by 4.8 points and reduces mean absolute error(MAE)by 0.006 compared with ZoomNeXt;on NC4K,it achieves a 3.6-point increase in F_(β).OnCAMO and CHAMELEON,it obtains 4.5-point increases in F_(β),respectively.These consistent gains substantiate the superiority and robustness of EGMFNet.展开更多
Accurate and efficient detection of building changes in remote sensing imagery is crucial for urban planning,disaster emergency response,and resource management.However,existing methods face challenges such as spectra...Accurate and efficient detection of building changes in remote sensing imagery is crucial for urban planning,disaster emergency response,and resource management.However,existing methods face challenges such as spectral similarity between buildings and backgrounds,sensor variations,and insufficient computational efficiency.To address these challenges,this paper proposes a novel Multi-scale Efficient Wavelet-based Change Detection Network(MewCDNet),which integrates the advantages of Convolutional Neural Networks and Transformers,balances computational costs,and achieves high-performance building change detection.The network employs EfficientNet-B4 as the backbone for hierarchical feature extraction,integrates multi-level feature maps through a multi-scale fusion strategy,and incorporates two key modules:Cross-temporal Difference Detection(CTDD)and Cross-scale Wavelet Refinement(CSWR).CTDD adopts a dual-branch architecture that combines pixel-wise differencing with semanticaware Euclidean distance weighting to enhance the distinction between true changes and background noise.CSWR integrates Haar-based Discrete Wavelet Transform with multi-head cross-attention mechanisms,enabling cross-scale feature fusion while significantly improving edge localization and suppressing spurious changes.Extensive experiments on four benchmark datasets demonstrate MewCDNet’s superiority over comparison methods:achieving F1 scores of 91.54%on LEVIR,93.70%on WHUCD,and 64.96%on S2Looking for building change detection.Furthermore,MewCDNet exhibits optimal performance on the multi-class⋅SYSU dataset(F1:82.71%),highlighting its exceptional generalization capability.展开更多
Tomato is a major economic crop worldwide,and diseases on tomato leaves can significantly reduce both yield and quality.Traditional manual inspection is inefficient and highly subjective,making it difficult to meet th...Tomato is a major economic crop worldwide,and diseases on tomato leaves can significantly reduce both yield and quality.Traditional manual inspection is inefficient and highly subjective,making it difficult to meet the requirements of early disease identification in complex natural environments.To address this issue,this study proposes an improved YOLO11-based model,YOLO-SPDNet(Scale Sequence Fusion,Position-Channel Attention,and Dual Enhancement Network).The model integrates the SEAM(Self-Ensembling Attention Mechanism)semantic enhancement module,the MLCA(Mixed Local Channel Attention)lightweight attention mechanism,and the SPA(Scale-Position-Detail Awareness)module composed of SSFF(Scale Sequence Feature Fusion),TFE(Triple Feature Encoding),and CPAM(Channel and Position Attention Mechanism).These enhancements strengthen fine-grained lesion detection while maintaining model lightweightness.Experimental results show that YOLO-SPDNet achieves an accuracy of 91.8%,a recall of 86.5%,and an mAP@0.5 of 90.6%on the test set,with a computational complexity of 12.5 GFLOPs.Furthermore,the model reaches a real-time inference speed of 987 FPS,making it suitable for deployment on mobile agricultural terminals and online monitoring systems.Comparative analysis and ablation studies further validate the reliability and practical applicability of the proposed model in complex natural scenes.展开更多
Distributed Denial of Service(DDoS)attacks are one of the severe threats to network infrastructure,sometimes bypassing traditional diagnosis algorithms because of their evolving complexity.PresentMachine Learning(ML)t...Distributed Denial of Service(DDoS)attacks are one of the severe threats to network infrastructure,sometimes bypassing traditional diagnosis algorithms because of their evolving complexity.PresentMachine Learning(ML)techniques for DDoS attack diagnosis normally apply network traffic statistical features such as packet sizes and inter-arrival times.However,such techniques sometimes fail to capture complicated relations among various traffic flows.In this paper,we present a new multi-scale ensemble strategy given the Graph Neural Networks(GNNs)for improving DDoS detection.Our technique divides traffic into macro-and micro-level elements,letting various GNN models to get the two corase-scale anomalies and subtle,stealthy attack models.Through modeling network traffic as graph-structured data,GNNs efficiently learn intricate relations among network entities.The proposed ensemble learning algorithm combines the results of several GNNs to improve generalization,robustness,and scalability.Extensive experiments on three benchmark datasets—UNSW-NB15,CICIDS2017,and CICDDoS2019—show that our approach outperforms traditional machine learning and deep learning models in detecting both high-rate and low-rate(stealthy)DDoS attacks,with significant improvements in accuracy and recall.These findings demonstrate the suggested method’s applicability and robustness for real-world implementation in contexts where several DDoS patterns coexist.展开更多
Advanced healthcare monitors for air pollution applications pose a significant challenge in achieving a balance between high-performance filtration and multifunctional smart integration.Electrospinning triboelectric n...Advanced healthcare monitors for air pollution applications pose a significant challenge in achieving a balance between high-performance filtration and multifunctional smart integration.Electrospinning triboelectric nanogenerators(TENG)provide a significant potential for use under such difficult circumstances.We have successfully constructed a high-performance TENG utilizing a novel multi-scale nanofiber architecture.Nylon 66(PA66)and chitosan quaternary ammonium salt(HACC)composites were prepared by electrospinning,and PA66/H multiscale nanofiber membranes composed of nanofibers(≈73 nm)and submicron-fibers(≈123 nm)were formed.PA66/H multi-scale nanofiber membrane as the positive electrode and negative electrode-spun PVDF-HFP nanofiber membrane composed of respiration-driven PVDF-HFP@PA66/H TENG.The resulting PVDF-HFP@PA66/H TENG based air filter utilizes electrostatic adsorption and physical interception mechanisms,achieving PM_(0.3)filtration efficiency over 99%with a pressure drop of only 48 Pa.Besides,PVDF-HFP@PA66/H TENG exhibits excellent stability in high-humidity environments,with filtration efficiency reduced by less than 1%.At the same time,the TENG achieves periodic contact separation through breathing drive to achieve self-power,which can ensure the long-term stability of the filtration efficiency.In addition to the air filtration function,TENG can also monitor health in real time by capturing human breathing signals without external power supply.This integrated system combines high-efficiency air filtration,self-powered operation,and health monitoring,presenting an innovative solution for air purification,smart protective equipment,and portable health monitoring.These findings highlight the potential of this technology for diverse applications,offering a promising direction for advancing multifunctional air filtration systems.展开更多
Defect detection in printed circuit boards(PCB)remains challenging due to the difficulty of identifying small-scale defects,the inefficiency of conventional approaches,and the interference from complex backgrounds.To ...Defect detection in printed circuit boards(PCB)remains challenging due to the difficulty of identifying small-scale defects,the inefficiency of conventional approaches,and the interference from complex backgrounds.To address these issues,this paper proposes SIM-Net,an enhanced detection framework derived from YOLOv11.The model integrates SPDConv to preserve fine-grained features for small object detection,introduces a novel convolutional partial attention module(C2PAM)to suppress redundant background information and highlight salient regions,and employs a multi-scale fusion network(MFN)with a multi-grain contextual module(MGCT)to strengthen contextual representation and accelerate inference.Experimental evaluations demonstrate that SIM-Net achieves 92.4%mAP,92%accuracy,and 89.4%recall with an inference speed of 75.1 FPS,outperforming existing state-of-the-art methods.These results confirm the robustness and real-time applicability of SIM-Net for PCB defect inspection.展开更多
The development of metallic mineral resources generates a significant amount of solid waste,such as tailings and waste rock.Cemented tailings and waste-rock backfill(CTWB)is an effective method for managing and dispos...The development of metallic mineral resources generates a significant amount of solid waste,such as tailings and waste rock.Cemented tailings and waste-rock backfill(CTWB)is an effective method for managing and disposing of this mining waste.This study employs a macro-meso-micro testing method to investigate the effects of the waste rock grading index(WGI)and loading rate(LR)on the uniaxial compressive strength(UCS),pore structure,and micromorphology of CTWB materials.Pore structures were analyzed using scanning electron microscopy(SEM)and mercury intrusion porosimetry(MIP).The particles(pores)and cracks analysis system(PCAS)software was used to quantitatively characterize the multi-scale micropores in the SEM images.The key findings indicate that the macroscopic results(UCS)of CTWB materials correspond to the microscopic results(pore structure and micromorphology).Changes in porosity largely depend on the conditions of waste rock grading index and loading rate.The inclusion of waste rock initially increases and then decreases the UCS,while porosity first decreases and then increases,with a critical waste rock grading index of 0.6.As the loading rate increases,UCS initially rises and then falls,while porosity gradually increases.Based on MIP and SEM results,at waste rock grading index 0.6,the most probable pore diameters,total pore area(TPA),pore number(PN),maximum pore area(MPA),and area probability distribution index(APDI)are minimized,while average pore form factor(APF)and fractal dimension of pore porosity distribution(FDPD)are maximized,indicating the most compact pore structure.At a loading rate of 12.0 mm/min,the most probable pore diameters,TPA,PN,MPA,APF,and APDI reach their maximum values,while FDPD reaches its minimum value.Finally,the mechanism of CTWB materials during compression is analyzed,based on the quantitative results of UCS and porosity.The research findings play a crucial role in ensuring the successful application of CTWB materials in deep metal mines.展开更多
With the rapid expansion of drone applications,accurate detection of objects in aerial imagery has become crucial for intelligent transportation,urban management,and emergency rescue missions.However,existing methods ...With the rapid expansion of drone applications,accurate detection of objects in aerial imagery has become crucial for intelligent transportation,urban management,and emergency rescue missions.However,existing methods face numerous challenges in practical deployment,including scale variation handling,feature degradation,and complex backgrounds.To address these issues,we propose Edge-enhanced and Detail-Capturing You Only Look Once(EHDC-YOLO),a novel framework for object detection in Unmanned Aerial Vehicle(UAV)imagery.Based on the You Only Look Once version 11 nano(YOLOv11n)baseline,EHDC-YOLO systematically introduces several architectural enhancements:(1)a Multi-Scale Edge Enhancement(MSEE)module that leverages multi-scale pooling and edge information to enhance boundary feature extraction;(2)an Enhanced Feature Pyramid Network(EFPN)that integrates P2-level features with Cross Stage Partial(CSP)structures and OmniKernel convolutions for better fine-grained representation;and(3)Dynamic Head(DyHead)with multi-dimensional attention mechanisms for enhanced cross-scale modeling and perspective adaptability.Comprehensive experiments on the Vision meets Drones for Detection(VisDrone-DET)2019 dataset demonstrate that EHDC-YOLO achieves significant improvements,increasing mean Average Precision(mAP)@0.5 from 33.2%to 46.1%(an absolute improvement of 12.9 percentage points)and mAP@0.5:0.95 from 19.5%to 28.0%(an absolute improvement of 8.5 percentage points)compared with the YOLOv11n baseline,while maintaining a reasonable parameter count(2.81 M vs the baseline’s 2.58 M).Further ablation studies confirm the effectiveness of each proposed component,while visualization results highlight EHDC-YOLO’s superior performance in detecting objects and handling occlusions in complex drone scenarios.展开更多
Impact craters are important for understanding the evolution of lunar geologic and surface erosion rates,among other functions.However,the morphological characteristics of these micro impact craters are not obvious an...Impact craters are important for understanding the evolution of lunar geologic and surface erosion rates,among other functions.However,the morphological characteristics of these micro impact craters are not obvious and they are numerous,resulting in low detection accuracy by deep learning models.Therefore,we proposed a new multi-scale fusion crater detection algorithm(MSF-CDA)based on the YOLO11 to improve the accuracy of lunar impact crater detection,especially for small craters with a diameter of<1 km.Using the images taken by the LROC(Lunar Reconnaissance Orbiter Camera)at the Chang’e-4(CE-4)landing area,we constructed three separate datasets for craters with diameters of 0-70 m,70-140 m,and>140 m.We then trained three submodels separately with these three datasets.Additionally,we designed a slicing-amplifying-slicing strategy to enhance the ability to extract features from small craters.To handle redundant predictions,we proposed a new Non-Maximum Suppression with Area Filtering method to fuse the results in overlapping targets within the multi-scale submodels.Finally,our new MSF-CDA method achieved high detection performance,with the Precision,Recall,and F1 score having values of 0.991,0.987,and 0.989,respectively,perfectly addressing the problems induced by the lesser features and sample imbalance of small craters.Our MSF-CDA can provide strong data support for more in-depth study of the geological evolution of the lunar surface and finer geological age estimations.This strategy can also be used to detect other small objects with lesser features and sample imbalance problems.We detected approximately 500,000 impact craters in an area of approximately 214 km2 around the CE-4 landing area.By statistically analyzing the new data,we updated the distribution function of the number and diameter of impact craters.Finally,we identified the most suitable lighting conditions for detecting impact crater targets by analyzing the effect of different lighting conditions on the detection accuracy.展开更多
A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue prob...A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).展开更多
The neutron diffusion equation plays a pivotal role in nuclear reactor analysis.Nevertheless,employing the physics-informed neural network(PINN)method for its solution entails certain limitations.Conventional PINN app...The neutron diffusion equation plays a pivotal role in nuclear reactor analysis.Nevertheless,employing the physics-informed neural network(PINN)method for its solution entails certain limitations.Conventional PINN approaches generally utilize a fully connected network(FCN)architecture that is susceptible to overfitting,training instability,and gradient vanishing as the network depth increases.These challenges result in accuracy bottlenecks in the solution.In response to these issues,the residual-based resample physics-informed neural network(R2-PINN)is proposed.It is an improved PINN architecture that replaces the FCN with a convolutional neural network with a shortcut(S-CNN).It incorporates skip connections to facilitate gradient propagation between network layers.Additionally,the incorporation of the residual adaptive resampling(RAR)mechanism dynamically increases the number of sampling points.This,in turn,enhances the spatial representation capabilities and overall predictive accuracy of the model.The experimental results illustrate that our approach significantly improves the convergence capability of the model and achieves high-precision predictions of the physical fields.Compared with conventional FCN-based PINN methods,R 2-PINN effectively overcomes the limitations inherent in current methods.Thus,it provides more accurate and robust solutions for neutron diffusion equations.展开更多
This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called...This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called Ⅰ-type basic scheme is developed for solving the equations and it is proved under the suitable conditions that this method has the computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4)),where τ,h_(x )and h_(y) are the calculation stepsizes of the method in t-,x-and y-direction,respectively.With the above method and Newton linearized technique,a Ⅱ-type basic scheme is also suggested.Based on the both basic schemes,the corresponding Ⅰ-and Ⅱ-type alternating direction implicit(ADI)schemes are derived.Finally,with a series of numerical experiments,the computational accuracy and efficiency of the four numerical schemes are further illustrated.展开更多
In this paper, we present a new algorithm to solve a kind of nonlinear time space-fractional partial differential equations on a finite domain. The method is based on B-spline wavelets approximations, some of these fu...In this paper, we present a new algorithm to solve a kind of nonlinear time space-fractional partial differential equations on a finite domain. The method is based on B-spline wavelets approximations, some of these functions are reshaped to satisfy on boundary conditions exactly. The Adams fractional method is used to reduce the problem to a system of equations. By multiscale method this system is divided into some smaller systems which have less computations. We get an approximated solution which is more accurate on some subdomains by combining the solutions of these systems. Illustrative examples are included to demonstrate the validity and applicability of our proposed technique, also the stability of the method is discussed.展开更多
Because of the challenge of compounding lightweight,high-strength Ti/Al alloys due to their considerable disparity in properties,Al 6063 as intermediate layer was proposed to fabricate TC4/Al 6063/Al 7075 three-layer ...Because of the challenge of compounding lightweight,high-strength Ti/Al alloys due to their considerable disparity in properties,Al 6063 as intermediate layer was proposed to fabricate TC4/Al 6063/Al 7075 three-layer composite plate by explosive welding.The microscopic properties of each bonding interface were elucidated through field emission scanning electron microscope and electron backscattered diffraction(EBSD).A methodology combining finite element method-smoothed particle hydrodynamics(FEM-SPH)and molecular dynamics(MD)was proposed for the analysis of the forming and evolution characteristics of explosive welding interfaces at multi-scale.The results demonstrate that the bonding interface morphologies of TC4/Al 6063 and Al 6063/Al 7075 exhibit a flat and wavy configuration,without discernible defects or cracks.The phenomenon of grain refinement is observed in the vicinity of the two bonding interfaces.Furthermore,the degree of plastic deformation of TC4 and Al 7075 is more pronounced than that of Al 6063 in the intermediate layer.The interface morphology characteristics obtained by FEM-SPH simulation exhibit a high degree of similarity to the experimental results.MD simulations reveal that the diffusion of interfacial elements predominantly occurs during the unloading phase,and the simulated thickness of interfacial diffusion aligns well with experimental outcomes.The introduction of intermediate layer in the explosive welding process can effectively produce high-quality titanium/aluminum alloy composite plates.Furthermore,this approach offers a multi-scale simulation strategy for the study of explosive welding bonding interfaces.展开更多
A nonlinear multi-scale interaction(NMI)model was proposed and developed by the first author for nearly 30 years to represent the evolution of atmospheric blocking.In this review paper,we first review the creation and...A nonlinear multi-scale interaction(NMI)model was proposed and developed by the first author for nearly 30 years to represent the evolution of atmospheric blocking.In this review paper,we first review the creation and development of the NMI model and then emphasize that the NMI model represents a new tool for identifying the basic physics of how climate change influences mid-to-high latitude weather extremes.The building of the NMI model took place over three main periods.In the 1990s,a nonlinear Schr?dinger(NLS)equation model was presented to describe atmospheric blocking as a wave packet;however,it could not depict the lifetime(10-20 days)of atmospheric blocking.In the 2000s,we proposed an NMI model of atmospheric blocking in a uniform basic flow by making a scale-separation assumption and deriving an eddyforced NLS equation.This model succeeded in describing the life cycle of atmospheric blocking.In the 2020s,the NMI model was extended to include the impact of a changing climate mainly by altering the basic zonal winds and the magnitude of the meridional background potential vorticity gradient(PVy).Model results show that when PVy is smaller,blocking has a weaker dispersion and a stronger nonlinearity,so blocking can be more persistent and have a larger zonal scale and weaker eastward movement,thus favoring stronger weather extremes.However,when PVy is much smaller and below a critical threshold under much stronger winter Arctic warming of global warming,atmospheric blocking becomes locally less persistent and shows a much stronger westward movement,which acts to inhibit local cold extremes.Such a case does not happen in summer under global warming because PVy fails to fall below the critical threshold.Thus,our theory indicates that global warming can render summer-blocking anticyclones and mid-to-high latitude heatwaves more persistent,intense,and widespread.展开更多
Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay di...Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.展开更多
文摘The short-range property of interactions between scales in incompressible turbulent flow was examined. Some formulae for the short-range eddy stress were given. A concept of resonant-range interactions between extremely contiguous scales was introduced and some formulae for the resonant-range eddy stress were also derived. Multi-scale equations for the incompressible turbulent flows were proposed. Key words turbulence - incompressible flow - interactions between scales - multi-scale equations MSC 2000 76F70
文摘The short-range property of interactions between scales in the compressible turbulent flow was examined. An estimation of the short-range scale scope and some formulae for the short-range eddy stress and heat transfer etc. were given. A concept of resonant-range interactions between extremely contiguous scales was introduced and some formulae for the resonant-range eddy stress and heat transfer etc. were also given. Multi-scale equations for the compressible turbulent flows were presented. The multi-scale equations are approximately closed and do not contain any empirical constants. The compressibility effects on turbulence are determined by the Farve averaged variables and the nonlinear relationships between the Farve- and physical-averaged variables.
基金Supported by the National Natural Science Foundation of China(12001074)the Research Innovation Program of Graduate Students in Hunan Province(CX20220258)+1 种基金the Research Innovation Program of Graduate Students of Central South University(1053320214147)the Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110025)。
文摘This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.
基金funded by the National Natural Science Foundation of China,grant numbers 52374156 and 62476005。
文摘Images taken in dim environments frequently exhibit issues like insufficient brightness,noise,color shifts,and loss of detail.These problems pose significant challenges to dark image enhancement tasks.Current approaches,while effective in global illumination modeling,often struggle to simultaneously suppress noise and preserve structural details,especially under heterogeneous lighting.Furthermore,misalignment between luminance and color channels introduces additional challenges to accurate enhancement.In response to the aforementioned difficulties,we introduce a single-stage framework,M2ATNet,using the multi-scale multi-attention and Transformer architecture.First,to address the problems of texture blurring and residual noise,we design a multi-scale multi-attention denoising module(MMAD),which is applied separately to the luminance and color channels to enhance the structural and texture modeling capabilities.Secondly,to solve the non-alignment problem of the luminance and color channels,we introduce the multi-channel feature fusion Transformer(CFFT)module,which effectively recovers the dark details and corrects the color shifts through cross-channel alignment and deep feature interaction.To guide the model to learn more stably and efficiently,we also fuse multiple types of loss functions to form a hybrid loss term.We extensively evaluate the proposed method on various standard datasets,including LOL-v1,LOL-v2,DICM,LIME,and NPE.Evaluation in terms of numerical metrics and visual quality demonstrate that M2ATNet consistently outperforms existing advanced approaches.Ablation studies further confirm the critical roles played by the MMAD and CFFT modules to detail preservation and visual fidelity under challenging illumination-deficient environments.
基金financially supported byChongqingUniversity of Technology Graduate Innovation Foundation(Grant No.gzlcx20253267).
文摘Camouflaged Object Detection(COD)aims to identify objects that share highly similar patterns—such as texture,intensity,and color—with their surrounding environment.Due to their intrinsic resemblance to the background,camouflaged objects often exhibit vague boundaries and varying scales,making it challenging to accurately locate targets and delineate their indistinct edges.To address this,we propose a novel camouflaged object detection network called Edge-Guided and Multi-scale Fusion Network(EGMFNet),which leverages edge-guided multi-scale integration for enhanced performance.The model incorporates two innovative components:a Multi-scale Fusion Module(MSFM)and an Edge-Guided Attention Module(EGA).These designs exploit multi-scale features to uncover subtle cues between candidate objects and the background while emphasizing camouflaged object boundaries.Moreover,recognizing the rich contextual information in fused features,we introduce a Dual-Branch Global Context Module(DGCM)to refine features using extensive global context,thereby generatingmore informative representations.Experimental results on four benchmark datasets demonstrate that EGMFNet outperforms state-of-the-art methods across five evaluation metrics.Specifically,on COD10K,our EGMFNet-P improves F_(β)by 4.8 points and reduces mean absolute error(MAE)by 0.006 compared with ZoomNeXt;on NC4K,it achieves a 3.6-point increase in F_(β).OnCAMO and CHAMELEON,it obtains 4.5-point increases in F_(β),respectively.These consistent gains substantiate the superiority and robustness of EGMFNet.
基金supported by the Henan Province Key R&D Project under Grant 241111210400the Henan Provincial Science and Technology Research Project under Grants 252102211047,252102211062,252102211055 and 232102210069+2 种基金the Jiangsu Provincial Scheme Double Initiative Plan JSS-CBS20230474,the XJTLU RDF-21-02-008the Science and Technology Innovation Project of Zhengzhou University of Light Industry under Grant 23XNKJTD0205the Higher Education Teaching Reform Research and Practice Project of Henan Province under Grant 2024SJGLX0126。
文摘Accurate and efficient detection of building changes in remote sensing imagery is crucial for urban planning,disaster emergency response,and resource management.However,existing methods face challenges such as spectral similarity between buildings and backgrounds,sensor variations,and insufficient computational efficiency.To address these challenges,this paper proposes a novel Multi-scale Efficient Wavelet-based Change Detection Network(MewCDNet),which integrates the advantages of Convolutional Neural Networks and Transformers,balances computational costs,and achieves high-performance building change detection.The network employs EfficientNet-B4 as the backbone for hierarchical feature extraction,integrates multi-level feature maps through a multi-scale fusion strategy,and incorporates two key modules:Cross-temporal Difference Detection(CTDD)and Cross-scale Wavelet Refinement(CSWR).CTDD adopts a dual-branch architecture that combines pixel-wise differencing with semanticaware Euclidean distance weighting to enhance the distinction between true changes and background noise.CSWR integrates Haar-based Discrete Wavelet Transform with multi-head cross-attention mechanisms,enabling cross-scale feature fusion while significantly improving edge localization and suppressing spurious changes.Extensive experiments on four benchmark datasets demonstrate MewCDNet’s superiority over comparison methods:achieving F1 scores of 91.54%on LEVIR,93.70%on WHUCD,and 64.96%on S2Looking for building change detection.Furthermore,MewCDNet exhibits optimal performance on the multi-class⋅SYSU dataset(F1:82.71%),highlighting its exceptional generalization capability.
基金Tianmin Tianyuan Boutique Vegetable Industry Technology Service Station(Grant No.2024120011003081)Development of Environmental Monitoring and Traceability System for Wuqing Agricultural Production Areas(Grant No.2024120011001866)。
文摘Tomato is a major economic crop worldwide,and diseases on tomato leaves can significantly reduce both yield and quality.Traditional manual inspection is inefficient and highly subjective,making it difficult to meet the requirements of early disease identification in complex natural environments.To address this issue,this study proposes an improved YOLO11-based model,YOLO-SPDNet(Scale Sequence Fusion,Position-Channel Attention,and Dual Enhancement Network).The model integrates the SEAM(Self-Ensembling Attention Mechanism)semantic enhancement module,the MLCA(Mixed Local Channel Attention)lightweight attention mechanism,and the SPA(Scale-Position-Detail Awareness)module composed of SSFF(Scale Sequence Feature Fusion),TFE(Triple Feature Encoding),and CPAM(Channel and Position Attention Mechanism).These enhancements strengthen fine-grained lesion detection while maintaining model lightweightness.Experimental results show that YOLO-SPDNet achieves an accuracy of 91.8%,a recall of 86.5%,and an mAP@0.5 of 90.6%on the test set,with a computational complexity of 12.5 GFLOPs.Furthermore,the model reaches a real-time inference speed of 987 FPS,making it suitable for deployment on mobile agricultural terminals and online monitoring systems.Comparative analysis and ablation studies further validate the reliability and practical applicability of the proposed model in complex natural scenes.
文摘Distributed Denial of Service(DDoS)attacks are one of the severe threats to network infrastructure,sometimes bypassing traditional diagnosis algorithms because of their evolving complexity.PresentMachine Learning(ML)techniques for DDoS attack diagnosis normally apply network traffic statistical features such as packet sizes and inter-arrival times.However,such techniques sometimes fail to capture complicated relations among various traffic flows.In this paper,we present a new multi-scale ensemble strategy given the Graph Neural Networks(GNNs)for improving DDoS detection.Our technique divides traffic into macro-and micro-level elements,letting various GNN models to get the two corase-scale anomalies and subtle,stealthy attack models.Through modeling network traffic as graph-structured data,GNNs efficiently learn intricate relations among network entities.The proposed ensemble learning algorithm combines the results of several GNNs to improve generalization,robustness,and scalability.Extensive experiments on three benchmark datasets—UNSW-NB15,CICIDS2017,and CICDDoS2019—show that our approach outperforms traditional machine learning and deep learning models in detecting both high-rate and low-rate(stealthy)DDoS attacks,with significant improvements in accuracy and recall.These findings demonstrate the suggested method’s applicability and robustness for real-world implementation in contexts where several DDoS patterns coexist.
基金financial support from the National Key Research and Development Program of China(2022YFB3804905)National Natural Science Foundation of China(22375047,22378068,and 22378071)+1 种基金Natural Science Foundation of Fujian Province(2022J01568)111 Project(No.D17005).
文摘Advanced healthcare monitors for air pollution applications pose a significant challenge in achieving a balance between high-performance filtration and multifunctional smart integration.Electrospinning triboelectric nanogenerators(TENG)provide a significant potential for use under such difficult circumstances.We have successfully constructed a high-performance TENG utilizing a novel multi-scale nanofiber architecture.Nylon 66(PA66)and chitosan quaternary ammonium salt(HACC)composites were prepared by electrospinning,and PA66/H multiscale nanofiber membranes composed of nanofibers(≈73 nm)and submicron-fibers(≈123 nm)were formed.PA66/H multi-scale nanofiber membrane as the positive electrode and negative electrode-spun PVDF-HFP nanofiber membrane composed of respiration-driven PVDF-HFP@PA66/H TENG.The resulting PVDF-HFP@PA66/H TENG based air filter utilizes electrostatic adsorption and physical interception mechanisms,achieving PM_(0.3)filtration efficiency over 99%with a pressure drop of only 48 Pa.Besides,PVDF-HFP@PA66/H TENG exhibits excellent stability in high-humidity environments,with filtration efficiency reduced by less than 1%.At the same time,the TENG achieves periodic contact separation through breathing drive to achieve self-power,which can ensure the long-term stability of the filtration efficiency.In addition to the air filtration function,TENG can also monitor health in real time by capturing human breathing signals without external power supply.This integrated system combines high-efficiency air filtration,self-powered operation,and health monitoring,presenting an innovative solution for air purification,smart protective equipment,and portable health monitoring.These findings highlight the potential of this technology for diverse applications,offering a promising direction for advancing multifunctional air filtration systems.
文摘Defect detection in printed circuit boards(PCB)remains challenging due to the difficulty of identifying small-scale defects,the inefficiency of conventional approaches,and the interference from complex backgrounds.To address these issues,this paper proposes SIM-Net,an enhanced detection framework derived from YOLOv11.The model integrates SPDConv to preserve fine-grained features for small object detection,introduces a novel convolutional partial attention module(C2PAM)to suppress redundant background information and highlight salient regions,and employs a multi-scale fusion network(MFN)with a multi-grain contextual module(MGCT)to strengthen contextual representation and accelerate inference.Experimental evaluations demonstrate that SIM-Net achieves 92.4%mAP,92%accuracy,and 89.4%recall with an inference speed of 75.1 FPS,outperforming existing state-of-the-art methods.These results confirm the robustness and real-time applicability of SIM-Net for PCB defect inspection.
基金Project(2022YFC2904103)supported by the National Key Research and Development Program of ChinaProjects(52374112,52274108)supported by the National Natural Science Foundation of China+1 种基金Projects(BX20220036,BX20230041)supported by the Postdoctoral Innovation Talents Support Program,ChinaProject(2232080)supported by the Beijing Natural Science Foundation,China。
文摘The development of metallic mineral resources generates a significant amount of solid waste,such as tailings and waste rock.Cemented tailings and waste-rock backfill(CTWB)is an effective method for managing and disposing of this mining waste.This study employs a macro-meso-micro testing method to investigate the effects of the waste rock grading index(WGI)and loading rate(LR)on the uniaxial compressive strength(UCS),pore structure,and micromorphology of CTWB materials.Pore structures were analyzed using scanning electron microscopy(SEM)and mercury intrusion porosimetry(MIP).The particles(pores)and cracks analysis system(PCAS)software was used to quantitatively characterize the multi-scale micropores in the SEM images.The key findings indicate that the macroscopic results(UCS)of CTWB materials correspond to the microscopic results(pore structure and micromorphology).Changes in porosity largely depend on the conditions of waste rock grading index and loading rate.The inclusion of waste rock initially increases and then decreases the UCS,while porosity first decreases and then increases,with a critical waste rock grading index of 0.6.As the loading rate increases,UCS initially rises and then falls,while porosity gradually increases.Based on MIP and SEM results,at waste rock grading index 0.6,the most probable pore diameters,total pore area(TPA),pore number(PN),maximum pore area(MPA),and area probability distribution index(APDI)are minimized,while average pore form factor(APF)and fractal dimension of pore porosity distribution(FDPD)are maximized,indicating the most compact pore structure.At a loading rate of 12.0 mm/min,the most probable pore diameters,TPA,PN,MPA,APF,and APDI reach their maximum values,while FDPD reaches its minimum value.Finally,the mechanism of CTWB materials during compression is analyzed,based on the quantitative results of UCS and porosity.The research findings play a crucial role in ensuring the successful application of CTWB materials in deep metal mines.
文摘With the rapid expansion of drone applications,accurate detection of objects in aerial imagery has become crucial for intelligent transportation,urban management,and emergency rescue missions.However,existing methods face numerous challenges in practical deployment,including scale variation handling,feature degradation,and complex backgrounds.To address these issues,we propose Edge-enhanced and Detail-Capturing You Only Look Once(EHDC-YOLO),a novel framework for object detection in Unmanned Aerial Vehicle(UAV)imagery.Based on the You Only Look Once version 11 nano(YOLOv11n)baseline,EHDC-YOLO systematically introduces several architectural enhancements:(1)a Multi-Scale Edge Enhancement(MSEE)module that leverages multi-scale pooling and edge information to enhance boundary feature extraction;(2)an Enhanced Feature Pyramid Network(EFPN)that integrates P2-level features with Cross Stage Partial(CSP)structures and OmniKernel convolutions for better fine-grained representation;and(3)Dynamic Head(DyHead)with multi-dimensional attention mechanisms for enhanced cross-scale modeling and perspective adaptability.Comprehensive experiments on the Vision meets Drones for Detection(VisDrone-DET)2019 dataset demonstrate that EHDC-YOLO achieves significant improvements,increasing mean Average Precision(mAP)@0.5 from 33.2%to 46.1%(an absolute improvement of 12.9 percentage points)and mAP@0.5:0.95 from 19.5%to 28.0%(an absolute improvement of 8.5 percentage points)compared with the YOLOv11n baseline,while maintaining a reasonable parameter count(2.81 M vs the baseline’s 2.58 M).Further ablation studies confirm the effectiveness of each proposed component,while visualization results highlight EHDC-YOLO’s superior performance in detecting objects and handling occlusions in complex drone scenarios.
基金the National Key Research and Development Program of China (Grant No.2022YFF0711400)the National Space Science Data Center Youth Open Project (Grant No. NSSDC2302001)
文摘Impact craters are important for understanding the evolution of lunar geologic and surface erosion rates,among other functions.However,the morphological characteristics of these micro impact craters are not obvious and they are numerous,resulting in low detection accuracy by deep learning models.Therefore,we proposed a new multi-scale fusion crater detection algorithm(MSF-CDA)based on the YOLO11 to improve the accuracy of lunar impact crater detection,especially for small craters with a diameter of<1 km.Using the images taken by the LROC(Lunar Reconnaissance Orbiter Camera)at the Chang’e-4(CE-4)landing area,we constructed three separate datasets for craters with diameters of 0-70 m,70-140 m,and>140 m.We then trained three submodels separately with these three datasets.Additionally,we designed a slicing-amplifying-slicing strategy to enhance the ability to extract features from small craters.To handle redundant predictions,we proposed a new Non-Maximum Suppression with Area Filtering method to fuse the results in overlapping targets within the multi-scale submodels.Finally,our new MSF-CDA method achieved high detection performance,with the Precision,Recall,and F1 score having values of 0.991,0.987,and 0.989,respectively,perfectly addressing the problems induced by the lesser features and sample imbalance of small craters.Our MSF-CDA can provide strong data support for more in-depth study of the geological evolution of the lunar surface and finer geological age estimations.This strategy can also be used to detect other small objects with lesser features and sample imbalance problems.We detected approximately 500,000 impact craters in an area of approximately 214 km2 around the CE-4 landing area.By statistically analyzing the new data,we updated the distribution function of the number and diameter of impact craters.Finally,we identified the most suitable lighting conditions for detecting impact crater targets by analyzing the effect of different lighting conditions on the detection accuracy.
基金supported by the National Natural Science Foundation of China(12401482)the second author was supported by the National Natural Science Foundation of China(12371371,12261160361,11971366)supported by the Open Research Fund of Hubei Key Laboratory of Computational Science,Wuhan University.
文摘A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).
基金supported by the Science and Technology on Reactor System Design Technology Laboratory(No.LRSDT12023108)supported in part by the Chongqing Postdoctoral Science Foundation(No.cstc2021jcyj-bsh0252)+2 种基金the National Natural Science Foundation of China(No.12005030)Sichuan Province to unveil the list of marshal industry common technology research projects(No.23jBGOV0001)Special Program for Stabilizing Support to Basic Research of National Basic Research Institutes(No.WDZC-2023-05-03-05).
文摘The neutron diffusion equation plays a pivotal role in nuclear reactor analysis.Nevertheless,employing the physics-informed neural network(PINN)method for its solution entails certain limitations.Conventional PINN approaches generally utilize a fully connected network(FCN)architecture that is susceptible to overfitting,training instability,and gradient vanishing as the network depth increases.These challenges result in accuracy bottlenecks in the solution.In response to these issues,the residual-based resample physics-informed neural network(R2-PINN)is proposed.It is an improved PINN architecture that replaces the FCN with a convolutional neural network with a shortcut(S-CNN).It incorporates skip connections to facilitate gradient propagation between network layers.Additionally,the incorporation of the residual adaptive resampling(RAR)mechanism dynamically increases the number of sampling points.This,in turn,enhances the spatial representation capabilities and overall predictive accuracy of the model.The experimental results illustrate that our approach significantly improves the convergence capability of the model and achieves high-precision predictions of the physical fields.Compared with conventional FCN-based PINN methods,R 2-PINN effectively overcomes the limitations inherent in current methods.Thus,it provides more accurate and robust solutions for neutron diffusion equations.
文摘This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called Ⅰ-type basic scheme is developed for solving the equations and it is proved under the suitable conditions that this method has the computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4)),where τ,h_(x )and h_(y) are the calculation stepsizes of the method in t-,x-and y-direction,respectively.With the above method and Newton linearized technique,a Ⅱ-type basic scheme is also suggested.Based on the both basic schemes,the corresponding Ⅰ-and Ⅱ-type alternating direction implicit(ADI)schemes are derived.Finally,with a series of numerical experiments,the computational accuracy and efficiency of the four numerical schemes are further illustrated.
文摘In this paper, we present a new algorithm to solve a kind of nonlinear time space-fractional partial differential equations on a finite domain. The method is based on B-spline wavelets approximations, some of these functions are reshaped to satisfy on boundary conditions exactly. The Adams fractional method is used to reduce the problem to a system of equations. By multiscale method this system is divided into some smaller systems which have less computations. We get an approximated solution which is more accurate on some subdomains by combining the solutions of these systems. Illustrative examples are included to demonstrate the validity and applicability of our proposed technique, also the stability of the method is discussed.
基金Opening Foundation of Key Laboratory of Explosive Energy Utilization and Control,Anhui Province(BP20240104)Graduate Innovation Program of China University of Mining and Technology(2024WLJCRCZL049)Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX24_2701)。
文摘Because of the challenge of compounding lightweight,high-strength Ti/Al alloys due to their considerable disparity in properties,Al 6063 as intermediate layer was proposed to fabricate TC4/Al 6063/Al 7075 three-layer composite plate by explosive welding.The microscopic properties of each bonding interface were elucidated through field emission scanning electron microscope and electron backscattered diffraction(EBSD).A methodology combining finite element method-smoothed particle hydrodynamics(FEM-SPH)and molecular dynamics(MD)was proposed for the analysis of the forming and evolution characteristics of explosive welding interfaces at multi-scale.The results demonstrate that the bonding interface morphologies of TC4/Al 6063 and Al 6063/Al 7075 exhibit a flat and wavy configuration,without discernible defects or cracks.The phenomenon of grain refinement is observed in the vicinity of the two bonding interfaces.Furthermore,the degree of plastic deformation of TC4 and Al 7075 is more pronounced than that of Al 6063 in the intermediate layer.The interface morphology characteristics obtained by FEM-SPH simulation exhibit a high degree of similarity to the experimental results.MD simulations reveal that the diffusion of interfacial elements predominantly occurs during the unloading phase,and the simulated thickness of interfacial diffusion aligns well with experimental outcomes.The introduction of intermediate layer in the explosive welding process can effectively produce high-quality titanium/aluminum alloy composite plates.Furthermore,this approach offers a multi-scale simulation strategy for the study of explosive welding bonding interfaces.
基金supported by the National Natural Science Foundation of China(Grant Nos.42150204 and 2288101)supported by the China National Postdoctoral Program for Innovative Talents(BX20230045)the China Postdoctoral Science Foundation(2023M730279)。
文摘A nonlinear multi-scale interaction(NMI)model was proposed and developed by the first author for nearly 30 years to represent the evolution of atmospheric blocking.In this review paper,we first review the creation and development of the NMI model and then emphasize that the NMI model represents a new tool for identifying the basic physics of how climate change influences mid-to-high latitude weather extremes.The building of the NMI model took place over three main periods.In the 1990s,a nonlinear Schr?dinger(NLS)equation model was presented to describe atmospheric blocking as a wave packet;however,it could not depict the lifetime(10-20 days)of atmospheric blocking.In the 2000s,we proposed an NMI model of atmospheric blocking in a uniform basic flow by making a scale-separation assumption and deriving an eddyforced NLS equation.This model succeeded in describing the life cycle of atmospheric blocking.In the 2020s,the NMI model was extended to include the impact of a changing climate mainly by altering the basic zonal winds and the magnitude of the meridional background potential vorticity gradient(PVy).Model results show that when PVy is smaller,blocking has a weaker dispersion and a stronger nonlinearity,so blocking can be more persistent and have a larger zonal scale and weaker eastward movement,thus favoring stronger weather extremes.However,when PVy is much smaller and below a critical threshold under much stronger winter Arctic warming of global warming,atmospheric blocking becomes locally less persistent and shows a much stronger westward movement,which acts to inhibit local cold extremes.Such a case does not happen in summer under global warming because PVy fails to fall below the critical threshold.Thus,our theory indicates that global warming can render summer-blocking anticyclones and mid-to-high latitude heatwaves more persistent,intense,and widespread.
文摘Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.
