In the field of image processing,the analysis of Synthetic Aperture Radar(SAR)images is crucial due to its broad range of applications.However,SAR images are often affected by coherent speckle noise,which significantl...In the field of image processing,the analysis of Synthetic Aperture Radar(SAR)images is crucial due to its broad range of applications.However,SAR images are often affected by coherent speckle noise,which significantly degrades image quality.Traditional denoising methods,typically based on filter techniques,often face challenges related to inefficiency and limited adaptability.To address these limitations,this study proposes a novel SAR image denoising algorithm based on an enhanced residual network architecture,with the objective of enhancing the utility of SAR imagery in complex electromagnetic environments.The proposed algorithm integrates residual network modules,which directly process the noisy input images to generate denoised outputs.This approach not only reduces computational complexity but also mitigates the difficulties associated with model training.By combining the Transformer module with the residual block,the algorithm enhances the network's ability to extract global features,offering superior feature extraction capabilities compared to CNN-based residual modules.Additionally,the algorithm employs the adaptive activation function Meta-ACON,which dynamically adjusts the activation patterns of neurons,thereby improving the network's feature extraction efficiency.The effectiveness of the proposed denoising method is empirically validated using real SAR images from the RSOD dataset.The proposed algorithm exhibits remarkable performance in terms of EPI,SSIM,and ENL,while achieving a substantial enhancement in PSNR when compared to traditional and deep learning-based algorithms.The PSNR performance is enhanced by over twofold.Moreover,the evaluation of the MSTAR SAR dataset substantiates the algorithm's robustness and applicability in SAR denoising tasks,with a PSNR of 25.2021 being attained.These findings underscore the efficacy of the proposed algorithm in mitigating speckle noise while preserving critical features in SAR imagery,thereby enhancing its quality and usability in practical scenarios.展开更多
Partial differential equations(PDEs)are important tools for scientific research and are widely used in various fields.However,it is usually very difficult to obtain accurate analytical solutions of PDEs,and numerical ...Partial differential equations(PDEs)are important tools for scientific research and are widely used in various fields.However,it is usually very difficult to obtain accurate analytical solutions of PDEs,and numerical methods to solve PDEs are often computationally intensive and very time-consuming.In recent years,Physics Informed Neural Networks(PINNs)have been successfully applied to find numerical solutions of PDEs and have shown great potential.All the while,solitary waves have been of great interest to researchers in the field of nonlinear science.In this paper,we perform numerical simulations of solitary wave solutions of several PDEs using improved PINNs.The improved PINNs not only incorporate constraints on the control equations to ensure the interpretability of the prediction results,which is important for physical field simulations,in addition,an adaptive activation function is introduced.By introducing hyperparameters in the activation function to change the slope of the activation function to avoid the disappearance of the gradient,computing time is saved thereby speeding up training.In this paper,the m Kd V equation,the improved Boussinesq equation,the Caudrey–Dodd–Gibbon–Sawada–Kotera equation and the p-g BKP equation are selected for study,and the errors of the simulation results are analyzed to assess the accuracy of the predicted solitary wave solution.The experimental results show that the improved PINNs are significantly better than the traditional PINNs with shorter training time but more accurate prediction results.The improved PINNs improve the training speed by more than 1.5 times compared with the traditional PINNs,while maintaining the prediction error less than 10~(-2)in this order of magnitude.展开更多
Physics-informed neural networks(PINNs)are known to suffer from optimization difficulty.In this work,we reveal the connection between the optimization difficulty of PINNs and activation functions.Specifically,we show ...Physics-informed neural networks(PINNs)are known to suffer from optimization difficulty.In this work,we reveal the connection between the optimization difficulty of PINNs and activation functions.Specifically,we show that PINNs exhibit high sensitivity to activation functions when solving PDEs with distinct properties.Existing works usually choose activation functions by inefficient trial-and-error.To avoid the inefficient manual selection and to alleviate the optimization difficulty of PINNs,we introduce adaptive activation functions to search for the optimal function when solving different problems.We compare different adaptive activation functions and discuss their limitations in the context of PINNs.Furthermore,we propose to tailor the idea of learning combinations of candidate activation functions to the PINNs optimization,which has a higher requirement for the smoothness and diversity on learned functions.This is achieved by removing activation functions which cannot provide higher-order derivatives from the candidate set and incorporating elementary functions with different properties according to our prior knowledge about the PDE at hand.We further enhance the search space with adaptive slopes.The proposed adaptive activation function can be used to solve different PDE systems in an interpretable way.Its effectiveness is demonstrated on a series of benchmarks.Code is available at https://github.com/LeapLabTHU/AdaAFforPINNs.展开更多
文摘In the field of image processing,the analysis of Synthetic Aperture Radar(SAR)images is crucial due to its broad range of applications.However,SAR images are often affected by coherent speckle noise,which significantly degrades image quality.Traditional denoising methods,typically based on filter techniques,often face challenges related to inefficiency and limited adaptability.To address these limitations,this study proposes a novel SAR image denoising algorithm based on an enhanced residual network architecture,with the objective of enhancing the utility of SAR imagery in complex electromagnetic environments.The proposed algorithm integrates residual network modules,which directly process the noisy input images to generate denoised outputs.This approach not only reduces computational complexity but also mitigates the difficulties associated with model training.By combining the Transformer module with the residual block,the algorithm enhances the network's ability to extract global features,offering superior feature extraction capabilities compared to CNN-based residual modules.Additionally,the algorithm employs the adaptive activation function Meta-ACON,which dynamically adjusts the activation patterns of neurons,thereby improving the network's feature extraction efficiency.The effectiveness of the proposed denoising method is empirically validated using real SAR images from the RSOD dataset.The proposed algorithm exhibits remarkable performance in terms of EPI,SSIM,and ENL,while achieving a substantial enhancement in PSNR when compared to traditional and deep learning-based algorithms.The PSNR performance is enhanced by over twofold.Moreover,the evaluation of the MSTAR SAR dataset substantiates the algorithm's robustness and applicability in SAR denoising tasks,with a PSNR of 25.2021 being attained.These findings underscore the efficacy of the proposed algorithm in mitigating speckle noise while preserving critical features in SAR imagery,thereby enhancing its quality and usability in practical scenarios.
文摘Partial differential equations(PDEs)are important tools for scientific research and are widely used in various fields.However,it is usually very difficult to obtain accurate analytical solutions of PDEs,and numerical methods to solve PDEs are often computationally intensive and very time-consuming.In recent years,Physics Informed Neural Networks(PINNs)have been successfully applied to find numerical solutions of PDEs and have shown great potential.All the while,solitary waves have been of great interest to researchers in the field of nonlinear science.In this paper,we perform numerical simulations of solitary wave solutions of several PDEs using improved PINNs.The improved PINNs not only incorporate constraints on the control equations to ensure the interpretability of the prediction results,which is important for physical field simulations,in addition,an adaptive activation function is introduced.By introducing hyperparameters in the activation function to change the slope of the activation function to avoid the disappearance of the gradient,computing time is saved thereby speeding up training.In this paper,the m Kd V equation,the improved Boussinesq equation,the Caudrey–Dodd–Gibbon–Sawada–Kotera equation and the p-g BKP equation are selected for study,and the errors of the simulation results are analyzed to assess the accuracy of the predicted solitary wave solution.The experimental results show that the improved PINNs are significantly better than the traditional PINNs with shorter training time but more accurate prediction results.The improved PINNs improve the training speed by more than 1.5 times compared with the traditional PINNs,while maintaining the prediction error less than 10~(-2)in this order of magnitude.
基金supported in part by the National Natural Science Foundation of China under Grants 62276150the Guoqiang Institute of Tsinghua University.
文摘Physics-informed neural networks(PINNs)are known to suffer from optimization difficulty.In this work,we reveal the connection between the optimization difficulty of PINNs and activation functions.Specifically,we show that PINNs exhibit high sensitivity to activation functions when solving PDEs with distinct properties.Existing works usually choose activation functions by inefficient trial-and-error.To avoid the inefficient manual selection and to alleviate the optimization difficulty of PINNs,we introduce adaptive activation functions to search for the optimal function when solving different problems.We compare different adaptive activation functions and discuss their limitations in the context of PINNs.Furthermore,we propose to tailor the idea of learning combinations of candidate activation functions to the PINNs optimization,which has a higher requirement for the smoothness and diversity on learned functions.This is achieved by removing activation functions which cannot provide higher-order derivatives from the candidate set and incorporating elementary functions with different properties according to our prior knowledge about the PDE at hand.We further enhance the search space with adaptive slopes.The proposed adaptive activation function can be used to solve different PDE systems in an interpretable way.Its effectiveness is demonstrated on a series of benchmarks.Code is available at https://github.com/LeapLabTHU/AdaAFforPINNs.
