Alpine regions face severe flood management challenges due to complex terrain,climate extremes,and sparse data.This commentary critiques limitations in current hydrological practices supporting China's Four-pre st...Alpine regions face severe flood management challenges due to complex terrain,climate extremes,and sparse data.This commentary critiques limitations in current hydrological practices supporting China's Four-pre strategy.Key barriers include poor data quality,model limitations,and fragmented systems.Thus,we recommend optimizing observation networks,using physicsinformed neural networks,and establishing unified data platforms.This integrated approach will enhance flood modeling reliability in data-scarce regions,providing actionable insights for adaptive flood governance in high-risk mountainous regions.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
基金the Science and Technology Projects of Xizang Autonomous Region(XZ202501ZY0145)Natural Science Foundation Youth Project of the Science and Technology Department of Sichuan Province(2024NSFSC0984)China Yangtze Power Co.Ltd(Z242302038).
文摘Alpine regions face severe flood management challenges due to complex terrain,climate extremes,and sparse data.This commentary critiques limitations in current hydrological practices supporting China's Four-pre strategy.Key barriers include poor data quality,model limitations,and fragmented systems.Thus,we recommend optimizing observation networks,using physicsinformed neural networks,and establishing unified data platforms.This integrated approach will enhance flood modeling reliability in data-scarce regions,providing actionable insights for adaptive flood governance in high-risk mountainous regions.
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.
