Artificial Neural Network(ANN)has become a powerful tool in the field of scientific research with its powerful information encapsulation ability and convenient variational optimization method.In particular,there have ...Artificial Neural Network(ANN)has become a powerful tool in the field of scientific research with its powerful information encapsulation ability and convenient variational optimization method.In particular,there have been many recent advances in computational physics to solve variational problems.Deep Neural Network(DNN)is used to represent the wave function to solve quantum many-body problems using variational optimization.In this work we used a new Physics-Informed Neural Network(PINN)to represent the Cumulative Distribution Function(CDF)of some classical problems in quantum mechanics and to obtain their ground state wave function and ground state energy through the CDF.By benchmarking against the exact solution,the error of the results can be controlled at a very low level.This new network architecture and optimization method can provide a new choice for solving quantum many-body problems.展开更多
Background,aim,and scope Soil saturated hydraulic conductivity(K_(s))is a key parameter in the hydrological cycle of soil;however,we have very limited understanding of K_(s)characteristics and the factors that inf lue...Background,aim,and scope Soil saturated hydraulic conductivity(K_(s))is a key parameter in the hydrological cycle of soil;however,we have very limited understanding of K_(s)characteristics and the factors that inf luence this key parameter in the Mu Us sandy land(MUSL).Quantifying the impact of changes in land use in the Mu Us sandy land on K_(s)will provide a key foundation for understanding the regional water cycle,but will also provide a scientific basis for the governance of the MUSL.Materials and methods In this study,we determined K_(s)and the basic physical and chemical properties of soil(i.e.,organic matter,bulk density,and soil particle composition)within the first 100 cm layer of four different land use patterns(farmland,tree,shrub,and grassland)in the MUSL.The vertical variation of K_(s)and the factors that influence this key parameter were analyzed and a transfer function for estimating K_(s)was established based on a multiple stepwise regression model.Results The K_(s)of farmland,tree,and shrub increased gradually with soil depth while that of grassland remained unchanged.The K_(s)of the four patterns of land use were moderately variable;mean K_(s)values were ranked as follows:grassland(1.38 mm·min^(-1))<tree(1.76 mm·min^(-1))<farmland(1.82 mm·min^(-1))<shrub(3.30 mm·min^(-1)).The correlation between K_(s)and organic matter,bulk density,and soil particle composition,varied across different land use patterns.A multiple stepwise regression model showed that silt,coarse sand,bulk density,and organic matter,were key predictive factors for the K_(s)of farmland,tree,shrub,and grassland,in the MUSL.Discussion The vertical distribution trend for K_(s)in farmland is known to be predominantly influenced by cultivation,fertilization,and other factors.The general aim is to improve the water-holding capacity of shallow soil on farmland(0-30 cm in depth)to conserve water and nutrients;research has shown that the K_(s)of farmland increases with soil depth.The root growth of tree and shrub in sandy land exerts mechanical force on the soil due to biophysical processes involving rhizospheres,thus leading to a significant change in K_(s).We found that shallow high-density fine roots increased the volume of soil pores and eliminated large pores,thus resulting in a reduction in shallow K_(s).Therefore,the K_(s)of tree and shrub increased with soil depth.Analysis also showed that the K_(s)of grassland did not change significantly and exhibited the lowest mean value when compared to other land use patterns.This finding was predominantly due to the shallow root system of grasslands and because this land use pattern is not subject to human activities such as cultivation and fertilization;consequently,there was no significant change in K_(s)with depth;grassland also had the lowest mean K_(s).We also established a transfer function for K_(s)for different land use patterns in the MUSL.However,the predictive factors for K_(s)in different land use patterns are known to be affected by soil cultivation methods,vegetation restoration modes,the distribution of soil moisture,and other factors,thus resulting in key differences.Therefore,when using the transfer function to predict K_(s)in other areas,it will be necessary to perform parameter calibration and further verification.Conclusions In the MUSL,the K_(s)of farmland,tree,and shrub gradually increased with soil depth;however,the K_(s)of grassland showed no significant variation in terms of vertical distribution.The mean K_(s)values of different land use patterns were ranked as follows:shrub>farmland>tree>grassland;all land use patterns showed moderate levels of variability.The K_(s)for different land use patterns exhibited differing degrees of correlation with soil physical and chemical properties;of these,clay,silt,sand,bulk density,and organic matter,were identified as important variables for predicting K_(s)in farmland,tree,shrub,and grassland,respectively.Recommendations and perspectives In this study,we used a stepwise multiple regression model to establish a transfer function prediction model for K_(s)for different land use patterns;this model possessed high estimation accuracy.The ability to predict K_(s)in the MUSL is very important in terms of the conservation of water and nutrients.展开更多
文摘Artificial Neural Network(ANN)has become a powerful tool in the field of scientific research with its powerful information encapsulation ability and convenient variational optimization method.In particular,there have been many recent advances in computational physics to solve variational problems.Deep Neural Network(DNN)is used to represent the wave function to solve quantum many-body problems using variational optimization.In this work we used a new Physics-Informed Neural Network(PINN)to represent the Cumulative Distribution Function(CDF)of some classical problems in quantum mechanics and to obtain their ground state wave function and ground state energy through the CDF.By benchmarking against the exact solution,the error of the results can be controlled at a very low level.This new network architecture and optimization method can provide a new choice for solving quantum many-body problems.
文摘Background,aim,and scope Soil saturated hydraulic conductivity(K_(s))is a key parameter in the hydrological cycle of soil;however,we have very limited understanding of K_(s)characteristics and the factors that inf luence this key parameter in the Mu Us sandy land(MUSL).Quantifying the impact of changes in land use in the Mu Us sandy land on K_(s)will provide a key foundation for understanding the regional water cycle,but will also provide a scientific basis for the governance of the MUSL.Materials and methods In this study,we determined K_(s)and the basic physical and chemical properties of soil(i.e.,organic matter,bulk density,and soil particle composition)within the first 100 cm layer of four different land use patterns(farmland,tree,shrub,and grassland)in the MUSL.The vertical variation of K_(s)and the factors that influence this key parameter were analyzed and a transfer function for estimating K_(s)was established based on a multiple stepwise regression model.Results The K_(s)of farmland,tree,and shrub increased gradually with soil depth while that of grassland remained unchanged.The K_(s)of the four patterns of land use were moderately variable;mean K_(s)values were ranked as follows:grassland(1.38 mm·min^(-1))<tree(1.76 mm·min^(-1))<farmland(1.82 mm·min^(-1))<shrub(3.30 mm·min^(-1)).The correlation between K_(s)and organic matter,bulk density,and soil particle composition,varied across different land use patterns.A multiple stepwise regression model showed that silt,coarse sand,bulk density,and organic matter,were key predictive factors for the K_(s)of farmland,tree,shrub,and grassland,in the MUSL.Discussion The vertical distribution trend for K_(s)in farmland is known to be predominantly influenced by cultivation,fertilization,and other factors.The general aim is to improve the water-holding capacity of shallow soil on farmland(0-30 cm in depth)to conserve water and nutrients;research has shown that the K_(s)of farmland increases with soil depth.The root growth of tree and shrub in sandy land exerts mechanical force on the soil due to biophysical processes involving rhizospheres,thus leading to a significant change in K_(s).We found that shallow high-density fine roots increased the volume of soil pores and eliminated large pores,thus resulting in a reduction in shallow K_(s).Therefore,the K_(s)of tree and shrub increased with soil depth.Analysis also showed that the K_(s)of grassland did not change significantly and exhibited the lowest mean value when compared to other land use patterns.This finding was predominantly due to the shallow root system of grasslands and because this land use pattern is not subject to human activities such as cultivation and fertilization;consequently,there was no significant change in K_(s)with depth;grassland also had the lowest mean K_(s).We also established a transfer function for K_(s)for different land use patterns in the MUSL.However,the predictive factors for K_(s)in different land use patterns are known to be affected by soil cultivation methods,vegetation restoration modes,the distribution of soil moisture,and other factors,thus resulting in key differences.Therefore,when using the transfer function to predict K_(s)in other areas,it will be necessary to perform parameter calibration and further verification.Conclusions In the MUSL,the K_(s)of farmland,tree,and shrub gradually increased with soil depth;however,the K_(s)of grassland showed no significant variation in terms of vertical distribution.The mean K_(s)values of different land use patterns were ranked as follows:shrub>farmland>tree>grassland;all land use patterns showed moderate levels of variability.The K_(s)for different land use patterns exhibited differing degrees of correlation with soil physical and chemical properties;of these,clay,silt,sand,bulk density,and organic matter,were identified as important variables for predicting K_(s)in farmland,tree,shrub,and grassland,respectively.Recommendations and perspectives In this study,we used a stepwise multiple regression model to establish a transfer function prediction model for K_(s)for different land use patterns;this model possessed high estimation accuracy.The ability to predict K_(s)in the MUSL is very important in terms of the conservation of water and nutrients.
