Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularl...Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularly deep learning(DL),applied and relevant to computational mechanics(solid,fluids,finite-element technology)are reviewed in detail.Both hybrid and pure machine learning(ML)methods are discussed.Hybrid methods combine traditional PDE discretizations with ML methods either(1)to help model complex nonlinear constitutive relations,(2)to nonlinearly reduce the model order for efficient simulation(turbulence),or(3)to accelerate the simulation by predicting certain components in the traditional integration methods.Here,methods(1)and(2)relied on Long-Short-Term Memory(LSTM)architecture,with method(3)relying on convolutional neural networks.Pure ML methods to solve(nonlinear)PDEs are represented by Physics-Informed Neural network(PINN)methods,which could be combined with attention mechanism to address discontinuous solutions.Both LSTM and attention architectures,together with modern and generalized classic optimizers to include stochasticity for DL networks,are extensively reviewed.Kernel machines,including Gaussian processes,are provided to sufficient depth for more advanced works such as shallow networks with infinite width.Not only addressing experts,readers are assumed familiar with computational mechanics,but not with DL,whose concepts and applications are built up from the basics,aiming at bringing first-time learners quickly to the forefront of research.History and limitations of AI are recounted and discussed,with particular attention at pointing out misstatements or misconceptions of the classics,even in well-known references.Positioning and pointing control of a large-deformable beam is given as an example.展开更多
Traditional Japanese Medicine originated from traditional Chinese medicine and was first introduced to Japan directly from the mainland of China or the Korean Peninsula.After its dissemination,integration,adaption,and...Traditional Japanese Medicine originated from traditional Chinese medicine and was first introduced to Japan directly from the mainland of China or the Korean Peninsula.After its dissemination,integration,adaption,and development in Japan for generations,it had evolved into Kampo medicine with Japanese characteristics and taken a leading role in Japanese medical practice.In history,there appeared successively schools such as Followers of Later Developments in Medicine,Followers of Classic Methods,Integrated School,and School of Textual Research.Alter Meiji Restoration,Kampo medicine experienced a tremendous impact by western medicine.However after World War II,with unremitting endeavors from learned scholars,traditional Japanese medicinje was revived again.展开更多
We study in this manuscript a new one-parameter model called sine inverse Rayleigh(SIR)model that is a new extension of the classical inverse Rayleigh model.The sine inverse Rayleigh model is aiming to provide morefit-...We study in this manuscript a new one-parameter model called sine inverse Rayleigh(SIR)model that is a new extension of the classical inverse Rayleigh model.The sine inverse Rayleigh model is aiming to provide morefit-ting for real data sets of purposes.The proposed extension is moreflexible than the original inverse Rayleigh(IR)model and it hasmany applications in physics and medicine.The sine inverse Rayleigh distribution can havea uni-model and right skewed probability density function(PDF).The hazard rate function(HRF)of sine inverse Rayleigh distribution can be increasing and J-shaped.Sev-eral of thenew model’s fundamental characteristics,namely quantile function,moments,incompletemoments,Lorenz and Bonferroni Curves are studied.Four classical estimation methods forthe population parameters,namely least squares(LS),weighted least squares(WLS),maximum likelihood(ML),and percentile(PC)methods are discussed,and the performanceof the four estimators(namely LS,WLS,ML and PC estimators)are also compared bynumerical implementa-tions.Finally,three sets of real data are utilized to compare the behavior of the four employed methods forfinding an optimal estimation of the new distribution.展开更多
The Babao River Basin is the "water tower" of the Heihe River Basin.The combination of vulnerable ecosystems and inhospitable natural environments substantially restricts the existence of humans and the sust...The Babao River Basin is the "water tower" of the Heihe River Basin.The combination of vulnerable ecosystems and inhospitable natural environments substantially restricts the existence of humans and the sustainable development of society and environment in the Heihe River Basin.Soil temperature(ST) is a critical soil variable that could affect a series of physical,chemical and biological soil processes,which is the guarantee of water conservation and vegetation growth in this region.To measure the temporal variation and spatial pattern of ST fluctuation in the Babao River Basin,fluctuation of ST at various depths were analyzed with ST data at depths of 4,10 and 20 cm using classical statistical methods and permutation entropy.The study results show the following: 1) There are variations of ST at different depths,although ST followed an obvious seasonal law.ST at shallower depths is higher than at deeper depths in summer,and vice versa in winter.The difference of ST between different depths is close to zero when ST is near 5℃ in March or –5℃ in September.2) In spring,ST at the shallower depths becomes higher than at deeper depths as soon as ST is above –5℃;this is reversed in autumn when ST is below 5℃.ST at a soil depth of 4 cm is the first to change,followed by ST at 10 and 20 cm,and the time that ST reaches the same level is delayed for 10–15 days.In chilling and warming seasons,September and February are,respectively,the months when ST at various depths are similar.3) The average PE values of ST for 17 sites at 4 cm are 0.765 in spring > 0.764 in summer > 0.735 in autumn > 0.723 in winter,which implies the complicated degree of fluctuations of ST.4) For the variation of ST at different depths,it appears that Max,Ranges,Average and the Standard Deviation of ST decrease by depth increments in soil.Surface soil is more complicated because ST fluctuation at shallower depths is more pronounced and random.The average PE value of ST for 17sites are 0.863 at a depth of 4 cm > 0.818 at 10 cm > 0.744 at 20 cm.5) For the variation of ST at different elevations,it appears that Max,Ranges,Average,Standard Deviation and ST fluctuation decrease with increasing elevation at the same soil depth.And with the increase of elevation,the decrease rates of Max,Range,Average,Standard Deviation at 4 cm are –0.89℃/100 m,–0.94℃/100 m,–0.43℃/100 m,and –0.25℃/100 m,respectively.In addition,this correlation decreased with the increase of soil depth.6) Significant correlation between PE values of ST at depths of 4,10 and 20 cm can easily be found.This finding implies that temperature can easily be transmitted within soil at depths between 4 and 20 cm.7) For the variation of ST on shady slope and sunny slope sides,it appears that the PE values of ST at 4,10 and 20 cm for 8 sites located on shady slope side are 0.868,0.824 and 0.776,respectively,whereas they are 0.858,0.810 and 0.716 for 9 sites located on sunny slope side.展开更多
文摘Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularly deep learning(DL),applied and relevant to computational mechanics(solid,fluids,finite-element technology)are reviewed in detail.Both hybrid and pure machine learning(ML)methods are discussed.Hybrid methods combine traditional PDE discretizations with ML methods either(1)to help model complex nonlinear constitutive relations,(2)to nonlinearly reduce the model order for efficient simulation(turbulence),or(3)to accelerate the simulation by predicting certain components in the traditional integration methods.Here,methods(1)and(2)relied on Long-Short-Term Memory(LSTM)architecture,with method(3)relying on convolutional neural networks.Pure ML methods to solve(nonlinear)PDEs are represented by Physics-Informed Neural network(PINN)methods,which could be combined with attention mechanism to address discontinuous solutions.Both LSTM and attention architectures,together with modern and generalized classic optimizers to include stochasticity for DL networks,are extensively reviewed.Kernel machines,including Gaussian processes,are provided to sufficient depth for more advanced works such as shallow networks with infinite width.Not only addressing experts,readers are assumed familiar with computational mechanics,but not with DL,whose concepts and applications are built up from the basics,aiming at bringing first-time learners quickly to the forefront of research.History and limitations of AI are recounted and discussed,with particular attention at pointing out misstatements or misconceptions of the classics,even in well-known references.Positioning and pointing control of a large-deformable beam is given as an example.
文摘Traditional Japanese Medicine originated from traditional Chinese medicine and was first introduced to Japan directly from the mainland of China or the Korean Peninsula.After its dissemination,integration,adaption,and development in Japan for generations,it had evolved into Kampo medicine with Japanese characteristics and taken a leading role in Japanese medical practice.In history,there appeared successively schools such as Followers of Later Developments in Medicine,Followers of Classic Methods,Integrated School,and School of Textual Research.Alter Meiji Restoration,Kampo medicine experienced a tremendous impact by western medicine.However after World War II,with unremitting endeavors from learned scholars,traditional Japanese medicinje was revived again.
文摘We study in this manuscript a new one-parameter model called sine inverse Rayleigh(SIR)model that is a new extension of the classical inverse Rayleigh model.The sine inverse Rayleigh model is aiming to provide morefit-ting for real data sets of purposes.The proposed extension is moreflexible than the original inverse Rayleigh(IR)model and it hasmany applications in physics and medicine.The sine inverse Rayleigh distribution can havea uni-model and right skewed probability density function(PDF).The hazard rate function(HRF)of sine inverse Rayleigh distribution can be increasing and J-shaped.Sev-eral of thenew model’s fundamental characteristics,namely quantile function,moments,incompletemoments,Lorenz and Bonferroni Curves are studied.Four classical estimation methods forthe population parameters,namely least squares(LS),weighted least squares(WLS),maximum likelihood(ML),and percentile(PC)methods are discussed,and the performanceof the four estimators(namely LS,WLS,ML and PC estimators)are also compared bynumerical implementa-tions.Finally,three sets of real data are utilized to compare the behavior of the four employed methods forfinding an optimal estimation of the new distribution.
基金National Key R&D Program of China,No.2017YFB0504102National Natural Science Foundation of China,No.41771537
文摘The Babao River Basin is the "water tower" of the Heihe River Basin.The combination of vulnerable ecosystems and inhospitable natural environments substantially restricts the existence of humans and the sustainable development of society and environment in the Heihe River Basin.Soil temperature(ST) is a critical soil variable that could affect a series of physical,chemical and biological soil processes,which is the guarantee of water conservation and vegetation growth in this region.To measure the temporal variation and spatial pattern of ST fluctuation in the Babao River Basin,fluctuation of ST at various depths were analyzed with ST data at depths of 4,10 and 20 cm using classical statistical methods and permutation entropy.The study results show the following: 1) There are variations of ST at different depths,although ST followed an obvious seasonal law.ST at shallower depths is higher than at deeper depths in summer,and vice versa in winter.The difference of ST between different depths is close to zero when ST is near 5℃ in March or –5℃ in September.2) In spring,ST at the shallower depths becomes higher than at deeper depths as soon as ST is above –5℃;this is reversed in autumn when ST is below 5℃.ST at a soil depth of 4 cm is the first to change,followed by ST at 10 and 20 cm,and the time that ST reaches the same level is delayed for 10–15 days.In chilling and warming seasons,September and February are,respectively,the months when ST at various depths are similar.3) The average PE values of ST for 17 sites at 4 cm are 0.765 in spring > 0.764 in summer > 0.735 in autumn > 0.723 in winter,which implies the complicated degree of fluctuations of ST.4) For the variation of ST at different depths,it appears that Max,Ranges,Average and the Standard Deviation of ST decrease by depth increments in soil.Surface soil is more complicated because ST fluctuation at shallower depths is more pronounced and random.The average PE value of ST for 17sites are 0.863 at a depth of 4 cm > 0.818 at 10 cm > 0.744 at 20 cm.5) For the variation of ST at different elevations,it appears that Max,Ranges,Average,Standard Deviation and ST fluctuation decrease with increasing elevation at the same soil depth.And with the increase of elevation,the decrease rates of Max,Range,Average,Standard Deviation at 4 cm are –0.89℃/100 m,–0.94℃/100 m,–0.43℃/100 m,and –0.25℃/100 m,respectively.In addition,this correlation decreased with the increase of soil depth.6) Significant correlation between PE values of ST at depths of 4,10 and 20 cm can easily be found.This finding implies that temperature can easily be transmitted within soil at depths between 4 and 20 cm.7) For the variation of ST on shady slope and sunny slope sides,it appears that the PE values of ST at 4,10 and 20 cm for 8 sites located on shady slope side are 0.868,0.824 and 0.776,respectively,whereas they are 0.858,0.810 and 0.716 for 9 sites located on sunny slope side.
