Background:Inadvertent intensive care unit(ICU)readmission is associated with longer length of stay and increased mortality.Conversely,delayed ICU discharge may represent inefficient use of resources.To better inform ...Background:Inadvertent intensive care unit(ICU)readmission is associated with longer length of stay and increased mortality.Conversely,delayed ICU discharge may represent inefficient use of resources.To better inform discharge timing,several hospitals have implemented machine learning models to predict readmission risk following discharge.However,these models are typically created locally and may not generalize well to other hospitals or patient populations.A single multi-hospital-based model might provide more accurate predictions and insight into features that are applicable across diverse clinical settings.Methods:This study involved a retrospective multi-center cohort from one academic hospital(Amsterdam University Medical Center[AUMC])and two large teaching hospitals(Maasstad Ziekenhuis[MSZ]and OLVG).Data from the latter two hospitals were combined to create a pooled model,which was tested on the academic hospital dataset.Data relating to all adult ICU patients were included,starting from the implementation of the electronic health record system until the commencement of model development for each hospital.An XGBoost model was trained to predict a composite outcome of readmission or mortality within 7 days and an autoencoder was used as an out-of-distribution(OOD)detector to capture dataset heterogeneity.Results:In total,44,837 patients were available for analysis across the three hospitals.The average readmission rates were 7.1%,6.9%,and 5.9%for MSZ,OLVG,and AUMC,respectively.Performance evaluation of the local models on AUMC data demonstrated weighted area under the receiver operating characteristic curves of 69.7%±0.8%,70.5%±0.5%,and 76.5%±1.9%,respectively,whereas the pooled model achieved a weighted area under the receiver operating characteristic curves of 71.1%±0.7%.The difference between internal and external performance was reduced when cardiac surgery patients were excluded.The key features across models were albumin levels and the use of oxygen therapy.Discussion:A single,multi-hospital-based model performed comparably on external datasets,especially when cardiac surgery patients were excluded.However,when applied externally,model predictions risk being uncalibrated for specific patient subgroups and require careful calibration before implementation.While external models were more stable than local ones over OOD scores,their performance was comparable after excluding cardiac surgery patients.Although pooling data marginally improved performance on external datasets,the incorporation of data from diverse hospitals is likely to provide greater benefits.展开更多
We propose a deep learning-based method,the Deep Ritz Method,for numerically solving variational problems,particularly the ones that arise from par-tial differential equations.The Deep Ritz Method is naturally nonline...We propose a deep learning-based method,the Deep Ritz Method,for numerically solving variational problems,particularly the ones that arise from par-tial differential equations.The Deep Ritz Method is naturally nonlinear,naturally adaptive and has the potential to work in rather high dimensions.The framework is quite simple and fits well with the stochastic gradient descent method used in deep learning.We illustrate the method on several problems including some eigenvalue problems.展开更多
Wediscuss the idea of using continuous dynamicalsystemstomodel generalhigh-dimensional nonlinear functions used in machine learning.We also discuss theconnection with deep learning.
A large class of stochastic differential games for several players is considered in this paper.The class includes Nash differential games as well as Stackelberg differential games.A mix is possible.The existence of fe...A large class of stochastic differential games for several players is considered in this paper.The class includes Nash differential games as well as Stackelberg differential games.A mix is possible.The existence of feedback strategies under general conditions is proved.The limitations concern the functionals in which the state and the controls appear separately.This is also true for the state equations.The controls appear in a quadratic form for the payoff and linearly in the state equation.The most serious restriction is the dimension of the state equation,which cannot exceed 2.The reason comes from PDE(partial differential equations) techniques used in studying the system of Bellman equations obtained by Dynamic Programming arguments.In the authors' previous work in 2002,there is not such a restriction,but there are serious restrictions on the structure of the Hamiltonians,which are violated in the applications dealt with in this article.展开更多
This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string...This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string of points which are moving randomly as Brownian motions and under elastic forces. Every two points on the same string or on two different strings also interact under a pairwise potential V. The dynamics of the system is described by a system of N coupled stochastic partial differential equations （SPDEs）. We show that the mean field limit as N -＋ c~ of the system is a self-consistent McKean-Vlasov type equation, under suitable assumptions on the initial and boundary conditions and regularity of V. We also prove that both the SPDE system of the polymers and the mean field limit equation are well-posed.展开更多
We study continuum and atomistic models for the elastodynamics of crystalline solids at zero temperature. We establish sharp criterion for the regime of validity of the nonlinear elastic wave equations derived from th...We study continuum and atomistic models for the elastodynamics of crystalline solids at zero temperature. We establish sharp criterion for the regime of validity of the nonlinear elastic wave equations derived from the well-known Cauchy-Born rule.展开更多
Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed:one uses the contour integral representation and conformal real〉ping,and the other is based on a version of the multip...Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed:one uses the contour integral representation and conformal real〉ping,and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple poles.Both representations have logarithmic computational complexity.They are of great interest for electronic structure calculations.展开更多
In this paper we study the behavior of a family of implicit numerical methods applied to stochastic differential equations with multiple time scales.We show by a combination of analytical arguments and numerical examp...In this paper we study the behavior of a family of implicit numerical methods applied to stochastic differential equations with multiple time scales.We show by a combination of analytical arguments and numerical examples that implicit methods in general fail to capture the effective dynamics at the slow time scale.This is due to the fact that such implicit methods cannot correctly capture non-Dirac invariant distributions when the time step size is much larger than the relaxation time of the system.展开更多
The main obstacle in sequential multiscale modeling is the pre-computation of the constitutive relationwhich often involvesmany independent variables.The constitutive relation of a polymeric fluid is a function of six...The main obstacle in sequential multiscale modeling is the pre-computation of the constitutive relationwhich often involvesmany independent variables.The constitutive relation of a polymeric fluid is a function of six variables,even after making the simplifying assumption that stress depends only on the rate of strain.Precomputing such a function is usually considered too expensive.Consequently the value of sequential multiscale modeling is often limited to“parameter passing”.Here we demonstrate that sparse representations can be used to drastically reduce the computational cost for precomputing functions of many variables.This strategy dramatically increases the efficiency of sequential multiscale modeling,making it very competitive in many situations.展开更多
We present a convergence analysis of a stochastic method for numerical modeling of complex fluids using Brownian configuration fields (BCF) for shear flows. The analysis takes into account the special structure of the...We present a convergence analysis of a stochastic method for numerical modeling of complex fluids using Brownian configuration fields (BCF) for shear flows. The analysis takes into account the special structure of the stochastic partial differential equations for shear flows. We establish the optimal rate of convergence. We also analyze the nature of the error by providing its leading order asymptotics.展开更多
文摘Background:Inadvertent intensive care unit(ICU)readmission is associated with longer length of stay and increased mortality.Conversely,delayed ICU discharge may represent inefficient use of resources.To better inform discharge timing,several hospitals have implemented machine learning models to predict readmission risk following discharge.However,these models are typically created locally and may not generalize well to other hospitals or patient populations.A single multi-hospital-based model might provide more accurate predictions and insight into features that are applicable across diverse clinical settings.Methods:This study involved a retrospective multi-center cohort from one academic hospital(Amsterdam University Medical Center[AUMC])and two large teaching hospitals(Maasstad Ziekenhuis[MSZ]and OLVG).Data from the latter two hospitals were combined to create a pooled model,which was tested on the academic hospital dataset.Data relating to all adult ICU patients were included,starting from the implementation of the electronic health record system until the commencement of model development for each hospital.An XGBoost model was trained to predict a composite outcome of readmission or mortality within 7 days and an autoencoder was used as an out-of-distribution(OOD)detector to capture dataset heterogeneity.Results:In total,44,837 patients were available for analysis across the three hospitals.The average readmission rates were 7.1%,6.9%,and 5.9%for MSZ,OLVG,and AUMC,respectively.Performance evaluation of the local models on AUMC data demonstrated weighted area under the receiver operating characteristic curves of 69.7%±0.8%,70.5%±0.5%,and 76.5%±1.9%,respectively,whereas the pooled model achieved a weighted area under the receiver operating characteristic curves of 71.1%±0.7%.The difference between internal and external performance was reduced when cardiac surgery patients were excluded.The key features across models were albumin levels and the use of oxygen therapy.Discussion:A single,multi-hospital-based model performed comparably on external datasets,especially when cardiac surgery patients were excluded.However,when applied externally,model predictions risk being uncalibrated for specific patient subgroups and require careful calibration before implementation.While external models were more stable than local ones over OOD scores,their performance was comparable after excluding cardiac surgery patients.Although pooling data marginally improved performance on external datasets,the incorporation of data from diverse hospitals is likely to provide greater benefits.
基金supported in part by the National Key Basic Research Program of China 2015CB856000Major Program of NNSFC under Grant 91130005,DOE Grant DE-SC0009248ONR Grant N00014-13-1-0338.
文摘We propose a deep learning-based method,the Deep Ritz Method,for numerically solving variational problems,particularly the ones that arise from par-tial differential equations.The Deep Ritz Method is naturally nonlinear,naturally adaptive and has the potential to work in rather high dimensions.The framework is quite simple and fits well with the stochastic gradient descent method used in deep learning.We illustrate the method on several problems including some eigenvalue problems.
基金with several collaborators,including Jiequn Han,Qianxiao Li,Jianfeng Lu and Cheng Tai.The author benefitted a great deal from discussions with them,particularly Jiequn Han.This work is supported in part by the Major Program of NNSFC under Grant91130005,ONR NO0014-13-1-0338 and DOE DE-SCo009248.
文摘Wediscuss the idea of using continuous dynamicalsystemstomodel generalhigh-dimensional nonlinear functions used in machine learning.We also discuss theconnection with deep learning.
基金supported by Office of Naval Research(ONR)(Grant No.N00014-13-1-0338)Major Program of National Natural Science Foundation of China(Grant No.91130005)
文摘We prove that for analytic functions in low dimension, the convergence rate of the deep neural network approximation is exponential.
基金supported by DAAD-PPP Hong Kong/Germany (No. G. HK 036/09)
文摘A large class of stochastic differential games for several players is considered in this paper.The class includes Nash differential games as well as Stackelberg differential games.A mix is possible.The existence of feedback strategies under general conditions is proved.The limitations concern the functionals in which the state and the controls appear separately.This is also true for the state equations.The controls appear in a quadratic form for the payoff and linearly in the state equation.The most serious restriction is the dimension of the state equation,which cannot exceed 2.The reason comes from PDE(partial differential equations) techniques used in studying the system of Bellman equations obtained by Dynamic Programming arguments.In the authors' previous work in 2002,there is not such a restriction,but there are serious restrictions on the structure of the Hamiltonians,which are violated in the applications dealt with in this article.
基金supported by National Natural Science Foundation of China(Grant No.91130005)the US Army Research Office(Grant No.W911NF-11-1-0101)
文摘This paper provides a mathematically rigorous foundation for self-consistent mean field theory of the polymeric physics. We study a new model for dynamics of mono-polymer systems. Every polymer is regarded as a string of points which are moving randomly as Brownian motions and under elastic forces. Every two points on the same string or on two different strings also interact under a pairwise potential V. The dynamics of the system is described by a system of N coupled stochastic partial differential equations （SPDEs）. We show that the mean field limit as N -＋ c~ of the system is a self-consistent McKean-Vlasov type equation, under suitable assumptions on the initial and boundary conditions and regularity of V. We also prove that both the SPDE system of the polymers and the mean field limit equation are well-posed.
基金an NSFgrant DMS 04-07866theproject"Research Team on Complex Systems"of the Chinese Academy of Sciences+1 种基金the National Basic Research Program(No.2005CB321704)the National Natural Science Foundation of China(No.10571172)
文摘We study continuum and atomistic models for the elastodynamics of crystalline solids at zero temperature. We establish sharp criterion for the regime of validity of the nonlinear elastic wave equations derived from the well-known Cauchy-Born rule.
基金supported by the Department of Energy(No.DE-FG02-03ER25587)the Office of Naval Research(No.N00014-01-1-0674)an Alfred P.Sloan Research Fellowship and a startup grant from University of Texas at Austin
文摘Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed:one uses the contour integral representation and conformal real〉ping,and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple poles.Both representations have logarithmic computational complexity.They are of great interest for electronic structure calculations.
基金ONR grant N00014-01-0674.TLi is partially supported by National Science Foundation of China grants 10401004the National Basic Research Program under grant 2005CB321704.
文摘In this paper we study the behavior of a family of implicit numerical methods applied to stochastic differential equations with multiple time scales.We show by a combination of analytical arguments and numerical examples that implicit methods in general fail to capture the effective dynamics at the slow time scale.This is due to the fact that such implicit methods cannot correctly capture non-Dirac invariant distributions when the time step size is much larger than the relaxation time of the system.
基金The work of Carlos J.Garcıa-Cervera is supported in part by NSF grants DMS-0411504 and DMS-0505738The work of Weiqing Ren is supported in part by NSF grant DMS-0604382The work of Jianfeng Lu and Weinan E is supported in part by ONR grant N00014-01-0674,DOE grant DE-FG02-03ER25587 and NSF grant DMS-0407866.
文摘The main obstacle in sequential multiscale modeling is the pre-computation of the constitutive relationwhich often involvesmany independent variables.The constitutive relation of a polymeric fluid is a function of six variables,even after making the simplifying assumption that stress depends only on the rate of strain.Precomputing such a function is usually considered too expensive.Consequently the value of sequential multiscale modeling is often limited to“parameter passing”.Here we demonstrate that sparse representations can be used to drastically reduce the computational cost for precomputing functions of many variables.This strategy dramatically increases the efficiency of sequential multiscale modeling,making it very competitive in many situations.
基金US ONR grant (No. N00014-01-1-0674)the Chinese Special Funds for Major State Research Projects (No.G1999032804), the Teaching and Research Award for outstanding young teachers from the Chinese MOE.
文摘We present a convergence analysis of a stochastic method for numerical modeling of complex fluids using Brownian configuration fields (BCF) for shear flows. The analysis takes into account the special structure of the stochastic partial differential equations for shear flows. We establish the optimal rate of convergence. We also analyze the nature of the error by providing its leading order asymptotics.
