Large biases exist in real-time ENSO prediction, which can be attributed to uncertainties in initial conditions and model parameters. Previously, a 4D variational （4D-Vat） data assimilation system was developed for ...Large biases exist in real-time ENSO prediction, which can be attributed to uncertainties in initial conditions and model parameters. Previously, a 4D variational （4D-Vat） data assimilation system was developed for an intermediate coupled model （ICM） and used to improve ENSO modeling through optimized initial conditions. In this paper, this system is further applied to optimize model parameters. In the ICM used, one important process for ENSO is related to the anomalous temperature of subsurface water entrained into the mixed layer （Te）, which is empirically and explicitly related to sea level （SL） variation. The strength of the thermocline effect on SST （referred to simply as ＂the thermocline effect＂） is represented by an introduced parameter, （l＇Te. A numerical procedure is developed to optimize this model parameter through the 4D-Var assimilation of SST data in a twin experiment context with an idealized setting. Experiments having their initial condition optimized only, and having their initial condition plus this additional model parameter optimized, are compared. It is shown that ENSO evolution can be more effectively recovered by including the additional optimization of this parameter in ENSO modeling. The demonstrated feasibility of optimizing model parameters and initial conditions together through the 4D-Var method provides a modeling platform for ENSO studies. Further applications of the 4D-Vat data assimilation system implemented in the ICM are also discussed.展开更多
An optimized nonlinear grey Bernoulli model was proposed by using a particle swarm optimization algorithm to solve the parameter optimization problem. In addition, each item in the first-order accumulated generating s...An optimized nonlinear grey Bernoulli model was proposed by using a particle swarm optimization algorithm to solve the parameter optimization problem. In addition, each item in the first-order accumulated generating sequence was set in turn as an initial condition to determine which alternative would yield the highest forecasting accuracy. To test the forecasting performance, the optimized models with different initial conditions were then used to simulate dissolved oxygen concentrations in the Guantlng reservoir inlet and outlet （China）. The empirical results show that the optimized model can remarkably improve forecasting accuracy, and the particle swarm optimization technique is a good tool to solve parameter optimization problems. What＇s more, the optimized model with an initial condition that performs well in in-sample simulation may not do as well as in out-of-sample forecasting.展开更多
In this paper we design the following two-step scheme to estimate the model parameter ω0 of the quantum system: first we utilize the Fisher information with respect to an intermediate variable v = cos(ω0 t) to deter...In this paper we design the following two-step scheme to estimate the model parameter ω0 of the quantum system: first we utilize the Fisher information with respect to an intermediate variable v = cos(ω0 t) to determine an optimal initial state and to seek optimal parameters of the POVM measurement operators; second we explore how to estimate ω0 from v by choosing t when a priori information knowledge of ω0 is available. Our optimal initial state can achieve the maximum quantum Fisher information. The formulation of the optimal time t is obtained and the complete algorithm for parameter estimation is presented. We further explore how the lower bound of the estimation deviation depends on the a priori information of the model.展开更多
The transition to turbulence in flows where the laminar profile is linearly stable requires perturbations of finite amplitude. ＂Optimal＂ perturbations are distinguished as extrema of certain functionals, and differe...The transition to turbulence in flows where the laminar profile is linearly stable requires perturbations of finite amplitude. ＂Optimal＂ perturbations are distinguished as extrema of certain functionals, and different functionals give different optima. We here discuss the phase space structure of a 2D simplified model of the transition to turbulence and discuss optimal perturbations with respect to three criteria： energy of the initial condition, energy dissipation of the initial condition, and amplitude of noise in a stochastic transition. We find that the states triggering the transition are different in the three cases, but show the same scaling with Reynolds number.展开更多
Most ocean-atmosphere coupled models have difficulty in predicting the E1 Nifio-Southern Oscillation （ENSO） when starting from the boreal spring season. However, the cause of this spring predictability barrier （SPB...Most ocean-atmosphere coupled models have difficulty in predicting the E1 Nifio-Southern Oscillation （ENSO） when starting from the boreal spring season. However, the cause of this spring predictability barrier （SPB） phenomenon remains elusive. We investigated the spatial characteristics of optimal initial errors that cause a significant SPB for E1 Nifio events by using the monthly mean data of the pre-industrial （PI） control runs from several models in CMIP5 experiments. The results indicated that the SPB-related optimal initial errors often present an SST pattern with positive errors in the central-eastern equatorial Pa- cific, and a subsurface temperature pattern with positive errors in the upper layers of the eastern equatorial Pacific, and nega- tive errors in the lower layers of the western equatorial Pacific. The SPB-related optimal initial errors exhibit a typical La Ni- fia-like evolving mode, ultimately causing a large but negative prediction error of the Nifio-3.4 SST anomalies for El Nifio events. The negative prediction errors were found to originate from the lower layers of the western equatorial Pacific and then grow to be large in the eastern equatorial Pacific. It is therefore reasonable to suggest that the E1 Nifio predictions may be most sensitive to the initial errors of temperature in the subsurface layers of the western equatorial Pacific and the Nifio-3.4 region, thus possibly representing sensitive areas for adaptive observation. That is, if additional observations were to be preferentially deployed in these two regions, it might be possible to avoid large prediction errors for E1 Nifio and generate a better forecast than one based on additional observations targeted elsewhere. Moreover, we also confirmed that the SPB-related optimal initial errors bear a strong resemblance to the optimal precursory disturbance for E1 Nifio and La Nifia events. This indicated that im- provement of the observation network by additional observations in the identified sensitive areas would also be helpful in de- tecting the signals provided by the precursory disturbance, which may greatly improve the ENSO prediction skill.展开更多
The K-core of a graph is the maximal subgraph within which each vertex is connected to at least K other vertices. It is a fundamental network concept for understanding threshold cascading processes with a discontinuou...The K-core of a graph is the maximal subgraph within which each vertex is connected to at least K other vertices. It is a fundamental network concept for understanding threshold cascading processes with a discontinuous percolation transition. A minimum attack set contains the smallest number of vertices whose removal induces complete collapse of the K-core. Here we tackle this prototypical optimal initial-condition problem from the spin-glass perspective of cycle-tree maximum packing and propose a cycle-tree guided attack(CTGA) message-passing algorithm. The good performance and time efficiency of CTGA are verified on the regular random and Erd?s-Rényi random graph ensembles. Our central idea of transforming a long-range correlated dynamical process to static structural patterns may also be instructive to other hard optimization and control problems.展开更多
This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, w...This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, where U is a control set, and x satisfies the ordinary equation x（s） = f（x（s）, u（x（s）, s））.It is proved that under the condition that the initial measure μ0 is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the corresponding Hamilton-Jacobi equation：Vt（t, x） ＋ sup u∈U = 0,V（0, x） = Φ0（x）.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 41705082, 41475101, 41690122(41690120))a Chinese Academy of Sciences Strategic Priority Project-the Western Pacific Ocean System (Grant Nos. XDA11010105 and XDA11020306)+1 种基金the National Programme on Global Change and Air–Sea Interaction (Grant Nos. GASI-IPOVAI06 and GASI-IPOVAI-01-01)the China Postdoctoral Science Foundation, and a Qingdao Postdoctoral Application Research Project
文摘Large biases exist in real-time ENSO prediction, which can be attributed to uncertainties in initial conditions and model parameters. Previously, a 4D variational （4D-Vat） data assimilation system was developed for an intermediate coupled model （ICM） and used to improve ENSO modeling through optimized initial conditions. In this paper, this system is further applied to optimize model parameters. In the ICM used, one important process for ENSO is related to the anomalous temperature of subsurface water entrained into the mixed layer （Te）, which is empirically and explicitly related to sea level （SL） variation. The strength of the thermocline effect on SST （referred to simply as ＂the thermocline effect＂） is represented by an introduced parameter, （l＇Te. A numerical procedure is developed to optimize this model parameter through the 4D-Var assimilation of SST data in a twin experiment context with an idealized setting. Experiments having their initial condition optimized only, and having their initial condition plus this additional model parameter optimized, are compared. It is shown that ENSO evolution can be more effectively recovered by including the additional optimization of this parameter in ENSO modeling. The demonstrated feasibility of optimizing model parameters and initial conditions together through the 4D-Var method provides a modeling platform for ENSO studies. Further applications of the 4D-Vat data assimilation system implemented in the ICM are also discussed.
基金supported by the National Natural Science Foundation of China (Nos. 51178018 and 71031001)
文摘An optimized nonlinear grey Bernoulli model was proposed by using a particle swarm optimization algorithm to solve the parameter optimization problem. In addition, each item in the first-order accumulated generating sequence was set in turn as an initial condition to determine which alternative would yield the highest forecasting accuracy. To test the forecasting performance, the optimized models with different initial conditions were then used to simulate dissolved oxygen concentrations in the Guantlng reservoir inlet and outlet （China）. The empirical results show that the optimized model can remarkably improve forecasting accuracy, and the particle swarm optimization technique is a good tool to solve parameter optimization problems. What＇s more, the optimized model with an initial condition that performs well in in-sample simulation may not do as well as in out-of-sample forecasting.
基金Supported by the National Natural Science Foundation of China under Grant Nos.61273202,61673389,and 61134008
文摘In this paper we design the following two-step scheme to estimate the model parameter ω0 of the quantum system: first we utilize the Fisher information with respect to an intermediate variable v = cos(ω0 t) to determine an optimal initial state and to seek optimal parameters of the POVM measurement operators; second we explore how to estimate ω0 from v by choosing t when a priori information knowledge of ω0 is available. Our optimal initial state can achieve the maximum quantum Fisher information. The formulation of the optimal time t is obtained and the complete algorithm for parameter estimation is presented. We further explore how the lower bound of the estimation deviation depends on the a priori information of the model.
基金supported in part by the German Research Foundation within FOR 1182
文摘The transition to turbulence in flows where the laminar profile is linearly stable requires perturbations of finite amplitude. ＂Optimal＂ perturbations are distinguished as extrema of certain functionals, and different functionals give different optima. We here discuss the phase space structure of a 2D simplified model of the transition to turbulence and discuss optimal perturbations with respect to three criteria： energy of the initial condition, energy dissipation of the initial condition, and amplitude of noise in a stochastic transition. We find that the states triggering the transition are different in the three cases, but show the same scaling with Reynolds number.
基金sponsored by the National Basic Research Program of China(Grant No.2012CB955200)the National Public Benefit(Meteorology)Research Foundation of China(Grant No.GYHY201306018)+2 种基金the National Natural Science Foundation of China(Grant Nos.41230420,41176013)Zhang Jing was supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)the Jiangsu Innovation Cultivation Project for Graduate Student(Grant No.CXZZ13_0502)
文摘Most ocean-atmosphere coupled models have difficulty in predicting the E1 Nifio-Southern Oscillation （ENSO） when starting from the boreal spring season. However, the cause of this spring predictability barrier （SPB） phenomenon remains elusive. We investigated the spatial characteristics of optimal initial errors that cause a significant SPB for E1 Nifio events by using the monthly mean data of the pre-industrial （PI） control runs from several models in CMIP5 experiments. The results indicated that the SPB-related optimal initial errors often present an SST pattern with positive errors in the central-eastern equatorial Pa- cific, and a subsurface temperature pattern with positive errors in the upper layers of the eastern equatorial Pacific, and nega- tive errors in the lower layers of the western equatorial Pacific. The SPB-related optimal initial errors exhibit a typical La Ni- fia-like evolving mode, ultimately causing a large but negative prediction error of the Nifio-3.4 SST anomalies for El Nifio events. The negative prediction errors were found to originate from the lower layers of the western equatorial Pacific and then grow to be large in the eastern equatorial Pacific. It is therefore reasonable to suggest that the E1 Nifio predictions may be most sensitive to the initial errors of temperature in the subsurface layers of the western equatorial Pacific and the Nifio-3.4 region, thus possibly representing sensitive areas for adaptive observation. That is, if additional observations were to be preferentially deployed in these two regions, it might be possible to avoid large prediction errors for E1 Nifio and generate a better forecast than one based on additional observations targeted elsewhere. Moreover, we also confirmed that the SPB-related optimal initial errors bear a strong resemblance to the optimal precursory disturbance for E1 Nifio and La Nifia events. This indicated that im- provement of the observation network by additional observations in the identified sensitive areas would also be helpful in de- tecting the signals provided by the precursory disturbance, which may greatly improve the ENSO prediction skill.
基金supported by the National Natural Science Foundation of China(Grant Nos.11975295,and 12047503)and the Chinese Academy of Sciences(Grant Nos.QYZDJ-SSW-SYS018,and XDPD15)。
文摘The K-core of a graph is the maximal subgraph within which each vertex is connected to at least K other vertices. It is a fundamental network concept for understanding threshold cascading processes with a discontinuous percolation transition. A minimum attack set contains the smallest number of vertices whose removal induces complete collapse of the K-core. Here we tackle this prototypical optimal initial-condition problem from the spin-glass perspective of cycle-tree maximum packing and propose a cycle-tree guided attack(CTGA) message-passing algorithm. The good performance and time efficiency of CTGA are verified on the regular random and Erd?s-Rényi random graph ensembles. Our central idea of transforming a long-range correlated dynamical process to static structural patterns may also be instructive to other hard optimization and control problems.
文摘This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, where U is a control set, and x satisfies the ordinary equation x（s） = f（x（s）, u（x（s）, s））.It is proved that under the condition that the initial measure μ0 is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the corresponding Hamilton-Jacobi equation：Vt（t, x） ＋ sup u∈U = 0,V（0, x） = Φ0（x）.
