Deep learning(DL)has become a crucial technique for predicting the El Niño-Southern Oscillation(ENSO)and evaluating its predictability.While various DL-based models have been developed for ENSO predictions,many f...Deep learning(DL)has become a crucial technique for predicting the El Niño-Southern Oscillation(ENSO)and evaluating its predictability.While various DL-based models have been developed for ENSO predictions,many fail to capture the coherent multivariate evolution within the coupled ocean-atmosphere system of the tropical Pacific.To address this three-dimensional(3D)limitation and represent ENSO-related ocean-atmosphere interactions more accurately,a novel this 3D multivariate prediction model was proposed based on a Transformer architecture,which incorporates a spatiotemporal self-attention mechanism.This model,named 3D-Geoformer,offers several advantages,enabling accurate ENSO predictions up to one and a half years in advance.Furthermore,an integrated gradient method was introduced into the model to identify the sources of predictability for sea surface temperature(SST)variability in the eastern equatorial Pacific.Results reveal that the 3D-Geoformer effectively captures ENSO-related precursors during the evolution of ENSO events,particularly the thermocline feedback processes and ocean temperature anomaly pathways on and off the equator.By extending DL-based ENSO predictions from one-dimensional Niño time series to 3D multivariate fields,the 3D-Geoformer represents a significant advancement in ENSO prediction.This study provides details in the model formulation,analysis procedures,sensitivity experiments,and illustrative examples,offering practical guidance for the application of the model in ENSO research.展开更多
We consider solving integral equations of the second kind defined on the half-line [0, infinity) by the preconditioned conjugate gradient method. Convergence is known to be slow due to the non-compactness of the assoc...We consider solving integral equations of the second kind defined on the half-line [0, infinity) by the preconditioned conjugate gradient method. Convergence is known to be slow due to the non-compactness of the associated integral operator. In this paper, we construct two different circulant integral operators to be used as preconditioners for the method to speed up its convergence rate. We prove that if the given integral operator is close to a convolution-type integral operator, then the preconditioned systems will have spectrum clustered around 1 and hence the preconditioned conjugate gradient method will converge superlinearly. Numerical examples are given to illustrate the fast convergence.展开更多
基金Supported by the Laoshan Laboratory(No.LSKJ202202402)the National Natural Science Foundation of China(No.42030410)+2 种基金the Startup Foundation for Introducing Talent of Nanjing University of Information Science&Technology,and Jiangsu Innovation Research Group(No.JSSCTD 202346)supported by the China National Postdoctoral Program for Innovative Talents(No.BX20240169)the China Postdoctoral Science Foundation(No.2141062400101)。
文摘Deep learning(DL)has become a crucial technique for predicting the El Niño-Southern Oscillation(ENSO)and evaluating its predictability.While various DL-based models have been developed for ENSO predictions,many fail to capture the coherent multivariate evolution within the coupled ocean-atmosphere system of the tropical Pacific.To address this three-dimensional(3D)limitation and represent ENSO-related ocean-atmosphere interactions more accurately,a novel this 3D multivariate prediction model was proposed based on a Transformer architecture,which incorporates a spatiotemporal self-attention mechanism.This model,named 3D-Geoformer,offers several advantages,enabling accurate ENSO predictions up to one and a half years in advance.Furthermore,an integrated gradient method was introduced into the model to identify the sources of predictability for sea surface temperature(SST)variability in the eastern equatorial Pacific.Results reveal that the 3D-Geoformer effectively captures ENSO-related precursors during the evolution of ENSO events,particularly the thermocline feedback processes and ocean temperature anomaly pathways on and off the equator.By extending DL-based ENSO predictions from one-dimensional Niño time series to 3D multivariate fields,the 3D-Geoformer represents a significant advancement in ENSO prediction.This study provides details in the model formulation,analysis procedures,sensitivity experiments,and illustrative examples,offering practical guidance for the application of the model in ENSO research.
文摘We consider solving integral equations of the second kind defined on the half-line [0, infinity) by the preconditioned conjugate gradient method. Convergence is known to be slow due to the non-compactness of the associated integral operator. In this paper, we construct two different circulant integral operators to be used as preconditioners for the method to speed up its convergence rate. We prove that if the given integral operator is close to a convolution-type integral operator, then the preconditioned systems will have spectrum clustered around 1 and hence the preconditioned conjugate gradient method will converge superlinearly. Numerical examples are given to illustrate the fast convergence.
