The recurrent neural network （RNN） model based on projective operator was studied. Different from the former study, the value region of projective operator in the neural network in this paper is a general closed con...The recurrent neural network （RNN） model based on projective operator was studied. Different from the former study, the value region of projective operator in the neural network in this paper is a general closed convex subset of n-dimensional Euclidean space and it is not a compact convex set in general, that is, the value region of projective operator is probably unbounded. It was proved that the network has a global solution and its solution trajectory converges to some equilibrium set whenever objective function satisfies some conditions. After that, the model was applied to continuously differentiable optimization and nonlinear or implicit complementarity problems. In addition, simulation experiments confirm the efficiency of the RNN.展开更多
Northeast China serves as an important crop production region.Accurately forecasting summer precipitation in Northeast China(NEC-PR)has been a challenge due to its wide range of time scales influenced by varying clima...Northeast China serves as an important crop production region.Accurately forecasting summer precipitation in Northeast China(NEC-PR)has been a challenge due to its wide range of time scales influenced by varying climatic conditions.This study presents a scale separation hybrid statistical model with recurrent neural network(SS-RNN)to predict the summer monthly NEC-PR.The SS-RNN model decomposes the multiple scales of the NEC-PR into several spatiotemporal intrinsic mode functions covering annual to decadal time scales.This strategy provides a way to derive appropriate predictors and establish predictive models for the primary spatial modes of the NEC-PR at various time scales.Our results demonstrate substantial improvements by the SS-RNN model in predicting the summer monthly NEC-PR as compared with dynamic models,particularly in predicting the spatial pattern of the NEC-PR.In this paper we take August,the month of the highest NEC-PR,to assess our model skill.Independent forecasts of the August NEC-PR over the period 2021–24 achieve significant spatial anomaly correlation coefficients,reaching a maximum value of 0.83.Additional verifications by station observations show that the model hits most station anomalies,achieving a mean predictive skill score of 90.展开更多
文摘The recurrent neural network （RNN） model based on projective operator was studied. Different from the former study, the value region of projective operator in the neural network in this paper is a general closed convex subset of n-dimensional Euclidean space and it is not a compact convex set in general, that is, the value region of projective operator is probably unbounded. It was proved that the network has a global solution and its solution trajectory converges to some equilibrium set whenever objective function satisfies some conditions. After that, the model was applied to continuously differentiable optimization and nonlinear or implicit complementarity problems. In addition, simulation experiments confirm the efficiency of the RNN.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFC3002803)the National Key Research and Development Program of China(Grant No.2024YFF0808402)the National Natural Science Foundation of China(Grant No.42375169)。
文摘Northeast China serves as an important crop production region.Accurately forecasting summer precipitation in Northeast China(NEC-PR)has been a challenge due to its wide range of time scales influenced by varying climatic conditions.This study presents a scale separation hybrid statistical model with recurrent neural network(SS-RNN)to predict the summer monthly NEC-PR.The SS-RNN model decomposes the multiple scales of the NEC-PR into several spatiotemporal intrinsic mode functions covering annual to decadal time scales.This strategy provides a way to derive appropriate predictors and establish predictive models for the primary spatial modes of the NEC-PR at various time scales.Our results demonstrate substantial improvements by the SS-RNN model in predicting the summer monthly NEC-PR as compared with dynamic models,particularly in predicting the spatial pattern of the NEC-PR.In this paper we take August,the month of the highest NEC-PR,to assess our model skill.Independent forecasts of the August NEC-PR over the period 2021–24 achieve significant spatial anomaly correlation coefficients,reaching a maximum value of 0.83.Additional verifications by station observations show that the model hits most station anomalies,achieving a mean predictive skill score of 90.
