Time series is a kind of data widely used in various fields such as electricity forecasting,exchange rate forecasting,and solar power generation forecasting,and therefore time series prediction is of great significanc...Time series is a kind of data widely used in various fields such as electricity forecasting,exchange rate forecasting,and solar power generation forecasting,and therefore time series prediction is of great significance.Recently,the encoder-decoder model combined with long short-term memory(LSTM)is widely used for multivariate time series prediction.However,the encoder can only encode information into fixed-length vectors,hence the performance of the model decreases rapidly as the length of the input sequence or output sequence increases.To solve this problem,we propose a combination model named AR_CLSTM based on the encoder_decoder structure and linear autoregression.The model uses a time step-based attention mechanism to enable the decoder to adaptively select past hidden states and extract useful information,and then uses convolution structure to learn the internal relationship between different dimensions of multivariate time series.In addition,AR_CLSTM combines the traditional linear autoregressive method to learn the linear relationship of the time series,so as to further reduce the error of time series prediction in the encoder_decoder structure and improve the multivariate time series Predictive effect.Experiments show that the AR_CLSTM model performs well in different time series predictions,and its root mean square error,mean square error,and average absolute error all decrease significantly.展开更多
In this paper we first compute the out-of-time-order correlators （OTOC） for both a phenomenological model and a random-field XXZ model in the many-body localized phase. We show that the OTOC decreases in power law i...In this paper we first compute the out-of-time-order correlators （OTOC） for both a phenomenological model and a random-field XXZ model in the many-body localized phase. We show that the OTOC decreases in power law in a many-body localized system at the scrambling time. We also find that the OTOC can also be used to distinguish a many-body localized phase from an Anderson localized phase, while a normal correlator cannot. Furthermore, we prove an exact theorem that relates the growth of the second Renyi entropy in the quench dynamics to the decay of the OTOC in equilibrium. This theorem works for a generic quantum system. We discuss various implications of this theorem.展开更多
基金Shanxi Provincial Key Research and Development Program Project Fund(No.201703D111011)。
文摘Time series is a kind of data widely used in various fields such as electricity forecasting,exchange rate forecasting,and solar power generation forecasting,and therefore time series prediction is of great significance.Recently,the encoder-decoder model combined with long short-term memory(LSTM)is widely used for multivariate time series prediction.However,the encoder can only encode information into fixed-length vectors,hence the performance of the model decreases rapidly as the length of the input sequence or output sequence increases.To solve this problem,we propose a combination model named AR_CLSTM based on the encoder_decoder structure and linear autoregression.The model uses a time step-based attention mechanism to enable the decoder to adaptively select past hidden states and extract useful information,and then uses convolution structure to learn the internal relationship between different dimensions of multivariate time series.In addition,AR_CLSTM combines the traditional linear autoregressive method to learn the linear relationship of the time series,so as to further reduce the error of time series prediction in the encoder_decoder structure and improve the multivariate time series Predictive effect.Experiments show that the AR_CLSTM model performs well in different time series predictions,and its root mean square error,mean square error,and average absolute error all decrease significantly.
基金supported by the National Key Research and Development Plan (2016YFA0301600)the National Natural Science Foundation of China (11325418)Tsinghua University Initiative Scientific Research Program
文摘In this paper we first compute the out-of-time-order correlators （OTOC） for both a phenomenological model and a random-field XXZ model in the many-body localized phase. We show that the OTOC decreases in power law in a many-body localized system at the scrambling time. We also find that the OTOC can also be used to distinguish a many-body localized phase from an Anderson localized phase, while a normal correlator cannot. Furthermore, we prove an exact theorem that relates the growth of the second Renyi entropy in the quench dynamics to the decay of the OTOC in equilibrium. This theorem works for a generic quantum system. We discuss various implications of this theorem.
