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There are many time series forecasting methods, but there are few research methods for long-term multivariate time series forecasting, which are mainly dominated by a series of forecasting models developed on the basis of a transformer. The aim of this study is to perform forecasting for multivariate time series data and to improve the forecasting accuracy of the model. In the recent past, it has appeared that the prediction effect of linear models surpasses that of the family of self-attention mechanism models, which encourages us to look for new methods to solve the problem of long-term multivariate time series forecasting. In order to overcome the problem that the temporal order of information is easily broken in the self-attention family and that it is difficult to capture information on long-distance data using recurrent neural network models, we propose a matrix attention mechanism, which is able to weight each previous data point equally without breaking the temporal order of the data, so that the overall data information can be fully utilized. We used the matrix attention mechanism as the basic module to construct the frequency domain block and time domain block. Since complex and variable seasonal component features are difficult to capture in the time domain, mapping them to the frequency domain reduces the complexity of the seasonal components themselves and facilitates data feature extraction. Therefore, we use the frequency domain block to extract the seasonal information with high randomness and poor regularity to help the model capture the local dynamics. The time domain block is used to extract the smooth floating trend component information to help the model capture long-term change patterns. This also improves the overall prediction performance of the model. It is experimentally demonstrated that our model achieves the best prediction results on three public datasets and one private dataset.

Traffic flow forecasting, as an integral part of intelligent transportation systems, plays a critical part in traffic planning. Previous studies have primarily focused on short-term traffic flow prediction, paying insufficient attention to long-term prediction. In this study, we propose a hybrid model that utilizes variational mode decomposition (VMD) and the auto-correlation mechanism for long-term prediction. In view of the periodic and stochastic characteristics of traffic flow, VMD is able to decompose the data into intrinsic mode functions with different frequencies, which in turn helps the model extract the internal features of the data and better capture the changes of traffic flow data in the cycle. Additionally, we improve the residual structure by adding a convolutional layer to propose a correction module and use it together with the auto-correlation mechanism to jointly build an encoder and decoder to extract features from different data components (intrinsic mode functions) and fuse the extracted features for output. To meet the requirements of long-term forecasting, we set the traffic flow forecast length to 4 levels: 96, 192, 336, and 720. We validated our model using the departure statistics dataset of a taxi parking lot at Beijing Capital International Airport and achieved the best prediction performance in terms of mean squared error and mean absolute error, compared to the baseline model.

After the discovery of bulk photovoltaic effect more than half a century ago, ferro-electrical and magneto-optical experiments have provided insights into various related topics, revealing above bandgap open voltages and non-central symmetrical current mechanisms. However, the nature of the photon-generated carriers responses and their microscopic mechanisms remain unclear. Here, all-inorganic perovskite Bi0.85Gd0.15Fe1−xMnxO3 thin films were prepared by a sol-gel process and the effects of Gd and Mn co-doped bismuth ferrites on their microtopography, grain boundries, multiferroic, and optical properties were studied. We discovered a simple “proof of principle” type new method that by one-step measuring the leakage current, one can demonstrate the value of photo generated current being the sum of ballistic current and shift current, which are combined to form the so-called bulk photovoltaic current, and can be related to the prototype intrinsic properties such as magneto-optical coupling and ferroelectric polarization. This result has significant potential influence on design principles for engineering multiferroic optoelectronic devices and future photovoltaic industry development.