Data filling method and device based on time sequence continuous deletion filling model

Abstract

The invention provides a data filling method and device based on a time sequence continuous deletion filling model, and relates to the technical field of artificial intelligence. The method comprises the steps of obtaining a training data set; respectively inputting the forward and backward input sequences into forward and backward prediction networks of a long-term filling module to obtain network output; a linear function is introduced to carry out weighted integration on network output to obtain long-term filling module output; inputting the true value of the to-be-predicted sequence and a randomly generated continuous missing mask into a short-term filling module to obtain a short-term filling module output; and outputting and inputting the long-term and short-term filling modules into the element weighting module to obtain a filling result. The invention provides the LSTI, and relates to a time sequence filling model which can automatically combine the output of the long-term filling module and the short-term filling module aiming at the continuous missing data of the time sequence. According to the method, long-term dependence and short-term dependence are respectively modeled through two specially designed expert models, so that continuous missing data can be effectively filled.

Description

Technical Field

[0001] The present invention relates to the technical field of artificial intelligence, and particularly to a data filling method and device based on a time series continuous missing value filling model. Background Art

[0002] Multivariate time series widely exist in various applications in the real world, such as meteorology, finance, engineering, scientific research, and healthcare. However, due to reasons such as sensor failures and communication interruptions, such data often contains missing values. Missing values not only weaken the integrity of the data but also reduce its interpretability, thus posing significant challenges to time series analysis. Therefore, how to effectively fill in the missing data becomes a key issue before performing downstream analysis.

[0003] In recent years, many studies have been devoted to using deep learning methods for missing value filling, and most of these methods mainly target the MCAR (Missing Completely at Random) scenario. However, in practical applications, missing values more often exhibit continuous or clustered patterns, which usually stem from external factors such as signal interruptions, environmental interferences, or device failures. For example, when a vehicle enters a tunnel, all satellite signals related to it may be blocked, resulting in continuous missing values with long intervals in the time series data.

[0004] In the aspect of time series imputation, deep learning models are good at capturing complex non-linear relationships in data. In early research, models based on RNN (Recurrent Neural Network) were widely used. GRU-D is a variant of GRU (Gated Recurrent Unit) for solving the problem of missing data in time series classification tasks. Subsequently, BRITS uses a bidirectional recursive dynamic system to impute missing values without making specific assumptions about the data. M-RNN imputes missing values based on the hidden states obtained from bidirectional RNNs. Since generative models are inherently suitable for imputation tasks, they have been widely used in missing value imputation. E2GAN embeds a GRU-based generator into an autoencoder framework. For spatio-temporal series imputation, NAOMI proposes a non-autoregressive model that combines a bidirectional encoder and a multi-resolution decoder. With the rise of diffusion models, CSDI, as a conditional score-based diffusion model, has shown excellent performance in the field of time series imputation. With the further development of deep learning, TimesNet extends the study of time variation to two-dimensional space and considers the multiple periodicities in time series data. NRTSI proposes a method to impute time series by treating them as a set of (time, data) pairs. SAITS achieves simultaneous reconstruction and imputation by weighted combination of two diagonal masked self-attention modules.

[0005] The above methods each have their own advantages, but they are all mainly designed for the completely random missing scenario. When faced with consecutive missing data with long time intervals, these methods often struggle to achieve ideal imputation results. Some studies attempt to combine prior knowledge in specific application fields to address this problem, such as air pollution prediction, water quality prediction, and electrical engineering applications. There are also methods that use statistical modeling for processing. However, these methods usually rely on complex processing flows and are not end-to-end architectures, so there are certain limitations in practical applications.

[0006] For time series prediction, time series prediction methods have the potential to fill in continuously missing data over long time intervals. Specifically, the values before the missing interval can be used to predict the entire missing segment. Some RNN-based models in early studies have demonstrated powerful prediction capabilities, such as LSTNet, which combines DNN (Deep Neural Network), RNN, and Skip-RNN networks. DeepAR adopts an autoregressive recurrent network architecture and outputs the probability of the prediction points. In recent years, Transformer-based models have gradually become mainstream. First, Informer significantly improves the training efficiency of Transformer through self-attention distillation; following that, Autoformer incorporates time series decomposition into the model, thereby enhancing the model's ability to discover time dependencies; Non-stationary Transformers adopt an innovative approach to introduce non-stationarity factors into the attention mechanism, avoiding the over-stabilization of time series data; PatchTST achieves excellent results by leveraging patch and channel independence; recently, iTransformer transposes the input matrix and reverses the roles of the attention mechanism and the feed-forward network, thus better capturing the correlations between multivariate time series.

[0007] Although prediction methods show some potential in filling in continuously missing data over long time intervals, there are still some problems in practical applications. First, the time series to be filled may contain multiple missing points, and it cannot be guaranteed that there is complete available data for prediction before each missing segment. Second, the endpoints of the predicted sequence often cannot be effectively aligned with the observations after the missing segment, resulting in a deviation between the subsequent predicted values and the actual values. Therefore, prediction methods cannot be directly applied to fill in continuously missing data over long time intervals. Summary of the Invention

[0008] To address the technical problem that most current filling methods usually assume that the test data is completely randomly missing. However, in practical applications, missing values often exhibit the characteristics of continuous and clustered distribution due to factors such as signal loss, environmental interference, or device failures. The mainstream filling methods have limited performance in dealing with long-interval continuous missing data. The fundamental reason lies in the difficulty of fully capturing long-term dependencies. Embodiments of the present invention provide a data filling method and device based on a time series continuous missing filling model. The technical solutions are as follows:

[0009] On the one hand, a data filling method based on a time series continuous missing filling model is provided. This method is implemented by a data filling device and includes:

[0010] S1. Obtain a training data set; the training data set includes a forward input sequence for forward prediction, the true value of the sequence to be predicted, and a backward input sequence for backward prediction.

[0011] S2. Input the forward input sequence and the backward input sequence into the forward prediction network and the backward prediction network of the long-term filling module respectively to obtain the forward prediction network output and the backward prediction network output; introduce a linear function to perform weighted integration on the forward prediction network output and the backward prediction network output to obtain the long-term filling module output, and construct the long-term filling module training loss.

[0012] S3. Input the true value of the sequence to be predicted and a randomly generated continuous missing mask into the short-term filling module to obtain the short-term filling module output, and construct the short-term filling module training loss; wherein, the short-term filling module includes a self-mapping network.

[0013] S4. Input the long-term filling module output, the short-term filling module output, the true value of the sequence to be predicted, and the continuous missing mask into the meta-weighting module to obtain the meta-weighting module output, and construct the meta-weighting module training loss; wherein, the meta-weighting module includes an independent multi-layer perceptron.

[0014] S5. Construct the long-short-term time series filling model loss according to the long-term filling module training loss, the short-term filling module training loss, and the meta-weighting module training loss, and train the long-short-term time series filling model to obtain the trained long-short-term time series filling model loss.

[0015] S6. Obtain a multi-variable time series to be filled with missing values, input it into the trained long-short-term time series filling model loss for missing data filling, and obtain the filling result.

[0016] Optionally, S2 includes:

[0017] S21. Input the forward input sequence into the forward prediction network of the long-term filling module to obtain the forward prediction network output; wherein, the forward prediction network output includes a forward backtracking prediction window and a forward prediction window.

[0018] S22. Reverse the time order of the backward input sequence, and input the reversed sequence into the backward prediction network of the long-term filling module to obtain the backward prediction network output; wherein, the backward prediction network output includes a backward backtracking prediction window and a backward prediction window.

[0019] S23. Introduce a linear function to perform weighted integration on the forward prediction window and the reversed backward backtracking prediction window to obtain the long-term filling module output, and construct the long-term filling module training loss.

[0020] Optionally, constructing the long-term filling module training loss in S23 includes:

[0021] S231. Construct a forward prediction loss based on the forward input sequence, the true value of the sequence to be predicted, and the output of the forward prediction network.

[0022] S232. Construct a backward prediction loss based on the backward input sequence, the true value of the sequence to be predicted, and the output of the reversed backward prediction network.

[0023] S233. Construct a consistency loss based on the forward prediction window and the reversed backward backtracking prediction window.

[0024] S234. Construct a training loss based on the difference between the prediction result of the long-term filling module and the true value of the sequence to be predicted.

[0025] S235. Construct a long-term filling module training loss based on the forward prediction loss, the backward prediction loss, the consistency loss, and the training loss.

[0026] Optionally, the forward prediction loss is as shown in the following formula (1):

[0027] (1)

[0028] The backward prediction loss is as shown in the following formula (2):

[0029] (2)

[0030] The consistency loss is as shown in the following formula (3):

[0031] (3)

[0032] The training loss is as shown in the following formula (4):

[0033] (4)

[0034] In the formula, represents the forward prediction loss, represents the forward input sequence, represents the true value of the sequence to be predicted, represents the output of the forward prediction network, represents the backward prediction loss, represents the backward input sequence, represents the output of the reversed backward prediction network, represents the consistency loss, represents the forward prediction window, represents the reversed backward backtracking prediction window, represents the training loss.

[0035] Optionally, the training loss of the short-term filling module in S3 is as shown in the following formula (5):

[0036] (5)

[0037] where

[0038] (6)

[0039] In the formula represents the training loss of the short-term filling module represents a randomly generated continuous missing mask represents the true value of the sequence to be predicted represents the output of the short-term filling module

[0040] Optionally, the training loss of the meta-weighting module in S4 is as shown in the following formula (7):

[0041] (7)

[0042] where

[0043] (8)

[0044] (9)

[0045] In the formula represents the training loss of the meta-weighting module represents a randomly generated continuous missing mask represents the true value of the sequence to be predicted represents the final filling result obtained by weighted summation using the weighted ratio of the output of the long-term filling module and the output of the short-term filling module represents the weighted ratio of the output of the long-term filling module and the output of the short-term filling module represents the output of the long-term filling module represents the output of the short-term filling module

[0046] On the other hand, a data filling device based on a time series continuous missing filling model is provided. The device is applied to a data filling method based on a time series continuous missing filling model. The device includes:

[0047] An acquisition module, configured to acquire a training data set; the training data set includes a forward input sequence for forward prediction, the true value of the sequence to be predicted, and a backward input sequence for backward prediction

[0048] The long-term filling module is used to input the forward input sequence and the backward input sequence into the forward prediction network and the backward prediction network of the long-term filling module respectively, to obtain the forward prediction network output and the backward prediction network output; a linear function is introduced to perform weighted integration on the forward prediction network output and the backward prediction network output, to obtain the long-term filling module output, and the long-term filling module training loss is constructed.

[0049] The short-term filling module is used to input the true value of the sequence to be predicted and the randomly generated continuous missing mask into the short-term filling module, to obtain the short-term filling module output, and the short-term filling module training loss is constructed; wherein, the short-term filling module includes a self-mapping network.

[0050] The meta-weighting module is used to input the long-term filling module output, the short-term filling module output, the true value of the sequence to be predicted and the continuous missing mask into the meta-weighting module, to obtain the meta-weighting module output, and the meta-weighting module training loss is constructed; wherein, the meta-weighting module includes an independent multi-layer perceptron.

[0051] The training module is used to construct the long-term and short-term time series filling model loss according to the long-term filling module training loss, the short-term filling module training loss and the meta-weighting module training loss, to train the long-term and short-term time series filling model, and to obtain the trained long-term and short-term time series filling model loss.

[0052] The output module is used to obtain the multi-variable time series to be filled with missing values, and input it into the trained long-term and short-term time series filling model loss to fill the missing data, to obtain the filling result.

[0053] Optionally, the long-term filling module is further used for:

[0054] S21. Input the forward input sequence into the forward prediction network of the long-term filling module, to obtain the forward prediction network output; wherein, the forward prediction network output includes a forward backtracking prediction window and a forward prediction window.

[0055] S22. Reverse the time order of the backward input sequence, and input the reversed sequence into the backward prediction network of the long-term filling module, to obtain the backward prediction network output; wherein, the backward prediction network output includes a backward backtracking prediction window and a backward prediction window.

[0056] S23. Introduce a linear function to perform weighted integration on the forward prediction window and the reversed backward backtracking prediction window, to obtain the long-term filling module output, and construct the long-term filling module training loss.

[0057] Optionally, the long-term filling module is further used for:

[0058] S231. Construct a forward prediction loss based on the forward input sequence, the true value of the sequence to be predicted, and the output of the forward prediction network.

[0059] S232. Construct a backward prediction loss based on the backward input sequence, the true value of the sequence to be predicted, and the output of the reversed backward prediction network.

[0060] S233. Construct a consistency loss based on the forward prediction window and the reversed backward backtracking prediction window.

[0061] S234. Construct a training loss based on the difference between the prediction result of the long-term filling module and the true value of the sequence to be predicted.

[0062] S235. Construct a long-term filling module training loss based on the forward prediction loss, the backward prediction loss, the consistency loss, and the training loss.

[0063] Optionally, the forward prediction loss is as shown in Equation (1) below:

[0064] (1)

[0065] The backward prediction loss is as shown in Equation (2) below:

[0066] (2)

[0067] The consistency loss is as shown in Equation (3) below:

[0068] (3)

[0069] The training loss is as shown in Equation (4) below:

[0070] (4)

[0071] In the formula, represents the forward prediction loss, represents the forward input sequence, represents the true value of the sequence to be predicted, represents the output of the forward prediction network, represents the backward prediction loss, represents the backward input sequence, represents the output of the reversed backward prediction network, represents the consistency loss, represents the forward prediction window, represents the reversed backward backtracking prediction window, represents the training loss.

[0072] Optionally, the short-term filling module training loss is as shown in Equation (5) below:

[0073] (5)

[0074] Wherein,

[0075] (6)

[0076] In the formula, represents the training loss of the short-term filling module, represents a randomly generated continuous missing mask, represents the true value of the sequence to be predicted, represents the output of the short-term filling module.

[0077] Optionally, the training loss of the meta-weighting module is as shown in the following formula (7):

[0078] (7)

[0079] Wherein,

[0080] (8)

[0081] (9)

[0082] In the formula, represents the training loss of the meta-weighting module, represents a randomly generated continuous missing mask, represents the true value of the sequence to be predicted, represents the final filling result obtained by weighted summation using the weighted ratio of the output of the long-term filling module and the output of the short-term filling module, represents the weighted ratio of the output of the long-term filling module and the output of the short-term filling module, represents the output of the long-term filling module, represents the output of the short-term filling module.

[0083] On the other hand, a data filling device is provided, and the data filling device includes: a processor; a memory, and computer-readable instructions are stored on the memory, and when the computer-readable instructions are executed by the processor, any one of the data filling methods in the above data filling method based on the time series continuous missing filling model is implemented.

[0084] On the other hand, a computer-readable storage medium is provided, and at least one instruction is stored in the storage medium, and the at least one instruction is loaded and executed by a processor to implement any one of the data filling methods in the above data filling method based on the time series continuous missing filling model.

[0085] The beneficial effects brought by the technical solutions provided in the embodiments of the present invention at least include:

[0086] Effectively coping with long - range continuous missing: By introducing forward and backward prediction networks and combining consistency regularization terms, LSTI can model long - term dependencies bidirectionally and effectively solve the problem of information breakage caused by long - time missing. Experimental results show that compared with the current optimal model on five real - world datasets, the average MSE of LSTI is reduced by 57.4%, and it performs more stably when the missing interval increases. Compared with traditional contrastive learning methods that only use normal samples, the present invention can better adapt to complex and changing real - world scenarios.

[0087] Compatible with multiple missing patterns and strong adaptability: Facing various types of continuous missing, LSTI shows strong adaptability. Especially in the Blackout scenario, it can still maintain excellent performance, significantly outperforming mainstream methods, demonstrating strong robustness to multiple types of missing patterns.

[0088] Modular structure and good scalability: Each sub - module of LSTI can use any time - series modeling backbone network (such as Transformer, RNN, TCN, etc.), with good "plug - and - play" ability, facilitating rapid migration and deployment in different fields. Brief Description of the Drawings

[0089] To more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following - described drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0090] Figure 1 It is a flowchart of a data filling method based on a time - series continuous missing filling model provided by an embodiment of the present invention;

[0091] Figure 2 It is an overall training process architecture diagram of LSTI provided by an embodiment of the present invention;

[0092] Figure 3 It is a schematic diagram showing the difference between completely random missing and continuous missing provided by an embodiment of the present invention;

[0093] Figure 4 It is a block diagram of a data filling device based on a time - series continuous missing filling model provided by an embodiment of the present invention;

[0094] Figure 5 It is a schematic structural diagram of a data filling device provided by an embodiment of the present invention. Detailed Embodiments

[0095] The following will describe the technical solutions in the present invention in conjunction with the drawings.

[0096] In the embodiments of the present invention, words such as "exemplarily" and "for example" are used to represent examples, illustrations or explanations. Any embodiment or design solution described as an "example" in the present invention should not be construed as being more preferred or having more advantages than other embodiments or design solutions. Rather, the use of the word "example" is intended to present concepts in a specific manner. In addition, in the embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one of the two.

[0097] In the embodiments of the present invention, "image" and "picture" can sometimes be used interchangeably. It should be noted that when the difference is not emphasized, the meanings they express are the same. "(of)", "corresponding", and "corresponding" can sometimes be used interchangeably. It should be noted that when the difference is not emphasized, the meanings they express are the same.

[0098] In the embodiments of the present invention, sometimes a subscript such as W1 may be written in a non-subscript form such as W1. When the difference is not emphasized, the meanings they express are the same.

[0099] To make the technical problems, technical solutions and advantages to be solved by the present invention clearer, the following will be described in detail with reference to the accompanying drawings and specific embodiments.

[0100] The embodiments of the present invention provide a data filling method based on a time series continuous missing value filling model. This method can be implemented by a data filling device, and the data filling device can be a terminal or a server. As Figure 1 shown in the flowchart of the data filling method based on the time series continuous missing value filling model, the processing flow of this method can include the following steps:

[0101] S1. Obtain a training data set.

[0102] In a feasible implementation manner, the present invention considers a multi-variable time series set , where represents the number of timestamps, represents the number of channels (or features). The goal of the filling task is to fill the missing values in . Formally, the observation mask is defined as , where when is missing, ; otherwise, .

[0103] In practical applications, continuous missing values may affect the matrix . The initial length of the continuous missing values is denoted as , and there are several random sub-matrices , where the value is missing. Specifically, the observation mask can be expressed as:

[0104] (1)

[0105] Where, represents the starting position randomly selected in the original data for the th missing interval, and represents the total number of missing intervals in the original data.

[0106] Specifically, let the input length of the prediction network be , the prediction length be , the training data set be denoted as , which contains the following three parts: the input sequence for forward prediction, the true value to be predicted, and the input sequence for backward prediction. The present invention reverses the time order of to obtain . Specifically, the formula is as follows:

[0107] (2)

[0108] This indicates that is a sub-matrix composed of the first rows of , while is a sub-matrix obtained by reversing the last rows of .

[0109] S2. Input the forward input sequence and the backward input sequence into the forward prediction network and the backward prediction network of the long-term imputation module respectively to obtain the forward prediction network output and the backward prediction network output; introduce a linear function to perform weighted integration on the forward prediction network output and the backward prediction network output to obtain the long-term imputation module output, and construct the long-term imputation module training loss.

[0110] Among them, the long-term imputation module: This module is used to capture the long-term dependencies in the time series. It consists of a forward and a backward prediction network, and introduces a consistency loss during the training phase to minimize the difference between the outputs of the two. During the imputation phase, the forward and backward networks respectively perform bidirectional prediction on the missing intervals in an autoregressive manner, and then perform weighted fusion on their prediction results.

[0111] Optionally, the above step S2 may include the following steps S21 - S23:

[0112] S21. Input the forward input sequence into the forward prediction network of the long-term filling module to obtain the output of the forward prediction network.

[0113] S22. Reverse the time order of the backward input sequence, and input the reversed sequence into the backward prediction network of the long-term filling module to obtain the output of the backward prediction network; wherein, the output of the backward prediction network includes a backward trace prediction window and a backward prediction window.

[0114] In a feasible implementation manner, and are respectively input into the forward prediction network and the backward prediction network to generate network outputs . Among them, contains a trace prediction window and a prediction window , is similar. Specifically, there are:

[0115] (3)

[0116] (4)

[0117] Among them, 、 and respectively represent 、 and 's time reversal results. The network outputs the values of the trace window and the prediction window simultaneously to ensure that the model output is consistent with the input in the time sequence structure, so as to achieve a more comprehensive training process and enhance the stability of the autoregressive process. Therefore, the forward prediction loss and the backward prediction loss need to be aligned with the true values of the trace window and the prediction window simultaneously:

[0118] (5)

[0119] (6)

[0120] Furthermore, the prediction windows and output by the two networks correspond to the same data segment . If both networks can effectively model long-term dependencies, their prediction results for the same segment should be highly consistent. Based on this, the present invention introduces a consistency loss function to further suppress potential error accumulation in the autoregressive process:

[0121] (7)

[0122] S23. Introduce a linear function to perform weighted integration on the forward prediction window and the backward backtracking prediction window after inversion to obtain the output of the long-term filling module, and construct the training loss of the long-term filling module.

[0123] In a feasible implementation, after obtaining the prediction results in two directions, the present invention integrates them into the final output of the long-term filling module. Intuitively, the values closer to the backtracking window in the prediction window usually have smaller cumulative errors. Therefore, the values in the front section of the missing interval should rely more on the prediction of the forward network, while the values in the back section should rely more on the prediction of the backward network. For this purpose, the present invention introduces a linear function to perform weighted integration on the two prediction results, and uses the difference between the integrated result and the true value as the basis for calculating the final training loss:

[0124] (8)

[0125] (9)

[0126] The overall training objective of the long-term filling module is the sum of the above losses:

[0127] (10)

[0128] In the formula, represents the forward prediction loss, represents the forward input sequence, represents the true value of the sequence to be predicted, represents the output of the forward prediction network, represents the backward prediction loss, represents the backward input sequence, represents the output of the backward prediction network after inversion, represents the consistency loss, represents the forward prediction window, represents the backward backtracking prediction window after inversion, represents the training loss.

[0129] Long-term Imputation Module, Bidirectional Autoregressive Imputation: Traditional methods often fail to model long-range dependencies when dealing with long continuous missing intervals, resulting in imputation results deviating from the true trend. To alleviate this problem, the present invention introduces two key design ideas to enhance the modeling effect of long-term dependencies. First, long-term dependency relationships can be learned from both the forward and backward directions of time. Therefore, the long-term imputation module consists of a forward prediction network (FPNet) and a backward prediction network (BPNet), proposing a bidirectional prediction structure that performs autoregressive prediction from both ends of the time series to capture forward and backward long-term dependency relationships and fill in missing values in an autoregressive manner. Second, the prediction results obtained from long-term dependencies in different directions should be consistent. Accordingly, in the training stage, the present invention introduces a consistency loss term to reduce the difference between the outputs of the two networks, thereby further improving the modeling ability of long-term dependencies and the imputation performance. In the imputation stage, a linear fusion strategy based on position weights is adopted to generate the final output by combining the forward and backward prediction results. This mechanism significantly enhances the model's fitting ability for long missing segments. Without the bidirectional long-term imputation module, the model will not be able to effectively model the long-term dependencies of the time series, and its performance will degrade severely, especially in the Blackout mode.

[0130] S3. Input the true values of the sequence to be predicted and the randomly generated continuous missing mask into the short-term imputation module to obtain the output of the short-term imputation module, and construct the training loss of the short-term imputation module; wherein, the short-term imputation module includes a self-mapping network.

[0131] Among them, the short-term imputation module (Short-term Imputer): This module focuses on modeling short-term local dependencies in the time series. Its core is a self-mapping network, which is trained with a randomly generated continuous missing mask. In the imputation stage, a sliding window mechanism is adopted to fill in each segment of the local missing area one by one.

[0132] In a feasible implementation, the missing data in the real world usually consists of single-point missing values and long continuous missing intervals. To adapt to various missing patterns, the present invention draws on the design idea of the basic imputation model and introduces a short-term imputation module to capture short-term dependency relationships in time series data. This module consists of a self-mapping network (Self-Mapping Network, SMNet). During the training process of the short-term imputation module, the training data used is , that is, the middle segment of the training data in the long-term imputation module. The present invention randomly generates a continuous missing mask , and inputs it together with the input data into the self-mapping network for training:

[0133] (11)

[0134] (12)

[0135] In the formula, represents the training loss of the short-term filling module, represents a randomly generated continuous missing mask, represents the true value of the sequence to be predicted, represents the output of the short-term filling module.

[0136] Short-term filling module, sliding window self-mapping filling: In the actual scenario, the missing data often presents multiple coexisting patterns. Relying solely on long-term filling will ignore the local structural information. Therefore, the present invention introduces a short-term filling module, which uses a sliding window and a random missing mask to train a self-mapping network to capture local temporal dependence features. This module can quickly recover the missing values in a short interval and is particularly effective in dealing with MCAR types or short missing segments. Without this module, the model will be insensitive to locally perturbed missing values and the filling accuracy will decrease.

[0137] S4. Input the output of the long-term filling module, the output of the short-term filling module, the true value of the sequence to be predicted, and the continuous missing mask into the meta-weighting module to obtain the output of the meta-weighting module and construct the training loss of the meta-weighting module; wherein, the meta-weighting module includes an independent multi-layer perceptron.

[0138] Among them, the meta-weighting module: This module dynamically learns the weighting ratio between the long-term and short-term filling results according to the characteristics of the specific input data, so as to achieve a more adaptable and accurate final filling result.

[0139] In a feasible implementation manner, in order to adaptively fill the data containing long-term and short-term missing values, the present invention designs a meta-weighting module. This module includes an independent multi-layer perceptron (Multilayer Perceptron, MLP) for learning the characteristics of the missing data, so as to adaptively assign weights to the outputs of the long-term filling module and the short-term filling module. During the training process, first obtain the output from the long-term filling module and the output from the short-term filling module , and then input the data and the missing mask into the meta-weighting module:

[0140] (13)

[0141] (14)

[0142] The training loss of the meta-weighted module is as follows:

[0143] (15)

[0144] The overall training objective of LSTI (Long Short-Term Imputer) is the sum of the losses of all modules:

[0145] (16)

[0146] In the formula, represents the training loss of the meta-weighted module, represents a randomly generated continuous missing mask, represents the true value of the sequence to be predicted, represents the final filling result obtained by weighted summation using the weighted ratio of the output of the long-term filling module and the output of the short-term filling module, represents the weighted ratio of the output of the long-term filling module and the output of the short-term filling module, represents the output of the long-term filling module, represents the output of the short-term filling module.

[0147] Meta-weighted fusion mechanism: Considering that different missing segments have different requirements for long-term and short-term dependencies, the present invention designs a meta-weighted module to dynamically learn the weighting coefficients of the long-term and short-term filling results according to the input data and the missing mask through an MLP network, realizing data-driven adaptive fusion. Experiments show that the weight change is positively correlated with the missing length, verifying its perception ability and rationality for the missing pattern. If this module is removed, the model will degenerate into fixed-ratio weighting, making it difficult to adapt to the information fusion requirements in different scenarios, and the overall performance will be restricted.

[0148] The overall architecture of LSTI is as Figure 2 shown. It consists of three core modules: (1) The long-term filling module, which consists of two prediction networks running in different directions; (2) The short-term filling module, which consists of a self-mapping module; (3) The meta-weighted module, which is used to learn how to weight the outputs of the two fillers to adapt to the characteristics of different input data. It should be emphasized that the basic backbone networks of the long-term filling module and the short-term filling module are highly replaceable, and current mainstream time series modeling structures, such as models based on Transformer, RNN or TCN, can be flexibly selected.

[0149] In summary, the core innovation of the present invention lies in the collaborative modeling of long-term and short-term dual modules, combined with consistency constraints and an adaptive weighting mechanism. These three aspects cooperate with each other from the perspectives of temporal dependence modeling, local structure restoration, and information fusion, and are closely linked. They are the key components for achieving robust filling performance and the key protected content of the present invention. If any one of these links is missing, the robustness and generalization ability of the overall system will be significantly reduced, making it difficult to meet the actual needs of complex time series filling tasks.

[0150] S5. Construct the loss of the long-short-term time series filling model based on the training losses of the long-term filling module, short-term filling module, and meta-weighting module, and train the long-short-term time series filling model to obtain the trained loss of the long-short-term time series filling model.

[0151] In a feasible implementation manner, according to the solutions in existing research, the present invention divides the missing patterns of continuous time series into four types: Disjoint, Overlap, MCAR_B, and Blackout. Each pattern corresponds to a specific form of long-interval continuous missing data. The present invention focuses on the most challenging Blackout pattern, which means that all channels are missing simultaneously at the same time position. This synchronous missing significantly increases the filling difficulty because it excludes the possibility of using information from other channels or time points to reconstruct the missing values. Figure 3 Shows the differences between MCAR and Blackout missing patterns.

[0152] Traditional filling methods perform poorly in dealing with such data, mainly because of their insufficient ability to model long-term dependencies. Some studies have tried to solve this problem in specific application scenarios, while others have dealt with it based on mathematical and statistical methods. However, these methods usually rely on domain knowledge, have complex processing flows, and do not have end-to-end deep learning capabilities, so they have limitations in terms of application scope and generalization ability.

[0153] To solve the problem of filling missing values in the Blackout pattern, the present invention proposes a specially designed model, LSTI (Long Short-Term Imputer). This model consists of three core modules:

[0154] First is the long-term filling module, which includes a forward prediction network and a backward prediction network. During the training phase, the present invention introduces a consistency loss to minimize the difference between the prediction results of the two networks; during the filling phase, these two networks fill the entire sequence in an autoregressive manner from the forward and backward directions respectively. The final filling result is obtained by weighted fusion of the prediction results in the two directions. This weighting strategy is based on the intuition that the closer a position in the prediction window is to the backtracking window, the smaller its cumulative error, so it should be more biased towards the prediction result of the forward network; while the closer a position is to the end of the sequence, it should be more biased towards the output of the backward network. This structure can effectively model the long-term dependencies in time series and is suitable for dealing with the filling problem of long-interval continuous missing values.

[0155] The second module is the short-term filling module. Since the missing data in the real world usually appears in multiple patterns (such as MCAR and long-interval continuous missing) intertwined, it is difficult to handle all situations relying only on long-term dependencies. Therefore, the model needs to have the ability to adapt to diverse missing patterns. The short-term filling module consists of a self-mapping network and is trained with randomly generated continuous missing masks to capture the short-term dependencies in time series.

[0156] Finally, LSTI introduces a meta-weighting module, which uses an independent MLP network to adaptively learn the importance of long-term and short-term dependencies in the current sample according to the input data and the missing mask, and then weights and fuses the outputs of the long-term and short-term filling modules accordingly to generate the final filling result. This structure enables the model to simultaneously capture and utilize the long-term and short-term dependencies in time series, achieving adaptive and efficient filling for multiple missing patterns.

[0157] The LSTI model proposed by the present invention comprehensively improves the model's adaptability and robustness to multiple missing patterns by integrating long-term and short-term dependency modeling, introducing bidirectional consistency prediction, and the meta-weighting mechanism. Experimental results show that this method is significantly superior to existing methods under multiple datasets, multiple missing rates, and missing lengths, and can stably and accurately fill long-interval continuous missing values. This research provides a new idea for the intelligent completion of complex time series data, has good generalization and application prospects, and is expected to promote the development of data-driven time series modeling and downstream analysis tasks.

[0158] S6. Obtain the multivariate time series to be filled with missing values, input it into the trained long-short-term time series filling model to perform missing data filling, and obtain the filling result.

[0159] In a feasible implementation, in real-world datasets, there are often multiple consecutive missing segments, which may cause the input of the network to also contain missing values. To solve this problem, the long-term filling module adopts a bidirectional autoregressive strategy during the filling process, filling the entire missing interval at once, so as to ensure that the input of the network is always a real value or a previously filled value, effectively avoiding the situation of missing data in the input. Among them, as long as it is a time series, the present invention can be used to fill missing values. For example, datasets in different fields such as Weather, Traffic, and Electricity.

[0160] In the forward prediction network, the present invention traverses the entire dataset from front to back along the time dimension. When it is detected that a certain data segment has missing values, and its corresponding missing mask is at that time, a data segment of length is selected from in front of this segment , and it is input into the forward prediction network:

[0161] (17)

[0162] Among them, represents the filling result of segment . The present invention uses to replace the original to ensure that there are no longer missing values in this segment. Subsequently, the entire dataset is continued to be scanned along the time axis, and the next data segment is processed in turn.

[0163] The backward prediction network performs the same autoregressive filling process on the entire missing segment in the opposite time direction. Subsequently, the present invention traverses all the original missing intervals again, and for each continuous missing segment , using the integration strategy of the formula , the filling results of the forward and backward directions are weighted and fused to obtain the final filling sequence .

[0164] Furthermore, the present invention uses a sliding window of length to divide the entire dataset, and inputs each data segment into the short-term filling module for filling. Finally, the short-term filling module outputs the filled data .

[0165] Furthermore, after obtaining the output of the long-term filling module and the output of the short-term filling module, the present invention uses the same sliding window as the short-term filling module to obtain from the original data and its missing mask Subsequently, these segmented data are input into the meta-weighting module to obtain For each window, the present invention adopts the formula To weight proportionally And To finally obtain the filled data.

[0166] In the embodiment of the present invention, the proposed method has achieved remarkable effects in the following aspects:

[0167] Effectively coping with long-range continuous missing: By introducing forward and backward prediction networks and combining consistency regularization terms, LSTI can bidirectionally model long-term dependencies and effectively solve the problem of information breakage caused by long-term missing. Experimental results show that compared with the current optimal model on five real datasets, LSTI reduces the average MSE by 57.4%, and performs more stably when the missing interval increases. Compared with traditional contrastive learning methods that only use normal samples, the present invention can better adapt to complex and changeable real-world scenarios.

[0168] Compatible with multiple missing patterns and strong adaptability: In the face of various continuous missing types, LSTI shows strong adaptability. Especially in the Blackout scenario, it can still maintain excellent performance, significantly superior to mainstream methods, demonstrating strong robustness to multiple types of missing patterns.

[0169] Structurally modular and with good scalability: Each sub-module of LSTI can use any time series modeling backbone network (such as Transformer, RNN, TCN, etc.), and has good "plug-and-play" ability, facilitating rapid migration and deployment in different fields.

[0170] Figure 4 It is a block diagram of a data filling device based on a time series continuous missing filling model shown according to an exemplary embodiment. This device is used for the data filling method based on the time series continuous missing filling model. Referring to Figure 4 This device includes an acquisition module 310, a long-term filling module 320, a short-term filling module 330, a meta-weighting module 340, a training module 350, and an output module 360. Among them:

[0171] The acquisition module 310 is used to acquire the training dataset; the training dataset includes a forward input sequence for forward prediction, the true value of the sequence to be predicted, and a backward input sequence for backward prediction.

[0172] The long-term filling module 320 is used to input the forward input sequence and the backward input sequence into the forward prediction network and the backward prediction network of the long-term filling module respectively, to obtain the output of the forward prediction network and the output of the backward prediction network; a linear function is introduced to perform weighted integration on the output of the forward prediction network and the output of the backward prediction network to obtain the output of the long-term filling module, and the training loss of the long-term filling module is constructed.

[0173] The short-term filling module 330 is used to input the true value of the sequence to be predicted and the randomly generated continuous missing mask into the short-term filling module to obtain the output of the short-term filling module, and construct the training loss of the short-term filling module; wherein, the short-term filling module includes a self-mapping network.

[0174] The meta-weighting module 340 is used to input the output of the long-term filling module, the output of the short-term filling module, the true value of the sequence to be predicted, and the continuous missing mask into the meta-weighting module to obtain the output of the meta-weighting module, and construct the training loss of the meta-weighting module; wherein, the meta-weighting module includes an independent multi-layer perceptron.

[0175] The training module 350 is used to construct the long-short-term time series filling model loss according to the training loss of the long-term filling module, the training loss of the short-term filling module, and the training loss of the meta-weighting module, and train the long-short-term time series filling model to obtain the trained long-short-term time series filling model loss.

[0176] The output module 360 is used to obtain the multivariate time series to be filled with missing values, input it into the trained long-short-term time series filling model loss for missing data filling, and obtain the filling result.

[0177] In the embodiments of the present invention, the proposed method has achieved remarkable effects in the following aspects:

[0178] Effectively coping with long-interval continuous missing: By introducing forward and backward prediction networks and combining consistency regularization terms, LSTI can bidirectionally model long-term dependencies and effectively solve the problem of information breakage caused by long-time missing. Experimental results show that compared with the current optimal model on five real datasets, the average MSE of LSTI is reduced by 57.4%, and it performs more stably when the missing interval increases. Compared with traditional contrastive learning methods that only use normal samples, the present invention can better adapt to complex and changing real-world scenarios.

[0179] Compatible with multiple missing patterns and strong adaptability: Facing various continuous missing types, LSTI shows strong adaptability. Especially in the Blackout scenario, it can still maintain excellent performance, significantly superior to mainstream methods, demonstrating strong robustness to multiple types of missing patterns.

[0180] Structurally modular with good scalability: Each sub-module of LSTI can use any time series modeling backbone network (such as Transformer, RNN, TCN, etc.), with good "plug-and-play" ability, facilitating rapid migration and deployment in different fields.

[0181] Figure 5 is a schematic structural diagram of a data filling device provided by an embodiment of the present invention. As Figure 5 shown, the data filling device may include the above-mentioned Figure 4 data filling device based on the time series continuous missing filling model shown. Optionally, the data filling device 410 may include a first processor 2001.

[0182] Optionally, the data filling device 410 may further include a memory 2002 and a transceiver 2003.

[0183] Among them, the first processor 2001 is connected to the memory 2002 and the transceiver 2003, and may be connected through a communication bus, for example.

[0184] Next, in conjunction with Figure 5 each component of the data filling device 410 will be specifically introduced:

[0185] Among them, the first processor 2001 is the control center of the data filling device 410, which may be a single processor or a collective term for multiple processing elements. For example, the first processor 2001 is one or more central processing units (CPUs), or may also be an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present invention, for example: one or more digital signal processors (DSPs), or one or more field programmable gate arrays (FPGAs).

[0186] Optionally, the first processor 2001 may execute various functions of the data filling device 410 by running or executing software programs stored in the memory 2002 and calling data stored in the memory 2002.

[0187] In a specific implementation, as an embodiment, the first processor 2001 may include one or more CPUs, such as Figure 5 CPU0 and CPU1 shown.

[0188] In a specific implementation, as an example, the data filling device 410 may also include multiple processors, such as Figure 5 the first processor 2001 and the second processor 2004 shown in Figure 5 . Each of these processors can be a single-core processor (single-CPU) or a multi-core processor (multi-CPU). The processor here can refer to one or more devices, circuits, and / or processing cores for processing data (such as computer program instructions).

[0189] Among them, the memory 2002 is used to store the software program for implementing the solution of the present invention and is controlled by the first processor 2001 for execution. The specific implementation method can refer to the above method embodiment and will not be elaborated here.

[0190] Optionally, the memory 2002 can be a read-only memory (ROM) or other types of static storage devices that can store static information and instructions, a random access memory (RAM) or other types of dynamic storage devices that can store information and instructions, or an electrically erasable programmable read-only memory (EEPROM), a compact disc read-only memory (CD-ROM), or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital versatile discs, Blu-ray discs, etc.), magnetic disk storage media, or any other medium that can be used to carry or store the desired program code in the form of instructions or data structures and can be accessed by a computer, but not limited thereto. The memory 2002 can be integrated with the first processor 2001 or exist independently and is coupled to the first processor 2001 through the interface circuit ( Figure 5 not shown in Figure 5 ) of the data filling device 410. The embodiments of the present invention do not make specific limitations on this.

[0191] The transceiver 2003 is used to communicate with a network device or with a terminal device.

[0192] Optionally, the transceiver 2003 can include a receiver and a transmitter ( Figure 5 not shown separately in Figure 5 ). Among them, the receiver is used to implement the receiving function, and the transmitter is used to implement the sending function.

[0193] Optionally, the transceiver 2003 can be integrated with the first processor 2001 or exist independently and is coupled to the first processor 2001 through the interface circuit ( Figure 5is not shown) and is coupled to the first processor 2001, which is not specifically limited in the embodiments of the present invention.

[0194] It should be noted that Figure 5 the structure of the data filling device 410 shown in does not constitute a limitation on the router. The actual knowledge structure recognition device may include more or fewer components than those shown, or combine certain components, or have different component arrangements.

[0195] In addition, for the technical effects of the data filling device 410, reference can be made to the technical effects of the data filling method based on the time series continuous missing filling model described in the above method embodiments, which will not be elaborated here.

[0196] It should be understood that the first processor 2001 in the embodiments of the present invention may be a central processing unit (CPU), and the processor may also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0197] It should also be understood that the memory in the embodiments of the present invention may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read-only memory (ROM), a programmable ROM (PROM), an erasable PROM (EPROM), an electrically erasable PROM (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example but not limitation, many forms of random access memory (RAM) are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchlink DRAM (SLDRAM), and direct rambus RAM (DR RAM).

[0198] The above embodiments can be implemented in whole or in part by software, hardware (such as circuits), firmware, or any combination thereof. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, the processes or functions described in the embodiments of the present invention are generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center by wired (such as infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server or a data center that contains one or more collections of available media. The available media can be magnetic media (such as floppy disks, hard disks, magnetic tapes), optical media (such as DVDs), or semiconductor media. The semiconductor media can be a solid-state drive.

[0199] It should be understood that the term "and / or" in this document is merely a description of the association relationship between associated objects, indicating that three relationships can exist. For example, A and / or B can represent: A exists alone, A and B exist simultaneously, and B exists alone. Here, A and B can be singular or plural. In addition, the character " / " in this document generally represents an "or" relationship between the associated objects before and after, but it may also represent an "and / or" relationship, which can be specifically understood by referring to the context.

[0200] In the present invention, "at least one" means one or more, and "a plurality" means two or more. "At least one of the following" or its similar expressions refer to any combination of these items, including any combination of single items or plural items. For example, at least one of a, b, or c can represent: a, b, c, a - b, a - c, b - c, or a - b - c, where a, b, and c can be single or multiple.

[0201] It should be understood that in various embodiments of the present invention, the magnitudes of the sequence numbers of the above processes do not mean the order of execution. The order of execution of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0202] Those of ordinary skill in the art can realize that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be implemented by electronic hardware, or by a combination of computer software and electronic hardware. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. Professional technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of the present invention.

[0203] Those skilled in the art can clearly understand that for the convenience and conciseness of description, the specific working processes of the above-described devices, apparatuses, and units can refer to the corresponding processes in the foregoing method embodiments and will not be elaborated herein.

[0204] In several embodiments provided by the present invention, it should be understood that the disclosed devices, apparatuses, and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the units is only a logical function division, and there can be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another device, or some features can be ignored or not executed. Another point is that the displayed or discussed coupling or direct coupling or communication connection to each other can be through some interfaces. The indirect coupling or communication connection of the devices or units can be in an electrical, mechanical, or other form.

[0205] The units described as separate components may or may not be physically separated. The components shown as units may or may not be physical units, that is, they can be located in one place, or distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0206] In addition, the functional units in each embodiment of the present invention can be integrated into one processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit.

[0207] When the above-mentioned functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art or a part of this technical solution can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The foregoing storage medium includes: various media that can store program codes, such as USB flash drives, mobile hard disks, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical discs.

[0208] As described above, the above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A data filling method based on a time series continuous missing value filling model, characterized in that, The method includes: S1. Obtain a training data set; the training data set includes a forward input sequence for forward prediction, the true value of the sequence to be predicted, and a backward input sequence for backward prediction; S2. Input the forward input sequence and the backward input sequence into the forward prediction network and the backward prediction network of the long-term filling module respectively to obtain the forward prediction network output and the backward prediction network output; introduce a linear function to perform weighted integration on the forward prediction network output and the backward prediction network output to obtain the long-term filling module output, and construct the long-term filling module training loss; S3. Input the true value of the sequence to be predicted and a randomly generated continuous missing mask into the short-term filling module to obtain the short-term filling module output, and construct the short-term filling module training loss; wherein, the short-term filling module includes a self-mapping network; S4. Input the long-term filling module output, the short-term filling module output, the true value of the sequence to be predicted, and the continuous missing mask into the meta-weighting module to obtain the meta-weighting module output, and construct the meta-weighting module training loss; wherein, the meta-weighting module includes an independent multi-layer perceptron; S5. Construct the long-short-term time series filling model loss according to the long-term filling module training loss, the short-term filling module training loss, and the meta-weighting module training loss, and train the long-short-term time series filling model to obtain the trained long-short-term time series filling model loss; S6. Obtain a multivariate time series to be filled with missing values, input it into the trained long-short-term time series filling model loss for missing data filling, and obtain the filling result.

2. The data filling method based on the time series continuous missing filling model according to claim 1, wherein The S2 includes: S21. Input the forward input sequence into the forward prediction network of the long-term filling module to obtain the forward prediction network output; wherein, the forward prediction network output includes a forward backtracking prediction window and a forward prediction window; S22. Reverse the time order of the backward input sequence, and input the reversed sequence into the backward prediction network of the long-term filling module to obtain the backward prediction network output; wherein, the backward prediction network output includes a backward backtracking prediction window and a backward prediction window; S23. Introduce a linear function to perform weighted integration on the forward prediction window and the reversed backward backtracking prediction window to obtain the long-term filling module output, and construct the long-term filling module training loss.

3. The data filling method based on the time series continuous missing filling model according to claim 2, characterized in that, The construction of the long-term filling module training loss in S23 includes: S231. Construct a forward prediction loss according to the forward input sequence, the true value of the sequence to be predicted, and the forward prediction network output; S232. Construct a backward prediction loss according to the backward input sequence, the true value of the sequence to be predicted, and the reversed backward prediction network output; S233. Construct a consistency loss according to the forward prediction window and the reversed backward backtracking prediction window; S234. Construct a training loss according to the difference between the long-term filling module prediction result and the true value of the sequence to be predicted; S235. Construct the long-term filling module training loss according to the forward prediction loss, the backward prediction loss, the consistency loss, and the training loss.

4. The data filling method based on the time series continuous missing value filling model according to claim 3, wherein The forward prediction loss is shown in the following formula (1): （1） The backward prediction loss is shown in the following formula (2): （2） The consistency loss is shown in the following formula (3): （3） The training loss is shown in the following formula (4): （4） Wherein, represents the forward prediction loss, represents the forward input sequence, represents the true value of the sequence to be predicted, represents the output of the forward prediction network, represents the backward prediction loss, represents the backward input sequence, represents the output of the reversed backward prediction network, represents the consistency loss, represents the forward prediction window, represents the reversed backward traceback prediction window, represents the training loss.

5. The data filling method based on the time series continuous missing value filling model according to claim 1, characterized in that, The training loss of the short-term filling module in S3 is shown in the following formula (5): （5） Wherein, （6） In the formula, represents the training loss of the short-term filling module, represents the randomly generated continuous missing mask, represents the true value of the sequence to be predicted, represents the output of the short-term filling module.

6. The data filling method based on the time series continuous missing value filling model according to claim 1, wherein The training loss of the meta-weighting module in S4 is shown in the following formula (7): （7） Wherein, （8） （9） In the formula, represents the training loss of the meta-weighted module, represents the randomly generated continuous missing mask, represents the true value of the sequence to be predicted, represents the final filling result obtained by weighted summation using the weighted ratio of the output of the long-term filling module and the output of the short-term filling module, represents the weighted ratio of the output of the long-term filling module and the output of the short-term filling module, represents the output of the long-term filling module, represents the output of the short-term filling module.

7. A data filling device based on a time series continuous missing value filling model, the data filling device based on the time series continuous missing value filling model is used to implement the data filling method based on the time series continuous missing value filling model according to any one of claims 1-6, characterized in that, The device includes: An acquisition module for acquiring a training data set; the training data set includes a forward input sequence for forward prediction, the true value of the sequence to be predicted, and a backward input sequence for backward prediction; A long-term filling module for inputting the forward input sequence and the backward input sequence into the forward prediction network and the backward prediction network of the long-term filling module respectively to obtain the forward prediction network output and the backward prediction network output; introducing a linear function to perform weighted integration on the forward prediction network output and the backward prediction network output to obtain the long-term filling module output, and constructing a long-term filling module training loss; A short-term filling module for inputting the true value of the sequence to be predicted and a randomly generated continuous missing mask into the short-term filling module to obtain the short-term filling module output, and constructing a short-term filling module training loss; wherein, the short-term filling module includes a self-mapping network; A meta-weighting module for inputting the long-term filling module output, the short-term filling module output, the true value of the sequence to be predicted, and the continuous missing mask into the meta-weighting module to obtain the meta-weighting module output, and constructing a meta-weighting module training loss; wherein, the meta-weighting module includes an independent multi-layer perceptron; A training module for constructing a long-short-term time series filling model loss according to the long-term filling module training loss, the short-term filling module training loss, and the meta-weighting module training loss, training the long-short-term time series filling model to obtain a trained long-short-term time series filling model loss; An output module for acquiring a multi-variable time series to be filled with missing values, inputting it into the trained long-short-term time series filling model loss for missing data filling to obtain a filling result.

8. The data filling device based on the time series continuous missing value filling model according to claim 7, wherein The step of inputting the forward input sequence and the backward input sequence into the forward prediction network and the backward prediction network of the long-term filling module respectively to obtain the forward prediction network output and the backward prediction network output; introducing a linear function to perform weighted integration on the forward prediction network output and the backward prediction network output to obtain the long-term filling module output, and constructing a long-term filling module training loss includes: S21. Input the forward input sequence into the forward prediction network of the long-term filling module to obtain the forward prediction network output; wherein, the forward prediction network output includes a forward retrospective prediction window and a forward prediction window; S22. Reverse the time order of the backward input sequence, and input the reversed sequence into the backward prediction network of the long-term filling module to obtain the backward prediction network output; wherein, the backward prediction network output includes a backward retrospective prediction window and a backward prediction window; S23. Introduce a linear function to perform weighted integration on the forward prediction window and the reversed backward retrospective prediction window to obtain the long-term filling module output, and construct a long-term filling module training loss.

9. A data filling device, characterized in that, The data filling device includes: A processor; A memory, on which computer-readable instructions are stored, and when the computer-readable instructions are executed by the processor, the method according to any one of claims 1 to 6 is implemented.

10. A computer-readable storage medium, characterized in that, Program code is stored in the computer-readable storage medium, and the program code can be called by the processor to execute the method according to any one of claims 1 to 6.

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