Symmetric Error Research Articles

Prediction of air quality index based on the SSA-BiLSTM-LightGBM model

The air quality index (AQI), as an indicator to describe the degree of air pollution and its impact on health, plays an important role in improving the quality of the atmospheric environment. Accurate prediction of the AQI can effectively serve people’s lives, reduce pollution control costs and improve the quality of the environment. In this paper, we constructed a combined prediction model based on real hourly AQI data in Beijing. First, we used singular spectrum analysis (SSA) to decompose the AQI data into different sequences, such as trend, oscillation component and noise. Then, bidirectional long short-term memory (BiLSTM) was introduced to predict the decomposed AQI data, and a light gradient boosting machine (LightGBM) was used to integrate the predicted results. The experimental results show that the prediction effect of SSA-BiLSTM-LightGBM for the AQI data set is good on the test set. The root mean squared error (RMSE) reaches 0.6897, the mean absolute error (MAE) reaches 0.4718, the symmetric mean absolute percentage error (SMAPE) reaches 1.2712%, and the adjusted R2 reaches 0.9995.

Automated Adolescence Scoliosis Detection Using Augmented U-Net With Non-square Kernels.

Purpose: Scoliosis is a deformity of the spine, and as a measure of scoliosis severity, Cobb angle is fundamental to the diagnosis of deformities that require treatment. Conventional Cobb angle measurement and assessment is usually done manually, which is inherently time-consuming, and associated with high inter- and intra-observer variability. While there exist automatic scoliosis measurement methods, they suffer from insufficient accuracy. In this work, we propose a two-step segmentation-based deep learning architecture to automate Cobb angle measurement for scoliosis assessment using X-Ray images. Methods: The proposed architecture involves two steps. In the first step, we utilize a novel Augmented U-Net architecture to generate segmentations of vertebrae. The second step includes a non-learning-based pipeline to extract landmark coordinates from the segmented vertebrae and filter undesirable landmarks. Results: Our proposed Augmented U-Net architecture achieved a Symmetric Mean Absolute Percentage Error of 9.2%, with approximately 90% of estimations having less than 10 degrees difference compared with the AASCE-MICCAI challenge 2019 dataset ground truths. We further validated the model using an internal dataset and achieved almost the same level of performance. Conclusion: The proposed architecture is robust in providing automated spinal vertebrae segmentations and Cobb angle measurement, and is potentially generalizable to real-world clinical settings.

Phytoclass: A pigment‐based chemotaxonomic method to determine the biomass of phytoplankton classes

AbstractPigment‐based chemotaxonomy is a widely utilized tool to determine the biomass of phytoplankton classes from pigment biomarkers. The CHEMTAX approach is sensitive to the initial estimates of pigment‐to‐chlorophyll a (Chl a) ratios for the phytoplankton classes required, even though these are modified by the CHEMTAX process. We present an alternative chemotaxonomic method that utilizes simulated annealing with a steepest descent algorithm to derive class abundances and pigment‐to‐Chl a ratios. The simulated annealing algorithm is tested on two synthetic datasets of Southern Ocean phytoplankton communities. Each dataset is composed of 1000 inversion samples (set of phytoplankton class abundances, pigment ratios, and pigment profiles) with sizes ranging between 5 and 60 individual samples. We show that the new simulated annealing approach displays higher accuracy than two common configurations of the CHEMTAX method, with lower differences between true and estimated class abundances. Symmetric mean absolute percentage error were 4.8–11%, compared to 18–70% with CHEMTAX approaches. Proportions of variance explained (R2) between true and estimated class abundances using the simulated annealing approach were 0.98–0.99 compared to 0.71–0.89 for CHEMTAX. Overall, this new methodology is capable of determining phytoplankton class abundances at higher accuracy than CHEMTAX without sensitivity to initial estimates of pigment‐to‐Chl a ratios.

Forecasting Future Monthly Patient Volume using Deep Learning and Statistical Models.

The variety of diseases is increasing day by day, and the demand for hospitals, especially for emergency and radiology units, is also increasing. As in other units, it is necessary to prepare the radiology unit for the future, to take into account the needs and to plan for the future. Due to the radiation emitted by the devices in the radiology unit, minimizing the time spent by the patients for the radiological image is of vital importance both for the unit staff and the patient. In order to solve the aforementioned problem, in this study, it is desired to estimate the monthly number of images in the radiology unit by using deep learning models and statistical-based models, and thus to be prepared for the future in a more planned way. For prediction processes, both deep learning models such as LSTM, MLP, NNAR and ELM, as well as statistical based prediction models such as ARIMA, SES, TBATS, HOLT and THETAF were used. In order to evaluate the performance of the models, the symmetric mean absolute percentage error (sMAPE) and mean absolute scaled error (MASE) metrics, which have been in demand recently, were preferred. The results showed that the LSTM model outperformed the deep learning group in estimating the monthly number of radiological case images, while the AUTO.ARIMA model performed better in the statistical-based group. It is believed that the findings obtained will speed up the procedures of the patients who come to the hospital and are referred to the radiology unit, and will facilitate the hospital managers in managing the patient flow more efficiently, increasing both the service quality and patient satisfaction, and making important contributions to the future planning of the hospital.

Feature Extraction and Prediction of Water Quality Based on Candlestick Theory and Deep Learning Methods

In environmental hydrodynamics, a research topic that has gained popularity is the transmission and diffusion of water pollutants. Various types of change processes in hydrological and water quality are directly related to meteorological changes. If these changing characteristics are classified effectively, this will be conducive to the application of deep learning theory in water pollution simulation. When periodically monitoring water quality, data were represented with a candlestick chart, and different classification features were displayed. The water quality data from the research area from 2012 to 2019 generated 24 classification results in line with the physics laws. Therefore, a deep learning water pollution prediction method was proposed to classify the changing process of pollution to improve the prediction accuracy of water quality, based on candlestick theory, visual geometry group, and gate recurrent unit (CT-VGG-GRU). In this method, after the periodic changes of water quality were represented by candlestick graphically, the features were extracted by the VGG network based on its advantages in graphic feature extraction. Then, this feature and other scenario parameters were fused as the input of the time series network model, and the pollutant concentration sequence at the predicted station constituted the output of the model. Finally, a hybrid model combining graphical and time series features was formed, and this model used continuous time series data from multiple stations on the Lijiang River watershed to train and validate the model. Experimental results indicated that, compared with other comparison models, such as the back propagation neural network (BPNN), support vector regression (SVR), GRU, and VGG-GRU, the proposed model had the highest prediction accuracy, especially for the prediction of extreme values. Additionally, the change trend of water pollution was closer to the real situation, which indicated that the process change information of water pollution could be fully extracted by the CT-VGG-GRU model based on candlestick theory. For the water quality indicators DO, CODMn, and NH3-N, the mean absolute errors (MAE) were 0.284, 0.113, and 0.014, the root mean square errors (RMSE) were 0.315, 0.122, and 0.016, and the symmetric mean absolute percentage errors (SMAPE) were 0.022, 0.108, and 0.127, respectively. The established CT-VGG-GRU model achieved superior computational performance. Using the proposed model, the classification information of the river pollution process could be obtained effectively and the time series information could also be retained, which made the application of the deep learning model to the transmission and diffusion process of river water pollution more explanatory. The proposed model can provide a new method for water quality prediction.

Prediction of temperature distribution in a furnace using the incremental deep extreme learning machine.

In this article, a data-driven model based on the incremental deep extreme learning machine (IDELM) algorithm is proposed to predict the temperature distribution in the furnace. To this end, computational fluid dynamics (CFD) simulations are carried out first to get temperature distributions under typical working conditions. Based on the air distribution mode, the simulation results are divided into six subclasses. Then the K-means clustering method is applied to find out the benchmark working condition of each subclass. Moreover, the random sampling method is used to extract samples to reduce computational complexity. Modeling inputs are selected according to the CFD boundary conditions and combustion mechanisms, and data sets are reconstructed based on the increments of each actual working condition from the benchmark working condition. Finally, an IDBN-based prediction model is built in each subclass. The experimental results show that the IDBN-based model has a promising predictive ability with less than 11% symmetric mean absolute percentage error.

A New Regression Model for Depression Severity Prediction Based on Correlation among Audio Features Using a Graph Convolutional Neural Network.

Recent studies have revealed mutually correlated audio features in the voices of depressed patients. Thus, the voices of these patients can be characterized based on the combinatorial relationships among the audio features. To date, many deep learning-based methods have been proposed to predict the depression severity using audio data. However, existing methods have assumed that the individual audio features are independent. Hence, in this paper, we propose a new deep learning-based regression model that allows for the prediction of depression severity on the basis of the correlation among audio features. The proposed model was developed using a graph convolutional neural network. This model trains the voice characteristics using graph-structured data generated to express the correlation among audio features. We conducted prediction experiments on depression severity using the DAIC-WOZ dataset employed in several previous studies. The experimental results showed that the proposed model achieved a root mean square error (RMSE) of 2.15, a mean absolute error (MAE) of 1.25, and a symmetric mean absolute percentage error of 50.96%. Notably, RMSE and MAE significantly outperformed the existing state-of-the-art prediction methods. From these results, we conclude that the proposed model can be a promising tool for depression diagnosis.

A Hybrid Neural Network Model for Short-Term Wind Speed Forecasting

This study proposes an effective wind speed forecasting model combining a data processing strategy, neural network predictor, and parameter optimization method. (a) Variational mode decomposition (VMD) is adopted to decompose the wind speed data into multiple subseries where each subseries contains unique local characteristics, and all the subseries are converted into two-dimensional samples. (b) A gated recurrent unit (GRU) is sequentially modeled based on the obtained samples and makes the predictions for future wind speed. (c) The grid search with rolling cross-validation (GSRCV) is designed to simultaneously optimize the key parameters of VMD and GRU. To evaluate the effectiveness of the proposed VMD-GRU-GSRCV model, comparative experiments based on hourly wind speed data collected from the National Renewable Energy Laboratory are implemented. Numerical results show that the root mean square error, mean absolute error, mean absolute percentage error, and symmetric mean absolute percentage error of this proposed model reach 0.2047, 0.1435, 3.77%, and 3.74%, respectively, which outperform the benchmark predictions using popular parameter optimization methods, data processing techniques, and hybrid neural network forecasting models.

Comprehensive analysis on error-robustness of FeFET computation-in-memory for hyperdimensional computing

This work comprehensively analyzes the error robustness of hyperdimensional computing (HDC) by using FeFET-based local multiply and global accumulate computation-in-memory. HDC trains and infers with hypervectors (HVs). Symmetric or asymmetric errors, which simulate read-disturb and data-retention errors of FeFET, are injected into Item memory and/or Associative memory before/after or during training in various cases when solving European language classification task. The detailed error injection reveals that HDC is acceptable for both symmetric and asymmetric error rate up to 10−1. Based on the detailed analysis of error robustness, training window slide (TWS) improves the error robustness against memory errors by removing data which contain different amount of errors. TWS shows 10 times higher error robustness. In addition, parallelization of HV encoding in training achieves fast training with up to 10 000 parallelism while maintaining the inference accuracy.

Machine Learning Predictive Models for Evaluating Risk Factors Affecting Sperm Count: Predictions Based on Health Screening Indicators.

In many countries, especially developed nations, the fertility rate and birth rate have continually declined. Taiwan's fertility rate has paralleled this trend and reached its nadir in 2022. Therefore, the government uses many strategies to encourage more married couples to have children. However, couples marrying at an older age may have declining physical status, as well as hypertension and other metabolic syndrome symptoms, in addition to possibly being overweight, which have been the focus of the studies for their influences on male and female gamete quality. Many previous studies based on infertile people are not truly representative of the general population. This study proposed a framework using five machine learning (ML) predictive algorithms-random forest, stochastic gradient boosting, least absolute shrinkage and selection operator regression, ridge regression, and extreme gradient boosting-to identify the major risk factors affecting male sperm count based on a major health screening database in Taiwan. Unlike traditional multiple linear regression, ML algorithms do not need statistical assumptions and can capture non-linear relationships or complex interactions between dependent and independent variables to generate promising performance. We analyzed annual health screening data of 1375 males from 2010 to 2017, including data on health screening indicators, sourced from the MJ Group, a major health screening center in Taiwan. The symmetric mean absolute percentage error, relative absolute error, root relative squared error, and root mean squared error were used as performance evaluation metrics. Our results show that sleep time (ST), alpha-fetoprotein (AFP), body fat (BF), systolic blood pressure (SBP), and blood urea nitrogen (BUN) are the top five risk factors associated with sperm count. ST is a known risk factor influencing reproductive hormone balance, which can affect spermatogenesis and final sperm count. BF and SBP are risk factors associated with metabolic syndrome, another known risk factor of altered male reproductive hormone systems. However, AFP has not been the focus of previous studies on male fertility or semen quality. BUN, the index for kidney function, is also identified as a risk factor by our established ML model. Our results support previous findings that metabolic syndrome has negative impacts on sperm count and semen quality. Sleep duration also has an impact on sperm generation in the testes. AFP and BUN are two novel risk factors linked to sperm counts. These findings could help healthcare personnel and law makers create strategies for creating environments to increase the country's fertility rate. This study should also be of value to follow-up research.

An improved Wavenet network for multi-step-ahead wind energy forecasting

Accurate multi-step-ahead wind speed (WS) and wind power (WP) forecasting are critical to the scheduling, planning, and maintenance of wind farms. Previous forecasting methods tend to focus on improving forecast accuracy by integrating different models and disaggregating data while neglecting the forecasting ability of basic models. In addition, traditional multi-step-ahead output strategies have limitations that constrain the forecasting capability of models. To overcome the above challenges, this study proposes a novel forecasting model called ED-Wavenet-TF. It adopts two Wavenet networks as Encoder and Decoder connected by the multi-head self-attention mechanism. And, teacher forcing is used as the multi-step-ahead output strategy for WS and WP forecasting. In the training phase, ED-Wavenet-TF uses a portion of the actual data to correct the errors at the intermediate forecasting steps, while in the forecasting phase, it runs through an inference loop to make forecasts. In this study, two WS datasets and two WP datasets are used to validate the performance of ED-Wavenet-TF with univariate input. The results show that compared with Wavenet, the symmetric mean absolute percentage error of ED-Wavenet-TF at four forecasting steps is lower by at least 4.8577% on average for the WS datasets and 8.9463% on average for the WP datasets. The advantages of ED-Wavenert-TF over ten comparable models are confirmed by four evaluation indicators and the Harvey, Leybourne, and Newbold statistical hypothesis test. Moreover, ED-Wavenet-TF is extended to make multi-step-ahead forecasts with multivariate inputs, whose effectiveness is demonstrated on another open WS dataset.

Error State Extended Kalman Filter Localization for Underground Mining Environments

The article addresses the issue of mobile robotic platform positioning in GNSS-denied environments in real-time. The proposed system relies on fusing data from an Inertial Measurement Unit (IMU), magnetometer, and encoders. To get symmetrical error gauss distribution for the measurement model and achieve better performance, the Error-state Extended Kalman Filter (ES EKF) is chosen. There are two stages of vector state determination: vector state propagation based on accelerometer and gyroscope data and correction by measurements from additional sensors. The error state vector is composed of the velocities along the x and y axes generated by combining encoder data and the orientation of the magnetometer around the axis z. The orientation angle is obtained from the magnetometer directly. The key feature of the algorithm is the IMU measurements’ isolation from additional sensor data, with its further summation in the correction step. Validation is performed by a simulation in the ROS (Robot Operating System) and the Gazebo environment on the grounds of the developed mathematical model. Trajectories for the ES EKF, Extended Kalman Filter (EKF), and Unscented Kalman Filter (UKF) algorithms are obtained. Absolute position errors for all trajectories are calculated with an EVO package. It is shown that using the simplified version of IMU’s error equations allows for the achievement of comparable position errors for the proposed algorithm, EKF and UKF.

Forecasting energy consumption demand of customers in smart grid using Temporal Fusion Transformer (TFT)

Energy consumption prediction has always remained a concern for researchers because of the rapid growth of the human population and customers joining smart grids network for smart home facilities. Recently, the spread of COVID-19 has dramatically increased energy consumption in the residential sector. Hence, it is essential to produce energy per the residential customers' requirements, improve economic efficiency, and reduce production costs. The previously published papers in the literature have considered the overall energy consumption prediction, making it difficult for production companies to produce energy per customers' future demand. Using the proposed study, production companies can accurately have energy per their customers' needs by forecasting future energy consumption demands.Scientists and researchers are trying to minimize energy consumption by applying different optimization and prediction techniques; hence this study proposed a daily, weekly, and monthly energy consumption prediction model using Temporal Fusion Transformer (TFT). This study relies on a TFT model for energy forecasting, which considers both primary and valuable data sources and batch training techniques. The model's performance has been related to the Long Short-Term Memory (LSTM), LSTM interpretable, and Temporal Convolutional Network (TCN) models. The model's performance has remained better than the other algorithms, with mean squared error (MSE), root mean squared error (RMSE), and mean absolute error (MAE) of 4.09, 2.02, and 1.50. Further, the overall symmetric mean absolute percentage error (sMAPE) of LSTM, LSTM interpretable, TCN, and proposed TFT remained at 29.78%, 31.10%, 36.42%, and 26.46%, respectively. The sMAPE of the TFT has proved that the model has performed better than the other deep learning models.

Quantification of Physiological Parameters of Rice Varieties Based on Multi-Spectral Remote Sensing and Machine Learning Models

Estimating plant physiological indicators with remote sensing technology is critical for ensuring precise field management. Compared with other remote sensing platforms, low-altitude unmanned aerial vehicles (UAVs) produce images with high spatial resolution that can be used to clearly identify vegetation. However, the information of UAV image data is relatively complex and difficult to analyze, which is the main problem limiting its large-scale use at present. In order to monitor plant physiological indexes from the multi-spectral data, a new method based on machine learning is studied in this paper. Using UAV for deriving the absorption coefficients of plant canopies and whole leaf area, this paper quantifies the effects of plant physiological indicators such as the soil and plant analyzer development (SPAD) value, whole leaf area, and dry matter accumulation on the relationship between the reflectance spectra. Nine vegetation indexes were then extracted as the sensitive vegetation indexes of the rice physiological indicators. Using the SVM model to predict the SPAD value of the plant, the mean squared error (MSE), root mean squared error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and symmetric mean absolute percentage error (SMAPE) values of the model were 1.90, 1.38, 0.13, 0.86, and 4.13, respectively. The results demonstrate that the rice plants display a considerable biochemical and spectral correlation. Using SVM to predict the SPAD value has a better effect because of a better adaptation and a higher accuracy than other models. This study suggests that the multi-spectral data acquired using UAV can quickly estimate field physiological indicators, which has potential in the pre-visual detection of SPAD value information in the field. At the same time, it can also be extended to the detection and inversion of other key variables of crops.

Defocused calibration for large field-of-view binocular cameras

In tunnel boring machine construction sites, on-site calibration of large field-of-view binocular cameras is still a challenging task due to factors such as the narrow spaces of the machines' mechanical structures, high pressure, or falling rocks. Therefore, a calibration method using a small plate in proximity to the camera (a defocused position safe for workers) is proposed in this paper to deal with the above challenges. First, a defocus-insensitive feature point encoding pattern is developed. Then feature points are extracted through a phase recovery network based on the Swin Transformer, and finally camera parameters are optimized based on virtual symmetric transfer errors. The relevant simulation and experimental data show that the relative error between the proposed method and the phase-shift method in feature extraction is 0.15 pixels, while the relative error between the proposed method and a high-precision laser tracker in three-dimensional measurement is 1.3%. The results demonstrate the feasibility of the method in a large field-of-view binocular camera for tunnel boring machine construction sites. Increasing the diversity of data sets and lightweight models will be the focus of future research.

Missing data reconstruction in attitude for quadrotor unmanned aerial vehicle based on deep regression model with different sensor failures

Forming a UAV cluster with multiple UAVs to collaborate in accomplishing tasks is the future development of battlefield. The UAV cluster can collaborate by communicating through inter-aircraft links and can quickly and accurately perform complex tasks such as path planning, collaborative reconnaissance, collaborative sensing and attack. In the process of Unmanned Aerial Vehicle (UAV) cooperative operation, obtaining the real-time attitude information of each UAV is preliminary to implement collaborative cooperation. However, in practice, due to the internal malfunction of sensors and mutual interference among UAVs, the acquired attitudes often suffer from data missing. This paper proposed a novel missing data reconstruction method for UAV’s attitude in the case of sensor failures. The attitude data of UAV is obtained through an advanced UAV simulation platform AirSim. Through fusing the temporal convolutional network (TCN) and Bi-directional long short-term memory (Bi-LSTM), a deep regression framework is established for missing data construction. In addition, we evaluate the reliability of the proposed method by comparing with different baseline models and different combinations of data missing. The performance of our method is quantified using metrics of root-mean-square-error (RMSE), mean absolute error (MAE), determination coefficient (DC), mean absolute percentage error (MAPE), and symmetric mean absolute percentage error (SMAPE) score. The averaged performance values of our proposed method outperform other baseline algorithms. The results of the experiment show that the study could well-address the issue of missing data reconstruction and provide reliable attitude data.

PERBANDINGAN METODE HOLT WINTER’S EXPONENTIAL SMOOTHING DAN EXTREME LEARNING MACHINE UNTUK PERAMALAN JUMLAH BARANG YANG DIMUAT PADA PENERBANGAN DOMESTIK DI BANDARA UTAMA SOEKARNO HATTA

The loading of goods carried out at the airport is an essential part of the transporting goods system. In this regard, it is necessary to have a prediction to make the right policy or to solve the problems that occur. Holt Winter's Exponential Smoothing, which one of the classic methods of analyzing time series data, and Extreme Learning Machine which is part of the artificial neural network method, are methods that can be used as a tool for forecasting problems. Holt Winter's Exponential Smoothing uses three times of smoothing on related data, which are level smoothing, trend smoothing, and season smoothing, while Extreme Learning Machine goes through three stages, which are normalization, training, and denormalization. In measuring the error rate in related forecasting, the symmetric Mean Absolute Percentage Error (sMAPE) value is used. The Holt Winter's Exponential Smoothing method Additive model produces a sMAPE value of 26.14%; while the Multiplicative model with the same method resulted in the sMAPE value of 25.69%. For the Extreme Learning Machine method, the sMAPE value is 49.85%. Based on the accuracy test using the sMAPE value, Holt Winter's Exponential Smoothing method Multiplicative model is the better method than Extreme Learning Machine

Heterogeneous Traffic Flow Detection Using CAV-Based Sensor With I-GAIN

This study proposes using connected automatic vehicles (CAVs) as traffic flow detectors to collect and exchange traffic flow data for heterogeneous traffic management and control. The proposed method includes the construction of a mathematical matrix to represent the status of the road section, the use of unsupervised machine learning to evaluate traffic data, and an improved generative adversarial imputation net (GAIN) to evaluate and impute missing traffic data. Next-generation simulation (NGSIM) data are used to verify the accuracy and robustness of the proposed method. One of the primary innovations of this study is the use of GAIN, a deep learning framework based on generative adversarial networks (GANs), to impute missing traffic data. GAIN has been shown to be more robust and stable when handling incomplete heterogeneous data than existing imputation methods. Additionally, this study contributes to the field by proposing the use of CAVs as sensors to detect mixed traffic flow, which could lead to more efficient and accurate traffic management and control. Experimental results demonstrate that the proposed method outperforms existing imputation methods, with a normalized root mean squared error and symmetric mean absolute percentage error of less than 0.2/0.3 and 0.08/0.13 in I-80 and Lankershim Boulevard, respectively. The findings of this study have important implications for the development and implementation of connected and automated vehicle technologies in the field of transportation.

The Golem: A General Data-Driven Model for Oil & Gas Forecasting Based on Recurrent Neural Networks

Oil & gas forecasting is one of the most critical issues in reservoir management. Physics-based simulations are the most common models used for production forecasts in oilfields. Previous works based on Machine Learning (ML) developed models focused on the oil rate as unique target variable, a forecasting by one-day output, and just one class of reservoir (synthetic or actual). This work introduces a general data-driven model based on Recurrent Neural Networks to forecast an adaptive sequence of timestamps for the complete production rates (oil, gas, and water), and we also included the wellbore pressure as target variable, for both classes of reservoirs as actual as synthetic. The first dataset was obtained from the synthetic benchmark UNISIM-II-H, which simulates a carbonate reservoir in the Brazilian pre-salt; the second dataset is from an actual reservoir, the Volve oilfield, a decommissioned reservoir in the Norwegian North Sea. The forecasting is calculated using an input sequence of daily values from the historical record of the production rates and the pressure; the output is also a set of the values to the next sequence of days for one selected production variable (oil, gas, water, or pressure). The size of both input and output sets is adaptive and its adjustment depends on the dataset size and the production time. We built the model and compared it between the Long Short-Term Memory (LSTM) and the Gated Recurrent Unit (GRU) implementations. We tuned the architectural parameters of the model, the input size of historical records, and the output forecasting days. We performed the training/testing procedures with several sizes for the training dataset from the target wellbore and tested with the remaining data to evaluate the model stability. We adopted the Symmetric Mean Absolute Percentage Error (SMAPE) and the coefficient of determination r-square (R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) metrics to compare our forecasting values to the production rates and the pressure, most of the results for both synthetic and actual oilfields exhibited that the model can follow an accurate trend of the production rates and the pressure; and the output values are approximated. Forecasting values from the designed model exhibited closer values when compared to the expected data from the wellbores in most of the experiments, some cases exhibited an SMAPE lower than 2 and R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> up to 0.99. The model can learn the behavior of each production variable according to the training set and the forecasting output can be adapted for a set of several timestamps.

Efficient 2D Mapping for Reversible Data Hiding

After the prediction, how to modify the 2D prediction error histogram (PEH) for reversible data hiding (RDH) is an important issue. In this letter, we propose an efficient 2D mapping strategy by considering the error pairs on two diagonal lines of the 2D PEH. The proposed 2D mapping can quickly adapt to the frequencies of the error pairs for different mapping area sizes. As a bonus, a satisfactory embedding performance can be achieved since in each group of two symmetrical error pairs the one with larger frequencies has priority to select more mapping ways. Experimental results have shown that it is low time-consuming and achieves better embedding performance in comparison with several classical and advanced 2D mappings.