Recurrent Unit Network Research Articles

SMS Spam Detection System Based on Deep Learning Architectures for Turkish and English Messages

Short Message Service (SMS) still continues its existence despite the emergence of different messaging services. It plays a part in our lives as a communication service. Companies use SMS for advertisement purposes due to the fact that e-mail filtering systems have rooted, short message systems are being undersold by the operators, and spam detection and blocking systems used for short messages are ineffective. Individuals falling victim to SMS spam messages sent by malevolent persons incur pecuniary and non-pecuniary losses. The aim of this study is to present a hybrid model proposal with the intention of detecting SMS spam messages. This detection model uses a gated recurrent unit (GRU) and convolutional neural network (CNN) as two deep learning methods. However, the fact that both algorithms require high memory capacities is a limitation. The design for this model was laid out by using two different datasets containing combined text messages written in the Turkish and English languages. The datasets used in the study are TurkishSMSCollection and the SMS Spam dataset from the UCI database. The testing process was performed on the dataset through benchmarking as well as other machine learning algorithms. It was revealed in the study that the hybrid CNN + GRU approach attained an accuracy of 99.07% by demonstrating a better performance compared to the other algorithms.

Bi-Level Interturn Short-Circuit Fault Monitoring for Wind Turbine Generators With Benchmark Dataset Development

Abstract Flourished wind energy market pushes the latest wind turbines (WTs) to further and harsher inland and offshore environment. Increased operation and maintenance cost calls for more reliable and cost effective condition monitoring systems. In this article, a bi-level condition monitoring framework for interturn short-circuit faults (ITSCFs) in WT generators is proposed. A benchmark dataset, consisting of 75 ITSCF scenarios and generator current signals of a specific WT, has been created and made publicly available on Zenodo. The data are simulated at a rate of 4 kHz. Based on the time and frequency features extracted from data processing, machine learning-based severity estimation and faulty phase identification modules can provide valuable diagnostic information for wind farm operators. Specifically, the performance of long short-term memory (LSTM) networks, gated recurrent unit (GRU) networks, and convolutional neural networks (CNNs) are analyzed and compared for severity estimation and faulty phase identification. For test-bed experimental reference, various numbers of scenarios for training the models are analyzed. Numerical experiments demonstrate the computational efficiency and robust denoising capability of the CNN algorithm. The GRU network, however, achieves the highest accuracy. The overall system performance improves significantly, from 87.76% with 16 training scenarios to 99.95% with 52 training scenarios, when tested on a set containing all 76 scenarios from an unforeseen period.

Detecting student attention through electroencephalography signals: a comparative analysis of deep learning models

<span lang="EN-MY">In the landscape of educational technology, understanding and optimizing student attention is important to enhance student’s learning experience. This study explores the potential of using electroencephalography (EEG) signals for discerning students' attention levels during educational tasks. With a cohort of 30 participants, EEG data were meticulously collected and subjected to robust preprocessing techniques, including independent component analysis (ICA) and principal component analysis (PCA). The research then employed different deep learning algorithm such as long short-term memory (LSTM), recurrent neural network (RNN), gated recurrent unit (GRU), multi-layer perceptron (MLP), and convolutional neural network (CNN) classifiers to predict students' attention. The results reveal notable variations in the classifiers' predictive performance. Our finding revealed that the LSTM model emerged as the top performer and achieved 96% of the accuracy. This study not only contributes to the advancement of attention detection in educational technology but also underscores the importance of preprocessing methodologies, such as ICA and PCA, in optimizing the performance of deep learning models for EEG-based applications.</span>

SOC Estimation of a Lithium-Ion Battery at Low Temperatures Based on a CNN-Transformer and SRUKF

As environmental regulations become stricter, the advantages of pure electric vehicles over fuel vehicles are becoming more and more significant. Due to the uncertainty of the actual operating conditions of the vehicle, accurate estimation of the state-of-charge (SOC) of the power battery under multi-temperature scenarios plays an important role in guaranteeing the safety, economy, and reliability of electric vehicles. In this paper, a SOC estimation method based on the fusion of convolutional neural network-transformer (CNN-Transformer) and square root unscented Kalman filter (SRUKF) for lithium-ion batteries in low-temperature scenarios is proposed. First, the CNN-Transformer base model is established. Then, the SRUKF algorithm is used to update the state of the Coulomb counting method results based on the base model results. Finally, ensemble learning theory is applied to estimate SOC in multi-temperature scenarios. Data is obtained from laboratory conditions at −20 °C, −7 °C, and 0 °C. The experimental results show that the SOC estimation method proposed in this study is stable in terms of the root mean square error (RMSE) being between 2.69% and 4.22%. The proposed base model is also compared with the long short-term memory (LSTM) network and gated recurrent unit (GRU) network to demonstrate its relative advantages.

Intelligent Dynamic Trajectory Planning of UAVs: Addressing Unknown Environments and Intermittent Target Loss

Precise trajectory planning is crucial in terms of enabling unmanned aerial vehicles (UAVs) to execute interference avoidance and target capture actions in unknown environments and when facing intermittent target loss. To address the trajectory planning problem of UAVs in such conditions, this paper proposes a UAV trajectory planning system that includes a predictor and a planner. Specifically, the system employs a bidirectional Temporal Convolutional Network (TCN) and Gated Recurrent Unit (GRU) network algorithm with an adaptive attention mechanism (BITCN-BIGRU-AAM) to train a model that incorporates the historical motion trajectory features of the target and motion intention the inferred by a Dynamic Bayesian Network (DBN). The resulting predictions of the maneuvering target are used as terminal inputs for the planner. An improved Radial Basis Function (RBF) network is utilized in combination with an offline–online trajectory planning method for real-time obstacle avoidance trajectory planning. Additionally, considering future practical applications, the predictor and planner adopt a parallel optimization and correction algorithm structure to ensure planning accuracy and computational efficiency. Simulation results indicate that the proposed method can accurately avoid dynamic interference and precisely capture the target during tasks involving dynamic interference in unknown environments and when facing intermittent target loss, while also meeting system computational capacity requirements.

Enhancing Facial Recognition: A Comprehensive Review of Deep Learning Approaches and Future Perspectives

This paper presents a comprehensive review of the application of deep learning in facial recognition, covering fundamental aspects from neural network architectures to advanced training methods. It starts with an introduction to the basic architectures such as Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs), including variations like Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) networks. The review extends to sophisticated architectures like AlexNet, GoogleNet, VGGNet, and ResNet, which have significantly pushed the boundaries of accuracy in face recognition tasks. The paper details the process of data preprocessing in face recognition, which involves critical steps such as face detection, alignment, and normalization to ensure uniformity in the input data, enhancing the accuracy of feature extraction. Various feature extraction methods are discussed, including CNN-based and Generative Adversarial Network (GAN)-based techniques, which have shown considerable promise in deriving complex facial features from raw images. Loss functions such as Euclidean distance loss, angular/cosine margin loss, and softmax loss variants are explored to understand their impact on enhancing the discriminative power of the facial recognition systems. The paper highlights the evolution from traditional models using eigenfaces and feature descriptors like Local Binary Patterns (LBP) to cutting-edge deep learning models that utilize deep identity features (DeepID) and triplet loss functions to improve recognition accuracy.

Deep Learning-Enhanced Autoencoder for Multi-Carrier Wireless Systems

In a multi-carrier (MC) system, the transmitted data are split across several sub-carriers as a crucial approach for achieving high data rates, reliability, and spectral efficiency. Deep learning (DL) enhances MC systems by improving signal representation, leading to more efficient data transmission and reduced bit error rates. In this paper, we propose an MC system supported by DL for operation on fading channels. Deep neural networks are utilized to model the modulation block, while a gated recurrent unit (GRU) network is used to model the demodulation blocks, acting as the encoder and decoder within an autoencoder (AE) architecture. The proposed scheme, known as MC-AE, differs from existing AE-based systems by directly processing channel state information and the received signal in a fully data-driven way, unlike traditional methods that rely on channel equalizers. This approach enables MC-AE to improve diversity and coding gains in fading channels by simultaneously optimizing the encoder and decoder. In this experiment, we evaluated the performance of the proposed model under both perfect and imperfect channel conditions and compared it with other models. Additionally, we assessed the performance of the MC-AE system against index modulation-based MC systems. The results demonstrate that the GRU-based MC-AE system outperforms the others.

Attention model of EEG signals based on reinforcement learning.

Applying convolutional neural networks to a large number of EEG signal samples is computationally expensive because the computational complexity is linearly proportional to the number of dimensions of the EEG signal. We propose a new Gated Recurrent Unit (GRU) network model based on reinforcement learning, which considers the implementation of attention mechanisms in Electroencephalogram (EEG) signal processing scenarios as a reinforcement learning problem. The model can adaptively select target regions or position sequences from inputs and effectively extract information from EEG signals of different resolutions at multiple scales. Just as convolutional neural networks benefit from translation invariance, our proposed network also has a certain degree of translation invariance, making its computational complexity independent of the EEG signal dimension, thus maintaining a lower learning cost. Although the introduction of reinforcement learning makes the model non differentiable, we use policy gradient methods to achieve end-to-end learning of the model. We evaluated our proposed model on publicly available EEG dataset (BCI Competition IV-2a). The proposed model outperforms the current state-of-the-art techniques in the BCI Competition IV- 2a dataset with an accuracy of 86.78 and 71.54% for the subject-dependent and subject-independent modes, respectively. In the field of EEG signal processing, attention models that combine reinforcement learning principles can focus on key features, automatically filter out noise and redundant data, and improve the accuracy of signal decoding.

Learning extreme vegetation response to climate drivers with recurrent neural networks

Abstract. The spectral signatures of vegetation are indicative of ecosystem states and health. Spectral indices used to monitor vegetation are characterized by long-term trends, seasonal fluctuations, and responses to weather anomalies. This study investigates the potential of neural networks in learning and predicting vegetation response, including extreme behavior from meteorological data. While machine learning methods, particularly neural networks, have significantly advanced in modeling nonlinear dynamics, it has become standard practice to approach the problem using recurrent architectures capable of capturing nonlinear effects and accommodating both long- and short-term memory. We compare four recurrent-based learning models, which differ in their training and architecture for predicting spectral indices at different forest sites in Europe: (1) recurrent neural networks (RNNs), (2) long short-term memory networks (LSTMs), (3) gated recurrent unit networks (GRUs), and (4) echo state networks (ESNs). While our results show minimal quantitative differences in their performances, ESNs exhibit slightly superior results across various metrics. Overall, we show that recurrent network architectures prove generally suitable for vegetation state prediction yet exhibit limitations under extreme conditions. This study highlights the potential of recurrent network architectures for vegetation state prediction, emphasizing the need for further research to address limitations in modeling extreme conditions within ecosystem dynamics.

Abstract 4136550: In-hospital cardiac arrest can be detected by Innovative smart healthcare syste

Background: Predicting in-hospital cardiac arrest (IHCA) is crucial for preventing patient fatalities. However, it remains challenging due to the irregularities in time series data across various features. Previous studies relied on traditional medical scoring systems, but their accuracy was limited as the models were overly simplistic. Recent research using machine learning methods has shown improved results. In our work, we employ deep learning and time series approaches, which are considered the most powerful models for addressing complex problems in recent years. Method/Research Design: The cohort study took place in a hospital in Taiwan from January 2016 to August 2022, involving 252,000 patients in general wards. Input data encompassed basic information, vital signs, Glasgow Coma Scale scores, medication, etc., to predict IHCA occurrences within 24 hours. Given the immediacy of IHCA events, we utilized left alignment to handle time series. Evaluation metrics included the area under the receiver operating characteristic curve (AUROC). Results: We compared three types of settings. The first was based on scoring systems, where the national early warning system (NEWS) achieved an AUROC of 0.756, and the modified early warning score (MEWS) reached 0.653. In the next setting, based on the data summary within a given time interval, the machine learning models XGBoost and deep learning model TabNet achieved AUROCs of 0.863 and 0.839, respectively. This indicates that machine learning outperforms traditional medical methods. The final setting involved time series analysis, where XGBoost and the Gate Recurrent Unit (GRU) network achieved 0.848 and 0.904, respectively, surpassing all previous settings. Conclusion: Our study demonstrates that learning-based methods outperform rule-based methods in predicting IHCA events. Machine learning algorithms offer more possibilities and have the potential to address complex problems effectively. Moreover, considering time series data rather than summarizing within fixed intervals preserves information and leads to better scores. Leveraging the time series deep learning method, GRU shows promising potential in significantly reducing the risk of IHCA events.

LLM GPT-3.5 study for sentiment analysis across Utkarsh server, Ohio supercomputer, Google Colab and PC

The major objective of the present research is to inspect sentiment analysis models that have been trained on Twitter corpus by utilising the Large Language Model (LLM) gpt-3–5-turbo-16k version of the Generative Pretrained Transformer (GPT 3.5) model. Such trained models include the Bidirectional long short-term memory neural network (BiLSTM), Convolutional Neural Networks, Gated Recurrent Unit and Recurrent Neural Network which were used to perform computational tasks on the Ohio Supercomputer and Utkarsh Server, in comparison to work conducted on Google Colab and a Personal Computer (PC).This research also looks at the performance as well as the computational aspects of these models in terms of accuracy, recall, F1-score, time/memory complexity and resource requirements (CPU/GPU) throughout the training and testing phases of each model. The training accuracies in this case were concentrated between 49.91 % and 99.98 % while those of the testing accuracies of the models accounts for about 50.00–75.00 %. For instance, models including BiLSTM and RNN usually exhibit more time complexity because of the nature of the models (sequential computation), on the contrary, CNNs are less time-consuming and are more effective in terms of storage modifying layered architecture. The use of supercomputers and specialized servers reduces training time, but resource constraints on platforms such as personal computers or Colab cause considerable divergence.

Advanced obstacle recognition and trajectory prediction for autonomous vehicles using 3D CNN and GRU

Abstract. Recent years have seen a rapid advancement in new energy vehicle technology, which has increased consumer demand for autonomous driving systems. However, current self-driving cars still face many technical barriers. Obstacle detection and obstacle trajectory prediction in dynamic environments is one of the main difficulties of the technique. To improve self-driving cars' capacity for route planning and decision-making in dynamic contexts, this thesis proposes an obstacle identification and trajectory prediction model that combines a gated recurrent unit (GRU) network with a three-dimensional convolutional neural network (3D CNN). The integrated framework utilises the feature recognition capability of 3D CNN and the prediction capability of GRU to accurately predict dynamic obstacles, thereby improving the performance of the model in various types of environments (e.g., visual SLAM). Experimental results based on publicly available datasets (e.g., KITTI and Argoverse) show that the proposed method has significant advantages in dynamic obstacle identification and prediction as well as overall model operation efficiency. The findings show that the integrated framework is useful and successful in advancing the creation of self-driving automobiles.

Prediction of Lithium-Ion Battery Health Using GRU-BPP

Accurate prediction of lithium-ion batteries’ (LIBs) state-of-health (SOH) is crucial for the safety and maintenance of LIB-powered systems. This study addresses the variability in degradation trajectories by applying gated recurrent unit (GRU) networks alongside principal component analysis (PCA), Granger causality, and K-means clustering to analyze the relationships between operating conditions—such as temperature and load profiles—and battery performance degradation. This paper uses a publicly accessible dataset derived by aging three prismatic LIB cells under a realistic forklift operation profile. First, we identify the features that are relevant to driving variance, then we employ the winning algorithm of K-means clustering for the classification of operational states. Granger causality later investigates the inter-group relationships. Our GRU-BPP model achieves an RMSE value of 0.167 and an MAE of 0.129 for the reference performance testing (RPT) dataset and an RMSE of 0.032 with an MAE of 0.025 for the aging dataset, thus outperformed benchmark methods such as GRU, LME, and XGBoost. These results further enhance the predictiveness and robustness of this approach and yield a holistic solution to the conventional challenges in battery management and their remaining useful life (RUL) predictions.

Technical Analysis of the Indonesian Stock Market with Gated Recurrent Unit and Temporal Convolutional Network

Big data is essential in the age of 4.0 industry as it becomes the basis of decision making. Deep learning research in the last few years has been proven effective in understanding complex big data patterns, especially in the finance sector. The rapid growth of the Indonesian stock market in the last 20 years, which was driven by globalization, prompted fluctuation in the Bursa Efek Jakarta (JKSE) which was influenced by stock prices, commodity prices, and exchange rate. This study identifies the main indicators of Indonesian stock market crisis, applies and compares deep learning models, particularly Gated Recurrent Unit (GRU) and Temporal Convolutional Network (TCN), in predicting stock prices. This study identified 20 JKSE crisis points between the 2002-2023 period with average return value at around -6%. All variables correlated positively with JKSE, with SET.BK as the highest correlated variable in lag 0. The American and European stock market, commodity price, and exchange rate tend to show a pattern opposite to the JKSE crisis. Predictor variables such as STI, HIS, KLSE, KS11, SET.BK, PSEI.PS, RUT, and USDIDR are chosen based on significant cross correlation and average return plot. Hyperparameter tuning and cross validation within a 3 years window concluded that the GRU model is accurate and efficient, with RMSE value at 43.35568 and MAE value at 33.66909 in the validation data.

State of charge estimation for lithium-ion batteries based on Gated Recurrent Unit neural network and an Adaptive Unscented Kalman Filter

Abstract For battery management systems, the accurate estimation of the state of charge (SOC) of lithium-ion batteries is crucial, yet it still poses challenges. Traditional model-based filtering methods typically require accurate battery models, but parameter uncertainties arise from various factors such as battery aging and temperature variations, leading to parameter uncertainties. In contrast, data-driven approaches can effectively capture SOC variations under different operating conditions and temperatures, but often exhibit significant prediction fluctuations. To address these challenges, a combined SOC estimation approach known as GRU-AUKF is presented in this paper. This method utilizes Gated Recurrent Unit (GRU) networks based on temperature, current, and voltage to estimate SOC, followed by filtering the output using an Adaptive Unscented Kalman Filter (AUKF) to reduce estimating errors. Experimental results demonstrate that when estimating battery SOC across different temperatures ranging from 0°C to 50°C, the RMSE is less than 1.68%, and the MAE is less than 1.44%. Compared to methods solely employing GRU models, the proposed GRU-AUKF method exhibits superior performance in enhancing estimation accuracy, thus validating its effectiveness.

Automated rice mapping using multitemporal Sentinel-1 SAR imagery using dynamic threshold and slope-based index methods

Rice cultivation plays a crucial role in food security and economic development, particularly in regions like India, due to its vast population and position as the top rice producer globally. This work introduces a novel framework, the Rice Mapping Method (RMM), which leverages Multitemporal Sentinel-1 Synthetic Aperture Radar (SAR) imagery for automated rice mapping. Contrary to the traditional approaches, RMM combines the Dynamic Threshold Method (DTM) for robust rice field identification and a slope-based index for classifying single and double cropping practices. By analyzing VH backscatter patterns and employing specific thresholds, DTM separates rice pixels from the other background pixels. The DTM, which relies on VH backscatter values during the growing season, has been tested across various rice cultivation landscapes, demonstrating high accuracy upto 0.95. DTM is also tested on different rice-growing areas such as the hilly Kodagu district, with an F1 Score of 0.96, and in the flooded delta region of Kuttanad, achieving an F1 Score of 0.93. The Slope-based Index I(r,c) is introduced to differentiate the single and double cropping pixels by calculating the index for the second season of cropping and gives F1 Score of 0.81. The DTM’s effectiveness in rice field identification is evaluated by comparing it to the classification of the Bi-directional Gated Recurrent Unit (Bi-GRU) network. Similarly, the Slope-based Index is compared with other established automated rice mapping methods to assess its accuracy in distinguishing cropping patterns. RMM was successfully applied in mapping rice-growing areas in the Udupi district for 2021, estimating Kharif and Rabi season areas, the estimated rice area is compared to official statistics by the Directorate of Economics and Statistics, Karnataka State. The proposed RMM approach offers a robust solution for mapping rice fields, particularly in regions with complex cropping landscapes, and enhances agricultural monitoring and decision-making processes contributing to sustainable rice production and food security initiatives.

Short-Term Prediction Model of Wave Energy Converter Generation Power Based on CNN-BiLSTM-DELA Integration

Wave energy is a promising source of sustainable clean energy, yet its inherent intermittency and irregularity pose challenges for stable grid integration. Accurate forecasting of wave energy power is crucial for reliable grid management. This paper introduces a novel approach that utilizes a Bidirectional Gated Recurrent Unit (BiGRU) network to fit the power matrix, effectively modeling the relationship between wave characteristics and energy output. Leveraging this fitted power matrix, the wave energy converter (WEC) output power is predicted using a model that incorporates a Convolutional Neural Network (CNN), a Bidirectional Long Short-Term Memory (BiLSTM) network, and deformable efficient local attention (DELA), thereby improving the accuracy and robustness of wave energy power prediction. The proposed method employs BiGRU to transform wave parameters into power outputs for various devices, which are subsequently processed by the CNN-BiLSTM-DELA model to forecast future generation. The results indicate that the CNN-BiLSTM-DELA model outperforms BiLSTM, CNN, BP, LSTM, CNN-BiLSTM, and GRU models, achieving the lowest mean squared error (0.0396 W) and mean absolute percentage error (3.7361%), alongside the highest R2 (98.69%), underscoring its exceptional forecasting accuracy. By enhancing power forecasting, the method facilitates effective power generation dispatch, thereby mitigating the adverse effects of randomness on the power grid.

Indoor Pedestrian Positioning Method Based on Ultra-Wideband with a Graph Convolutional Network and Visual Fusion.

To address the challenges of low accuracy in indoor positioning caused by factors such as signal interference and visual distortions, this paper proposes a novel method that integrates ultra-wideband (UWB) technology with visual positioning. In the UWB positioning module, the powerful feature-extraction ability of the graph convolutional network (GCN) is used to integrate the features of adjacent positioning points and improve positioning accuracy. In the visual positioning module, the residual results learned from the bidirectional gate recurrent unit (Bi-GRU) network are compensated into the mathematical visual positioning model's solution results to improve the positioning results' continuity. Finally, the two positioning coordinates are fused based on particle filter (PF) to obtain the final positioning results and improve the accuracy. The experimental results show that the positioning accuracy of the proposed UWB positioning method based on a GCN is less than 0.72 m in a single UWB positioning, and the positioning accuracy is improved by 55% compared with the Chan-Taylor algorithm. The proposed visual positioning method based on Bi-GRU and residual fitting has a positioning accuracy of 0.42 m, 71% higher than the Zhang Zhengyou visual positioning algorithm. In the fusion experiment, 80% of the positioning accuracy is within 0.24 m, and the maximum error is 0.66 m. Compared with the single UWB and visual positioning, the positioning accuracy is improved by 56% and 52%, respectively, effectively enhancing indoor pedestrian positioning accuracy.

GRU-IKF scene taxiing trajectory prediction model based on attention mechanism

Aircraft taxi trajectory prediction helps solve operational problems such as airport taxiing conflicts and long waiting times, ensuring airport safety while improving service levels and increasing airport throughput. In view of the fact that the performance of machine learning models depends on good data sets, a method for predicting taxi trajectories of aircraft on the ground based on attention mechanism, fusion of gated recurrent unit (GRU) and improved Kalman filter algorithm (IKF) is proposed. Firstly, three independent gated recurrent unit networks are used to capture the motion state and temporal dependency of aircraft at future moments, and the attention mechanism is introduced to enhance the ability to extract data difference features and learn the mapping relationship from input to output; then, it is fused with the improved extended Kalman filter to integrate the output results of the neural network into the state prediction and update process to improve the accuracy of the predicted trajectory sequence. Finally, the effectiveness of the model was verified using the actual taxiing trajectory of aircraft at Lukou Airport. The simulation results show that the model can effectively and accurately predict the taxiing trajectory of aircraft on the surface, with an overall mean square error of about 0.00128. Compared with the single recurrent neural network (RNN), long short-term memory network (LSTM) and GRU model, the RMSE is reduced by 72.9%and respectively 39.9%, 54.7%and the prediction time is 40 ms. It can accurately and quickly predict the taxiing trajectory, which helps to reduce the operating load of the airport surface management system.

Physical information-guided multidirectional gated recurrent unit network fusing attention to solve the Black-Scholes equation

Reasonable option pricing is crucial in the financial derivatives market. Finding analytical solutions for the Black-Scholes (BS) equation, particularly for American options or with fluctuating volatility and interest rates, is challenging. BS equations exhibit strong time-series characteristics, with asset prices typically adhering to geometric Brownian motion. To address the BS equations, we propose a sequence-to-sequence model guided by physical information (PI), called PiMGA. The PiMGA fuses a multidirectional gated recurrent unit (GRU) network with an attention module, where multidirectional GRU enhances the coding performance of the input sequences and the attention module balances the feature weights of the hidden variables. Prior physical knowledge in BS equations is jointly used as a constraint, forming the penalty function for objective optimization. This allows PiMGA to serve as an efficient approximation function in the learning paradigm of physically informed machine learning to solve BS equations. BS equations with various complexities illustrate the accuracy and feasibility of PiMGA for numerical solutions. Furthermore, the out-of-distribution generalization ability of PiMGA is verified by predicting the Nasdaq 100 index.