Bayesian Learning Algorithm Research Articles

Bayesian additive regression trees for predicting childhood asthma in the CHILD cohort study

BackgroundAsthma is a heterogeneous disease that affects millions of children and adults. There is a lack of objective gold standard diagnosis that spans the ages; instead, diagnoses are made by clinician assessment based on a cluster of signs, symptoms and objective tests dependent on age. Yet, there is a clear morbidity associated with chronic asthma symptoms. Machine learning has become a popular tool to improve asthma diagnosis and classification. There is a paucity of literature on the use of Bayesian machine learning algorithms to predict asthma diagnosis in children. This paper develops a prediction model using the Bayesian additive regression trees (BART) and compares its performance to various machine learning algorithms in predicting the diagnosis of childhood asthma.MethodsClinically relevant variables collected at or before 3 years of age from 2794 participants in the CHILD Cohort Study were used to predict physician-diagnosed asthma at age 5. BART and six other commonly used machine learning algorithms, namely adaptive boosting, logistic regression, decision tree, neural network, random forest, and support vector machine were trained. Measures of performance including sensitivity, specificity, and area under the receiver operating characteristic (ROC) curve were calculated. The confidence intervals were calculated using Bootstrapping samples. Important predictors and interaction effects associated with asthma were also identified using BART.ResultsBART, logistic regression and random forest showed the highest area under the ROC curve compared to other machine learning algorithms. Based on BART, recurrent wheeze, respiratory infection and food sensitization at 3 years of age were the most important predictors. The three most important interaction effects were found to be interaction terms of respiratory infection at 3 years and recurrent wheezing at 3 years, maternal asthma and paternal asthma, and maternal wheezing and inhalant sensitization of child at 3 years.ConclusionsBART demonstrated promising prediction performance when compared to other machine learning algorithms. Future research could validate the BART in an external cohort to evaluate its reliability and generalizability.

A fast temporal multiple sparse Bayesian learning-based channel estimation method for time-varying underwater acoustic OFDM systems

In this paper, a fast temporal multiple sparse Bayesian learning (FTMSBL)-based channel estimation method for underwater acoustic (UWA) orthogonal frequency division multiplexing (OFDM) systems is proposed, which is optimized using the fast marginalized likelihood maximization method. The algorithm fully uses the consistent sparse structure and time-domain correlation properties of channels to improve the reconstruction performance and computational efficiency, offering better performance and higher computational efficiency than the traditional Bayesian learning algorithms. At the same time, the FTMSBL algorithm does not require computing the inverse of large matrices and consumes very little storage resources in the operation, making it suitable for hardware implementation. Simulation and sea trial results show that the FTMSBL-based underwater channel estimation algorithm achieves higher channel estimation accuracy than the orthogonal matching tracking algorithm, and the system bit error rate (BER) is significantly reduced; specifically, the FTMSBL algorithm can achieve optimal performance in strong time-dependent channels.

Development of a Bayesian Deep Learning algorithm using multicentre pre-anaesthesia assessment data to predict surgical duration, blood loss, and patient placement (the Pre-Anesthesia AI Tool)

Development of a Bayesian Deep Learning algorithm using multicentre pre-anaesthesia assessment data to predict surgical duration, blood loss, and patient placement (the Pre-Anesthesia AI Tool)

A TMSBL underwater acoustic channel estimation method based on dictionary learning denoising

The shallow sea underwater acoustic channel exhibits a significant sparse multipath structure. The temporally multiple sparse Bayesian learning (TMSBL) algorithm can effectively estimate this sparse multipath channel. However, the complexity of the algorithm is high, the signal-to-noise ratio (SNR) of shallow-sea underwater acoustic communication is low, and the estimation performance of the TMSBL algorithm is greatly affected by noise. To address this problem, an improved TMSBL underwater acoustic channel estimation method based on a dictionary learning noise reduction algorithm is proposed. Firstly, the K-Singular Value Decomposition (K-SVD) dictionary learning method is used to reduce the noise of the received pilot matrix, reducing the influence of noise on the signal. Then, the Generalized Orthogonal Matching Pursuit (GOMP) channel estimation method is combined to obtain a priori information such as the perceptual matrix and hyperparameter matrix for TMSBL channel estimation; and the noise variance is obtained by using the null subcarrier calculation instead of iteratively updating the noise variance in the TMSBL, to improve the estimation accuracy and reduce the algorithmic complexity. Finally, the TMSBL channel estimation method is used to estimate the underwater acoustic channels of different symbols jointly. The simulation results show that the normalized mean square error of the channel estimation of the improved TMSBL method is reduced by about 92.2% compared with the TMSBL algorithm, obtaining higher estimation accuracy; running time is reduced by about 45.6%, and there is also better performance in terms of the running speed, which provides a reference for underwater acoustic channel estimation.

Off-Grid Underwater Acoustic Source Direction-of-Arrival Estimation Method Based on Iterative Empirical Mode Decomposition Interval Threshold.

To solve the problem that the hydrophone arrays are disturbed by ocean noise when collecting signals in shallow seas, resulting in reduced accuracy and resolution of target orientation estimation, a direction-of-arrival (DOA) estimation algorithm based on iterative EMD interval thresholding (EMD-IIT) and off-grid sparse Bayesian learning is proposed. Firstly, the noisy signal acquired by the hydrophone array is denoised by the EMD-IIT algorithm. Secondly, the singular value decomposition is performed on the denoised signal, and then an off-grid sparse reconstruction model is established. Finally, the maximum a posteriori probability of the target signal is obtained by the Bayesian learning algorithm, and the DOA estimate of the target is derived to achieve the orientation estimation of the target. Simulation analysis and sea trial data results show that the algorithm achieves a resolution probability of 100% at an azimuthal separation of 8° between adjacent signal sources. At a low signal-to-noise ratio of -9 dB, the resolution probability reaches 100%. Compared with the conventional MUSIC-like and OGSBI-SVD algorithms, this algorithm can effectively eliminate noise interference and provides better performance in terms of localization accuracy, algorithm runtime, and algorithm robustness.

A Kronecker product accelerated efficient sparse Gaussian Process (E-SGP) for flow emulation

In this paper, we introduce an efficient sparse Gaussian process (E-SGP) for the surrogate modelling of fluid mechanics. This novel Bayesian machine learning algorithm enables efficient model training using databases of different structures. It extends the approximated sparse GP algorithm by combining the concept of efficient GP (E-GP) and variational energy free sparse Gaussian processes (VEF-SGP). The developed E-SGP approach leverages the arbitrariness of inducing points and the monotonically increasing nature of the objective function with respect to the number of inducing points in VEF-SGP. By specifying the inducing points on the orthogonal grid/input subspace and using the Kronecker product, E-SGP significantly enhances computational efficiency without imposing constraints on the covariance matrix or increasing the number of parameters that need to be optimised during training.The E-SGP algorithm outperforms E-GP not only in terms of scalability but also in model quality, as evidenced by mean standardised logarithmic loss (MSLL). The computational complexity of E-GP grows cubically with an increasing structured training database, while E-SGP maintains computational efficiency as the model resolution (i.e., the number of inducing points) remains the same. The examples show that E-SGP produces more accurate predictions compared to E-GP when model resolutions are similar. In the application to a partially structured database, E-GP benefits from more training data but comes with higher computational demands, while E-SGP achieves a comparable level of accuracy but is more computationally efficient, making E-SGP a potentially preferable choice for fluid mechanics. Furthermore, E-SGP can produce more reasonable estimates of model uncertainty, whilst E-GP is more likely to produce over-confident predictions. In the application to partially structured databases, the performance of E-SGP is also compared to the structured Gaussian processes latent variable model (SGPLVM). In this case, E-SGP and SGPLVM both exhibit robust performance. However, E-SGP demonstrates a slight advantage over SGPLVM, particularly in terms of MSLL, indicating that E-SGP is better at producing trustworthy and accurate estimates of the uncertainty in the predictions. . While SGPLVM also improves computational efficiency by exploiting the Kronecker product and a small number of inducing points, E-SGP's orthogonal grid specification of inducing points further enhances its scalability and robustness, making it a superior choice for complex fluid mechanics problems with partially structured data.

Multi-Objective Bayesian Optimization for Laminate-Inspired Mechanically Reinforced Piezoelectric Self-Powered Sensing Yarns.

Piezoelectric fiber yarns produced by electrospinning offer a versatile platform for intelligent devices, demonstrating mechanical durability and the ability to convert mechanical strain into electric signals. While conventional methods involve twisting a single poly(vinylidene fluoride-co-trifluoroethylene)(P(VDF-TrFE)) fiber mat to create yarns, by limiting control over the mechanical properties, an approach inspired by composite laminate design principles is proposed for strengthening. By stacking multiple electrospun mats in various sequences and twisting them into yarns, the mechanical properties of P(VDF-TrFE) yarn structures are efficiently optimized. By leveraging a multi-objective Bayesian optimization-based machine learning algorithm without imposing specific stacking restrictions, an optimal stacking sequence is determined that simultaneously enhances the ultimate tensile strength (UTS) and failure strain by considering the orientation angles of each aligned fiber mat as discrete design variables. The conditions on the Pareto front that achieve a balanced improvement in both the UTS and failure strain are identified. Additionally, applying corona poling induces extra dipole polarization in the yarn state, successfully fabricating mechanically robust and high-performance piezoelectric P(VDF-TrFE) yarns. Ultimately, the mechanically strengthened piezoelectric yarns demonstrate superior capabilities in self-powered sensing applications, particularly in challenging environments and sports scenarios, substantiating their potential for real-time signal detection.

Bayesian quadrature policy optimization for spacecraft proximity maneuvers and docking

Advancing autonomous spacecraft proximity maneuvers and docking (PMD) is crucial for enhancing the efficiency and safety of inter-satellite services. One primary challenge in PMD is the accurate a priori definition of the system model, often complicated by inherent uncertainties in the system modeling and observational data. To address this challenge, we propose a novel Lyapunov Bayesian actor-critic reinforcement learning algorithm that guarantees the stability of the control policy under uncertainty. The PMD task is formulated as a Markov decision process that involves the relative dynamic model, the docking cone, and the cost function. By applying Lyapunov theory, we reformulate temporal difference learning as a constrained Gaussian process regression, enabling the state-value function to act as a Lyapunov function. Additionally, the proposed Bayesian quadrature policy optimization method analytically computes policy gradients, effectively addressing stability constraints while accommodating informational uncertainties in the PMD task. Experimental validation on a spacecraft air-bearing testbed demonstrates the significant and promising performance of the proposed algorithm.

Complex-valued multi-frequency electrical impedance tomography based on deep neural networks

The utilization of multi-frequency electrical impedance tomography (mfEIT), a non-invasive imaging technique, allows for the visualization of the conductivity distribution in biological tissues across different frequencies. However, the analysis of phase angle information within complex impedance remains a challenge, as most existing deep learning-based mfEIT algorithms are limited to real number processing. To mitigate this limitation, this study proposes a comlex reconstruction method which is inspired by the idea of combining deep learning with traditional reconstruction algorithm. It uses a spare Bayesian learning algorithm in the preprocessing stage that can perform complex arithmetic operations, and fully learns and makes use of the correlation between the real and imaginary parts to reconstruc the distribution of complex-valued conductivity in the measurement area. After that, an altered UNet network is used to further optimize the pre-reconstruction outcomes. The experimental outcomes validate the efficacy of the proposed algorithm in accurately reconstructing the complex-valued conductivity distributions of diverse biological tissues, such as potato and pig kidney, across different frequencies. Furthermore, the algorithm exhibits exceptional performance in mitigating the presence of image artifacts during the reconstruction process.

A data-driven Bayesian network of management and organizational factors for human reliability analysis in the process industry

According to historical statistical data, management and organizational factors (MOFs) contribute more to process accidents than technique factors. Under the umbrella of socio-tech system theory, human reliability analysis (HRA) has become a critical part of systemic probability risk analysis. In many HRA techniques, MOFs are among the performance shaping factors (PSFs). However, the interactions and causality of MOFs to human errors are still difficult to quantify and lack validation. To fill these gaps, a framework is proposed, considering data source selection, CBN construction algorithm comparison, and results validation. The case study employed the open access eMARS database as a data source. The optimized hybrid structure learning algorithm and Bayesian criteria parameter learning algorithm are employed to build a Causal Bayesian Network (CBN) of (MOFs) that lead to human error. The proposed kernel CBN is validated through prediction accuracy and sensitivity analysis. For theoretical contribution, the validated kernel BN could generally serve as the heart part of more specific CBNs as a basis for future works. For practical applications, an application shows the model's ability to quantify the contribution of MOFs to system reliability. The results show that human-machine interacting system reliability is most sensitive to organizational factors such as adequate training and procedures.

Knowledge-aided multi-dictionary block sparsity-aware STAP for airborne polarimetric conformal array radar

Airborne polarimetric conformal array radar has gained increased attention recently. However, the conformal array configuration and polarization factors may lead to non-stationary clutter, which significantly degrades the performance of space–time adaptive processing (STAP), particularly in short-range clutter environments. In this paper, we introduce a knowledge-aided multi-dictionary block sparse Bayesian learning (KA-MDBSBL) algorithm to improve the clutter suppression performance. Using prior knowledge, the proposed algorithm designs multi-dictionary matrices for each training sample, rather than a single dictionary matrix for the cell under test (CUT). We take advantage of the identical clutter profile under each dictionary matrix. In the multi-dictionary case, we enforce shared sparsity in the clutter profiles. Additionally, we utilize the inherent block structure of the dictionary matrix to jointly recover clutter and noise power through a fast convergence learning framework. Subsequently, the clutter plus noise covariance matrix is reconstructed using precisely estimated clutter and noise power, along with the dictionary matrix corresponding to the CUT. Numerical simulations are included to demonstrate the effectiveness and superiority of the proposed algorithm.

Fast estimation of array shape and direction of arrival using sparse Bayesian learning for manoeuvring towed line array

AbstractThe sparse Bayesian learning (SBL) algorithm has demonstrated its advantage in the direction of arrival (DOA) estimation. However, it requires a lot of computational cost to iteratively estimate the SBL hyperparameters from measurement data. This paper focuses on fast estimating the array shape and DOAs using SBL for a short towed line array (TLA) during manoeuvring. A parabolic model is utilised to describe the bent TLA whose bow as a hyperparameter is estimated in the SBL iterative process. Then, the basis vector pruning strategy is considered in the iteration to reduce computational cost by neglecting the impossible directions of signal presence. The converged speed of the joint estimation algorithm is further improved by approximately calculating the posterior probability density with the message passing approach. The effectiveness of the optimising joint estimation algorithm is verified using the experimental results from South China Sea.

Bayesian network structure learning with a new ensemble weights and edge constraints setting mechanism

Bayesian networks (BNs) are highly effective in handling uncertain problems, which can assist in decision-making by reasoning with limited and incomplete information. Learning a faithful directed acyclic graph (DAG) from a large number of complex samples of a joint distribution is currently a challenging combinatorial problem. Due to the growing volume and complexity of data, some Bayesian structure learning algorithms are ineffective and lack the necessary precision to meet the required needs. In this paper, we propose a new PCCL-CC algorithm. To ensure the accuracy of the network structure, we introduce the new ensemble weights and edge constraints setting mechanism. In this mechanism, we employ a method that estimates the interaction between network nodes from multiple perspectives and divides the learning process into multiple stages. We utilize an asymmetric weighted ensemble method and adaptively adjust the network structure. Additionally, we propose a causal discovery method that effectively utilizes the causal relationships among data samples to correct the network structure and mitigate the influence of Markov equivalence classes (MEC). Experimental results on real datasets demonstrate that our approach outperforms state-of-the-art methods.

Airborne Radar Space–Time Adaptive Processing Algorithm Based on Dictionary and Clutter Power Spectrum Correction

Sparse recovery space–time adaptive processing (SR-STAP) technology improves the moving target detection performance of airborne radar. However, the sparse recovery method with a fixed dictionary usually leads to an off-grid effect. This paper proposes a STAP algorithm for airborne radar based on dictionary and clutter power spectrum joint correction (DCPSJC-STAP). The algorithm first performs nonlinear regression in a non-stationary clutter environment with unknown yaw angles, and it corrects the corresponding dictionary for each snapshot by updating the clutter ridge parameters. Then, the corrected dictionary is combined with the sparse Bayesian learning algorithm to iteratively update the required hyperparameters, which are used to correct the clutter power spectrum and estimate the clutter covariance matrix. The proposed algorithm can effectively overcome the off-grid effect and improve the moving target detection performance of airborne radar in actual complex clutter environments. Simulation experiments verified the effectiveness of this algorithm in improving clutter estimation accuracy and moving target detection performance.

Multiplicative Basis Function Based Adaptive DOA Estimation in Optimal MIMO Sparse Antenna Reconfiguration Model

Direction of arrival (DOA) estimation using sparse signal representation has gained significant attention in recent decades. The spatial signals utilized for DOA estimation are reconstructed through a novel compressive sensing (CS) approach. In this study, we used a CS approach to ascertain the adaptive underdetermined DOA for multiple inputs and multiple output (MIMO) sparse media. Accurate DOA estimation through the CS approach contributes to enhanced signal investigation and the suppression of undesired noise in a sparse channel. The method proposed herein encompasses the development and execution of a novel multiplicative basis function known as the multi-kernel supported non-negative sparse Bayesian learning (NNSBL) algorithm, which is implemented on predefined grid values. Concurrently, stochastic grey wolf optimization (GWO) is virtually applied to increase the degrees of freedom (DOF) on a minimum redundancy array (MRA) while considering an optimal antenna reconfiguration model. The advantages of this proposed approach include the generation of a distinct manifold matrix for precise beam steering, resulting in improved DOA estimation accuracy. Additionally, an augmentation of DOF using GWO was observed, with low computational complexity. The simulated result of proposed algorithm leads to the attainment of optimal minimum root mean square error (RMSE) across various optimal wavelengths of the stochastic sources. Finally, a comparative analysis of RMSE and convergence plots confirms the superior performance and high potentiality of the proposed method in comparison to existing techniques across different SNR values. Notably, there is significant reduction in RMSE which is suitable for precise DOA estimation in signal processing applications.

A High-Resolution Time Reversal Method for Target Localization in Reverberant Environments

Reverberation in real environments is an important factor affecting the high resolution of target sound source localization (SSL) methods. Broadband low-frequency signals are common in real environments. This study focuses on the localization of this type of signal in reverberant environments. Because the time reversal (TR) method can overcome multipath effects and realize adaptive focusing, it is particularly suitable for SSL in a reverberant environment. On the basis of the significant advantages of the sparse Bayesian learning algorithm in the estimation of wave direction, a novel SSL is proposed in reverberant environments. First, the sound propagation model in a reverberant environment is studied and the TR focusing signal is obtained. We then use the sparse Bayesian framework to locate the broadband low-frequency sound source. To validate the effectiveness of the proposed method for broadband low-frequency targeting in a reverberant environment, simulations and real data experiments were performed. The localization performance under different bandwidths, different numbers of microphones, signal-to-noise ratios, reverberation times, and off-grid conditions was studied in the simulation experiments. The practical experiment was conducted in a reverberation chamber. Simulation and experimental results indicate that the proposed method can achieve satisfactory spatial resolution in reverberant environments and is robust.

From green-washing to innovation-washing: Environmental information intangibility and corporate green innovation in China

We use a sample of China's listed firms and employ a naïve Bayesian machine learning algorithm to reveal that environmental information intangibility superficially promotes green innovation. We demonstrate that this effect is channelled through the acquisition of institutional resources, including bank loans and government subsidies. The impact of environmental information intangibility on green innovation is most pronounced in state-owned enterprises, large firms, and politically connected firms. Furthermore, we confirm that environmental information intangibility does not lead to improvements in innovation efficiency or quality. This implies that green innovation may serve as a symbolic environmental activity. Our findings contribute to the research on environmental information intangibility, greenwashing behaviour, and their relationship to green innovation.

Finding community structure in Bayesian networks by heuristic K-standard deviation method

When constructing a Bayesian network for high-dimensional data, due to the complex relationships among distinct nodes, the difficulty in detecting the community structure will directly restrict the feasibility of the divide-and-conquer learning algorithm. This study attempts to solve this problem from the shortest path perspective and proposes the heuristic K-standard deviation algorithm. Firstly, we design a novel heuristic function and drive the A* algorithm to find the shortest paths between nodes in the Bayesian network. In addition, the new heuristic function is theoretically proved to be admissible and consistent. Experiments on different synthetic datasets and benchmark Bayesian networks verify that the proposed heuristic K-standard deviation algorithm generally gets better clustering performance than other representative algorithms and improves the efficiency and accuracy of the conventional Bayesian network structure learning algorithms, especially for high-dimensional data.

Real-Time Epidemiology and Acute Care Need Monitoring and Forecasting for COVID-19 via Bayesian Sequential Monte Carlo-Leveraged Transmission Models.

COVID-19 transmission models have conferred great value in informing public health understanding, planning, and response. However, the pandemic also demonstrated the infeasibility of basing public health decision-making on transmission models with pre-set assumptions. No matter how favourably evidenced when built, a model with fixed assumptions is challenged by numerous factors that are difficult to predict. Ongoing planning associated with rolling back and re-instituting measures, initiating surge planning, and issuing public health advisories can benefit from approaches that allow state estimates for transmission models to be continuously updated in light of unfolding time series. A model being continuously regrounded by empirical data in this way can provide a consistent, integrated depiction of the evolving underlying epidemiology and acute care demand, offer the ability to project forward such a depiction in a fashion suitable for triggering the deployment of acute care surge capacity or public health measures, and support quantitative evaluation of tradeoffs associated with prospective interventions in light of the latest estimates of the underlying epidemiology. We describe here the design, implementation, and multi-year daily use for public health and clinical support decision-making of a particle-filtered COVID-19 compartmental model, which served Canadian federal and provincial governments via regular reporting starting in June 2020. The use of the Bayesian sequential Monte Carlo algorithm of particle filtering allows the model to be regrounded daily and adapt to new trends within daily incoming data-including test volumes and positivity rates, endogenous and travel-related cases, hospital census and admissions flows, daily counts of dose-specific vaccinations administered, measured concentration of SARS-CoV-2 in wastewater, and mortality. Important model outputs include estimates (via sampling) of the count of undiagnosed infectives, the count of individuals at different stages of the natural history of frankly and pauci-symptomatic infection, the current force of infection, effective reproductive number, and current and cumulative infection prevalence. Following a brief description of the model design, we describe how the machine learning algorithm of particle filtering is used to continually reground estimates of the dynamic model state, support a probabilistic model projection of epidemiology and health system capacity utilization and service demand, and probabilistically evaluate tradeoffs between potential intervention scenarios. We further note aspects of model use in practice as an effective reporting tool in a manner that is parameterized by jurisdiction, including the support of a scripting pipeline that permits a fully automated reporting pipeline other than security-restricted new data retrieval, including automated model deployment, data validity checks, and automatic post-scenario scripting and reporting. As demonstrated by this multi-year deployment of the Bayesian machine learning algorithm of particle filtering to provide industrial-strength reporting to inform public health decision-making across Canada, such methods offer strong support for evidence-based public health decision-making informed by ever-current articulated transmission models whose probabilistic state and parameter estimates are continually regrounded by diverse data streams.

First principles molecular dynamics simulation and thermal decomposition kinetics study of CL-20.

2,4,6,8,10, 12-hexanitro-2,4,6,8,10, 12-hexazepane (CL-20) is a new energetic material with high performance and low sensitivity. In-depth study of the thermal decomposition mechanism of CL-20 is a necessary condition to improve its performance, ensure its safety, and optimize its application. On the basis of a large number of empirical force fields used in molecular dynamics simulation in the past, the machine learning augmented first-principles molecular dynamics method was used for the first time to simulate the thermal decomposition reaction of CL-20 at 2200 K, 2500 K, 2800 K, and 3000 K isothermal temperature. The main stable resulting compounds are N2, CO2, CO, H2O, andH2, where CO2 and H2O continue to decompose at higher temperatures. The initial decomposition pathways are denitration by N-N fracture, ring-opening by C-N bond fracture, and redox reaction involving NO2 and CL-20. After ring opening, two main compounds, fused tricyclic pyrazine and azadicyclic, were formed, which were decomposed continuously to form monocyclic pyrazine and pyrazole ring structures. The most common fragments formed during decomposition are those containing two, three, four, and six carbons. The formation rule and quantity of main small molecule intermediates and resulting stable products under different simulated temperatures were analyzed. Based on ab initio Bayesian active learning algorithm, efficient and accurate prediction of CL-20 is made using the dynamic machine learning function of Vienna Ab-Initio Simulation Package (VASP), which constructs the energy potential surface by learning a large number of data based on AIMD calculations. The result is a machine learning force field (MLFF). Then the molecular dynamics of CL-20 was simulated using the trained MLFF model. PAW pseudopotentials and generalized gradient approximation (GGA), namely, Perdew-Burke-Ernzerhof (PBE) functional, are used in the calculation. The plane wave truncation energy (ENCUT) is set to 550 eV, and using the Gaussian broadening, the thermal broadening size of the single-electron orbital is 0.05 eV. A van der Waals revision of the system with Grimme Version 3. The energy convergence accuracy (EDIFF) of electron self-consistent iteration is set to 1E-5 eV and 1E-6 eV, respectively. The two-step structure optimization is carried out using 1'1'1 k point grid and conjugate gradient method. The ENCUT was changed to 500 eV and EDIFF to 1E-5 eV, and NVT integration (ISIF = 2) of Langevin thermostat was used for machine learning force field training and AIMD simulation of the system.