Coal and gas outburst prediction method and system based on physical information neural network

Abstract

The invention discloses a coal and gas outburst prediction method and system based on a physical information neural network. The coal and gas outburst prediction method comprises the steps that S1, geological parameters, gas dynamic parameters and mining activity parameters of a target area are collected and preprocessed; s2, based on the preprocessed data, performing correlation analysis by using a statistical method and a machine learning algorithm to screen out key features highly related to coal and gas outburst events; s3, according to a physical mechanism of coal and gas outburst, constructing a key physical equation to determine physical information; s4, constructing a physical information-based PINN network structure, and performing training by using a comprehensive loss function considering data driving loss and physical driving loss; s5, applying the trained PINN model to actual coal and gas outburst prediction, inputting real-time monitoring data, and outputting a classification result of the occurrence probability; according to the method, dependence on large-scale training data is reduced, and the model generalization ability and prediction precision are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of coal mine safety production, and more specifically, to a coal and gas outburst prediction method and system based on a physics-informed neural network. Background Art

[0002] During the coal mining process, coal and gas outburst is a serious natural disaster with extremely strong destructiveness and suddenness, posing a great threat to the lives of miners and the production activities of coal mines; in order to effectively prevent the occurrence of coal and gas outburst accidents, accurate prediction technology is particularly important.

[0003] Currently, the existing coal and gas outburst prediction methods are mainly divided into two categories: one is the prediction method based on physical mechanisms, and the other is the prediction method based on data-driven.

[0004] The prediction method based on physical mechanisms realizes the prediction of outburst by establishing a physical model of coal and gas outburst and considering the relationships among factors such as in-situ stress, gas pressure, and coal seam properties; however, this method requires very accurate understanding of the geological conditions and physical parameters of the coal mine, and the process of establishing and solving the model is relatively complex, making it difficult to apply to the actual coal mine environment.

[0005] The data-driven prediction method uses historical monitoring data to establish a prediction model through statistical analysis, machine learning and other means. Common methods include neural networks, support vector machines, grey systems, etc.; these methods can capture the laws of coal and gas outburst to a certain extent, but they usually require a large amount of training data and have high requirements for the quality of data; in actual applications, due to problems such as missing and noisy mine monitoring data, the prediction accuracy and reliability of the model are limited; in addition, when a disaster occurs, the on-site environment is often chaotic and dangerous, the data acquisition equipment may be damaged, and the safety evacuation of personnel is prioritized, making it extremely difficult to obtain accurate data, further affecting the training and optimization of the data-driven model.

[0006] Therefore, how to reduce the dependence on large-scale training data, significantly improve the generalization ability and prediction accuracy of the model, and enhance the adaptability to different mining areas and mining conditions is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0007] In view of this, the present invention provides a coal and gas outburst prediction method and system based on a physics-informed neural network, aiming to realize the rapid and accurate prediction of coal and gas outburst by obtaining the data to be processed in the target area, performing data preprocessing, embedding physical laws, feature engineering and neural network training.

[0008] To achieve the above object, the present invention adopts the following technical solutions:

[0009] A coal and gas outburst prediction method based on a physics-informed neural network, comprising the following steps:

[0010] S1. Collect data including but not limited to geological parameters, gas dynamic parameters, and mining activity parameters in the target area, and preprocess the data;

[0011] S2. Based on the preprocessed data, use statistical methods and machine learning algorithms for correlation analysis, and screen out key features highly correlated with coal and gas outburst events, removing redundant or irrelevant features;

[0012] S3. According to the physical mechanism of coal and gas outburst, construct key physical equations to determine physical information;

[0013] S4. Construct a PINN network structure based on physical information, and train it with a comprehensive loss function considering data-driven loss and physical-driven loss;

[0014] S5. Apply the trained PINN model to actual coal and gas outburst prediction, input real-time monitoring data, and output the classification result of the occurrence probability.

[0015] Preferably, in step S1, the content of preprocessing the data includes: adding Gaussian noise to enhance data robustness, and normalizing the data to map it to a suitable interval.

[0016] Preferably, in step S2, the key features extracted include: initial gas emission velocity, coal seam firmness coefficient, gas content, gas desorption content, and mining depth.

[0017] Preferably, in step S2, the methods of using statistical methods and machine learning algorithms for correlation analysis include: recursive feature elimination method, gradually eliminating unimportant features based on the performance of the PINN model; and principal component analysis, extracting main features through dimensionality reduction, retaining key information while reducing the feature dimension.

[0018] Preferably, in step S3, the key physical equations include: stress-strain relationship, gas adsorption-desorption equilibrium, permeability dynamic model, and in-situ stress balance equation.

[0019] Preferably, in step S4, the PINN network structure includes an input layer, multiple hidden layers, and an output layer;

[0020] The input layer receives the processed feature data, and the number of neurons matches the feature dimension, ensuring that the PINN model can comprehensively capture multi-dimensional information related to coal and gas outburst;

[0021] The hidden layer performs non - linear transformation through activation functions, and extracts and transforms high - level abstract representations of input features layer by layer;

[0022] The output layer uses the Softmax activation function to convert the feature vector transmitted from the hidden layer into a probability distribution of whether coal and gas outburst occurs, and the number of its neurons corresponds to the number of categories of classification labels;

[0023] An optimization algorithm is used to adjust the network parameters to minimize the loss function. The loss function of PINN consists of the weighted sum of data - driven loss and physics - driven loss.

[0024] Preferably, the PINN model prediction formula is:

[0025]

[0026] Among them, represents the predicted output of the PINN model, which is the risk of coal and gas outburst; represents the input data, including geological parameters, gas dynamic parameters, and mining activity parameters; represents the mapping function of the neural network, which is determined by the network structure and parameters decide; include the weights and biases in the network, which are learned through training data; the physical constraints represent the physical laws embedded in the loss function.

[0027] Preferably, the comprehensive loss function of the PINN model is the weighted sum of the data - driven loss function and the physics - driven loss function, specifically:

[0028]

[0029] Among them, represents the true label or actual observation value of the th sample, represents the predicted value of the PINN model for the th sample, represents the total number of samples, represents the predicted stress of the th sample, represents the elastic modulus of the material, which reflects the proportional relationship between stress and strain in the elastic deformation stage of the material, represents the actual strain of the th sample, represents the predicted adsorption amount of the th sample, represents the maximum adsorption amount of gas, represents the gas pressure of the th sample, is the adsorption characteristic pressure, denotes the predicted permeability of the \(i\)-th sample, denotes the reference permeability of the \(i\)-th sample, denotes the gas pressure of the \(i\)-th sample, denotes the reference pressure of the \(i\)-th sample, which is used to normalize the current pressure, denotes the empirical index of the \(i\)-th sample, denotes the divergence of the stress tensor, denotes the density of coal and rock, denotes the acceleration due to gravity, and \(\lambda_1, \lambda_2, \lambda_3, \lambda_4, \lambda_5\) are weight coefficients.

[0030] A coal and gas outburst prediction system based on a physics-informed neural network, based on the described coal and gas outburst prediction method based on a physics-informed neural network, includes a data acquisition and preprocessing module, a feature engineering module, a physical information determination module, a model construction and training module, and a prediction module;

[0031] The data acquisition and preprocessing module is used to collect data including but not limited to geological parameters, gas dynamic parameters, and mining activity parameters of the target area, and preprocess the data;

[0032] The feature engineering module is used to perform correlation analysis on the preprocessed data using statistical methods and machine learning algorithms, screen out key features highly relevant to coal and gas outburst events, and remove redundant or irrelevant features;

[0033] The model construction and training module is used to construct key physical equations according to the physical mechanism of coal and gas outburst to determine physical information and construct a PINN network structure based on physical information, and train with a comprehensive loss function considering data-driven loss and physical-driven loss;

[0034] The prediction module is used to apply the trained PINN model to actual coal and gas outburst prediction, input real-time monitoring data, and output the classification result of the occurrence probability.

[0035] A processing terminal includes a memory and a processor. A computer program that can run on the processor is stored in the memory. When the processor executes the computer program, the described coal and gas outburst prediction method based on a physics-informed neural network is implemented.

[0036] As can be seen from the above technical solutions, compared with the prior art, the present invention discloses a coal and gas outburst prediction method and system based on a physics-informed neural network, which combines physical laws with data-driven approaches, making up for the lack of physical consistency in pure data-driven models and improving the scientificity and accuracy of predictions. By embedding physical information, the model has stronger adaptability to different mining areas and mining conditions, and its generalization ability is significantly improved. It can process input data in a timely manner and give prediction results, meeting the timeliness requirements for coal and gas outburst early warning in coal mine safety production. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings according to the provided drawings without creative efforts.

[0038] Figure 1 Schematic diagram of a coal and gas outburst prediction method based on a physics-informed neural network provided by the present invention;

[0039] Figure 2 Schematic diagram of the PINN network structure based on physical information provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art without creative efforts based on the embodiments of the present invention belong to the scope of protection of the present invention.

[0041] The embodiments of the present invention disclose a coal and gas outburst prediction method based on a physics-informed neural network, as Figure 1 , including the following steps:

[0042] S1. Collect data including but not limited to geological parameters, gas dynamic parameters, and mining activity parameters of the target area, and preprocess the data;

[0043] S2. Based on the preprocessed data, use statistical methods and machine learning algorithms for correlation analysis, and screen out features highly correlated with coal and gas outburst events, removing redundant or irrelevant features;

[0044] S3. According to the physical mechanism of coal and gas outburst, construct key physical equations to determine physical information;

[0045] S4. Construct a PINN network structure based on physical information and train it with a comprehensive loss function that considers data-driven loss and physical-driven loss;

[0046] S5. Apply the trained PINN model to the actual prediction of coal and gas outbursts, input real-time monitoring data, and output the classification results of occurrence probability.

[0047] In this embodiment, the geological parameters include elastic modulus and ground stress distribution, the gas dynamic parameters include concentration and pressure, and the mining activity parameter data include mining depth and drilling parameters;

[0048] In actual applications, professional geological exploration equipment is used on-site in the mining area to collect detailed information such as the thickness, elastic modulus and ground stress distribution of the coal seam. These parameters can reflect the physical properties of the coal seam and the geological environment in which it is located; high-precision gas sensors are used in the mine to monitor the concentration and pressure changes of gas in real time. Monitoring of gas concentration helps to understand the accumulation of gas in the coal seam, and gas pressure is an important indicator for assessing the hazard of gas outbursts; key parameters in the mining process are recorded, such as the mining depth, the specific size and spacing of the drill holes, etc. These parameters have a direct impact on the destruction of the coal seam and the release of gas, and are an important basis for predicting coal and gas outbursts.

[0049] In order to further implement the above technical solution, step S1, preprocessing the data includes: adding Gaussian noise to enhance data robustness, and normalizing the data to map it to a suitable interval;

[0050] Preprocessing also includes cleaning the collected raw data to remove data points with obvious errors or anomalies. For example, abnormally high or low value data caused by a gas sensor failure is eliminated. At the same time, missing data is filled in to ensure data integrity.

[0051] For the original data Add Gaussian noise:

[0052]

[0053] in, is the standard deviation of Gaussian noise, is a random number that follows a standard normal distribution;

[0054] The specific method is to use the standard deviation of Gaussian noise according to the statistical characteristics of the original data. Set to 0.01 and generate random numbers that follow a standard normal distribution , calculate the noise value according to the formula and add it to the original data;

[0055] Normalize the data after adding noise and map it to the interval [0,1], which helps to eliminate the dimensional differences between different feature data and enables the model to learn the patterns in the data more effectively. The normalization formula is:

[0056]

[0057] where and are the minimum and maximum values of the data after adding noise respectively, and x noise is the noise data.

[0058] To further implement the above technical solution, in step S2, the key features extracted include: initial gas emission velocity, coal seam firmness coefficient, gas content, gas desorption content, and mining depth;

[0059] The initial gas emission velocity, i.e., the initial velocity of gas released from the coal seam, is an important dynamic index for evaluating the risk of gas outburst; the coal seam firmness coefficient, which reflects the anti - fragmentation ability of the coal seam and directly affects the possibility of gas outburst; the gas content, i.e., the total amount of gas in the coal seam, is an important basic parameter for gas outburst risk; the gas desorption content, the amount of gas desorbed from the coal seam, is closely related to gas pressure and coal seam characteristics; and the mining depth. As the mining depth increases, the in - situ stress and gas pressure usually increase, thus significantly affecting the gas outburst risk.

[0060] To further implement the above technical solution, in step S2, the methods for performing correlation analysis using statistical methods and machine learning algorithms include: recursive feature elimination method, which gradually eliminates unimportant features based on the performance of the PINN model; and principal component analysis, which extracts the main features through dimensionality reduction, retaining key information while reducing the feature dimension.

[0061] Through step S2, the quality of the input data of the PINN model can be ensured, the prediction performance can be improved, and at the same time, the consumption of computing resources can be reduced. The reasonable selection and processing of these features provide comprehensive input information for the PINN model, enhancing the scientificity and accuracy of the prediction.

[0062] To further implement the above technical solution, in step S3, the key physical equations include: stress - strain relationship, gas adsorption - desorption equilibrium, permeability dynamic model, and in - situ stress balance equation;

[0063] Specifically:

[0064] The stress - strain relationship equation describes the deformation characteristics of the coal seam under in - situ stress. Through parameters such as elastic modulus and Poisson's ratio, it relates stress and strain, reflecting the mechanical behavior of the coal seam:

[0065]

[0066] Among them, represents stress, represents elastic modulus, represents strain;

[0067] The gas adsorption-desorption equilibrium, i.e., the Langmuir model, depicts the occurrence state of gas in coal seams. Through parameters such as the maximum adsorption amount and adsorption characteristic pressure, it reveals the adsorption and desorption processes of gas in coal seams:

[0068]

[0069] Among them, is the maximum adsorption amount, is the adsorption characteristic pressure, reflecting the occurrence state of gas;

[0070] The dynamic model equation of permeability reflects the law of the change of coal seam permeability with pore pressure. The accurate estimation of permeability is crucial for understanding the flow characteristics of gas in coal seams:

[0071]

[0072] Among them, is permeability, is the reference permeability, is the pore pressure, is the characteristic pressure;

[0073] The in-situ stress balance equation ensures the stress balance of the coal seam under static conditions, comprehensively considering factors such as the stress tensor, coal-rock density, and gravitational acceleration:

[0074]

[0075] Among them, is the stress tensor, is the coal-rock density, is the gravitational acceleration.

[0076] To further implement the above technical solution, such as Figure 2 , step S4, the PINN network structure includes an input layer, multiple hidden layers, and an output layer;

[0077] The input layer receives the processed feature data, and the number of neurons matches the feature dimension to ensure that the PINN model can comprehensively capture the multi-dimensional information related to coal and gas outbursts;

[0078] The hidden layers perform non-linear transformations through activation functions, layer by layer extracting and transforming the high-level abstract representations of the input features;

[0079] It includes 4 - 6 hidden layers, and each layer contains 128 - 256 neurons;

[0080] The output layer uses the Softmax activation function to convert the feature vector transmitted from the hidden layer into a probability distribution of whether coal and gas outburst occurs, and the number of its neurons corresponds to the number of categories of classification labels;

[0081] An optimization algorithm is used to adjust the network parameters to minimize the loss function. The loss function of PINN is composed of the weighted sum of data-driven loss and physics-driven loss.

[0082] To further implement the above technical solution, the PINN model prediction formula is:

[0083]

[0084] where represents the predicted output of the PINN model, which is the risk of coal and gas outburst; represents the input data, including geological parameters, gas dynamic parameters, and mining activity parameters; represents the mapping function of the neural network, which is determined by the network structure and parameters ; includes the weights and biases in the network, which are learned through training data; the physical constraints represent the physical laws embedded in the loss function.

[0085] In this implementation, the on-site drilling method is adopted to observe whether there are phenomena such as hole spraying, drill jamming, and other dynamic phenomena that can represent outburst, and the dynamic phenomena are used to evaluate whether there is outburst risk and conduct grade classification, including no outburst risk, denoted as 1; general outburst risk, denoted as 2; serious outburst risk, denoted as 3.

[0086] To further implement the above technical solution, the comprehensive loss function of the PINN model consists of data-driven loss and physics-driven loss. The data-driven loss is the mean square error between the model prediction value and the actual value, and the physics-driven loss is the mean square error of the physical equation residual. The two are weighted and summed to obtain the final loss function, specifically:

[0087] The data-driven loss function is and the physics-driven loss function is: , , , ;

[0088] The data-driven loss function and the physics-driven loss function are weighted and summed to obtain the loss function of the PINN model:

[0089]

[0090] where represents the The true label or actual observation of a sample, denotes the predicted value of the PINN model for the th sample, denotes the total number of samples, denotes the th predicted stress of a sample, denotes the elastic modulus of the material, reflecting the proportional relationship between stress and strain in the elastic deformation stage of the material, denotes the th actual strain of a sample, denotes the th predicted adsorption capacity of a sample, denotes the maximum adsorption capacity of gas, denotes the th gas pressure of a sample, is the adsorption characteristic pressure, denotes the predicted permeability of the th sample, denotes the reference permeability of the th sample, denotes the gas pressure of the th sample, denotes the reference pressure of the th sample, used to normalize the current pressure, denotes the empirical index of the th sample, denotes the divergence of the stress tensor, denotes the density of coal and rock, denotes the acceleration due to gravity, and λ1, λ2, λ3, λ4, λ5 are weight coefficients.

[0091] When training the PINN model, physical information is embedded by incorporating physical laws as constraints into the loss function. Physical laws are presented in the form of differential equations, such as the stress-strain relationship, gas adsorption-desorption equilibrium, permeability dynamic model, and in-situ stress balance equation in coal and gas outburst prediction. After their residuals are calculated by automatic differentiation technology, they become physical information loss terms. The model loss function is composed of a weighted sum of data-driven loss (measuring the difference between prediction and observation) and physics-driven loss (ensuring that the prediction conforms to physical laws). During training, the Adam optimization algorithm adjusts the parameters to minimize the comprehensive loss function (in terms of parameter settings, the learning rate is set to 0.001, the training epoch is 500, the batch size is 64, and the weight decay coefficient is 0.0001), enabling the model to be consistent with the observed data while satisfying physical laws. This method reduces the dependence on large-scale training data, significantly improves the model's generalization ability and prediction accuracy, enhances the adaptability to different mining areas and mining conditions, and provides a solid foundation for the accurate prediction of coal and gas outbursts.

[0092] In practical applications, as the mine is being exploited, the geological conditions and mining environment are constantly changing, and the gas emission volume and in-situ stress distribution also change accordingly. To adapt to these changes, the PINN model is updated regularly. Specifically, after the newly collected data undergoes the same data preprocessing and feature engineering processes as before, it is added to the original training set. Then, the PINN model is retrained using the Adam optimization algorithm, and the network parameters are adjusted to adapt to the new data patterns and mine conditions. During the retraining process, the model performance is evaluated through techniques such as cross-validation to ensure a balance between prediction accuracy and generalization ability.

[0093] A coal and gas outburst prediction system based on a physics-informed neural network, based on a coal and gas outburst prediction method based on a physics-informed neural network, includes a data collection and preprocessing module, a feature engineering module, a model construction and training module, and a prediction module.

[0094] The data collection and preprocessing module is used to collect data including but not limited to geological parameters, gas dynamic parameters, and mining activity parameters of the target area, and preprocess the data.

[0095] The feature engineering module is used to perform correlation analysis on the preprocessed data using statistical methods and machine learning algorithms, screen out key features highly correlated with coal and gas outburst events from them, and remove redundant or irrelevant features.

[0096] The model construction and training module is used to construct key physical equations based on the physical mechanism of coal and gas outbursts to determine physical information and construct a PINN network structure based on physical information, and train it with a comprehensive loss function considering data-driven loss and physical-driven loss.

[0097] The prediction module is used to apply the trained PINN model to actual coal and gas outburst predictions, input real-time monitoring data, and output the classification results of occurrence probabilities.

[0098] A processing terminal includes a memory and a processor. A computer program that can run on the processor is stored in the memory. When the processor executes the computer program, it implements a coal and gas outburst prediction method based on a physics-informed neural network.

[0099] In this specification, the various embodiments are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. The same or similar parts among the various embodiments can be referred to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the description of the method part.

[0100] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the broadest scope consistent with the principles and novel features disclosed herein.

Claims

1. A coal and gas outburst prediction method based on a physics-informed neural network, characterized in that It includes the following steps: S1. Collect data on geological parameters, gas dynamic parameters, mining activity parameters, etc. in the target area, and preprocess the data; S2. Based on the preprocessed data, use statistical methods and machine learning algorithms for correlation analysis, and screen out key features highly correlated with coal and gas outburst events, removing redundant or irrelevant features; S3. According to the physical mechanism of coal and gas outburst, construct key physical equations to determine physical information; S4. Construct a PINN network structure based on physical information, and train it with a comprehensive loss function considering data-driven loss and physical-driven loss; S5. Apply the trained PINN model to actual coal and gas outburst prediction, input real-time monitoring data, and output the classification result of the occurrence probability.

2. The coal and gas outburst prediction method based on the physics-informed neural network according to claim 1, characterized in that, In step S1, the content of preprocessing the data includes: adding Gaussian noise to enhance data robustness, and normalizing the data to map it to a suitable interval.

3. A coal and gas outburst prediction method based on a physics-informed neural network according to claim 1, characterized in that, In step S2, the key features extracted include: initial gas emission velocity, coal seam firmness coefficient, gas content, gas desorption content, and mining depth.

4. A coal and gas outburst prediction method based on a physics-informed neural network according to claim 1, characterized in that, In step S2, the methods of using statistical methods and machine learning algorithms for correlation analysis include: recursive feature elimination method, gradually removing unimportant features based on the performance of the PINN model; and principal component analysis, extracting main features through dimensionality reduction, reducing the feature dimension while retaining key information.

5. A coal and gas outburst prediction method based on a physics-informed neural network according to claim 1, characterized in that, In step S3, the key physical equations include: stress-strain relationship, gas adsorption-desorption equilibrium, permeability dynamic model, and in-situ stress balance equation.

6. The coal and gas outburst prediction method based on a physics-informed neural network according to claim 1, characterized in that, In step S4, the PINN network structure includes an input layer, multiple hidden layers, and an output layer; The input layer receives the processed feature data, and the number of neurons matches the feature dimension to ensure that the PINN model can comprehensively capture multi-dimensional information related to coal and gas outburst; The hidden layer performs non-linear transformation through activation functions, and layer by layer extracts and transforms the high-level abstract representation of the input features; The output layer uses the Softmax activation function to convert the feature vector transmitted from the hidden layer into the probability distribution of the occurrence of coal and gas outburst, and the number of its neurons corresponds to the number of categories of classification labels; An optimization algorithm is used to adjust the network parameters to minimize the loss function. The loss function of PINN is composed of the weighted sum of data-driven loss and physical-driven loss.

7. A coal and gas outburst prediction method based on a physics-informed neural network according to claim 1, characterized in that The prediction formula of the PINN model is: ； Among them, represents the predicted output of the model, which is the risk of coal and gas outburst; represents the input data, including geological parameters, gas dynamic parameters, and mining activity parameters; represents the mapping function of the neural network, which is determined by the network structure and parameters decided; including the weights and biases in the network, which are obtained by learning from the training data; the physical constraints represent the physical laws embedded in the loss function.

8. A coal and gas outburst prediction method based on a physics-informed neural network according to claim 1, characterized in that, The comprehensive loss function of the PINN model is the weighted sum of the data-driven loss function and the physical-driven loss function, specifically: ； Among them, represents the true label or actual observation value of the th sample, represents the predicted value of the PINN model for the th sample, represents the total number of samples, represents the th sample's predicted stress, represents the elastic modulus of the material, reflecting the proportional relationship between stress and strain in the elastic deformation stage of the material, represents the th sample's actual strain, represents the th sample's predicted adsorption capacity, represents the maximum adsorption capacity of gas, represents the th sample's gas pressure, is the adsorption characteristic pressure, represents the predicted permeability of the th sample, represents the reference permeability of the th sample, represents the gas pressure of the th sample, represents the reference pressure of the th sample, used to normalize the current pressure, represents the empirical exponent of the th sample, represents the divergence of the stress tensor, represents the density of coal and rock, represents the acceleration due to gravity, and λ1, λ2, λ3, λ4, λ5 are weight coefficients.

9. A coal and gas outburst prediction system based on a physics-informed neural network, characterized in that, A method for predicting coal and gas outburst based on physical information neural network according to any one of claims 1-8, including a data acquisition and preprocessing module, a feature engineering module, a model construction and training module, and a prediction module; The data acquisition and preprocessing module is used to collect data on geological parameters, gas dynamic parameters, mining activity parameters, etc. in the target area, and preprocess the data; A feature engineering module, which is used to perform correlation analysis based on the preprocessed data by using statistical methods and machine learning algorithms, screen out key features highly relevant to coal and gas outburst events from them, and remove redundant or irrelevant features; A model construction and training module, which is used to construct key physical equations according to the physical mechanism of coal and gas outburst to determine physical information and construct a PINN network structure based on physical information, and train it with a comprehensive loss function considering data-driven loss and physical-driven loss; A prediction module, which is used to apply the trained PINN model to actual coal and gas outburst prediction, input real-time monitoring data, and output the classification result of the occurrence probability.

10. A processing terminal, characterized in that, It includes a memory and a processor. A computer program that can run on the processor is stored in the memory. When the processor executes the computer program, it implements a method for predicting coal and gas outburst based on a physics-informed neural network according to any one of claims 1-8.

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