Graph network-based downhole gas concentration prediction method fusing physical information
By constructing a graph network model that integrates physical information, the problems of perception lag and poor data generalization ability in downhole gas concentration prediction are solved, achieving high-precision and robust gas concentration prediction and enhancing the interpretability of the model.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHONGQING UNIV
- Filing Date
- 2026-03-18
- Publication Date
- 2026-06-12
AI Technical Summary
Existing technologies for monitoring downhole gas concentrations suffer from problems such as sensing lag, difficulty in obtaining parameters, and poor data generalization ability, resulting in low accuracy and poor robustness in predicting hazardous gas concentrations in downholes.
A graph network model integrating physical information is constructed. By building a graph structure that integrates physics and causality, the partial differential equation of gas transport is used as a physical constraint. By combining graph convolutional networks and temporal convolutional networks, spatiotemporal characteristics that conform to physical laws are learned to achieve gas concentration prediction.
It improves the accuracy and robustness of downhole gas concentration prediction, enhances the interpretability of the model, and can provide high-precision prediction results under complex multiphysics coupling effects.
Smart Images
Figure CN122196442A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of coal mine safety monitoring and gas concentration prediction technology, specifically relating to a graph network method for predicting underground gas concentration that integrates physical information. Background Technology
[0002] With the increasing depth and intensity of coal mining, the challenges to mine safety are becoming increasingly severe. Among these challenges, major accidents caused by hazardous gases such as methane (mainly composed of gas) and carbon monoxide remain the most prominent risks threatening miners' lives and hindering the sustainable development of the industry due to their suddenness and destructive power. Therefore, accurate and timely prediction and early warning of hazardous gas concentrations underground are of paramount importance for ensuring safe coal mine production.
[0003] Currently, the monitoring and prediction of downhole gas concentrations mainly rely on the following types of technologies.
[0004] (1) Sensor network-based monitoring system: By deploying fixed sensors at key locations underground, gas concentration data is collected in real time and threshold alarms are triggered. Although this type of system can provide real-time monitoring, it is essentially a "post-event" perception, that is, it only issues an alarm when the gas concentration exceeds the standard, and there is a significant perception lag. In addition, due to the limited number and location of sensor points, the system is difficult to fully see the gas movement in the deep goaf, dead corners of roadways and other monitoring blind spots, and it cannot provide effective early warning for sudden abnormal gas outbursts.
[0005] (2) Numerical simulation techniques based on physical equations: This method attempts to reveal the mechanistic laws of gas transport and diffusion in the well by establishing complex fluid dynamics models (such as computational fluid dynamics, CFD). However, this type of method heavily relies on precise boundary conditions and physical parameters (such as wind speed field, medium porosity, source term intensity, etc.), which are often difficult to obtain in real time and accurately in the complex and variable downhole environment. Therefore, the practicality of numerical simulation technology is greatly limited and it is difficult to use for real-time prediction in the field.
[0006] (3) Data-driven deep learning methods: In recent years, with the development of artificial intelligence technology, deep learning models represented by recurrent neural networks (RNN), long short-term memory networks (LSTM), and temporal convolutional networks (TCN) have been widely used in time series data prediction tasks. Some studies have also begun to try to combine graph convolutional networks (GCN) to model the spatial correlation between different monitoring points. However, purely data-driven models are highly dependent on the completeness of historical data. When faced with rare extreme conditions (such as large-scale pressure surges or tectonic zone surges) that have not appeared in the training samples, the model has poor generalization ability, and the prediction results often lose physical meaning and are difficult to gain engineering reliance.
[0007] In summary, existing technologies are either limited by the "sensing lag" of point-based monitoring, "limited practicality" due to the difficulty in obtaining parameters, or "poor generalization ability" due to reliance on data. None of these technologies effectively solve the challenge of accurately predicting the concentration of hazardous gases in underground mines under the complex coupling of multiple physics fields. Therefore, a new method that deeply integrates physical mechanisms and data-driven advantages is urgently needed to overcome the shortcomings of existing technologies and achieve high-precision, high-robustness prediction of hazardous gases in coal mines. Summary of the Invention
[0008] In view of this, the purpose of this invention is to provide a graph network method for predicting downhole gas concentration that integrates physical information. By constructing a graph structure that integrates physics and causality, and using the partial differential equation of gas transport as a physical constraint, the network is guided to learn spatiotemporal characteristics that conform to physical laws, aiming to improve the accuracy and robustness of predicting hazardous gas concentrations in downholes.
[0009] To achieve the above objectives, the present invention provides the following technical solution: A graph network-based method for predicting downhole gas concentration by incorporating physical information includes the following steps: Step 1: Based on the physical connectivity of the monitoring node set and the underground roadway, construct a spatial adjacency matrix; based on the historical gas concentration data of each monitoring node, construct a causal adjacency matrix using a time-series causal analysis algorithm; merge the spatial adjacency matrix and the causal adjacency matrix to obtain a combined adjacency matrix; Step 2: Input the node feature matrix within the historical time window into the spatiotemporal feature encoder. The spatiotemporal feature encoder uses a graph convolutional network to aggregate spatial information of the node features at each historical time step based on the combined adjacency matrix. Then, it uses a temporal convolutional network to capture temporal dependencies and generates a global conditional vector that condenses historical spatiotemporal information through a temporal attention mechanism. Step 3: Construct a physical information constraint module. Input the global condition vector and combined adjacency matrix into the coordinate learner and output the predicted coordinates of each node. Input the time information, predicted coordinates, and global condition vector into the physical information decoder and output the predicted future gas concentration values and corresponding physical parameters of each node. Step 4: Based on the convection-diffusion-reaction partial differential equation, at randomly sampled spatiotemporal points, use automatic differentiation technology to calculate the physical residual between the concentration prediction value output by the physical information decoder and the physical parameters; Step 5: Construct a total loss function that includes a physical loss function and a data loss function, and train the model to obtain a trained gas concentration prediction model; wherein, the physical loss function is constructed based on the physical residual, and the data loss function is constructed based on the error between the predicted future gas concentration value and the actual monitored value; Step 6: Input the real-time monitoring data into the gas concentration prediction model and output the prediction results of the downhole gas concentration at future times.
[0010] Furthermore, in step one, the set of monitoring nodes is defined based on the actual layout of the downhole working face and the location of the sensor deployment, and is represented as follows: in: For monitoring node data sets; The number of monitoring nodes; For node vectors; The types of gas data for each monitoring node; For gas monitoring data; Spatial adjacency matrix The element is defined as: in: Spatial adjacency matrix The matrix elements in the matrix.
[0011] Furthermore, in step one, the temporal causality analysis algorithm is the Granger causality test, and the method for constructing the causal adjacency matrix is as follows: For any two monitoring nodes and The same gas concentration sequence ,in Establish the inclusion and exclusion of nodes based on the historical window length. Two autoregressive models for the lag term: in: The maximum lag order; and These are the regression coefficients; and For model residuals; and There are two monitoring nodes. and exist Gas concentration at the time step; Calculate the sum of squared residuals for each of the two models. and ,structure Statistic: according to Distributed computation value Quantization nodes For nodes Causal strength: in: gas Next node For nodes The causal strength; gas Next node For nodes Granger causality test value; Various gases The causal adjacency matrix is obtained by weighting and combining the causal strengths. Its elements are: in: Causal adjacency matrix Matrix elements in; The types of gas data for each monitoring node; and the weights of the gases.
[0012] Furthermore, in step one, the spatial adjacency matrix is... With causal adjacency matrix The fusion method is the Hadamard product, which yields a combined adjacency matrix. : in: It is a spatial adjacency matrix; It is a causal adjacency matrix; This indicates element-wise multiplication.
[0013] Furthermore, in step two, the spatiotemporal feature encoder includes: Graph convolutional network layers are used to receive the node feature matrices at each historical time step. and the adjacency matrix with added self-loops By aggregating information from neighboring nodes, the graph coding features for each time step are output. : in: To add a self-loop to the combined adjacency matrix; for The degree matrix, and ; For the first Hidden layer state; For the first Layer trainable weight matrix; It is the ReLU activation function; To hide the dimension.
[0014] A temporal convolutional network layer consists of multiple stacked residual blocks, each containing a causal dilated convolution for encoding features of the graph. Perform convolutions along the time dimension to capture long-term dependencies; The temporal attention layer is used to perform a weighted summation of the graph-encoded features at all time steps to generate the global conditional vector. : Where: attention weight It is calculated by a learnable attention network.
[0015] Furthermore, in step three, the coordinate learner includes: Graph convolutional layers, used to apply the global conditional vector Expanded to a matrix at the node level As input, based on the combined adjacency matrix By fusing neighborhood information, we obtain aggregated node features. : in: To add a self-loop to the combined adjacency matrix; for The degree matrix; The weight matrix is trainable. For feature dimensions; Multilayer perceptron Used to aggregate the features of each node Mapped to 3D spatial predicted coordinates : in: Node features The Row, i.e., node Aggregation characteristics; It is a fully connected network used to map 1D features to 3D spatial coordinates.
[0016] Furthermore, in step three, the physical information decoder is a multilayer perceptron. Its input is time. Predicted coordinates of nodes and global condition vector The combination of , the output is: in: For nodes At any moment Predicted gas concentration values; For nodes The diffusion coefficient at that location; For nodes Wind speed vector at the location; For nodes Attenuation rate at the location; For nodes Source term strength at the location.
[0017] Furthermore, in step four, the convection-diffusion-reaction partial differential equation is: in: This is the diffusion term, representing the net diffusion caused by the concentration gradient; For the convection term, it represents the concentration change caused by the gas carried by the wind speed; This is a decay term, directly proportional to concentration; The source term represents the gas production rate; Gas concentration; For time; For gradient operators; Let be the diffusion coefficient tensor; This is the wind speed vector; The attenuation rate; Physical residuals Automatic differentiation at randomly sampled spatiotemporal points The above calculation yields: in: This represents the concentration prediction value output by the decoder at the sampling point; The gas diffusion coefficient; This is the wind speed vector; The gas decay rate; Through automatic differential calculation; For spatial gradient; The diffusion term, under the isotropic assumption, equals Laplace ; For convection terms; This is the attenuation term; For source terms.
[0018] Furthermore, in step five, the total loss function is expressed as: in: This is the total loss function; The data loss function is composed of the mean square error between the future predicted value and the actual sensor observation value. For physical loss, is the mean of the sum of squares of physical residuals at all monitoring nodes; The weighting coefficients are used to balance the two losses; Predict the number of steps for the future; For nodes At any moment The predicted concentration; For nodes At any moment The true concentration label; For at a point in spacetime The physical residuals calculated above; For nodes The predicted coordinates; For the first Time coordinates of each sampling point: This represents the number of sampling points in the physical loss.
[0019] The beneficial effects of this invention are as follows: This invention presents a graph network-based downhole gas concentration prediction method that integrates physical information. By deeply fusing physical mechanisms and data-driven approaches, it achieves high-precision and robust prediction of downhole gas concentration. The technical effects are as follows: (1) Enhance spatiotemporal representation capability: By constructing a combined graph that integrates physical spatial adjacency and Granger causality, it can reflect the physical constraints of the tunnel and dynamically capture the driving relationship of gas migration, thereby enhancing the model's ability to model complex spatiotemporal relationships. (2) Ensure physical consistency of prediction results: The residual of the convection-diffusion-reaction equation is used as the physical loss function to guide the network to learn a solution that conforms to the gas transport law; even in the face of extreme working conditions that do not appear in the training samples, the model output is still constrained by the physical equation, which significantly improves the generalization ability and engineering reliability. (3) Enhance model interpretability: While learning the concentration prediction, the decoder outputs physical parameters such as diffusion coefficient, wind speed, and source term, so that the model is no longer a "black box" and provides quantitative basis for engineers to invert the field conditions and understand the causes of the prediction.
[0020] In summary, this invention addresses the problem of low prediction accuracy and poor generalization ability in existing downhole gas prediction methods that rely on pure data-driven approaches and lack physical mechanism support. By constructing a graph structure that integrates physics and causality, and using the partial differential equation of gas transport as a physical constraint, the network is guided to learn spatiotemporal characteristics that conform to physical laws. This effectively improves the accuracy and robustness of downhole hazardous gas concentration prediction, and achieves the physical rationality of the results and the interpretability of the process. Attached Figure Description
[0021] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration: Figure 1 This is a flowchart of the graph network downhole gas concentration prediction method that integrates physical information according to the present invention. Detailed Implementation
[0022] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.
[0023] This embodiment proposes a graph network-based method for predicting downhole gas concentration by integrating physical information. By constructing a deep learning architecture for graph networks and using a gas transport model coupled with multiple physics fields as physical constraints, and combining the fusion mechanism of the physical information neural network PINN with graph networks, the method achieves joint learning of physical laws and spatial topological relationships, thereby enabling accurate prediction and early warning of hazardous gas concentrations in coal mines.
[0024] like Figure 1 As shown in the figure, the graph network downhole gas concentration prediction method that integrates physical information in this embodiment includes the following steps.
[0025] Step 1: Construct a spatial adjacency matrix based on the physical connectivity between the monitoring node set and the underground roadway; construct a causal adjacency matrix based on the historical gas concentration data of each monitoring node using a time-series causal analysis algorithm; merge the spatial adjacency matrix with the causal adjacency matrix to obtain a combined adjacency matrix.
[0026] (1) Construction of spatial topology map of mine monitoring nodes.
[0027] Based on the actual working face layout and sensor deployment locations, a set of monitoring nodes is defined as follows: in: For monitoring node data sets; This refers to the number of monitoring nodes, i.e., the gas data monitoring points at different locations; For node vectors; The types of gas data for each monitoring node (e.g., CO, O2, etc.); This refers to the monitoring data of the gas, i.e., its concentration.
[0028] A spatial adjacency matrix is constructed based on the physical connectivity of underground roadways. Its elements are defined as: in: Spatial adjacency matrix The matrix elements in the matrix.
[0029] (2) Constructing a temporal dependency graph based on Granger causality.
[0030] To capture the dynamic driving relationships between nodes during gas migration, Granger causality tests are performed using historical monitoring data. The Granger causality test determines whether a time series helps predict another time series by comparing the residuals of the autoregressive model with and without predictor variables. In this embodiment, the time-series causal analysis algorithm is the Granger causality test. Specifically, the method for constructing the causal adjacency matrix is as follows.
[0031] For any two monitoring nodes The same gas concentration sequence : in: This is the length of the historical window (i.e., the length of the time series used for analysis).
[0032] To test Is it correct? It has predictive capabilities and can establish a list of nodes that include and do not include nodes. Two autoregressive models with lag terms.
[0033] use Its own lagged term prediction : in: The maximum lag order indicates that the past is considered at most. The impact of each time step; These are regression coefficients, reflecting... The contribution of its own lag term to the current value; For model residuals; For monitoring nodes exist Gas concentration at time step.
[0034] join in The lagged terms: in: These are regression coefficients, reflecting... Lagged terms Additional predictive power; for model residuals; and Two monitoring nodes exist Gas concentration at time step.
[0035] Calculate the sum of squared residuals for each of the two models. and : structure Statistic, to test "all" The null hypothesis that "both are zero": in: This represents the average reduction in residuals resulting from each additional lag term. Variance residuals of an unrestricted model.
[0036] According to the F-distribution, it can be calculated value This indicates that the null hypothesis is true (i.e., ... no When the Granger cause is observed, the current The probability of the value; The smaller the value, the stronger the evidence against the null hypothesis. right The more significant the predictive power, the better. That is, this embodiment is based on... Calculated values of distribution Quantization node-to-node Causal strength: in: gas Next node For nodes The causal strength; gas Next node For nodes Granger causality test value. The larger the value, the more likely it is to be a node. Gas concentration changes on nodes The stronger the predictive power of the future concentration, the stronger the correlation between the two points.
[0037] Various gases The causal adjacency matrix is obtained by weighting and combining the causal strengths. Its elements are: in: Causal adjacency matrix Matrix elements in; The types of gas data for each monitoring node; gas The weight.
[0038] By fusing the spatial topology graph with the causal graph, we obtain the adjacency matrix. Specifically, in this embodiment, the spatial adjacency matrix is... With causal adjacency matrix The fusion method is the Hadamard product, resulting in a combined adjacency matrix. for: in: It is a spatial adjacency matrix; It is a causal adjacency matrix; This indicates element-wise multiplication.
[0039] This operation ensures that only spatially adjacent edges with significant causal dependencies are retained in the final graph structure, which reflects both physical connectivity and strengthens dynamic driving relationships.
[0040] Step 2: Input the node feature matrix within the historical time window into the spatiotemporal feature encoder. The spatiotemporal feature encoder uses a graph convolutional network to aggregate spatial information of the node features at each historical time step based on the combined adjacency matrix. Then, it uses a temporal convolutional network to capture temporal dependencies and generates a global conditional vector that condenses historical spatiotemporal information through a temporal attention mechanism.
[0041] In the spatiotemporal feature encoder of this embodiment, spatial information is aggregated for the node features of each historical time step through a graph convolutional network (GCN), and then temporal dependencies are captured through a causal temporal convolutional network (TCN). Finally, a temporal attention mechanism is used to generate a global conditional vector, which condenses the historical spatiotemporal information.
[0042] That is, the spatiotemporal feature encoder in this embodiment includes a graph convolutional network layer, a temporal convolutional network layer, and a temporal attention layer.
[0043] Graph convolutional network layers are used at each historical time step Receive node feature matrix and the adjacency matrix with added self-loops By aggregating information from neighboring nodes to update node representations, the graph coding features at each time step are output. : in: To add a self-loop to the combined adjacency matrix; for The degree matrix, and ; For the first Hidden layer state, initial ; For the first Layer trainable weight matrix; It is the ReLU activation function; This is the hidden dimension. After passing through multiple GCNs, the graph-encoded features at each time step are obtained. , To hide dimensions, spatial topology and causal dependency information were captured.
[0044] The temporal convolutional network layer consists of multiple stacked residual blocks, each containing causal dilated convolution, batch normalization, ReLU activation, and Dropout. Dilated convolutions increase the receptive field for encoding features in the graph. Perform convolutions along the time dimension to capture long-term dependencies.
[0045] The temporal attention layer is used to perform a weighted summation of the graph-encoded features at all time steps to generate the global conditional vector. : Where: attention weight It is calculated by a learnable attention network, highlighting the impact of key historical moments.
[0046] Step 3: Construct a physical information constraint module. Input the global condition vector and combined adjacency matrix into the coordinate learner to output the predicted coordinates of each node. Input the time information, predicted coordinates, and global condition vector into the physical information decoder to output the predicted future gas concentration values and corresponding physical parameters of each node.
[0047] In this step, the global condition vector It deeply integrates with physical laws, including learnable nodal spatial coordinate mapping, a decoder based on convection-diffusion reaction equations, and physical residual calculation. Its goal is to ensure that the model output not only fits the data but also satisfies the physical equations of gas transport.
[0048] (1) Coordinate learner This embodiment designs a normalized coordinate learner, which includes a graph convolutional layer and a multilayer perceptron. .
[0049] Graph convolutional layers are used to apply global conditional vectors. Expanded to a matrix at the node level As input, based on the combined adjacency matrix By fusing neighborhood information, we obtain aggregated node features. : in: yes Expanding the matrix into a node-level representation by... copy Each row is identical; To add a self-loop to the combined adjacency matrix; for The degree matrix; The weight matrix is trainable. The aggregated node features; For feature dimensions.
[0050] Multilayer perceptron Used to aggregate the features of each node Mapped to 3D spatial predicted coordinates : in: Node features The Row, i.e., node Aggregation characteristics; It is a fully connected network used to... 3D features are mapped to 3D spatial coordinates.
[0051] (2) Physical information decoder In this embodiment, the physical information decoder is a multilayer perceptron. Its input is time. Predicted coordinates of nodes and global condition vector The combination of , the output is: in: For nodes At any moment Predicted gas concentration values; For nodes The diffusion coefficient at that location; For nodes Wind speed vector at the location; For nodes Attenuation rate at the location; For nodes Source term strength at the location.
[0052] Step 4: Based on the convection-diffusion-reaction partial differential equation, at randomly sampled spatiotemporal points, use automatic differentiation technology to calculate the physical residual between the concentration prediction value output by the physical information decoder and the physical parameters.
[0053] In this embodiment, the partial differential equation governing the physical laws of downhole gas transport, namely the convection-diffusion-reaction partial differential equation, is expressed as: in: This is the diffusion term, representing the net diffusion caused by the concentration gradient; For the convection term, it represents the concentration change caused by the gas carried by the wind speed; For attenuation terms (such as adsorption, chemical reactions, etc.), they are proportional to concentration. The source term represents the gas production rate; The gas concentration is denoted by time. and spatial coordinates The function; For time; Let be the partial derivative of concentration with respect to time, representing the rate of change of concentration; For gradient operators; Let be the diffusion coefficient tensor; This is the wind speed vector; This represents the attenuation rate.
[0054] Embedded physical constraints, physical residuals Automatic differentiation at randomly sampled spatiotemporal points The above calculation, that is, the calculation of derivatives of each order through automatic differentiation: in: This represents the concentration prediction value output by the decoder at the sampling point; The gas diffusion coefficient; This is the wind speed vector; The gas decay rate; Through automatic differential calculation; For spatial gradient; The diffusion term, under the isotropic assumption, equals Laplace ; For convection terms; This is the attenuation term; For source terms.
[0055] Step 5: Construct a total loss function that includes a physical loss function and a data loss function, and train the model to obtain a trained gas concentration prediction model; wherein, the physical loss function is constructed based on the physical residual, and the data loss function is constructed based on the error between the predicted future gas concentration value and the actual monitored value.
[0056] In this embodiment, physical loss is defined as the mean of the sum of squared residuals at all sampling points, ensuring that the model output satisfies the convection-diffusion-reaction equation, without requiring additional labeled data. Data loss measures the error between the model's predicted values for future times and the actual sensor observations, using mean squared error: The constructed total loss function is expressed as: in: This is the total loss function; The data loss function is composed of the mean square error between the future predicted value and the actual sensor observation value. For physical loss, is the mean of the sum of squares of physical residuals at all monitoring nodes; The weighting coefficients are used to balance the two losses; Predict the number of steps for the future; For nodes At any moment The predicted concentration; For nodes At any moment The true concentration label; For at a point in spacetime The physical residuals calculated above; For nodes The predicted coordinates; Time coordinates of the sampling points: This represents the number of sampling points in the physical loss.
[0057] Accordingly, this embodiment proposes a new underground gas concentration prediction model for coal mines. By integrating physical information neural networks and graph networks, it achieves joint learning of physical laws and spatial topological relationships, thereby enabling accurate prediction and early warning of hazardous gas concentrations in coal mines.
[0058] Step 6: Input the real-time monitoring data into the gas concentration prediction model and output the prediction results of the downhole gas concentration at future times.
[0059] This embodiment addresses the problems of low prediction accuracy and poor generalization ability of traditional methods in predicting underground gas concentrations in coal mines, which are caused by complex physical field coupling, spatiotemporal correlations, and limited monitoring data. It proposes a graph network-based underground gas concentration prediction method that integrates physical information. This method effectively combines the convection-diffusion-reaction physical equations based on gas transport mechanisms with a spatiotemporal data-driven model based on graph networks. Using physical residuals as constraints to guide network training, it significantly improves the accuracy, robustness, and physical consistency of underground hazardous gas concentration prediction, providing reliable technical support for early warning of mine safety production.
[0060] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.
Claims
1. A graph network-based method for predicting downhole gas concentration by integrating physical information, characterized in that: Includes the following steps: Step 1: Based on the physical connectivity of the monitoring node set and the underground roadway, construct a spatial adjacency matrix; based on the historical gas concentration data of each monitoring node, construct a causal adjacency matrix using a time-series causal analysis algorithm; merge the spatial adjacency matrix and the causal adjacency matrix to obtain a combined adjacency matrix; Step 2: Input the node feature matrix within the historical time window into the spatiotemporal feature encoder. The spatiotemporal feature encoder uses a graph convolutional network to aggregate spatial information of the node features at each historical time step based on the combined adjacency matrix. Then, it uses a temporal convolutional network to capture temporal dependencies and generates a global conditional vector that condenses historical spatiotemporal information through a temporal attention mechanism. Step 3: Construct a physical information constraint module. Input the global condition vector and combined adjacency matrix into the coordinate learner and output the predicted coordinates of each node. Input the time information, predicted coordinates, and global condition vector into the physical information decoder and output the predicted future gas concentration values and corresponding physical parameters of each node. Step 4: Based on the convection-diffusion-reaction partial differential equation, at randomly sampled spatiotemporal points, use automatic differentiation technology to calculate the physical residual between the concentration prediction value output by the physical information decoder and the physical parameters; Step 5: Construct a total loss function that includes a physical loss function and a data loss function, and train the model to obtain a trained gas concentration prediction model; wherein, the physical loss function is constructed based on the physical residual, and the data loss function is constructed based on the error between the predicted future gas concentration value and the actual monitored value; Step 6: Input the real-time monitoring data into the gas concentration prediction model and output the prediction results of the downhole gas concentration at future times.
2. The graph network downhole gas concentration prediction method integrating physical information according to claim 1, characterized in that: In step one, the set of monitoring nodes is defined based on the actual layout of the downhole working face and the location of the sensor deployment, and is represented as follows: in: For monitoring node data sets; The number of monitoring nodes; For node vectors; The types of gas data for each monitoring node; For gas monitoring data; Spatial adjacency matrix The element is defined as: in: Spatial adjacency matrix The matrix elements in the matrix.
3. The graph network downhole gas concentration prediction method integrating physical information according to claim 1, characterized in that: In step one, the temporal causality analysis algorithm is the Granger causality test, and the method for constructing the causal adjacency matrix is as follows: For any two monitoring nodes and The same gas concentration sequence ,in Establish the inclusion and exclusion of nodes based on the historical window length. Two autoregressive models for the lag term: in: The maximum lag order; and These are the regression coefficients; and For model residuals; and There are two monitoring nodes. and exist Gas concentration at the time step; Calculate the sum of squared residuals for each of the two models. and Construct statistics: according to Distributed computation value Quantization nodes For nodes Causal strength: in: gas Next node to node The causal strength; gas Next node to node Granger causality test value; Various gases The causal adjacency matrix is obtained by weighting and combining the causal strengths. Its elements are: in: Causal adjacency matrix Matrix elements in; The types of gas data for each monitoring node; gas The weight.
4. The graph network downhole gas concentration prediction method integrating physical information according to claim 1, characterized in that: In step one, the spatial adjacency matrix is... With causal adjacency matrix The fusion method is the Hadamard product, which yields a combined adjacency matrix. : in: It is a spatial adjacency matrix; It is a causal adjacency matrix; This indicates element-wise multiplication.
5. The graph network downhole gas concentration prediction method integrating physical information according to claim 1, characterized in that: In step two, the spatiotemporal feature encoder includes: Graph convolutional network layers are used at each historical time step to receive the node feature matrix and the combined adjacency matrix with self-loops added. By aggregating information from neighboring nodes, the graph coding features for each time step are output. : in: To add a self-loop to the combined adjacency matrix; for The degree matrix, and ; For the first Hidden layer state; For the first Layer trainable weight matrix; It is the ReLU activation function; To hide dimensions; A temporal convolutional network layer consists of multiple stacked residual blocks, each containing a causal dilated convolution for encoding features of the graph. Perform convolutions along the time dimension to capture long-term dependencies; The temporal attention layer is used to perform a weighted summation of the graph-encoded features at all time steps to generate the global conditional vector. : Where: attention weight It is calculated by a learnable attention network.
6. The graph network downhole gas concentration prediction method integrating physical information according to claim 1, characterized in that: In step three, the coordinate learner includes: Graph convolutional layers, used to apply the global conditional vector Expanded to a matrix at the node level As input, based on the combined adjacency matrix By fusing neighborhood information, we obtain aggregated node features. : in: To add a self-loop to the combined adjacency matrix; for The degree matrix; The weight matrix is trainable. For feature dimensions; Multilayer perceptron Used to aggregate the features of each node Mapped to 3D spatial predicted coordinates : in: Node features The Row, i.e., node Aggregation characteristics; It is a fully connected network used to... 3D features are mapped to 3D spatial coordinates.
7. The graph network downhole gas concentration prediction method integrating physical information according to claim 1, characterized in that: In step three, the physical information decoder is a multilayer perceptron. Its input is time. Predicted coordinates of nodes and global condition vector The combination of , the output is: in: For nodes At any moment Predicted gas concentration values; For nodes The diffusion coefficient at that location; For nodes Wind speed vector at the location; For nodes Attenuation rate at the location; For nodes Source term strength at the location.
8. The graph network downhole gas concentration prediction method integrating physical information according to claim 1, characterized in that: In step four, the convection-diffusion-reaction partial differential equation is: in: This is the diffusion term, representing the net diffusion caused by the concentration gradient; For the convection term, it represents the concentration change caused by the gas carried by the wind speed; This is a decay term, directly proportional to concentration; The source term represents the gas production rate; Gas concentration; For time; For gradient operators; Let be the diffusion coefficient tensor; is the wind speed vector; is the attenuation rate; Physical residuals Automatic differentiation at randomly sampled spatiotemporal points The above calculation yields: Where: is the concentration prediction value output by the decoder at the sampling point; is the gas diffusion coefficient; This is the wind speed vector; The gas decay rate; Through automatic differential calculation; For spatial gradient; The diffusion term, under the isotropic assumption, equals Laplace ; For convection; for attenuation; For source terms.
9. The graph network downhole gas concentration prediction method integrating physical information according to claim 1, characterized in that: In step five, the total loss function is expressed as: in: This is the total loss function; The data loss function is composed of the mean square error between the future predicted value and the actual sensor observation value. For physical loss, is the mean of the sum of squares of physical residuals at all monitoring nodes; The weighting coefficients are used to balance the two losses; Predict the number of steps for the future; For nodes The predicted concentration at time; For the node at time The true concentration label; for a point in time and space. The physical residuals calculated above; For nodes The predicted coordinates; Let be the time coordinate of the i-th sampling point; be the number of sampling points in the physical loss.