A method for predicting the seismic possibility of hydraulic fracturing

Abstract

The present invention provides a method for predicting the possibility of hydraulic fracturing earthquakes, which relates to the technical field of hydraulic fracturing. The method includes constructing a physical constraint depth operator network model combined with the importance sampling method; collecting and processing data under different scenarios as training data; performing iterative training on the physical constraint depth operator network model to obtain the weights of the physical constraint depth operator network model at the optimal step; initializing the physical constraint depth operator network model, and obtaining the prediction result of the possibility of hydraulic fracturing earthquakes in the target scenario according to the target hydraulic fracturing earthquake prediction task data. The present invention incorporates importance sampling into the depth operator network, and by calculating the importance of each function in the function set and adaptively changing the sampling distribution, it accelerates model convergence and improves model stability, solves the problems of difficult training, slow convergence speed, and low solution accuracy in the scenario of unlabeled data, and makes a more accurate prediction of the possibility of hydraulic fracturing earthquakes.

Description

Technical Field

[0001] The present invention belongs to the technical field of hydraulic fracturing, and particularly relates to a method for predicting the possibility of hydraulic fracturing-induced earthquakes. Background Art

[0002] Hydraulic fracturing technology has become the standard method for the energy industry to extract deep gas storage, ore storage, and heat storage. Hydraulic fracturing is accompanied by processes such as injecting fracturing fluid into the deep underground to form a fracture zone, establishing a fluid channel to extract oil and gas energy, and reinjecting wastewater. Due to the existence of natural fracture zones or weak zones such as faults underground, the above industrial activities may cause obstacles to underground mining and even induce earthquakes. Most of the induced earthquakes related to fluid injection occur in the basement rock, which is 1 to 4 kilometers deeper than the target formation. These instability problems caused by fluid injection will seriously hinder the efficient progress of energy extraction activities, and at the same time pose a threat to production safety and the lives of surrounding residents. Therefore, it is crucial to clarify the stability problems caused during the fluid injection process.

[0003] In hydraulic fracturing activities, the possibility of fluid injection-induced earthquakes can be represented by the following mathematical model:

[0004]

[0005] Wherein, represents the seismic activity rate relative to the steady-state seismic activity rate at a reference stress rate of ; represents time; represents the Coulomb stress rate; represents that the characteristic time scale is related to the physical properties of the lithosphere (such as creep behavior or rheological properties), and is also related to the external stress loading rate that triggers earthquakes. Solving this ordinary differential equation can predict the seismic activity rate. However, the Coulomb stress rate in the above formula needs to be calculated and estimated through spline curve fitting and a solver, and there is no explicit expression, so that the equation has no analytical solution expression and can only rely on numerical solution methods for approximate calculation.

[0006] Traditional numerical solution methods include the finite difference method (FDM), the finite element method (FEM), and the finite volume method (FVM). These methods approximate the solution of the fluid state in space and time by discretizing the equations. For example, the finite difference method approximates differential operations at discrete nodes and is suitable for some simple geometric structures but is not flexible enough in the complex fractures of hydraulic fracturing. The finite element method, although suitable for dealing with complex geological structures and boundary conditions, has a high computational cost and is not suitable for real-time simulation. The finite volume method is popular for its good description of conservation equations but has insufficient accuracy when dealing with highly nonlinear conditions. Although traditional numerical solution methods are quite mature, they still face the problems of long calculation time and high resource consumption.

[0007] In recent years, the progress of deep learning technology has provided new ideas for PDE solving. Among them, the Deep Operator Network (DeepONet) is an innovative deep learning model for fast solving partial differential equations. The core of the Deep Operator Network is its ability to learn the mapping relationship from the input to the output of partial differential equations, that is, to directly obtain the distribution of the solution through training without discretely solving point by point step by step. By inputting initial conditions, boundary conditions, etc., the Deep Operator Network can directly predict the pressure distribution and fluid flow pattern in the entire region, greatly shortening the calculation time. For the hydraulic fracturing process, the application advantages of the Deep Operator Network are particularly obvious: after training, it can achieve real-time prediction of the fluid pressure and flow in the fracture network. This enables engineers to adjust the injection parameters in real time according to the model results, optimize the fracturing process, and reduce the consumption of computing resources.

[0008] The subsequently proposed Physics-informed DeepONet adds an additional partial differential equation loss term to the loss function of the Deep Operator Network, thus greatly reducing or even completely avoiding the dependence on labeled training data and further expanding the application scenarios of the Deep Operator Network. For the sake of simplicity, the "Deep Operator Network" in the following text refers to the Deep Operator Network integrated with physical constraints.

[0009] Although the Deep Operator Network avoids problems such as long calculation time, discretized grids, and difficulty in solving inverse problems of traditional numerical solvers to a certain extent. However, for some complex partial differential equation problems, few-label data problems, and unlabeled data problems, the Deep Operator Network has problems such as high training difficulty, slow convergence speed, and low solution accuracy. In the context of hydraulic fracturing, the prediction of seismic activity rate is also one of them. Summary of the Invention

[0010] In view of the above deficiencies in the prior art, the present invention provides a method for predicting the likelihood of hydraulic fracturing earthquakes, which solves the problems of difficult training, slow convergence speed, and low solution accuracy of the depth operator network in the scenario of unlabeled data, and thus enables a more accurate prediction of the likelihood of hydraulic fracturing earthquakes.

[0011] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for predicting the likelihood of hydraulic fracturing earthquakes, comprising the following steps:

[0012] S1. Construct a physical constraint depth operator network model PDIS incorporating the importance sampling method;

[0013] S2. Collect and process data of the seismic activity rate mathematical model under different scenarios as training data;

[0014] S3. Use the training data and partial differential equation constraints to iteratively train the physical constraint depth operator network model PDIS to obtain the weights of the physical constraint depth operator network model PDIS at the optimal step;

[0015] S4. Initialize the physical constraint depth operator network model PDIS using the weights obtained in step S3, and obtain the prediction result of the likelihood of hydraulic fracturing earthquakes in the target scenario according to the target hydraulic fracturing earthquake prediction task data.

[0016] The beneficial effects of the present invention are as follows: By constructing the physical constraint depth operator network model PDIS, the present invention integrates importance sampling into the depth operator network, accelerates model convergence, improves model stability by calculating the importance of each function in the function set and adaptively changing the sampling distribution, solves the problems of difficult training, slow convergence speed, and low solution accuracy of the depth operator network in the scenario of unlabeled data, and thus enables a more accurate prediction of the likelihood of hydraulic fracturing earthquakes.

[0017] Further, the expression of the bias reweighted loss function of the physical constraint depth operator network model PDIS is as follows:

[0018]

[0019]

[0020]

[0021] Among them, represents the bias reweighted loss function of the physical constraint depth operator network model PDIS, represents the function set of the current batch, obtained by the importance sampling method of functions at the start of a training iteration, i represents the i th function, Denote the sampling weight corresponding to the i th function, denote the loss function of the physical constraint depth operator network, denote the function dataset N the i th function in, denote the collocation coordinate set input to the backbone network, denote the weight parameter of the physical constraint depth operator network model, , and respectively denote the partial differential equation loss, initial condition loss, and boundary condition loss in the physical constraint method, and both denote weights, denote the original sampling probability of the i th function, denote the function sampling probability, denote the function dataset.

[0022] The beneficial effect of the above further scheme is that the bias reweighted loss function is used to implement the physical constraint of the partial differential equation, while preventing the convergence bias caused by the change of the sampling distribution. While changing the sampling distribution and accelerating the training convergence, the bias reweighted loss function ensures that the convergence direction remains unchanged, which is an essential part of the correct implementation of the importance sampling method.

[0023] Furthermore, the training data includes the Coulomb stress rate data under different scenarios, irrelevant constant parameters and initial boundary conditions under different scenarios, where the Coulomb stress rate data includes the discrete point set of the Coulomb stress rate and the spline curve fitting representation.

[0024] The beneficial effect of the above further scheme is that in the earthquake activity rate prediction scenario, obtaining sufficient Coulomb stress rate data includes the discrete point set of the Coulomb stress rate and the spline curve fitting representation, ensuring the convergence stability of the training result of the physical constraint depth operator network model PDIS and the generalization ability of the model.

[0025] Furthermore, the step S3 includes the following steps:

[0026] S301. Initialize the bias weight parameter of the physical constraint depth operator network model PDIS, and generate a sampling point set uniformly distributed in the time dimension;

[0027] S302. At the beginning of an iteration, input the Coulomb stress rate The discrete point set and the sampling point set, and according to the output of the physical constraint depth operator network model PDIS and the Coulomb stress rate The spline curve of , by calculating the Coulomb stress rate of each group one by one The total sum of the partial differential equation errors of the data on the sampling point set, obtaining the Coulomb stress rate of each group The function sampling probability;

[0028] S303. Perform batch sampling according to the function sampling probability, and use the sampled Coulomb stress rate Data and the randomly generated time coordinate sequence are used as the inputs of the branch network and the backbone network respectively, and the output of the physical constraint depth operator network model PDIS is obtained. Among them, the output of the physical constraint depth operator network model PDIS is the prediction result of the hydraulic fracturing seismic possibility under the target scenario;

[0029] S304. Based on the output of the physical constraint depth operator network model PDIS, calculate the bias reweighted loss and perform gradient optimization to adjust the parameters of the physical constraint depth operator network model PDIS;

[0030] S305. Repeat steps S301 to S304 until the iteration ends and retain the weights of the physical constraint depth operator network model PDIS at the optimal step. Among them, the physical constraint depth operator network model PDIS includes a backbone network and a branch network.

[0031] The beneficial effect of the above further solution is that in step S03, the physical constraint depth operator network model PDIS calculates the importance of the discrete point set of the Coulomb stress rate under different scenarios, adaptively changes the sampling distribution, thereby accelerating the model convergence, improving the stability of the prediction result of the hydraulic fracturing seismic activity rate, and at the same time improving the accuracy of the network model for predicting the hydraulic fracturing seismic possibility.

[0032] Furthermore, the expression of the function sampling probability in step S302 is as follows:

[0033]

[0034]

[0035] Among them, represents the function sampling probability, S represents the set of sampling point sets, represents that the input function is at the time the partial differential equation loss at the position, represents that the input function is at the time the partial differential equation loss at the position, and respectively represent the N th n th i functions in the function dataset, represents the k th time coordinate in the uniform time coordinate sequence within the target time interval, represents the weight parameters of the physical constraint depth operator network model PDIS, represents the predicted result of the hydraulic fracturing seismic probability under the output target scenario, represents the characteristic time scale, represents the Coulomb stress rate.

[0036] The beneficial effect of the above further solution is that by calculating the sum of the partial differential equation losses of each input function (i.e., the discretized representation of the Coulomb stress rate under different scenarios) on the uniform grid, the PDIS weights of the physical constraint depth operator network model approximately obtain the importance distribution of each function without adding too many additional calculation steps, facilitating subsequent function sampling.

[0037] Furthermore, the step S4 includes the following steps:

[0038] S401. Initialize the physical constraint depth operator network model PDIS using the PDIS weights of the physical constraint depth operator network model with the optimal step;

[0039] S402. Obtain the discretized point set representation of the Coulomb stress rate under the target scenario and use it as the input of the branch network;

[0040] S403. Randomly generate a time coordinate sequence in the target prediction time interval and use it as the input of the backbone network;

[0041] S404. Perform forward propagation according to the input results of step S402 and step S403;

[0042] S405. According to the forward propagation result, perform an inner product operation on the outputs of the backbone network and the branch network to obtain the predicted result of the hydraulic fracturing seismic probability under the target scenario.

[0043] The beneficial effect of the above further solution is that by loading the trained physical constraint depth operator network model PDIS, the present invention can output the predicted result of the seismic activity rate for a given coordinate according to any input function (the discretized representation of the Coulomb stress rate under different physical scenarios), thereby realizing the prediction of hydraulic fracturing earthquakes. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a schematic structural diagram of the physical constraint depth operator network model PDIS.

[0045] Figure 2 It is a schematic diagram of the importance sampling process.

[0046] Figure 3 It is the method flow chart of the present invention. Detailed implementation manners

[0047] The following describes the detailed implementation manners of the present invention to facilitate those skilled in the art of this technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the detailed implementation manners. For those of ordinary skill in the art of this technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions created using the concept of the present invention are within the scope of protection.

[0048] Embodiment

[0049] The hydraulic fracturing earthquake likelihood prediction method of the present invention is based on a Physics-informed Deep Operator Network with Importance Sampling (PDIS). It mainly predicts the likelihood of earthquakes induced by hydraulic fracturing activities through PDIS. As Figure 3 shown, the present invention provides a hydraulic fracturing earthquake likelihood prediction method, and its implementation method is as follows:

[0050] S1. Construct a physical constraint depth operator network model PDIS combined with the importance sampling method;

[0051] In this embodiment, as Figure 1 shown ( Figure 1 where represents the i th function , x represents the input coordinates; b From 1 to b p are the p outputs of the branch network, t From 1 to t p are the p outputs of the main network. The function of both is to obtain the predicted value of the final network at the input function , input coordinates x through the inner product; in the loss function, M represents the function set of the current batch, i is the function subscript from 1 to M , represents the sampling weight, X representsx a set of represents the weight parameters of the physical constraint depth operator network model, and both represent weights), the physical constraint depth operator network model PDIS includes:

[0052] a backbone network, which is used to obtain the time position of the seismic activity rate according to the time coordinate sequence of the randomly generated target prediction time interval;

[0053] a branch network, which is used to receive the discrete point set representation of the Coulomb stress rate in the obtained target scenario;

[0054] an output layer, which is used to perform an inner product operation on the outputs of the backbone network and the branch network to obtain the predicted result of the hydraulic fracturing earthquake possibility in the target scenario.

[0055] In this embodiment, the physical constraint depth operator network model PDIS is a physical constraint depth operator model combined with the importance sampling method, and its purpose is to fit the solution operator of a class of partial differential equations during the training process, so as to achieve the purpose of quickly solving this class of partial differential equations. In the scenario of the present invention, the purpose of the physical constraint depth operator network model PDIS is to solve the partial differential equation of the fluid injection-induced seismic activity rate in the hydraulic fracturing scenario, so as to be able to predict the change of the seismic activity rate with time under different Coulomb stress rate curves. Therefore, there is an urgent need to propose a new method for predicting the possibility of hydraulic fracturing earthquakes, which can avoid the problems of large computational resource consumption and limited grids in traditional numerical solution methods, and further improve the convergence speed of deep learning during the training process and the solution accuracy of partial differential equations, so as to predict the hydraulic fracturing process more efficiently and accurately, and avoid instability problems to the greatest extent, and ensure the safe and efficient progress of energy extraction activities.

[0056] In this embodiment, the physical constraint depth operator network model PDIS includes: a backbone network, a branch network and a bias reweighting loss function. Among them, the backbone network is usually composed of a fully connected network, and its input is the coordinate position of a collocation point (i.e., the time coordinate sequence of the target time interval), which is used to define the position of the objective function (i.e., the seismic activity rate); the branch network can be composed of a fully connected layer, a convolutional layer or other network structures, and its input is the discrete sampling points of a function (i.e., the discrete point set of the Coulomb stress rate), usually a vector, and the inner product of the outputs of the backbone network and the branch network is finally used to obtain the predicted value of the objective function under the current input function and input coordinates. The bias reweighting loss function is used to implement the physical constraint of the partial differential equation and prevent the convergence deviation caused by the change of the sampling distribution.

[0057] In this embodiment, during a training iteration, first, the importance sampling probabilities of each function in the function set are calculated. Subsequently, function importance sampling is performed to obtain the function batch for the current iteration. Then, a coordinate batch is randomly sampled. Finally, the sampled data of both is used to train the network, calculate the deviation reweighted loss, and optimize the network model parameters.

[0058] Function sampling probability: In the physical constraint depth operator network model PDIS, the function sampling probability is the ratio of the sum of the loss function values of the sampling point set in its domain to the sum of all functions:

[0059]

[0060] Among them, S represents the set of sampling point sets, which is generated by uniform sampling within the entire domain, represents the function data set, represents the partial differential equation loss at the position when the input function is i.e., the mean square error between the actual calculation result of the partial differential equation expression and the target value. Through the above process, the present invention can evaluate the error magnitude of each function in the function set, making it more likely for important functions to be selected for training. In the hydraulic fracturing seismic prediction scenario of the present invention, is the uniform time coordinate sequence within the target time interval, S corresponds to the data set discretely represented by the Coulomb stress rate under different environmental conditions. That is, in the hydraulic fracturing seismic prediction scenario of the present invention, the input function set is actually the data set discretely represented by the Coulomb stress rate under different environmental conditions; the set of sampling point sets is actually the uniform time coordinate sequence within the target time interval, represents the partial differential equation loss at the position when the input function is i.e., the mean square error between the actual calculation result of the partial differential equation expression and the target value. Through the above process, the present invention can evaluate the error magnitude of each function in the function set, making it more likely for important functions to be selected for training. In the hydraulic fracturing seismic prediction scenario of the present invention, is the uniform time coordinate sequence within the target time interval, corresponds to the data set discretely represented by the Coulomb stress rate under different environmental conditions. That is, in the hydraulic fracturing seismic prediction scenario of the present invention, the input function set is actually the data set discretely represented by the Coulomb stress rate under different environmental conditions; the set of sampling point sets is actually the uniform time coordinate sequence within the target time interval,

[0061]

[0062] Among them, represents the function sampling probability, S represents the set of sampling point sets, represents the partial differential equation loss at the position when the input function is i.e., the mean square error between the actual calculation result of the partial differential equation expression and the target value. Through the above process, the present invention can evaluate the error magnitude of each function in the function set, making it more likely for important functions to be selected for training. In the hydraulic fracturing seismic prediction scenario of the present invention, represents the partial differential equation loss at the position when the input function is i.e., the mean square error between the actual calculation result of the partial differential equation expression and the target value. Through the above process, the present invention can evaluate the error magnitude of each function in the function set, making it more likely for important functions to be selected for training. In the hydraulic fracturing seismic prediction scenario of the present invention, i.e., the mean square error between the actual calculation result of the partial differential equation expression and the target value. Through the above process, the present invention can evaluate the error magnitude of each function in the function set, making it more likely for important functions to be selected for training. In the hydraulic fracturing seismic prediction scenario of the present invention, represents the partial differential equation loss at the position when the input function is and respectively represent the function data set N in the nThe i -th function and the -th function, k denote the -th time coordinate of the uniform time coordinate sequence within the target time interval, denote the predicted result of the hydraulic fracturing seismic possibility under the output target scenario, denote the Coulomb stress rate, n from 1 to , denote the N -th function in the function set n , that is, the Coulomb stress rate under different environmental conditions -th representation in the discretized representation, n denote the k -th representation from 1 to S , which is S the k -th element in the set, that is, the k -th time coordinate of the uniform time coordinate sequence within the target time interval, denote the characteristic time scale, which is regarded as a constant in this method. The specific value usually comes from experimental data or observational fitting, and is related to the physical properties of the lithosphere (such as creep behavior or rheological properties), and is also related to the external stress loading rate that triggers earthquakes.

[0063] In this embodiment, as shown in the above formula, the present invention calculates the partial differential equation error of each function on the sampling point set before the start of training, and then calculates the sampling probability of each function in equal proportion. is the coordinate set obtained by uniform sampling in the domain, and its purpose is to ensure the accurate estimation of the function error while minimizing the growth of performance overhead. When the sum of the errors of the function on the sampling point set is larger, the sampling probability is also larger. Such an importance sampling method makes the network adaptively tilt the sampling distribution towards the high-error data points during the training process, so that the convergence speed of the network can be increased, and at the same time, the convergence stability and prediction accuracy of the network can be improved. The schematic diagram of the sampling process can be seen in Figure 2 .

[0064] In this embodiment, the total loss function of the physical constraint depth operator network model PDIS is:

[0065]

[0066] where denote the function set of the current batch, which is obtained by the importance sampling method of the function at the start of a training iteration, The collocation coordinate set representing the main network input consists of parts such as the coordinates within the domain and the coordinates on the domain boundary, etc. is the i sampling weight corresponding to the th function, which is multiplied by the corresponding loss of the function to achieve the deviation reweighting operation.

[0067]

[0068] The three terms in the formula respectively correspond to the partial differential equation loss, the initial condition loss, and the boundary condition loss in the physical constraint method. The coefficients of the latter two terms are used to adjust the proportion of the three parts of the loss.

[0069] For the sampling weight of the function, its magnitude is equal to the ratio of the random sampling probability to the importance sampling probability:

[0070]

[0071] Among them, represents the deviation reweighting loss function of the physical constraint depth operator network model PDIS, represents the function set of the current batch, which is obtained by the importance sampling method of the function at the start of a training iteration, i represents the i th function, represents the i sampling weight corresponding to the th function, represents the loss function of the physical constraint depth operator network, N represents the i th function in the function data set, represents the collocation coordinate set input to the backbone network, , and respectively represent the partial differential equation loss, the initial condition loss, and the boundary condition loss in the physical constraint method, and both represent weights, represents the i original sampling probability of the th function, represents the function sampling probability,

[0072] S2. Collect and process the data of the seismic activity rate mathematical model under different scenarios as training data;

[0073] In this embodiment, the training data includes the Coulomb stress rate data under different scenarios, the irrelevant constant parameters and the initial boundary conditions under different scenarios. Among them, the Coulomb stress rate data includes the discrete point set of the Coulomb stress rate and the representation of the spline curve fitting. The Coulomb stress rate curve after discretization is used as the input function of the branch network. In this embodiment, the Coulomb stress rate is the most important training data, which represents the change rate of the stress state on the fault plane in the prediction of the seismic activity rate. It combines the changes of the shear stress and the effective normal stress into one quantity, reflecting the sliding tendency of the fault in the earthquake-induced environment. In this embodiment, a set of Coulomb stress rate data includes two parts: the discrete point set of the Coulomb stress rate and the representation of the spline curve fitting. Among them, the former is used as the input of the branch network, and the latter is used as an additional variable for the loss of the partial differential equation during the training process. Collecting sufficient Coulomb stress rate data can provide enough training samples for the subsequent physical constraint depth operator network model PDIS to fit the solution operator, thereby improving the generalization ability of the model and ensuring that the model can correctly learn the mapping relationship from the Coulomb stress rate data to the seismic activity rate. In this embodiment, the training data includes the Coulomb stress rate data under different scenarios, the irrelevant constant parameters and the initial boundary conditions under different scenarios. Among them, the Coulomb stress rate data includes the discrete point set of the Coulomb stress rate and the representation of the spline curve fitting. The Coulomb stress rate curve after discretization is used as the input function of the branch network.

[0074] In this embodiment, the Coulomb stress rate is the most important training data, which represents the change rate of the stress state on the fault plane in the prediction of the seismic activity rate. It combines the changes of the shear stress and the effective normal stress into one quantity, reflecting the sliding tendency of the fault in the earthquake-induced environment. In this embodiment, the Coulomb stress rate is the most important training data, which represents the change rate of the stress state on the fault plane in the prediction of the seismic activity rate. It combines the changes of the shear stress and the effective normal stress into one quantity, reflecting the sliding tendency of the fault in the earthquake-induced environment.

[0075] In this embodiment, a set of Coulomb stress rate data includes two parts: the discrete point set of the Coulomb stress rate and the representation of the spline curve fitting. Among them, the former is used as the input of the branch network, and the latter is used as an additional variable for the loss of the partial differential equation during the training process. Collecting sufficient Coulomb stress rate data can provide enough training samples for the subsequent physical constraint depth operator network model PDIS to fit the solution operator, thereby improving the generalization ability of the model and ensuring that the model can correctly learn the mapping relationship from the Coulomb stress rate data to the seismic activity rate. In this embodiment, a set of Coulomb stress rate data includes two parts: the discrete point set of the Coulomb stress rate and the representation of the spline curve fitting. Among them, the former is used as the input of the branch network, and the latter is used as an additional variable for the loss of the partial differential equation during the training process. Collecting sufficient Coulomb stress rate data can provide enough training samples for the subsequent physical constraint depth operator network model PDIS to fit the solution operator, thereby improving the generalization ability of the model and ensuring that the model can correctly learn the mapping relationship from the Coulomb stress rate data to the seismic activity rate. In this embodiment, the training data includes the Coulomb stress rate data under different scenarios, the irrelevant constant parameters and the initial boundary conditions under different scenarios. Among them, the Coulomb stress rate data includes the discrete point set of the Coulomb stress rate and the representation of the spline curve fitting. The Coulomb stress rate curve after discretization is used as the input function of the branch network.

[0076] S3. Use the training data and the partial differential equation constraints to iteratively train the physical constraint depth operator network model PDIS to obtain the weights of the physical constraint depth operator network model PDIS with the optimal step. The implementation method is as follows:

[0077] S301. Initialize the bias weight parameters of the physical constraint depth operator network model PDIS and generate a sampling point set uniformly distributed in the time dimension.

[0078] S302. At the beginning of an iteration, input the discrete point set of the Coulomb stress rate and the sampling point set, and calculate the total error of the partial differential equation of each group of Coulomb stress rate data on the sampling point set according to the output of the physical constraint depth operator network model PDIS and the spline curve of the Coulomb stress rate, so as to obtain the function sampling probability of each group of Coulomb stress rate data. S303. Perform batch sampling according to the function sampling probability, and sample the Coulomb stress rate In this embodiment, the training data includes the Coulomb stress rate data under different scenarios, the irrelevant constant parameters and the initial boundary conditions under different scenarios. Among them, the Coulomb stress rate data includes the discrete point set of the Coulomb stress rate and the representation of the spline curve fitting. The Coulomb stress rate curve after discretization is used as the input function of the branch network. In this embodiment, the training data includes the Coulomb stress rate data under different scenarios, the irrelevant constant parameters and the initial boundary conditions under different scenarios. Among them, the Coulomb stress rate data includes the discrete point set of the Coulomb stress rate and the representation of the spline curve fitting. The Coulomb stress rate curve after discretization is used as the input function of the branch network. In this embodiment, the training data includes the Coulomb stress rate data under different scenarios, the irrelevant constant parameters and the initial boundary conditions under different scenarios. Among them, the Coulomb stress rate data includes the discrete point set of the Coulomb stress rate and the representation of the spline curve fitting. The Coulomb stress rate curve after discretization is used as the input function of the branch network.

[0079] S303. Perform batch sampling according to the function sampling probability, and sample the Coulomb stress rate The data and the randomly generated time coordinate sequence are used as the inputs of the branch network and the backbone network respectively, and the output of the physical constraint depth operator network model PDIS is obtained. Among them, the output of the physical constraint depth operator network model PDIS is the prediction result of the hydraulic fracturing seismic possibility under the target scenario;

[0080] S304. Calculate the deviation reweighted loss based on the output of the physical constraint depth operator network model PDIS, and perform gradient optimization to adjust the parameters of the physical constraint depth operator network model PDIS;

[0081] S305. Repeat steps S301 to S304 until the iteration ends and retain the weights of the physical constraint depth operator network model PDIS at the optimal step. Among them, the physical constraint depth operator network model PDIS includes a backbone network and a branch network.

[0082] In this embodiment, during the training process, first, the bias weight parameters of the physical constraint depth operator network model PDIS are initialized, and at the same time, a sampling point set uniformly distributed in the time dimension is generated for subsequent evaluation of the importance of the function. Subsequently, at the beginning of an iteration, the Coulomb stress rate discrete point set and the sampling point set are input. According to the output of the physical constraint depth operator network model PDIS and the spline curve interpolation of the Coulomb stress rate, the sum of the partial differential equation errors of each group of Coulomb stress rate data on the sampling point set is calculated one by one, so as to be equivalently transformed into calculating the sampling probability of each group of Coulomb stress rate Then, batch sampling is performed according to the sampling probability, and the sampled Coulomb stress rate data and the randomly generated time coordinate sequence are used as the inputs of the branch network and the main network respectively to obtain the network output. Calculate the deviation reweighted loss based on the model output, and perform gradient optimization to adjust the model parameters. Repeat the above steps until the iteration ends and retain the weights of the physical constraint depth operator network model PDIS at the optimal step.

[0083] S4. Initialize the physical constraint depth operator network model PDIS using the weights obtained in step S3, and obtain the prediction result of the hydraulic fracturing seismic possibility under the target scenario according to the target hydraulic fracturing seismic prediction task data. The implementation method is as follows:

[0084] S401. Initialize the physical constraint depth operator network model PDIS using the weights of the physical constraint depth operator network model PDIS at the optimal step;

[0085] S402. Obtain the discrete point set representation of the Coulomb stress rate under the target scenario and use it as the input of the branch network;

[0086] S403. Randomly generate a time coordinate sequence for the target prediction time interval as the input to the backbone network;

[0087] S404. Perform forward propagation based on the input results of step S402 and step S403;

[0088] S405. According to the forward propagation result, perform an inner product operation on the outputs of the backbone network and the branch network to obtain the prediction result of the hydraulic fracturing earthquake possibility in the target scenario.

[0089] In this embodiment, when the physical constraint depth operator network model PDIS is predicting, first use the optimal physical constraint depth operator network model PDIS parameters to initialize the physical constraint depth operator network model PDIS. Then, obtain the discrete point set representation of the Coulomb stress rate in the target scenario through detection or simulation, etc., as the input to the branch network; then, generate a time coordinate sequence for the target prediction time interval as the input to the backbone network. Finally, input the data into the initialized physical constraint depth operator network model PDIS, and after forward propagation, obtain the output result, that is, the prediction result of the hydraulic fracturing fluid-induced earthquake possibility in the target scenario. In summary, compared with traditional numerical solvers, the present invention has fewer hyperparameters and does not require time grid division with a fixed step size. For the Coulomb stress rate curve without an explicit expression, the present invention can directly use the discretization result as the input to the network model without additional preprocessing operations. Compared with the existing depth operator network, the present invention can adaptively select training batches according to the importance of the Coulomb stress rate curve, accelerate model training, and improve convergence stability and accuracy.

[0090] In the present invention, specific embodiments are used to elaborate the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

[0091]

[0092] Those of ordinary skill in the art will realize that the embodiments described here are for helping readers understand the principle of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various specific deformations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed in the present invention, and these deformations and combinations are still within the protection scope of the present invention.

[0092] Those of ordinary skill in the art will realize that the embodiments described here are for helping readers understand the principle of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various specific deformations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed in the present invention, and these deformations and combinations are still within the protection scope of the present invention.

Claims

1. A method for predicting the possibility of hydraulic fracturing earthquakes, characterized in that, It includes the following steps: S1. Construct a physics-constrained deep operator network model PDIS that combines the importance sampling method; The expression of the bias reweighted loss function of the physics-constrained deep operator network model PDIS is as follows: Among them, represents the bias reweighted loss function of the physical constraint depth operator network model PDIS, represents the function set of the current batch, which is obtained by the importance sampling method of functions at the start of a training iteration, i represents the i th function, represents the i th sampling weight corresponding to the th function, represents the loss function of the physical constraint depth operator network, N represents the i th function in the function data set represents the collocation point coordinate set input to the backbone network, represents the weight parameters of the physical constraint depth operator network model, , and respectively represent the partial differential equation loss, the initial condition loss, and the boundary condition loss in the physical constraint method, and both represent weights, represents the original sampling probability of the i th function, represents the function sampling probability, represents the function data set; S2. Collect and process the data of the seismic activity rate mathematical model under different scenarios as training data; S3. Use the training data and partial differential equation constraints to iteratively train the physics-constrained deep operator network model PDIS to obtain the weights of the physics-constrained deep operator network model PDIS at the optimal step, specifically: S301. Initialize the bias weight parameters of the physics-constrained deep operator network model PDIS and generate a sampling point set uniformly distributed in the time dimension; S302. At the beginning of an iteration, input the discrete point set and sampling point set of the Coulomb stress rate and, based on the output of the physical constraint depth operator network model PDIS and the spline curve of the Coulomb stress rate , by calculating the total sum of the partial differential equation errors of each group of Coulomb stress rate data on the sampling point set, obtain the function sampling probability of each group of Coulomb stress rate ; S303. Perform batch sampling according to the function sampling probability, and use the sampled Coulomb stress rate data and the randomly generated time coordinate sequence as the inputs of the branch network and the backbone network respectively, and obtain the output of the physical constraint depth operator network model PDIS, where the output of the physical constraint depth operator network model PDIS is the prediction result of the hydraulic fracturing seismic possibility under the target scenario; S304. Based on the output of the physics-constrained deep operator network model PDIS, calculate the bias reweighted loss and perform gradient optimization to adjust the parameters of the physics-constrained deep operator network model PDIS; S305. Repeat steps S301 to S304 until the iteration ends and retain the weights of the physics-constrained deep operator network model PDIS at the optimal step, where the physics-constrained deep operator network model PDIS includes a backbone network and a branch network; S4. Initialize the physics-constrained deep operator network model PDIS with the weights obtained in step S3, and obtain the prediction result of the hydraulic fracturing earthquake possibility in the target scenario according to the target hydraulic fracturing earthquake prediction task data.

2. The hydraulic fracturing seismic probability prediction method according to claim 1, wherein The training data includes Coulomb stress rate data under different scenarios, irrelevant constant parameters under different scenarios, and initial boundary conditions. Among them, the Coulomb stress rate data includes a discrete point set of the Coulomb stress rate and a representation fitted by a spline curve. The data, irrelevant constant parameters under different scenarios, and initial boundary conditions, where the Coulomb stress rate data includes a discrete point set of the Coulomb stress rate and a spline curve fitting representation.

3. The hydraulic fracturing seismic possibility prediction method according to claim 1, wherein, The expression of the function sampling probability in step S302 is as follows: Among them, represents the function sampling probability, S represents the set of sampling point sets, represents that the input function is when the partial differential equation loss at the represents that the input function is when the partial differential equation loss at the and respectively represent the N in the function data set n the i th function and the represents the k th time coordinate in the uniform time coordinate sequence within the target time interval, represents the weight parameters of the physical constraint depth operator network model, represents the predicted result of the hydraulic fracturing seismic possibility under the output target scenario, represents the characteristic time scale, represents the Coulomb stress rate.

4. The hydraulic fracturing seismic probability prediction method according to claim 1, wherein Step S4 includes the following steps: S401. Initialize the physics-constrained deep operator network model PDIS with the weights of the physics-constrained deep operator network model PDIS at the optimal step; S402. Obtain the Coulomb stress rate under the target scenario and represent it as a discrete point set, which is used as the input of the branch network; S403. Randomly generate a time coordinate sequence in the target prediction time interval as the input of the backbone network; S404. Perform forward propagation according to the input results of steps S402 and S403; S405. According to the forward propagation result, perform an inner product operation on the outputs of the backbone network and the branch network to obtain the prediction result of the hydraulic fracturing earthquake possibility in the target scenario.

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