Method for predicting multi-working-condition hydraulic fracture geometry, computer device and medium

Abstract

The present application relates to a kind of multi-working condition hydraulic fracture geometry prediction method, computer equipment and medium, the multi-working condition hydraulic fracture geometry prediction method includes obtaining target construction parameter, and sampling in the value range of the target construction parameter, obtain multiple different working condition parameter values, and generate independent PINN task for each working condition parameter value, construct the support set and query set corresponding to each PINN task for each PINN task;PINN meta parameter is set globally shared, and PINN network of each PINN task is initialized using the meta parameter, the support set of each task is used to train its PINN network, and the updated PINN network parameter of each task is obtained;Using the updated PINN network parameter of each task and query set to build meta loss, and based on meta loss optimization meta parameter and loss weight prediction network parameter, obtain the updated meta parameter and loss weight prediction network.

Description

Technical Field

[0001] This invention relates to the field of petroleum technology, and in particular to a method, computer equipment, and medium for predicting the geometry of hydraulic fractures under multiple operating conditions. Background Technology

[0002] Accurate prediction of hydraulic fracturing fracture geometry (HFG) is crucial for optimizing construction parameters, controlling fracturing effects, increasing reservoir stimulation volume, and ultimately improving oil and gas recovery. In actual fracturing operations, operating parameters need to be dynamically adjusted according to engineering objectives, and the evolution of fracture geometry varies significantly under different operating conditions. Therefore, achieving accurate and rapid prediction of HFG under multiple operating conditions is a critical technical problem that urgently needs to be solved. Existing methods for HFG prediction mainly include Physical Information Neural Networks (PINNs), but traditional PINNs are typically trained for a single operating condition, requiring retraining once operating parameters change, resulting in insufficient rapid adaptation capabilities across operating conditions.

[0003] The above content is only used to help understand the technical solution of the present invention and does not represent an admission that the above content is prior art. Summary of the Invention

[0004] The main objective of this invention is to provide a method, computer equipment, and medium for predicting the geometry of hydraulic fractures under multiple operating conditions, aiming to solve the aforementioned technical problems in the prior art.

[0005] To achieve the above objectives, the present invention provides a method for predicting the geometry of hydraulic fractures under multiple operating conditions, the method comprising: Obtain the target construction parameters, sample within the range of the target construction parameters to obtain multiple different working condition parameter values, generate an independent PINN task for each working condition parameter value, and construct the corresponding support set and query set for each PINN task; Set globally shared PINN meta-parameters, and use these meta-parameters to initialize the PINN network for each PINN task. Train the PINN network for each task using the support set of each task to obtain the updated PINN network parameters for each task. The meta-loss function is constructed using the updated PINN network parameters and query set for each task, and the meta-parameters are optimized based on the meta-loss function to obtain the updated meta-parameters and loss weight prediction network. When a new target working condition that has not participated in the aforementioned learning and training occurs, the updated meta-parameters are used to initialize the target task PINN network, and the optimized loss weight prediction network is used to generate loss weights for the current task. A dataset is constructed for the target working condition to train the PINN network and obtain a model for predicting the crack width of the target working condition.

[0006] Preferably, in the multi-condition hydraulic fracture geometry prediction method, the step of setting globally shared PINN meta-parameters, initializing the PINN network for each PINN task using these meta-parameters, and training the PINN network using the support set of each task to obtain the updated PINN network parameters for each task includes: For each PINN task, the globally shared PINN meta-parameters are copied to the current PINN task as its network parameters. Input the operating parameters corresponding to the current PINN task into the loss weight prediction network to obtain the data loss weight and physical loss weight corresponding to the current PINN task. Based on the support set, data loss weights, and physical loss weights of the current PINN task, construct the PINN loss function on the support set; The gradient of the current PINN task is updated using the PINN loss function on the support set as the optimization objective.

[0007] Preferably, in the method for predicting the geometry of hydraulic fractures under multiple operating conditions, in the step of constructing a PINN loss function on the support set based on the support set, data loss weights, and physical loss weights of the current PINN task, the PINN loss function on the support set is: ; in, To support PINN tasks on the assembly The data loss term, in which the network parameters used are: ; To support PINN tasks on the assembly The physical loss term, in which the network parameters used are ; for ; and PINN tasks on the support set The weights of the data loss term and the physical loss term; ; ; H represents the number of observation data points used for training; m represents the m-th observation sample point; For at a point in spacetime The output value of the network; For at a point in spacetime The true value of the crack; F is the number of physical points used for training; For the first The spatiotemporal coordinates of a physical point; h is the height of the crack; It is the plane strain modulus; v and ν are Young's modulus and Poisson's ratio, respectively; μ is the viscosity of the fracturing fluid; C L The filtration loss coefficient; In order to be in The crack in time is half-length; ; q represents the fracturing fluid injection rate.

[0008] Preferably, in the method for predicting the geometry of hydraulic fractures under multiple operating conditions, in the step of inputting the operating condition parameters corresponding to the current PINN task into the loss weight prediction network to obtain the data loss weight and physical loss weight corresponding to the current PINN task, the loss weight prediction network is a multilayer perceptron that takes the operating condition parameters as input and outputs data loss weight and physical loss weight.

[0009] Preferably, in the multi-condition hydraulic fracture geometry prediction method, the step of updating the gradient of the current PINN task using the PINN loss function on the support set as the optimization objective is as follows: ; in, The learning rate for the inner loop; and These are the network parameters before and after the update, respectively. For PINN task The loss on the support set is relevant to the network parameters. The gradient.

[0010] Preferably, in the multi-condition hydraulic fracture geometry prediction method, in the step of constructing the meta-loss function using the updated PINN network parameters and query sets from each task, the total loss of each PINN task on its corresponding query set is: ; The total loss of each PINN task on its corresponding query set is summed and averaged to obtain the meta-loss function: ; in, For the PINN task on the query set The data loss term, in which the network parameters used are: ; For the PINN task on the query set The physical loss term, in which the network parameters used are ; for ; and PINN tasks on the query set The weights of the data loss term and the physical loss term; n is the total number of PINN tasks.

[0011] Preferably, in the multi-condition hydraulic fracture geometry prediction method, the step of obtaining updated meta-parameters and loss weight prediction network based on meta-loss optimization of meta-parameters and loss weight prediction network parameters includes: The gradient descent algorithm is used to update the gradients of the meta-parameters and the loss weight prediction network parameters, specifically including: ; ; in, The outer loop learning rate is the meta-parameter θ. β is the outer loop learning rate of the loss weight prediction network parameter ψ.

[0012] The process involves acquiring target construction parameters, sampling within the range of these parameters to obtain multiple different working condition parameter values, generating an independent PINN task for each working condition parameter value, and constructing a corresponding support set and query set for each PINN task, including: Select a variable parameter from the set of construction parameters as the target construction parameter, and sample multiple working condition parameter values ​​within its range; use each sampled value as a fixed parameter in the PKN partial differential equation to generate n independent PINN tasks; generate training data in a given spatiotemporal domain for each PINN task; and construct the corresponding support set and query set for each PINN task.

[0013] To achieve the above objectives, the present invention also provides a computer device, comprising: At least one processor; and, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, which enables the at least one processor to perform the above-described method for predicting the geometry of hydraulic fractures under multiple operating conditions.

[0014] To achieve the above objectives, the present invention also provides a computer-readable storage medium, characterized in that it stores a computer program, which, when executed by a controller, implements the above-described method for predicting the geometry of hydraulic fractures under multiple operating conditions.

[0015] The present invention has at least the following beneficial effects: This invention acquires target construction parameters and samples them within their range to obtain multiple different working condition parameter values. For each working condition parameter value, an independent PINN task is generated, and a corresponding support set and query set are constructed for each PINN task. Globally shared PINN meta-parameters are set, and these meta-parameters are used to initialize the PINN network for each PINN task. The PINN network for each task is trained using its support set to obtain updated PINN network parameters for each task. A meta-loss is constructed using the updated PINN network parameters and query set for each task, and the meta-parameters and loss weight prediction network parameters are optimized based on the meta-loss to obtain updated meta-parameters and loss weight prediction network. When a new target working condition that has not participated in the aforementioned learning and training occurs, the updated meta-parameters are used to initialize the target task PINN network, and the updated loss weight prediction network is used to generate loss weights for the target task. A dataset is constructed for the target working condition to train the PINN network and obtain a model for predicting the crack width of the target working condition. By constructing a three-stage prediction framework of "parameter sampling and task generation - dual-objective meta-learning training - rapid adaptation to the target task," significant technical advancements have been achieved in prediction accuracy, convergence speed, and generalization ability. Regarding prediction accuracy, the standardized mean square error (SMSE) of this invention is as low as 0.96%, a reduction of approximately 77% compared to the traditional PINN's 4.18%, and a reduction of approximately 66% compared to the 2.85% of PINN+Meta-init which only uses meta-learning initialization; the mean absolute error (MAE) is reduced to 2.06 × 10⁻⁶. -4 It also outperforms all the comparison models. In terms of convergence speed, this invention only requires 35 rounds of gradient updates to achieve convergence, which is 20 rounds less than the 55 rounds of the traditional PINN, a reduction of 36.4%.

[0016] When the test conditions were extended to low viscosity (μ=0.003) and high viscosity (μ=0.2) conditions outside the training range, the present invention still achieved the lowest SMSE of 2.13% and 3.65%, respectively, which are significantly better than PINN+Meta-init, traditional PINN, and pure data-driven DNN. The synergistic achievement of the above technical effects is attributed to the simultaneous optimization of two types of objectives in the present invention: first, learning the fracture width prediction network meta-parameters that can be quickly transferred between different working conditions, so that the model does not need to start training from a random initial point under new working conditions; second, learning the prediction network that can adaptively output data loss weights and physical loss weights according to working condition parameters, so that the model can dynamically balance the constraints of observation data and PKN control equations, thereby achieving high-precision, high-efficiency, and strong generalization prediction of fracture geometry under different construction parameters, providing reliable technical support for the optimization of hydraulic fracturing construction parameters and the control of fracturing effects. Attached Figure Description

[0017] Figure 1 The flowchart of the multi-condition hydraulic fracture geometry prediction method provided by the present invention in the first embodiment; Figure 2 A framework diagram of the multi-condition hydraulic fracture geometry prediction method provided by the present invention; Figure 3 A basic architecture diagram of a physical information neural network for crack width prediction; Figure 4a The convergence curve represents the data loss. Figure 4b The convergence curve of the PDE loss; Figure 5 SMSE comparison charts for different models under different working conditions; Figure 6 This is a schematic diagram of an embodiment of the computer device provided by the present invention.

[0018] The objectives, features, and advantages of this invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0019] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The present invention will be described in detail below with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0020] In this embodiment of the invention, the term "and / or" describes the relationship between associated objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. The character " / " generally indicates that the preceding and following associated objects have an "or" relationship.

[0021] It should be noted that the terms "first," "second," etc., in the specification, claims, and drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0022] In this embodiment of the invention, the term "multiple" refers to two or more, and other quantifiers are similar.

[0023] In this invention, unless otherwise stated, directional terms such as "upper," "lower," "top," and "bottom" are generally used in relation to the direction shown in the accompanying drawings, or in relation to the vertical, perpendicular, or gravitational direction of the component itself; similarly, for ease of understanding and description, "inner" and "outer" refer to the inner and outer contours of each component itself, but the above directional terms are not intended to limit this invention.

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details are presented in the embodiments of the present invention to facilitate a better understanding of the invention. However, the technical solutions claimed in the present invention can be implemented even without these technical details and various variations and modifications based on the following embodiments. The division of the following embodiments is for ease of description and should not constitute any limitation on the specific implementation of the present invention. The various embodiments can be combined with and referenced by each other without contradiction.

[0025] Research on HFG prediction under multiple operating conditions is still limited, and there are currently two main types of technical solutions.

[0026] The first approach employs the parametric PINN method for multi-condition prediction. This approach uses fracturing fluid viscosity, injection rate, and other condition parameters along with spatiotemporal coordinates as network inputs, embedding governing equations into the loss function to cover multiple conditions with a single network. For example, Ryu et al. used parametric PINN to incorporate fracturing fluid viscosity, injection rate, and spatiotemporal coordinates into the network, achieving HFG prediction under different conditions. However, this approach has significant drawbacks: as the range of conditions expands, the model needs to increase network capacity and sampling point density, leading to slower training and significantly increased optimization difficulty, thus limiting its practicality under a wide range of variable conditions.

[0027] The second approach employs neural operator methods for multi-condition prediction. This approach learns an infinite-dimensional mapping from condition parameters to PDE solution functions, eliminating the need to retrain the network for each new condition. For example, Wang et al. proposed a semi-physical information multi-input operator network that uses multi-condition parameters such as crack spacing and matrix permeability as independent inputs to directly learn the mapping from parameters to crack geometry. However, this type of method heavily relies on a large number of pre-generated high-fidelity samples to cover the parameter space. If the training data coverage is insufficient, the model's prediction accuracy under unseen conditions will significantly decrease, and obtaining a large number of high-fidelity samples itself constitutes a huge computational burden.

[0028] In summary, existing methods all have their limitations in multi-condition HFG prediction: parameterized PINN faces optimization bottlenecks due to the expanded range of conditions, and neural operators are limited by the coverage of training data. Both methods struggle to balance generalization ability across conditions, training efficiency, and prediction accuracy. Therefore, a novel prediction method is urgently needed that can achieve fast and accurate HFG prediction under multiple conditions while also possessing strong generalization ability.

[0029] To address this, the present invention provides a method for predicting the geometry of hydraulic fractures under multiple operating conditions. Please refer to [link to relevant documentation]. Figures 1 to 3 The method for predicting the geometry of hydraulic fractures under multiple operating conditions includes steps S1000 to S4000.

[0030] Step S1000: Obtain target construction parameters, sample within the range of target construction parameters to obtain multiple different working condition parameter values, generate an independent PINN task for each working condition parameter value, and construct a corresponding support set and query set for each PINN task.

[0031] It should be noted that the continuously changing operating parameters are discretized into multiple specific PINN tasks, and a training dataset (support set) and an evaluation dataset (query set) are prepared for each PINN task.

[0032] Specifically, step S1000 includes steps S1100 to S1400.

[0033] Step S1100 selects a variable parameter from the set of construction parameters as the target construction parameter, and samples multiple working condition parameter values ​​within its value range.

[0034] For example, the set of construction parameters in the hydraulic fracturing process. ,in, This represents the different construction parameters that affect the evolution of the geometric morphology of hydraulic fractures, where N is the number of construction parameters.

[0035] Will As a variable parameter under multiple working conditions, i.e., the target construction parameter, within its value range Sampling was performed to obtain n different operating condition parameter values. .

[0036] Step S1200 uses each sampled value as a fixed parameter in the PKN partial differential equation to generate n independent PINN tasks.

[0037] Each partial differential equation with fixed operating parameters is treated as a PINN task, thus generating n tasks: Each PINN task This corresponds to a specific fracturing condition.

[0038] Step S1300 For each PINN task, in a given spatiotemporal domain Internally generated training data. Among them, The spatial position along the crack axis. For fracturing time, This is a preset spatial range. For the PINN task... The Nordgren closed-form analytical solution corresponding to the PKN model is used to calculate the spatiotemporal points. True value of crack width at [location] .

[0039] Step S1400 constructs the corresponding support set and query set for each PINN task. For the generated n PINN tasks... Based on the true value of the crack width of each PINN task The spatiotemporal domain Ω constructs a corresponding support set for each task. With query set For each PINN task, the initial conditions of the spatiotemporal domain Ω are first determined ( H data points are uniformly sampled on the boundary conditions (x=0 or x=L) to form the observation data; then, F data points are selected within the spatiotemporal domain Ω using Latin hypercube sampling to form the physical collocation points. The observation data points contain spatiotemporal coordinates and the true value of the crack width, while the physical collocation points only contain spatiotemporal coordinates. Together, they constitute the support set. Query set The same construction rules are used, but the sets do not overlap with the support sets.

[0040] Step S2000 sets globally shared PINN meta-parameters and uses these meta-parameters to initialize the PINN network for each PINN task. The PINN network for each task is trained using the support set of each task to obtain the updated PINN network parameters for each task.

[0041] It should be noted that step S2000 is the inner loop of the dual-objective meta-learning. Each PINN task starts from the globally shared meta-parameters, performs a small number of gradient updates using its own support set, and obtains specific network parameters that accurately describe its respective task. The model parameters are then quickly updated using the support set of each task to obtain model parameters adapted to each task.

[0042] It should be noted that after parameter sampling and task generation are completed, this invention enters the dual-objective meta-learning training phase. The purpose of this phase is twofold: firstly, to learn a set of fracture width prediction network meta-parameters that can rapidly migrate between different hydraulic fracturing tasks. On the other hand, we learn a loss weight prediction network that can adaptively generate loss weights based on different operating parameters. .

[0043] Step S2000 includes steps S2100 to S2400.

[0044] Step S2100: For each PINN task, the globally shared PINN meta-parameters are copied to the current PINN task as the network parameters of the current PINN task.

[0045] Specifically, the network parameters for the current PINN task are initialized. This is done for each task. Independent task adaptation process. First, globally shared meta-parameters... Copy as the initial task parameters for this task: .

[0046] Step S2200 inputs the operating parameters corresponding to the current PINN task into the loss weight prediction network to obtain the data loss weight and physical loss weight corresponding to the current PINN task. The loss weight prediction network is a multilayer perceptron that takes the operating parameters as input and outputs data loss weight and physical loss weight.

[0047] Step S2300 constructs the PINN loss function on the support set based on the support set, data loss weights, and physical loss weights of the current PINN task.

[0048] Specifically, the PINN loss function on the support set is: ; in, To support PINN tasks on the assembly The data loss term, in which the network parameters used are: ; To support PINN tasks on the assembly The physical loss term, in which the network parameters used are ; for ; and PINN tasks on the support set The weights of the data loss term and the physical loss term; ; ; H represents the number of observation data points used for training; m represents the m-th observation sample point; For at a point in spacetime The output value of the network; For at a point in spacetime The true value of the crack; F is the number of physical points used for training; For the first The spatiotemporal coordinates of a physical point; h is the height of the crack; It is the plane strain modulus; v and ν are Young's modulus and Poisson's ratio, respectively; μ is the viscosity of the fracturing fluid; C L The filtration loss coefficient; In order to be in The crack in time is half-length; ; q represents the fracturing fluid injection rate.

[0049] Step S2400 uses the PINN loss function on the support set as the optimization objective to perform gradient updates on the current PINN task.

[0050] Specifically, the update method is as follows: ; in, The learning rate for the inner loop; and These are the network parameters before and after the update, respectively. For PINN task The loss on the support set is relevant to the network parameters. The gradient.

[0051] It should be noted that after several gradient updates on the support set, the initialization parameters of the current PINN task... Updated to parameters ᵢ′。 This inner loop process is executed independently for each sampling task; therefore, each PINN task corresponds to a set of updated parameters. { }

[0052] Step S3000 uses the updated PINN network parameters and query set from each task to construct the meta-loss, and optimizes the meta-parameters and loss weight prediction network parameters based on the meta-loss to obtain the updated meta-parameters and loss weight prediction network.

[0053] It should be noted that step S3000 is the outer loop of the dual-objective meta-learning. The goal of the outer loop is to construct the loss using the updated parameters and query set from the inner loop, and then use the loss to optimize the meta-parameters and loss weight network parameters.

[0054] After completing the inner loop update for each PINN task, the model uses the updated parameters Φᵢ′ as the network parameters for the corresponding task, and then updates the query set for that task. Input the network to obtain the loss of the task on the query set. Simultaneously, input the operating parameters. Input the loss weight prediction network to obtain the data loss weight and physical loss weight corresponding to the task. In the step of constructing the meta-loss function using the updated PINN network parameters and query set for each task, the total loss of each PINN task on its corresponding query set is: ; After obtaining the loss of each task on its query set, these losses are summed and averaged to construct the meta-loss function of the outer loop. Specifically, the total loss of each PINN task on its corresponding query set is summed and averaged to obtain the meta-loss function: ; in, For the PINN task on the query set The data loss term, in which the network parameters used are: ; For the PINN task on the query set The physical loss term, in which the network parameters used are ; for ; and PINN tasks on the query set The weights of the data loss term and the physical loss term; n is the total number of PINN tasks.

[0055] The steps of optimizing the meta-parameters and loss weight prediction network parameters based on the meta-loss to obtain the updated meta-parameters and loss weight prediction network include: The gradient descent algorithm is used to update the gradients of the meta-parameters and the loss weight prediction network parameters, specifically including: ; ; in, The outer loop learning rate is the meta-parameter θ. β is the outer loop learning rate of the loss weight prediction network parameter ψ.

[0056] After multiple outer loop iterations, the model finally learns a set of meta-parameters θ, which enables rapid transfer between different tasks; simultaneously, the model also learns a prediction network. It can be based on operating parameters Output the loss weights for the corresponding task.

[0057] Step S4000: When a new target working condition that has not participated in the aforementioned learning and training occurs, the updated meta-parameters are used to initialize the target task PINN network, the updated loss weight prediction network is used to generate loss weights for the target task, and a dataset is constructed for the target working condition to train the PINN network to obtain a model for predicting the crack width of the target working condition.

[0058] When operating parameters that did not participate in the aforementioned dual-objective meta-learning training occur... When the new target operating condition is met, this invention directly uses the meta-parameters obtained during the dual-target meta-learning stage. As initial parameters for the target task PINN network This initialization method enables the target task network to start training from a region with better parameters, thereby reducing training time under new conditions.

[0059] At the same time, the target operating condition parameters Input the loss weight prediction network after training The data loss weights corresponding to the target working condition are obtained. and physical loss weights .

[0060] Following the same data construction method as in the parameter sampling and task generation phases, a small number of observation data points and physical coordinate points are sampled for the target task. The observation data points are obtained by sampling initial and boundary conditions in the spatiotemporal domain, while the physical coordinate points are obtained by sampling within the spatiotemporal domain. Based on the above data and loss weights, the PINN loss function for the target task is constructed, and a small number of gradient updates are performed on the network parameters of the target task. ; γ represents the learning rate during the training phase of the target task; The parameters of the target task network after the s-th update; The target task network uses the meta-parameters θ obtained during the dual-objective meta-learning stage as initial parameters; For the task The loss on the query set is related to the network parameters. gradient, For the task Loss on the query set.

[0061] After a small number of gradient updates, the loss of the target task can converge quickly, thus obtaining a crack width model that can accurately predict the target working condition.

[0062] To achieve the above objectives, the present invention also provides a computer device, such as... Figure 6 As shown, the mobile terminal includes at least one processor 601; and a memory 602 communicatively connected to the at least one processor 601; wherein the memory 602 stores instructions that can be executed by the at least one processor 601, the instructions being executed by the at least one processor 601 to enable the at least one processor 601 to perform the above-described method for predicting the geometry of hydraulic fractures under multiple operating conditions.

[0063] The memory 602 and processor 601 are connected via a bus, which may include any number of interconnecting buses and bridges. The bus connects various circuits of one or more processors 601 and memory 602 together. The bus can also connect various other circuits, such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and therefore will not be described further herein. A bus interface provides an interface between the bus and the transceiver. The transceiver can be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by processor 601 is transmitted over a wireless medium via an antenna, which further receives data and transmits it to processor 601.

[0064] Processor 601 is responsible for managing the bus and general processing, and can also provide various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory 602 can be used to store data used by processor 601 during operation.

[0065] To achieve the above objectives, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor 601, implements the above-described method for predicting the geometry of hydraulic fractures under multiple operating conditions.

[0066] That is, those skilled in the art will understand that all or part of the steps in the methods described above can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0067] This invention employs a dual-objective meta-learning mechanism to simultaneously learn transferable initialization parameters across different operating conditions and an adaptive loss weight prediction network. This allows the model to avoid the slow convergence and low accuracy problems associated with traditional PINN random initialization and fixed loss weights when facing new operating conditions not previously trained on. Consequently, it improves the accuracy, adaptability, and generalization ability of multi-operating-condition hydraulic fracture geometry prediction. To further verify the effectiveness of this invention, several aspects will be discussed in detail below.

[0068] (1) Accuracy of crack geometric prediction under target working conditions In terms of quantitative error, as shown in Table 1, the standardized mean square error (SMSE) of the DOM-PINN method of this invention is 0.96%, significantly lower than that of DNN (5.24%), traditional PINN (4.18%), and PINN+Meta-init (2.85%). Simultaneously, the mean absolute error (MAE) of DOM-PINN is reduced to 2.06 × 10⁻⁶. -4 It is also superior to other comparative models.

[0069] From the loss convergence curves, the proposed DOM-PINN model converges to lower final loss values ​​in both data loss and PDE loss, outperforming other comparative models overall. Specifically, the lower data loss indicates a smaller deviation between the model's predicted crack width and the true value, while the lower PDE loss indicates that the prediction results better satisfy the constraints of the PKN governing equations. This also indirectly demonstrates that the proposed method has higher crack width prediction accuracy under the target working condition.

[0070] Table 1 Comparison of Model Prediction Accuracy and Convergence Rounds

[0071] (2) Convergence speed under target operating conditions From the perspective of quantitative error, as shown in Table 1, during the target operating condition adaptation phase, traditional PINN requires 55 update rounds to achieve convergence, while the DOM-PINN proposed in this invention only requires 35 update rounds to achieve convergence, reducing the number of convergence rounds by 20 rounds, or approximately 36.4%. From the perspective of loss convergence properties, by Figure 4a It can be seen that PINN+Meta-init and DOM-PINN both exhibit faster degradation rates than traditional PINN in the early stages of training. This indicates that the initialization parameters obtained through dual-objective meta-learning can provide a better starting point for the target task, thereby significantly enhancing the model's rapid adaptability.

[0072] (3) Improve the generalization ability of the model.

[0073] To verify the prediction capability of the proposed method under different operating conditions outside the training range, this invention designed a comparative experiment including distributed interpolation and distributed extrapolation. Experimental results show that DOM-PINN has the lowest prediction error under operating condition μ=0.01 within the training parameter range. When the test conditions are expanded to low viscosity condition μ=0.003 and high viscosity condition μ=0.2 outside the training range, DOM-PINN still achieves the lowest SMSE of 2.13% and 3.65%, respectively, both outperforming PINN+Meta-init, traditional PINN, and DNN. Further specific results are detailed in [link to relevant documentation]. Figure 5 The results demonstrate that the initialization parameters obtained through multi-condition meta-learning in this invention can improve the model's ability to quickly adapt to unseen conditions, thereby enabling the model to maintain higher prediction accuracy under both in-distribution and out-of-distribution conditions.

[0074] Example S1, Set of Construction Parameters Below are two construction parameters and their corresponding ranges.

[0075] Table 2 Examples of Construction Parameters

[0076] Using fracturing fluid viscosity as the target construction parameter, and sampling within the range of the target construction parameter, multiple different operating condition parameter values ​​are obtained. An independent PINN task is generated for each operating condition parameter value, and a corresponding support set and query set are constructed for each PINN task. For example, 50 sampled values ​​are used. , thus obtaining 50 PINN tasks.

[0077] S2, the loss weight predictor, employs a multilayer perceptron; the network parameters are... This is represented as (where the multilayer perceptron contains one input layer, two hidden layers, each hidden layer containing 32 neurons, with Tanh activation functions and an output layer added between layers). For each PINN task, the input... Output the data loss weights for the current task. and physical loss weights .

[0078] The PINN model, for each PINN task, takes the following inputs: x (representing the spatial position along the fracture axis) and t (representing the pumping time during hydraulic fracturing).

[0079] Network architecture: Employs a multilayer perceptron; network parameters are used... Let's represent it as follows. (The multilayer perceptron contains one input layer, six hidden layers, each hidden layer contains 300 neurons, and Tanh activation functions and an output layer are added between the layers).

[0080] Output: w (the width of the crack predicted by the network).

[0081] S3, inner loop. Input: meta-parameters The support set for each task, the data loss weights and physical loss weights for each task (predicted by the loss weight predictor).

[0082] Output: Parameters obtained after 10 update iterations for each task. . Corresponding task , Corresponding task .

[0083] S4, outer loop. Input the parameters obtained from the inner loop. The query set for each PINN task. Output the meta-parameters updated 1000 times by the outer loop. A loss weight prediction network that has undergone 1000 iterations of outer loop updates. .

[0084] S5, when a new target operating condition (operating condition parameters are) occurs that has not participated in the aforementioned learning and training, When the value is 0.01, the updated meta-parameters are used to initialize the target task PINN network, and a dataset is built for the target working condition to train the PINN network to obtain a model for predicting the crack width of the target working condition.

[0085] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for predicting the geometry of hydraulic fractures under multiple operating conditions, characterized in that, include: Obtain the target construction parameters, sample within the range of the target construction parameters to obtain multiple different working condition parameter values, generate an independent PINN task for each working condition parameter value, and construct the corresponding support set and query set for each PINN task; Set globally shared PINN meta-parameters and initialize the PINN network for each PINN task using these meta-parameters. Train the PINN network for each task using the support set to obtain the updated PINN network parameters for each task. This includes copying the globally shared PINN meta-parameters to the current PINN task as its network parameters; inputting the operating condition parameters corresponding to the current PINN task into the loss weight prediction network to obtain the data loss weights and physical loss weights corresponding to the current PINN task; constructing the PINN loss function on the support set based on the current PINN task's support set, data loss weights, and physical loss weights; and performing gradient updates for the current PINN task using the PINN loss function on the support set as the optimization objective. The loss weight prediction network is a multilayer perceptron that takes the operating condition parameters as input and outputs data loss weights and physical loss weights. The meta-loss is constructed using the updated PINN network parameters and query set for each task, and the meta-parameters and loss weight prediction network parameters are optimized based on the meta-loss to obtain the updated meta-parameters and loss weight prediction network. When a new target working condition that has not participated in the aforementioned learning and training occurs, the updated meta-parameters are used to initialize the target task PINN network, the updated loss weight prediction network is used to generate loss weights for the target task, and a dataset is constructed for the target working condition to train the PINN network to obtain a model for predicting the crack width of the target working condition.

2. The method for predicting the geometry of hydraulic fractures under multiple operating conditions as described in claim 1, characterized in that, In the step of constructing the PINN loss function on the support set based on the support set, data loss weights, and physical loss weights of the current PINN task, the PINN loss function on the support set is as follows: ； in, To support PINN tasks on the assembly The data loss term, in which the network parameters used are: ; To support PINN tasks on the assembly The physical loss term, in which the network parameters used are ; for ; and PINN tasks on the support set The weights of the data loss term and the physical loss term; ； ； H represents the number of observation data points used for training; m represents the m-th observation sample point; For at a point in spacetime The output value of the network; For at a point in spacetime The true value of the crack; F is the number of physical points used for training; For the first The spatiotemporal coordinates of a physical point; h is the height of the crack; It is the plane strain modulus; v and ν are Young's modulus and Poisson's ratio, respectively; μ is the viscosity of the fracturing fluid; C L The filtration loss coefficient; In order to be in The crack in time is half-length; ; q represents the fracturing fluid injection rate.

3. The method for predicting the geometry of hydraulic fractures under multiple operating conditions as described in claim 2, characterized in that, In the step of updating the gradient of the current PINN task with the PINN loss function on the support set as the optimization objective, the update method is as follows: ； in, The learning rate for the inner loop; and These are the network parameters before and after the update, respectively. For PINN task The loss on the support set is relevant to the network parameters. The gradient.

4. The method for predicting the geometry of hydraulic fractures under multiple operating conditions as described in claim 1, characterized in that, In the step of constructing the meta-loss function using the updated PINN network parameters and query sets from each task, the total loss for each PINN task on its corresponding query set is: ； The total loss of each PINN task on its corresponding query set is summed and averaged to obtain the meta-loss function: ； in, For the PINN task on the query set The data loss term, in which the network parameters used are: ; For the PINN task on the query set The physical loss term, in which the network parameters used are ; for ; and PINN tasks on the query set The weights of the data loss term and the physical loss term; n is the total number of PINN tasks.

5. The method for predicting the geometry of hydraulic fractures under multiple operating conditions as described in claim 4, characterized in that, The steps of optimizing the meta-parameters and loss weight prediction network parameters based on the meta-loss to obtain the updated meta-parameters and loss weight prediction network include: The gradient descent algorithm is used to update the gradients of the meta-parameters and the loss weight prediction network parameters, specifically including: ； ； in, The outer loop learning rate is the meta-parameter θ. β is the outer loop learning rate of the loss weight prediction network parameter ψ.

6. The method for predicting the geometry of hydraulic fractures under multiple operating conditions as described in claim 1, characterized in that, The process involves acquiring target construction parameters, sampling within the range of these parameters to obtain multiple different working condition parameter values, generating an independent PINN task for each working condition parameter value, and constructing a corresponding support set and query set for each PINN task, including: Select a variable parameter from the set of construction parameters as the target construction parameter, and sample multiple working condition parameter values ​​within its range; use each sampled value as a fixed parameter in the PKN partial differential equation to generate n independent PINN tasks; generate training data in a given spatiotemporal domain for each PINN task; and construct the corresponding support set and query set for each PINN task.

7. A computer device, characterized in that, include: At least one processor; as well as, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the multi-condition hydraulic fracture geometry prediction method as described in any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that, The system contains a computer program that, when executed by a controller, implements the method for predicting the geometry of hydraulic fractures under multiple operating conditions as described in any one of claims 1 to 6.

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