Fracture propagation simulation method and device based on cascade model, equipment and medium

Abstract

The application provides a crack propagation simulation method and device based on a cascade model, equipment and a medium, relating to the fields of image processing, artificial intelligence and hydraulic fracturing simulation in oil and gas development. In view of the problems that the existing high-fidelity simulation has large calculation cost, the scene adaptability of the data-driven model is insufficient, and it is difficult to balance the stability of time series prediction and high-resolution detail recovery, a crack propagation simulation method based on a cascade model is proposed. High-resolution and low-resolution crack propagation data under the same physical constraint condition are used to train a low-resolution time series prediction model, and a target super-resolution reconstruction model is selected from a super-resolution reconstruction model candidate pool according to high-resolution data, and then the two are cascaded to simulate the initial crack propagation data and output the target crack propagation simulation result. The simulation accuracy can be improved while reducing the calculation cost, the adaptability in different physical constraint scenes can be enhanced, and the recovery effect of crack tip, turning area and local morphological details can be improved.

Description

Technical Field

[0001] This application relates to the fields of image processing, artificial intelligence and hydraulic fracturing simulation in oil and gas development, and in particular to a method, apparatus, equipment and medium for simulating fracture propagation based on a cascade model. Background Technology

[0002] In predicting the propagation of hydraulic fracturing fractures, existing technologies typically employ high-fidelity numerical simulations or data-driven surrogate models to analyze the dynamic evolution of fracture width, length, and height.

[0003] However, high-fidelity numerical simulations incur significantly higher computational costs when spatial resolution is increased, making it difficult to meet the requirements of multi-parameter optimization and real-time prediction. While data-driven surrogate models can improve computational efficiency, their adaptability to different geological conditions and parameter combinations is limited, and the reliability of prediction results lacks effective characterization, affecting the stability of engineering applications.

[0004] Therefore, how to balance prediction accuracy and computational efficiency in crack propagation simulation, and improve the model's adaptability to different scenarios and the reliability of results, has become a technical problem that needs to be solved. Summary of the Invention

[0005] This application provides a crack propagation simulation method, apparatus, device, and medium based on a cascaded model. By comprehensively utilizing the efficient evolution capability of low-resolution data and the fine description capability of high-resolution data in the crack propagation prediction process, it achieves efficient and accurate simulation of the target crack propagation simulation results, thereby balancing prediction accuracy and computational efficiency, and improving the adaptability of the cascaded model used for crack propagation simulation to different physical constraint scenarios and the reliability of prediction results.

[0006] Firstly, this application provides a crack propagation simulation method based on a cascade model, the method comprising:

[0007] Multiple sets of crack propagation data are acquired. Each set of crack propagation data includes low-resolution crack propagation data and high-resolution crack propagation data corresponding to at least two time steps under the same physical constraint. The high-resolution crack propagation data is generated by simulation using a first simulation grid, and the low-resolution crack propagation data is generated by simulation using a second simulation grid. The spatial discretization accuracy of the first simulation grid is higher than that of the second simulation grid.

[0008] Based on low-resolution crack propagation data, a pre-set time series prediction model is trained to obtain a pre-trained time series prediction model. The pre-trained time series prediction model is used to predict the low-resolution crack propagation data of the next time step based on the low-resolution crack propagation data of the previous time step and the physical constraints that match the current set of crack propagation data.

[0009] Based on high-resolution crack propagation data, the candidate models in the preset super-resolution reconstruction model candidate pool are analyzed to select the target super-resolution reconstruction model. The target super-resolution reconstruction model is used to map the low-resolution crack propagation data of the next time step to reconstruct high-resolution crack propagation data.

[0010] The pre-trained temporal prediction model is concatenated with the target super-resolution reconstruction model to obtain a concatenated model for crack propagation simulation.

[0011] Obtain the initial crack propagation data to be simulated, and input the initial crack propagation data into the cascaded model to obtain the target crack propagation simulation results.

[0012] In one possible implementation, the preset time-series prediction model adopts a U-shaped network architecture, which includes an encoder path, a decoder path, and a jump connection structure connecting the encoder path and the decoder path.

[0013] The encoder path is used to extract and downsample the low-resolution crack propagation data of the previous time step, while the decoder path is used to upsample and reconstruct the extracted features to output the low-resolution crack propagation data of the next time step.

[0014] In one possible implementation, the candidate models in a pre-defined super-resolution reconstruction model candidate pool are analyzed based on high-resolution crack propagation data to select the target super-resolution reconstruction model, including:

[0015] Low-resolution crack propagation data is input into each candidate model in the candidate pool to obtain the corresponding reconstructed high-resolution crack propagation data.

[0016] Calculate the peak signal-to-noise ratio and structural similarity index between reconstructed high-resolution crack propagation data and high-resolution crack propagation data;

[0017] The peak signal-to-noise ratio and structural similarity index are weighted according to preset weights to obtain the scores of each candidate model;

[0018] The candidate model with the highest score is selected from the candidate pool as the target super-resolution reconstruction model.

[0019] In one possible implementation, a pre-trained temporal prediction model is cascaded with a target super-resolution reconstruction model to obtain a cascaded model for crack propagation simulation, comprising:

[0020] The model parameters of the pre-trained temporal prediction model and the target super-resolution reconstruction model are fixed;

[0021] The output of the pre-trained temporal prediction model is directly connected to the input of the target super-resolution reconstruction model to build an end-to-end inference pipeline.

[0022] The inference pipeline is configured to: receive low-resolution crack propagation data at the current time step, output intermediate low-resolution crack propagation data for the next time step through a pre-trained time-series prediction model, and map the intermediate low-resolution crack propagation data to reconstructed high-resolution crack propagation data for the next time step through a target super-resolution reconstruction model.

[0023] In one possible implementation, initial crack propagation data to be simulated is acquired, and the initial crack propagation data is input into a cascaded model to obtain the target crack propagation simulation results, including:

[0024] Obtain the initial crack propagation data to be simulated. The initial crack propagation data includes the crack data at the initial moment and the target physical constraints.

[0025] The crack data and target physical constraints at the initial moment are used as the extended data at the current time step;

[0026] Input the current time step expansion data into the cascaded model to obtain the high-resolution crack propagation simulation results for the next time step;

[0027] If the preset simulation termination time has not been reached, a downsampling operation is performed on the high-resolution crack propagation simulation results of the next time step to obtain the downsampled crack propagation data of the next time step.

[0028] The steps are: using the downsampled crack propagation data of the next time step and the target physical constraints as the new current time step propagation data, and returning to input the current time step propagation data into the cascaded model to obtain the high-resolution crack propagation simulation results of the next time step.

[0029] When the preset simulation termination time is reached, the target crack propagation simulation result is obtained based on the high-resolution crack propagation simulation results of the next time step generated each time step.

[0030] In one possible implementation, inputting initial crack propagation data into a cascaded model to obtain the target crack propagation simulation results further includes:

[0031] In the inference process of the cascaded model, a Monte Carlo dropout mechanism or an ensemble learning mechanism is introduced to perform multiple random forward propagations and obtain multiple sets of high-resolution crack propagation simulation results.

[0032] The results of multiple high-resolution crack propagation simulations are aggregated to calculate the average crack width and generate a crack width average map.

[0033] Based on the variance of multiple high-resolution crack propagation simulation results, a prediction uncertainty map is generated. The prediction uncertainty map is used to identify areas in the crack propagation path where the prediction confidence is lower than a preset threshold.

[0034] Secondly, this application provides a crack propagation simulation device based on a cascade model, the device comprising:

[0035] The acquisition module is used to acquire multiple sets of crack propagation data. Each set of crack propagation data includes low-resolution crack propagation data and high-resolution crack propagation data corresponding to at least two time steps under the same physical constraint. The high-resolution crack propagation data is generated by simulation using a first simulation grid, and the low-resolution crack propagation data is generated by simulation using a second simulation grid. The spatial discretization accuracy of the first simulation grid is higher than that of the second simulation grid.

[0036] The training module is used to train a preset time series prediction model based on low-resolution crack propagation data to obtain a pre-trained time series prediction model. The pre-trained time series prediction model is used to predict the low-resolution crack propagation data of the next time step based on the low-resolution crack propagation data of the previous time step and the physical constraints that match the current set of crack propagation data.

[0037] The filtering module is used to analyze each candidate model in the preset super-resolution reconstruction model candidate pool based on high-resolution crack propagation data, and filter out the target super-resolution reconstruction model. The target super-resolution reconstruction model is used to map the low-resolution crack propagation data of the next time step into the reconstructed high-resolution crack propagation data.

[0038] The cascade module is used to cascade the pre-trained temporal prediction model with the target super-resolution reconstruction model to obtain a cascaded model for crack propagation simulation.

[0039] The prediction module is used to acquire the initial crack propagation data to be simulated and input the initial crack propagation data into the cascaded model to obtain the target crack propagation simulation results.

[0040] In one possible implementation, in the training module, the preset temporal prediction model adopts a U-shaped network architecture, which includes an encoder path, a decoder path, and a skip connection structure connecting the encoder path and the decoder path.

[0041] The encoder path is used to extract and downsample the low-resolution crack propagation data of the previous time step, while the decoder path is used to upsample and reconstruct the extracted features to output the low-resolution crack propagation data of the next time step.

[0042] In one possible implementation, the filtering module is specifically used for:

[0043] Low-resolution crack propagation data is input into each candidate model in the candidate pool to obtain the corresponding reconstructed high-resolution crack propagation data.

[0044] Calculate the peak signal-to-noise ratio and structural similarity index between reconstructed high-resolution crack propagation data and high-resolution crack propagation data;

[0045] The peak signal-to-noise ratio and structural similarity index are weighted according to preset weights to obtain the scores of each candidate model;

[0046] The candidate model with the highest score is selected from the candidate pool as the target super-resolution reconstruction model.

[0047] In one possible implementation, the cascade module is specifically used for:

[0048] The model parameters of the pre-trained temporal prediction model and the target super-resolution reconstruction model are fixed;

[0049] The output of the pre-trained temporal prediction model is directly connected to the input of the target super-resolution reconstruction model to build an end-to-end inference pipeline.

[0050] The inference pipeline is configured to: receive low-resolution crack propagation data at the current time step, output intermediate low-resolution crack propagation data for the next time step through a pre-trained time-series prediction model, and map the intermediate low-resolution crack propagation data to reconstructed high-resolution crack propagation data for the next time step through a target super-resolution reconstruction model.

[0051] In one possible implementation, the prediction module is specifically used for:

[0052] Obtain the initial crack propagation data to be simulated. The initial crack propagation data includes the crack data at the initial moment and the target physical constraints.

[0053] The crack data and target physical constraints at the initial moment are used as the extended data at the current time step;

[0054] Input the current time step expansion data into the cascaded model to obtain the high-resolution crack propagation simulation results for the next time step;

[0055] If the preset simulation termination time has not been reached, a downsampling operation is performed on the high-resolution crack propagation simulation results of the next time step to obtain the downsampled crack propagation data of the next time step.

[0056] The steps are: using the downsampled crack propagation data of the next time step and the target physical constraints as the new current time step propagation data, and returning to input the current time step propagation data into the cascaded model to obtain the high-resolution crack propagation simulation results of the next time step.

[0057] When the preset simulation termination time is reached, the target crack propagation simulation result is obtained based on the high-resolution crack propagation simulation results of the next time step generated each time step.

[0058] In one possible implementation, the prediction module is further configured to:

[0059] In the inference process of the cascaded model, a Monte Carlo dropout mechanism or an ensemble learning mechanism is introduced to perform multiple random forward propagations and obtain multiple sets of high-resolution crack propagation simulation results.

[0060] The results of multiple high-resolution crack propagation simulations are aggregated to calculate the average crack width and generate a crack width average map.

[0061] Based on the variance of multiple high-resolution crack propagation simulation results, a prediction uncertainty map is generated. The prediction uncertainty map is used to identify areas in the crack propagation path where the prediction confidence is lower than a preset threshold.

[0062] Thirdly, this application provides an electronic device, including: a processor, and a memory communicatively connected to the processor.

[0063] The memory stores the instructions that the computer executes.

[0064] The processor executes computer execution instructions stored in memory to implement a crack propagation simulation method based on a cascade model, as described in the first aspect of the invention.

[0065] Fourthly, this application provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement a crack propagation simulation method based on a cascade model, as described in the first aspect of the invention.

[0066] Fifthly, this application provides a computer program product, including a computer program, which, when executed by a processor, is used to implement a crack propagation simulation method based on a cascade model, as described in the first aspect of the invention.

[0067] Based on the implementation methods provided in the above aspects, this application can be further combined to provide more implementation methods.

[0068] This application provides a crack propagation simulation method, apparatus, device, and medium based on a cascaded model. By acquiring low-resolution crack propagation data and high-resolution crack propagation data under the same physical constraints, it forms the data foundation for temporal evolution learning and high-resolution reconstruction analysis, respectively. The trained temporal prediction model is cascaded with the selected target super-resolution reconstruction model. It can efficiently predict the low-resolution crack propagation data of the next time step based on the low-resolution crack propagation data of the previous time step and the matching physical constraints, and then map it to reconstruct high-resolution crack propagation data. In this way, while reducing the computational cost of high-resolution direct simulation, it obtains target crack propagation simulation results with both high spatial detail representation ability and temporal prediction ability, thereby improving the efficiency, accuracy, and adaptability of crack propagation simulation to different scenarios. Attached Figure Description

[0069] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0070] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0071] Figure 1 A schematic diagram illustrating an application scenario of a crack propagation simulation method based on a cascade model, provided in an embodiment of this application.

[0072] Figure 2 A flowchart illustrating a crack propagation simulation method based on a cascade model provided in this application embodiment;

[0073] Figure 3 A comparison chart of the statistical distribution of crack geometric parameters obtained by simulation at different mesh resolutions in embodiments of this application;

[0074] Figure 4 This is a schematic diagram of the U-shaped network architecture provided in the embodiments of this application;

[0075] Figure 5 A comparative diagram of crack propagation super-resolution reconstruction results of various models provided in the embodiments of this application;

[0076] Figure 6 A schematic diagram illustrating the super-resolution reconstruction effect and error analysis of the crack width field of the cascaded model provided in this application embodiment;

[0077] Figure 7A schematic diagram of the quantification results of the crack width field uncertainty provided in the embodiments of this application;

[0078] Figure 8 A schematic diagram of a crack propagation simulation device based on a cascade model provided in this application embodiment;

[0079] Figure 9 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0080] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0081] In the embodiments of this application, the terms "first" and "second" are used to distinguish identical or similar items with substantially the same function and effect. Those skilled in the art will understand that the terms "first" and "second" do not limit the quantity or execution order, and that "first" and "second" do not necessarily imply difference. It should be noted that in the embodiments of this application, the words "exemplary" or "for example" are used to indicate that something is being used as an example, illustration, or description. Any embodiment or design scheme described as "exemplary" or "for example" in this application should not be construed as being better or more advantageous than other embodiments or design schemes. Specifically, the use of "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner. In the embodiments of this application, "at least one" refers to one or more, and "more than one" refers to two or more.

[0082] It should be noted that the phrase "at...time" in the embodiments of this application can refer to the instant at which a certain situation occurs, or to a period of time after the occurrence of a certain situation; the embodiments of this application do not specifically limit this. Furthermore, the crack propagation simulation method based on a cascade model provided in the embodiments of this application is merely an example; a crack propagation simulation method based on a cascade model may also include more or less content.

[0083] Hydraulic fracturing fracture propagation simulation belongs to the field of unconventional oil and gas resource development and digital simulation technology. It is mainly used for predicting and analyzing fracture width, length, height, and propagation path during the stimulation of shale oil and gas, hot dry rock, and other reservoirs. This type of application typically relies on fracture propagation data, geophysical constraint information, and simulation computing platforms to design fracturing schemes, evaluate processes, and predict results.

[0084] In existing technologies, crack propagation prediction typically employs high-fidelity numerical simulation methods or data-driven surrogate models. The former generally uses simulation meshes with varying spatial discretization precision to solve the crack evolution process under given physical constraints step-by-step, thereby obtaining high-precision crack propagation results. The latter, on the other hand, learns the mapping relationship between historical crack propagation data to quickly predict the crack state in subsequent time steps, thus reducing the computational burden of direct solutions.

[0085] However, as spatial resolution increases, high-fidelity numerical simulations suffer from significantly increased computational scale and solution overhead, making them unsuitable for batch optimization analysis and near-real-time prediction requirements under multiple parameter combinations. While data-driven surrogate models can improve computational efficiency, they often suffer from insufficient adaptability under different geological conditions, pumping parameters, and fracture evolution morphologies, especially in simultaneously achieving both temporal prediction stability and high-resolution detail recovery capabilities.

[0086] Furthermore, when low-resolution predictions are directly used for engineering decisions, details such as fracture tips, turning zones, and local morphology are easily distorted. Conversely, relying solely on a single reconstruction model for high-resolution restoration may reduce the reliability of the results due to insufficient model matching. These shortcomings directly impact the accuracy of fracturing scheme evaluation, parameter optimization, and fracture propagation trend assessment.

[0087] Therefore, how to balance prediction accuracy and computational efficiency in crack propagation simulation, and improve scene adaptability under different physical constraints, has become an urgent technical problem to be solved.

[0088] Based on this, this application proposes a fracture propagation simulation method, apparatus, device, and medium based on a cascaded model, which can be used in image processing, artificial intelligence, and hydraulic fracturing simulation in oil and gas development, aiming to solve the above-mentioned technical problems of the prior art. This method provides a fracture propagation simulation method based on a cascaded model. It acquires low-resolution and high-resolution fracture propagation data corresponding to the same physical constraints, trains a time-series prediction model for low-resolution prediction in the next time step, and selects a target super-resolution reconstruction model from a candidate pool of super-resolution reconstruction models based on the high-resolution fracture propagation data. Then, it cascades the pre-trained time-series prediction model with the target super-resolution reconstruction model to simulate the initial fracture propagation data and output the target fracture propagation simulation result.

[0089] To better understand the solutions of the embodiments of this application, an application scenario involved in the embodiments of this application will be introduced below.

[0090] For specific application scenarios of this application, please refer to [link / reference needed]. Figure 1 . Figure 1This diagram illustrates an application scenario of a crack propagation simulation method based on a cascade model, as provided in this application. It should be noted that... Figure 1 The examples shown are merely application scenarios that can be applied to the embodiments of this application, in order to help those skilled in the art understand the technical content of this application, but do not mean that the embodiments of this application cannot be used in other devices, systems, environments or scenarios.

[0091] like Figure 1 As shown, the application scenario includes: a data processing server 101 and a user terminal 102.

[0092] The data processing server 101 is used to execute the crack propagation simulation method based on a cascaded model provided in this application embodiment. Specifically, the data processing server 101 can acquire multiple sets of crack propagation data to train a preset time-series prediction model and select a target super-resolution reconstruction model, and construct a cascaded model. After receiving the initial crack propagation data to be simulated, the cascaded model can be used for inference calculation to generate the target crack propagation simulation results (e.g., high-resolution data including a crack width mean map and a prediction uncertainty map).

[0093] User terminal 102 is used to communicate and interact with data processing server 101. User terminal 102 can send simulation requests and initial crack propagation data (such as crack data at the initial moment and target physical constraints) to data processing server 101, and receive target crack propagation simulation results returned by data processing server 101. Then, through the display interface, it can intuitively display the dynamic evolution process of crack propagation, the distribution of key physical quantities, or the uncertainty area of ​​prediction, for researchers or engineers to analyze and make decisions.

[0094] It should be noted that the data processing server 101 can be a standalone physical server, a server cluster consisting of multiple servers, or a cloud computing platform. The user terminal 102 can be a personal computer, workstation, tablet computer, or smartphone, or other device with data display and interactive functions. Data transmission between the two can be achieved through wired networks, wireless networks (such as Wi-Fi, 5G), or other communication protocols.

[0095] Figure 2 This is a flowchart illustrating a crack propagation simulation method based on a cascade model, provided as an embodiment of this application. The execution entity in this embodiment can be... Figure 1 The data processing server 101 in the illustrated embodiment can also be other computer-related devices, and this embodiment does not impose any particular limitations on it. Figure 2 As shown, the method includes:

[0096] S201. Obtain multiple sets of crack propagation data.

[0097] Each set of crack propagation data includes low-resolution crack propagation data and high-resolution crack propagation data corresponding to at least two time steps under the same physical constraint. The high-resolution crack propagation data is generated by simulation using a first simulation grid, and the low-resolution crack propagation data is generated by simulation using a second simulation grid. The spatial discretization accuracy of the first simulation grid is higher than that of the second simulation grid.

[0098] In this embodiment, fracture propagation data is used to characterize the spatial propagation state of fractures at different time steps during fracturing. The data content may include fracture length, fracture width, fracture height, fracture-occupied area, fracture tip location, or a two-dimensional or three-dimensional field distribution reflecting fracture morphology. The first simulation grid is used to generate high-resolution fracture propagation data. Its grid cell size (e.g., 2-meter grid) is smaller than the second simulation grid, enabling finer-grained characterization of fracture tips, turning regions, and local morphological changes. The second simulation grid is used to generate low-resolution fracture propagation data. Its grid cell size is larger (e.g., 5-meter grid), used to generate fracture propagation input suitable for time-series learning with lower computational overhead. Physical constraints are scenario constraint information corresponding to the same set of fracture propagation data. These constraints may include at least one of the following: geostress parameters, rock elastic modulus, Poisson's ratio, interlayer stress difference, reservoir thickness, natural fracture distribution parameters, pump injection rate, construction fluid viscosity, sand addition parameters, and construction time regime, used to ensure that the same set of data corresponds to the same physical evolution scenario.

[0099] In practice, the implementing entity can be a crack propagation simulation platform deployed on a local workstation, edge computing node, or cloud server. This platform can receive raw samples from historical simulation libraries, field inversion databases, or offline numerical simulation systems, and perform condition matching, time step alignment, and resolution pairing processing on the samples.

[0100] In one possible embodiment, multiple sets of crack propagation data can be generated through a dual-grid simulation method. That is, for the same set of physical constraints, numerical simulation of crack propagation is performed on the first simulation grid and the second simulation grid respectively to obtain a high-resolution sequence and a low-resolution sequence describing the same crack propagation process. Then, the two sequences are registered according to a unified time axis so that each low-resolution crack propagation data can correspond to the high-resolution crack propagation data at the same physical moment.

[0101] After receiving multiple sets of candidate samples, the platform first reads the physical constraint identifier associated with each set of samples, groups crack propagation data with the same constraint number, and then checks whether each set of data contains at least two adjacent time steps. Subsequently, the high-resolution crack propagation data and low-resolution crack propagation data are formatted uniformly, for example, into matrix, tensor, or regular grid array format, and the crack propagation region is normalized and encoded to ensure that data under different physical quantities meet the input requirements for subsequent model training.

[0102] In one possible embodiment, the crack propagation state can be represented using a two-dimensional grid field, where the grid values ​​characterize the crack width or the probability of crack presence. In another possible embodiment, the crack propagation state can be represented using a multi-channel tensor. After the above processing, the generated dataset includes multiple sample groups. Each sample group can store low-resolution and high-resolution crack propagation data at multiple consecutive time steps under the same physical constraints. Time step indexes, condition indexes, and resolution mapping relationships can be established for subsequent training of preset time-series prediction models and analysis of super-resolution reconstruction models.

[0103] Based on the above analysis, this step provides a consistent data foundation for subsequent learning of crack propagation time evolution and resolution mapping by constructing dual-resolution corresponding data under the same physical constraints. This enables the cascaded model to maintain physical scene consistency and establish stable correlations between different spatial accuracies during inference.

[0104] S202. Based on low-resolution crack propagation data, train a pre-set time series prediction model to obtain a pre-trained time series prediction model.

[0105] The pre-trained time-series prediction model is used to predict the low-resolution crack propagation data for the next time step based on the low-resolution crack propagation data of the previous time step and the physical constraints that match the current set of crack propagation data.

[0106] In this embodiment, the time-series prediction model is used to establish the evolution relationship of low-resolution crack propagation state over time. Its input includes at least the low-resolution crack propagation data of the previous time step and the physical constraints matching that data, and its output is the low-resolution crack propagation data of the next time step. The preset time-series prediction model can adopt a model structure suitable for time-series field prediction. The physical constraints serve as auxiliary inputs during training, not directly replacing the crack propagation field, but can participate in network computation through vector concatenation, conditional channel expansion, or feature modulation, ensuring that the network output remains consistent with the corresponding geological conditions and construction parameters.

[0107] In practice, adjacent time-step sample pairs can be extracted from the multiple sets of crack propagation data generated above to form a training sample set. The low-resolution crack propagation data from the previous time step is recorded as the input sample, and the low-resolution crack propagation data from the next time step is recorded as the supervision label. Physical constraints of the same set are simultaneously loaded as conditional features. If the physical constraints contain scalar parameters, standardization can be performed first, and then the conditional vector can be formed. If the physical constraints contain spatial distribution information, they can be resampled to a spatial size consistent with the second simulation grid and used as an additional input channel. During training, low-resolution crack propagation data and physical constraints can be fed into a pre-set temporal prediction model in batches. The pre-set temporal prediction model forward computes the predicted low-resolution crack propagation data for the next time step, and then the difference between the prediction result and the supervision label is used as the loss function input into the backpropagation process to update the model parameters.

[0108] Once the training rounds have reached a preset number or the validation set error has converged, the obtained model parameters can be saved to form a pre-trained temporal prediction model. During the inference phase, this pre-trained temporal prediction model can receive low-resolution crack propagation data from the previous time step along with matching physical constraints, output low-resolution crack propagation data for the next time step, and can recursively generate multiple low-resolution crack propagation sequences for subsequent time steps.

[0109] In one possible embodiment, the low-resolution crack propagation data output by the pre-trained temporal prediction model can continue to be used as input for the next round, thereby achieving time-step rolling prediction. In another possible embodiment, the pre-trained temporal prediction model can output low-resolution crack propagation data for multiple future time steps at once, and then provide it to the subsequent target super-resolution reconstruction model for reconstruction processing in chronological order.

[0110] Based on the above analysis, this step first learns the temporal evolution of crack propagation at a low-resolution level, transforming the high-overhead high-resolution temporal series solution into a lower-dimensional temporal series prediction problem, thereby providing stable and continuous temporal input for subsequent super-resolution reconstruction.

[0111] S203. Analyze each candidate model in the preset super-resolution reconstruction model candidate pool based on high-resolution crack propagation data, and select the target super-resolution reconstruction model.

[0112] The target super-resolution reconstruction model is used to map the low-resolution crack propagation data of the next time step to reconstruct high-resolution crack propagation data.

[0113] In this embodiment, the super-resolution reconstruction model candidate pool is a set of models containing multiple candidate reconstruction models, used to recover high-resolution spatial details from low-resolution crack propagation data. The target super-resolution reconstruction model is an adapted model determined after analysis, used to receive the low-resolution crack propagation data of the next time step and output reconstructed high-resolution crack propagation data corresponding to the first simulation mesh. The high-resolution crack propagation data serves as a reference ground truth in this step, used to evaluate the ability of each candidate model to recover crack propagation details and boundary information.

[0114] In practice, a super-resolution evaluation sample can be constructed based on the aforementioned multiple sets of crack propagation data, where low-resolution crack propagation data and corresponding high-resolution crack propagation data are stored in pairs. Each candidate model in the super-resolution reconstruction model candidate pool receives the low-resolution crack propagation data and generates corresponding reconstructed high-resolution crack propagation data. Subsequently, the reconstructed high-resolution crack propagation data output by each candidate model can be compared with the actual high-resolution crack propagation data to form a model score.

[0115] In practical processing, if there are many candidate models, batch inference can be performed based on a unified validation set first, and then the corresponding scoring results can be recorded according to the model number to form a candidate model performance table. The model with the best analysis results (i.e., the model with the highest score) can be determined as the target super-resolution reconstruction model. Its model parameters, input size, upsampling ratio, and output channel configuration are written into the model configuration file for subsequent cascading calls.

[0116] Based on the above analysis, this step uses high-resolution reference data to screen candidate models in multiple super-resolution reconstruction model candidate pools, so that the final target super-resolution reconstruction model matches the crack propagation detail recovery task, thereby maintaining the spatial resolution of crack tip, turning region and local morphology in subsequent simulation output.

[0117] S204. The pre-trained temporal prediction model is cascaded with the target super-resolution reconstruction model to obtain a cascaded model for crack propagation simulation.

[0118] In this embodiment, the cascaded model is a holistic processing model used for crack propagation simulation. Its core is to continuously connect the output of the pre-trained temporal prediction model with the input of the target super-resolution reconstruction model in the data stream, forming an end-to-end inference process that first performs low-resolution temporal prediction and then high-resolution reconstruction. The pre-trained temporal prediction model is responsible for predicting the crack propagation state of the next time step in the low-resolution space corresponding to the second simulation grid, while the target super-resolution reconstruction model is responsible for mapping this low-resolution crack propagation state to the high-resolution space corresponding to the first simulation grid, thereby outputting the high-resolution crack propagation result.

[0119] In practical implementation, a unified inference interface can be established in the model deployment environment. The interface input includes the low-resolution crack propagation data for the current time step, the physical constraints corresponding to the current simulation scene, and necessary time step identifiers. The pre-trained temporal prediction model first performs forward computation on the input data to obtain the low-resolution crack propagation data for the next time step. Subsequently, this output can be tensor rearranged, scale-checked, and channel-aligned according to the input format of the target super-resolution reconstruction model, and then directly input into the target super-resolution reconstruction model to generate the corresponding reconstructed high-resolution crack propagation data. If the target super-resolution reconstruction model requires auxiliary conditional input, the physical constraints can be synchronously input into the conditional branch of the target super-resolution reconstruction model using the same encoding method, ensuring that the reconstruction result not only depends on the low-resolution morphology but also remains consistent with the actual physical scene.

[0120] In one possible embodiment, the cascading process can be implemented using a software pipeline approach, that is, two models are deployed sequentially within the same computation graph, with intermediate results stored in a memory buffer and passed directly.

[0121] In another possible embodiment, the cascading process can be implemented using a service orchestration approach. Specifically, a pre-trained temporal prediction model acts as the upstream service, outputting low-resolution crack propagation data, while the target super-resolution reconstruction model acts as the downstream service, receiving the result and returning reconstructed high-resolution crack propagation data. Regardless of the implementation, a fixed data correspondence is established between the two, including the low-resolution output size, high-resolution target size, data type, and normalization method, to ensure input-output consistency after model concatenation. For multi-time-step crack propagation simulation, after completing the high-resolution output at a certain time step, the cascaded model can retain the corresponding low-resolution crack propagation data from the same time step as the input basis for the pre-trained temporal prediction model at the next time step, thus forming a recursive processing chain.

[0122] After this step is completed, a cascaded model object that can be directly executed for inference can be obtained. The cascaded model object contains pre-trained temporal prediction model parameters, target super-resolution reconstruction model parameters, input-output mapping relationships, and inference scheduling logic.

[0123] Based on the above analysis, it can be seen that this step combines temporal evolution prediction and spatial detail restoration into the same processing link, enabling crack propagation simulation to output high-resolution results with low computational complexity, while maintaining the synchronous expression of temporal continuity and spatial resolution.

[0124] S205. Obtain the initial crack propagation data to be simulated, and input the initial crack propagation data into the cascade model to obtain the target crack propagation simulation results.

[0125] In this embodiment, the initial crack propagation data is the starting state data used for cascaded model inference. Its spatial resolution is consistent with the input requirements of the time-series prediction model. It can be the measured crack initiation state under the simulated working condition, the inversion result at the initial stage of construction, or the initial simulation state generated based on the target working condition. The initial crack propagation data includes crack data at the initial moment and the target physical constraints. The target crack propagation simulation result is the crack propagation result output by the cascaded model. It can be represented as high-resolution crack propagation data at a single target time step, or as a high-resolution crack propagation sequence at multiple consecutive time steps. This result corresponds to the first simulation grid and can be used for subsequent fracturing scheme evaluation, crack propagation trend analysis, and parameter comparison.

[0126] In practice, the system first receives basic information about the scenario to be simulated, including reservoir parameters, construction parameters, and the simulation time range. Initial fracture propagation data is then extracted from the on-site monitoring system, historical engineering database, or a preset working condition input interface. If the initial fracture propagation data originates from actual monitoring and its resolution differs from the second simulation grid, interpolation, cropping, or resampling can be performed to convert it into a low-resolution format recognizable by the pre-trained time-series prediction model. Simultaneously, the physical constraints corresponding to the scenario to be simulated can be standardized and encoded in the same way as during the training phase to ensure consistent input distribution for the cascaded model. Subsequently, the initial fracture propagation data (including the matched target physical constraints) can be input into the cascaded model. The cascaded model can first output low-resolution fracture propagation data for the next time step, and then output the corresponding reconstructed high-resolution fracture propagation data. If the simulation task requires multiple subsequent time steps, the cascaded inference can be repeated until the preset simulation termination time is reached.

[0127] In one possible embodiment, high-resolution crack propagation data can be saved for each simulation time step, and these data can be arranged into a sequence of target crack propagation simulation results in chronological order. Each result in the sequence corresponds to an evolution moment of the crack propagation process under the same physical constraints. In another possible embodiment, only the high-resolution crack propagation data at the target time can be output, and derived parameters such as crack length, width, height, and main propagation direction can be extracted simultaneously as a result summary. To ensure the stability of the inference process, boundary checks can be performed on the results after each round of output, such as determining whether the crack region exceeds the simulation region or whether the crack width exceeds the set physical range. If an anomaly is detected, re-normalization or termination of inference can be triggered. Finally, the target crack propagation simulation results can be written to a result database or simulation display interface for subsequent processing.

[0128] Based on the above analysis, this step applies the trained cascaded model to the actual crack propagation simulation task. Starting from the initial crack propagation data, it gradually generates high-resolution crack propagation results under the target physical constraints, thereby achieving crack propagation prediction that balances computational efficiency and output details.

[0129] This application provides a method for simulating crack propagation based on a cascaded model. The method includes acquiring low-resolution and high-resolution crack propagation data corresponding to the same physical constraints; training a pre-set temporal prediction model based on the low-resolution crack propagation data; selecting a target super-resolution reconstruction model from a candidate pool of super-resolution reconstruction models based on the high-resolution crack propagation data; cascading the pre-trained temporal prediction model and the target super-resolution reconstruction model; and inputting the initial crack propagation data to be simulated into the cascaded model to obtain the target crack propagation simulation result. In this application embodiment, by first learning the temporal evolution of crack propagation in the low-resolution space corresponding to the second simulation grid, and then performing detailed reconstruction in the high-resolution space corresponding to the first simulation grid, the high-fidelity crack propagation simulation is divided into two continuous processing stages: temporal prediction and super-resolution mapping. Under the same physical constraints, a correspondence between low-resolution and high-resolution models is established, enabling the crack propagation simulation to output high-resolution results while maintaining temporal continuity. This method is applicable to crack propagation prediction scenarios under different combinations of geological and construction parameters.

[0130] Building upon the aforementioned embodiments, the preset temporal prediction model further employs a U-shaped network architecture. This architecture includes an encoder path, a decoder path, and a skip connection structure connecting the encoder and decoder paths. The encoder path is used to extract and downsample the low-resolution crack propagation data from the previous time step, while the decoder path is used to upsample and reconstruct the extracted features to output the low-resolution crack propagation data for the next time step.

[0131] In practical implementation, the encoder path can consist of several convolutional and pooling modules sequentially. Each convolutional module extracts local texture and crack boundary features, while the pooling module reduces the feature map size and expands the receptive field. The decoder path can consist of several deconvolutional modules, upsampling modules, or interpolation and reconstruction modules to progressively restore the feature map size. The network input is the low-resolution crack extension data from the previous time step, and the output is the low-resolution crack extension data from the next time step. The spatial dimensions of the output correspond to the spatial dimensions of the low-resolution crack extension data from the input time step. The kernel size of the convolutional modules can be set to 3×3, and the number of channels can be configured to increase or decrease with the network depth.

[0132] When this U-shaped network architecture is working, the encoder first performs multi-level representation of the input data and forms deep features. Then, the decoder, combined with skip connections, recovers the crack propagation morphology, thereby completing the prediction output of the low-resolution crack propagation data for the next time step. Since the encoding stage preserves information about the crack tip, turning region, and local details, the decoding stage can simultaneously utilize this information during the reconstruction process, ensuring that the prediction results remain consistent in both overall trend and local morphology.

[0133] By adopting the aforementioned U-shaped network architecture, the temporal prediction model can simultaneously acquire global evolutionary features and local detail features during crack propagation, and maintain good spatial continuity and boundary integrity when outputting low-resolution crack propagation data for the next time step. The skip connection structure effectively transmits shallow details, reduces information loss caused by downsampling, makes crack propagation morphology prediction more stable, and can provide more regular low-resolution input for subsequent super-resolution reconstruction.

[0134] In one possible implementation, the candidate models in a pre-defined super-resolution reconstruction model candidate pool are analyzed based on high-resolution crack propagation data to select the target super-resolution reconstruction model. This includes: inputting low-resolution crack propagation data into each candidate model in the candidate pool to obtain the corresponding reconstructed high-resolution crack propagation data; calculating the peak signal-to-noise ratio and structural similarity index between the reconstructed high-resolution crack propagation data and the high-resolution crack propagation data; weighting the peak signal-to-noise ratio and structural similarity index according to pre-defined weights to obtain the score of each candidate model; and selecting the candidate model with the highest score from the candidate pool as the target super-resolution reconstruction model.

[0135] In practical implementation, the candidate pool for super-resolution reconstruction models can consist of multiple super-resolution reconstruction networks. The network parameters of each candidate model can be pre-initialized and loaded into the same inference environment. After inputting the same set of low-resolution crack propagation data into each candidate model, each model outputs reconstructed high-resolution crack propagation data. Subsequently, the outputs of each model can be aligned and compared with high-resolution crack propagation data acquired or simulated under the same physical constraints. The peak signal-to-noise ratio (PSNR) and structural similarity index are calculated, and a candidate model score is generated based on preset weights. This score can be a weighted sum of the PSNR and structural similarity index, or a linear combination of the PSNR and structural similarity index after normalization, ensuring uniformity of the dimensions of different indicators. Finally, the candidate model with the highest score can be selected as the target super-resolution reconstruction model.

[0136] During the process, candidate models can be reconstructed in parallel on the same low-resolution crack propagation data. Then, a reconstruction quality index can be calculated based on real high-resolution crack propagation data, and the models are comprehensively ranked to determine the target super-resolution reconstruction model that best matches the current crack propagation scenario. This target super-resolution reconstruction model can then be used to map the next time-step low-resolution crack propagation data output by the time-series prediction model to a high-resolution result.

[0137] In practical implementation, the weighting ratio of Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) can be dynamically adjusted according to the physical characteristics of the crack morphology. PSNR is used to measure pixel-level accuracy (such as crack width error), while SSIM is used to assess structural consistency (such as crack tip sharpness). The comprehensive scoring formula can be: Score = 0.6 × PSNR + 0.4 × SSIM, ensuring the physical rationality and visual consistency of the high-resolution crack morphology.

[0138] After adopting this implementation method, the selection process of the target super-resolution reconstruction model takes into account both pixel error and structural consistency, which enables the subsequent reconstruction results to maintain a high degree of consistency in crack tip morphology, turning region and local detail representation, thereby improving the credibility and scene adaptability of the target crack propagation simulation results based on the cascade model.

[0139] In one possible implementation, a pre-trained temporal prediction model and a target super-resolution reconstruction model are cascaded to obtain a cascaded model for crack propagation simulation. This includes fixing the model parameters of both the pre-trained temporal prediction model and the target super-resolution reconstruction model. The output of the pre-trained temporal prediction model is directly connected to the input of the target super-resolution reconstruction model to construct an end-to-end inference pipeline. The inference pipeline is configured to: receive low-resolution crack propagation data at the current time step; output intermediate low-resolution crack propagation data for the next time step via the pre-trained temporal prediction model; and map the intermediate low-resolution crack propagation data to reconstructed high-resolution crack propagation data for the next time step via the target super-resolution reconstruction model.

[0140] In actual operation, the low-resolution crack propagation data of the current time step is processed by a pre-trained temporal prediction model to obtain intermediate low-resolution crack propagation data for the next time step, which characterizes the crack evolution trend. This intermediate low-resolution crack propagation data is then input into the target super-resolution reconstruction model, which recovers the crack tip, turning region, and local texture details, and outputs reconstructed high-resolution crack propagation data for the next time step. This cascading relationship allows temporal evolution prediction and spatial detail recovery to be completed continuously in the same inference chain, thus forming a unified output result for crack propagation simulation.

[0141] After adopting the above cascaded method, the pre-trained temporal prediction model is responsible for maintaining the temporal continuity of crack evolution, while the target super-resolution reconstruction model is responsible for supplementing high-resolution spatial details. The two infer continuously under fixed parameter conditions, which can enable the target crack propagation simulation results to have both temporal consistency and spatial representation integrity, and reduce the detail bias when low-resolution results are directly used for engineering judgment.

[0142] In one possible implementation, the process involves acquiring initial crack propagation data to be simulated and inputting this data into a cascaded model to obtain the target crack propagation simulation result. This includes: acquiring the initial crack propagation data to be simulated, which includes crack data at the initial time step and target physical constraints; using the initial crack data and target physical constraints as the current time step propagation data; inputting the current time step propagation data into the cascaded model to obtain the high-resolution crack propagation simulation result for the next time step; performing downsampling on the high-resolution crack propagation simulation result for the next time step before a preset simulation termination time is reached, obtaining downsampled crack propagation data for the next time step; using the downsampled crack propagation data and target physical constraints as the new current time step propagation data, and returning to the step of inputting the current time step propagation data into the cascaded model to obtain the high-resolution crack propagation simulation result for the next time step; and obtaining the target crack propagation simulation result based on the high-resolution crack propagation simulation results generated for each next time step when the preset simulation termination time is reached.

[0143] In practical implementation, the initial fracture geometry, fracture width field, or fracture leading edge distribution can be read from the scenario to be simulated, and the target physical constraints matching the scenario can be loaded simultaneously. These constraints can consist of reservoir stress field, rock mechanics parameters, injection pressure curve, and boundary constraints. Subsequently, the initial fracture data and the target physical constraints can be concatenated to form the current time-step extended data. This data is then input into the cascaded pre-trained time-series prediction model and the target super-resolution reconstruction model to obtain the intermediate low-resolution fracture extension data for the next time step, which is then mapped to the high-resolution fracture extension simulation result for the next time step. If the current simulation time has not reached the preset simulation termination time, the high-resolution result can be downsampled according to a preset grid ratio, sampling interval, or interpolation rule to form the downsampled fracture extension data for the next time step. This downsampled data is then recombine with the target physical constraints to form new current time-step extended data, which is then input into the cascaded model again for iterative inference. If the preset simulation termination time has been reached, the high-resolution fracture extension simulation results generated at each time step can be summarized in chronological order to obtain the target fracture extension simulation result.

[0144] This scheme downsamples the high-resolution output of each time step and feeds it back to the cascaded model before the preset simulation termination time. This allows the crack propagation state to advance continuously under unified physical constraints while maintaining consistency between temporal input and output. Since the termination condition is controlled by the preset simulation termination time, the cascaded model can complete multiple rounds of inference and form a complete crack propagation trajectory within a limited time range. Using this method, the output results simultaneously include high-resolution crack morphology and temporal evolution information at each time step, improving the continuity and completeness of the crack propagation simulation.

[0145] Building upon the aforementioned embodiments, the process further includes inputting initial crack propagation data into a cascaded model to obtain target crack propagation simulation results. This further involves introducing a Monte Carlo dropout mechanism or ensemble learning mechanism during the inference process of the cascaded model, performing multiple random forward propagations to obtain a set of multiple high-resolution crack propagation simulation results. These multiple high-resolution crack propagation simulation results are then aggregated to calculate the mean crack width, generating a mean crack width map. Based on the variance of the multiple high-resolution crack propagation simulation results, a prediction uncertainty map is generated. This prediction uncertainty map is used to identify regions in the crack propagation path where the prediction confidence is below a preset threshold.

[0146] In the specific implementation, the initial crack propagation data is input into the cascaded pre-trained temporal prediction model and the target super-resolution reconstruction model. The model output is the high-resolution crack propagation simulation result at the corresponding time step. During inference, if a Monte Carlo dropout mechanism is used, the dropout layer in the encoder, decoder, or reconstruction network can remain enabled, and forward propagation can be repeated multiple times for the same input. If an ensemble learning mechanism is used, multiple inference models with different structures or parameters can be applied to the same input, resulting in multiple high-resolution results. Subsequently, the obtained results are statistically analyzed pixel-wise or grid-wise along the crack width dimension, the mean is calculated, and mapped to a crack width mean map. Simultaneously, a prediction uncertainty map can be generated based on the variance of the results at each location, and regions with variance higher than a corresponding threshold or confidence lower than a preset threshold are marked as low-confidence regions.

[0147] In its implementation, the Monte Carlo dropout mechanism can be activated in the convolutional module of the decoder layer, generating 10 predictions by randomly dropping some neurons. The variance threshold is set to the 95th quantile of the variance distribution to ensure that only crack regions that significantly deviate from the mean (such as tips and turning regions) are labeled as low-confidence regions.

[0148] This method obtains output distribution information by repeatedly performing random inference on the same crack propagation input, and uses a mean plot and an uncertainty plot to characterize the expected shape and fluctuation range of crack propagation, respectively. This allows the target crack propagation simulation results to maintain high resolution while providing interpretable confidence indicators. Consequently, crack tips, turning regions, and local width variation areas can be identified simultaneously, and their corresponding simulation results and risk area markers can be directly used for crack propagation analysis.

[0149] This application provides a fracture propagation simulation method based on a cascade model, which can be applied to the horizontal well fracturing design optimization scenario in shale oil blocks during unconventional oil and gas resource development.

[0150] Taking a horizontal well in a shale oil block as an example, it is necessary to quickly predict the fracture propagation morphology under different combinations of injection parameters and rock mechanics parameters. The design of fracturing parameter combinations includes an injection flow rate of 15-24 cubic meters per minute (m³ / min) and a viscosity of 5-25 millipascal-second (mPa·s), and optimization of the fracture propagation path to maximize the Stimulated Reservoir Volume (SRV).

[0151] The geological conditions of this block are complex, and there are significant uncertainties in the rock mechanical parameters, including a Young's modulus of 40-50 gigapascals (GPa) and a principal stress difference of 20-30 megapascals (MPa). Therefore, it is necessary to assess the risk of natural fracture activation through high-resolution fracture simulation, while taking into account the simulation accuracy of key physical characteristics such as fracture tip and direction and the computational cost of high-resolution numerical simulation, and combining uncertainty quantification for risk decision-making.

[0152] In one possible implementation, multiple sets of fracture propagation data are first acquired. Each set of fracture propagation data corresponds to the same physical constraint condition and simultaneously includes low-resolution and high-resolution fracture propagation data from at least two time steps. For the aforementioned shale oil block scenario, 5000 sets of parameter combinations can be randomly generated using a high-fidelity hydraulic fracturing simulator (Pseudo Three-Dimensional Hydraulic Fracture Simulator, PL3D) under both 5-meter coarse and 2-meter fine grid conditions. Rock mechanics parameters include Young's modulus of 20-50 GPa, Poisson's ratio of 0.2-0.35, and principal stress of 40-70 MPa. Pumping parameters include injection rate of 8-24 m³ / min and viscosity of 5-25 mPa·s. High-resolution fracture propagation data can be generated using a 2-meter fine grid simulation, while low-resolution fracture propagation data can be generated using a 5-meter coarse grid simulation. The spatial discretization accuracy of the 2-meter fine grid is higher than that of the 5-meter coarse grid.

[0153] Under each set of parameters, the simulator can output crack width map, rock mechanics parameter map and pumping parameter map every 5 minutes. Finally, about 100,000 paired samples are generated and divided into training set, validation set and test set in a ratio of 7:2:1. The size of low resolution crack map can be 73×10 pixels, and the size of high resolution crack map can be 181×24 pixels.

[0154] Figure 3 A comparison diagram of the statistical distribution of crack geometric parameters obtained by simulating different mesh resolutions in the embodiments of this application. Figure 3 This diagram illustrates the difference in crack width distribution between 5-meter and 2-meter grids under the same pumping parameters. The top subplots show the frequency distribution of crack width at injection times of 5, 15, and 25 minutes. The bottom subplots show the frequency distribution of crack length at the corresponding time points. Gray bars and black fitted curves represent simulation results with fine grids, while pink bars and red fitted curves represent simulation results with coarse grids.

[0155] like Figure 3 As shown, this application analyzes the influence of grid resolution on the accuracy of hydraulic fracturing simulation through comparative experiments. Figure 3The study demonstrates the statistical differences in crack morphology parameters obtained by numerical simulation using a 5-meter coarse grid and a 2-meter fine grid, while keeping the pumping parameters consistent.

[0156] Specifically, the top subplots reflect the evolution of fracture width. The horizontal axis represents fracture width in millimeters (mm), and the vertical axis represents sample frequency. Observing the three sets of data with injection times of 5 minutes, 15 minutes, and 25 minutes, it can be seen that the fracture width generally increases with continuous fracturing fluid injection (the distribution curve shifts to the right). However, comparing the simulation results of the two grids reveals that the coarse grid (pink / red curve) generally predicts a higher mean fracture width than the fine grid (gray / black curve), and the distribution pattern shows a significant deviation. This indicates that due to numerical discretization errors, low-resolution grids often overestimate the average fracture opening degree, leading to a distortion in the assessment of reservoir conductivity.

[0157] The lower subplots further reveal the distribution characteristics of crack length. Data shows that the crack length distribution simulated by the fine mesh is relatively concentrated and conforms to physical laws, while the simulation results of the coarse mesh exhibit different peak positions and dispersion at different times. Especially in the later stages of injection (e.g., 25 minutes), there is a significant gap between the crack extension range predicted by the coarse mesh and the high-resolution baseline, failing to accurately capture the propagation behavior of the crack tip.

[0158] In conclusion, Figure 3 This intuitively demonstrates the negative impact of the grid effect on the prediction accuracy of fracture geometry (width and length). This further underscores the necessity of the method proposed in this application: by introducing high-resolution simulation data as a monitoring signal, or by using a cascaded model to perform super-resolution reconstruction of coarse-grid results, grid-dependent errors can be effectively eliminated, thereby more accurately characterizing the fracture network morphology and providing a reliable basis for the accurate assessment of reservoir stimulation volume.

[0159] Based on low-resolution fracture propagation data from each dataset, time-series training samples are constructed. The low-resolution fracture propagation data from the previous time step and its corresponding physical constraints are used as input, while the low-resolution fracture propagation data from the next time step is used as the supervised output. This process trains the pre-trained time-series prediction model, resulting in a pre-trained model. In this shale oil block example, the time-series prediction model can adopt a U-shaped network architecture, i.e., a U-Net network structure, including encoder paths, decoder paths, and skip connections connecting the encoder and decoder paths. The input is the multi-channel feature map from the previous time step, which can consist of a fracture width map and parameter maps such as Young's modulus, Poisson's ratio, principal stress, injection displacement, and viscosity. The output is the low-resolution fracture width map from the next time step. The encoder path can extract and downsample the input low-resolution fracture propagation data from the previous time step. Specifically, a 4-layer downsampling encoder can be used, increasing the number of channels from 64 to 512. The decoder path can perform upsampling and reconstruction on the extracted features. Specifically, a 4-layer upsampling decoder can be used, reducing the number of channels from 512 to 64. Under the action of the skip connection structure, shallow detail features and multi-scale features are fused to output low-resolution crack extension data for the next time step.

[0160] In one embodiment of this application, the training process of the cascaded model can employ a combination of various loss functions. For example, a weighted combination of mean squared error loss and edge-aware loss (such as gradient difference loss calculated based on the Laplacian operator) can be used as the total loss function, wherein the Laplacian operator is used to extract the edge features of the crack to calculate the difference between the predicted edge and the real edge, thereby improving the cascaded model's ability to reconstruct high-frequency details such as crack tips.

[0161] For optimization, the Adam optimizer can be used, with an initial learning rate of 0.0001 and a decay strategy (e.g., decreasing to 0.5 times the original rate every 100 epochs). The batch size during training can be set to 32, and the training epochs to 500. This training process can be performed on general-purpose computing devices, such as servers equipped with graphics processing units (GPUs). Testing has shown that the cascaded model achieves high prediction accuracy on the test set.

[0162] Figure 4 This is a schematic diagram of the U-shaped network architecture provided in an embodiment of this application. Figure 4 As shown, the network includes an encoder downsampling path on the left, a decoder upsampling path on the right, and a skip connection structure connecting the two. The input is low-resolution crack width field data at time T. After multiple convolutional, pooling, and feature fusion processes, the output is the predicted low-resolution crack width field data at time T+1. Figure 2The document also shows the kernel size (e.g., 3×3, 1×1), pooling method (2×2), upsampling operation (2×2), and distribution of regularization layers used in each layer.

[0163] After training the time-series prediction model, a pre-defined pool of candidate super-resolution reconstruction models can be analyzed based on high-resolution crack propagation data. Low-resolution crack propagation data is input into each candidate model in the pool to obtain the reconstructed high-resolution crack propagation data output by each model. Each reconstruction result is then compared with its corresponding high-resolution crack propagation data, and the peak signal-to-noise ratio (PSNR) and structural similarity index are calculated. These PNR and structural similarity indices are weighted according to pre-defined weights to obtain a score for each candidate model. The candidate model with the highest score is selected from the pool as the target super-resolution reconstruction model. In this example, a candidate pool of heterogeneous super-resolution models is constructed, including Sparse and Self-Taught Convolutional Neural Network (SCNN), Fourier Neural Operator (FNO), Swin-Conv-UNet (SCUNet), and Swin Transformer for Image Restoration (SwinIR). A Super-Resolution Generative Adversarial Network (SRGAN) model is also validated and compared. Each candidate model takes a low-resolution crack image (e.g., 73×10 pixels) and a 20-dimensional physical constraint vector as input, and outputs a high-resolution crack image (e.g., 181×24 pixels). The 20-dimensional physical constraint vector includes Young's modulus, Poisson's ratio, principal stress, injection displacement, viscosity, and their first-order and second-order difference features. The model's PSNR and SSIM were calculated on the validation set. The SRGAN model achieved a PSNR of 38.1 dB and an SSIM of 0.96, thus it was selected as the target super-resolution reconstruction model. This target super-resolution reconstruction model maps physical constraint vectors to feature maps through fully connected layers and performs channel concatenation with image features.

[0164] Figure 5 A comparative diagram showing the super-resolution reconstruction results of crack propagation for various models provided in the embodiments of this application. For example... Figure 5As shown, the three columns in the figure represent crack evolution samples under different working conditions. From top to bottom, each column contains: a coarse mesh simulator, a fine mesh simulator, and reconstruction results from the Generative Adversarial Network (GAN) super-resolution model, Fourier neural operator, U-Net (UNet) super-resolution model, Convolutional Neural Network (CNN) super-resolution model, Swin image restoration network, and bilinear interpolation. Figure 5 The performance differences of each method in restoring detailed features such as crack morphology, edge sharpness, and width distribution are visually demonstrated.

[0165] Subsequently, the model parameters of the pre-trained temporal prediction model and the target super-resolution reconstruction model are fixed. The output of the pre-trained temporal prediction model is directly connected to the input of the target super-resolution reconstruction model, constructing an end-to-end inference pipeline. This allows the low-resolution fracture propagation data of the current time step to first pass through the pre-trained temporal prediction model to output intermediate low-resolution fracture propagation data for the next time step, and then be mapped by the target super-resolution reconstruction model to reconstruct high-resolution fracture propagation data for the next time step. In the above example, the trained U-Net model and the SRGAN super-resolution model are integrated end-to-end to form a super-resolution-temporal cascade pipeline. During actual simulation, the initial fracture propagation data to be simulated is first obtained. The initial fracture propagation data includes the fracture data at the initial time and the target physical constraints. Taking well A as an example, the initial fracture map, rock mechanics parameters, and pumping parameters of well A are input, and parallel inference with 500 sets of parameter combinations is executed through batch scheduling using a graphics processing unit (GPU). After the current time step propagation data enters the cascaded model, the high-resolution fracture propagation simulation results for the next time step are output. If the preset simulation termination time has not been reached, a downsampling operation is performed on the high-resolution crack propagation simulation results for the next time step to obtain downsampled crack propagation data for the next time step. This downsampled crack propagation data, along with the target physical constraints, is then used as the new current time step propagation data and input into the cascaded model. The high-resolution crack propagation simulation results for subsequent time steps are generated iteratively. When the preset simulation termination time is reached, the high-resolution crack propagation simulation results for the next time step generated in each iteration are summarized to form the target crack propagation simulation result.

[0166] Figure 6 This diagram illustrates the super-resolution reconstruction effect and error analysis of the crack width field in the cascaded model provided in this embodiment of the application. Figure 6As shown in the figure, this figure illustrates the temporal prediction performance of the cascaded model for the crack width field at different injection times (10 minutes, 25 minutes, 40 minutes, and 55 minutes). Each set of results, from top to bottom, includes: the coarse-grid simulation input at time t, the fine-grid simulation ground truth at time t+1, the super-resolution reconstruction result generated by the model at time t+1, and the corresponding error distribution map. The comparison shows that the reconstruction results highly match the fine-grid simulation ground truth in terms of crack morphology, expansion range, and peak width. Furthermore, the error map shows that the main deviations are concentrated in the crack edge region, and the overall error is controlled at a low level, indicating that the cascaded model can effectively capture the dynamic evolution characteristics of cracks and possesses high reconstruction accuracy and stability.

[0167] In the inference process of the cascaded model, a Monte Carlo dropout mechanism can be introduced to perform multiple random forward propagations on the same current time step of the extended data, resulting in multiple sets of high-resolution crack propagation simulation results, which are then aggregated. In this example, Monte Carlo dropout technology is enabled in the SRGAN super-resolution model, and the same input is subjected to 10 random forward propagations. The pixel-level mean and standard deviation are calculated for the 10 high-resolution crack width maps obtained. Based on the aggregated results, the mean crack width is calculated and a mean crack width map is generated. At the same time, a prediction uncertainty map is generated based on the variance of the multiple high-resolution crack propagation simulation result sets, and regions with prediction confidence levels below a preset threshold in the crack propagation path are marked in the prediction uncertainty map. In the crack tip region, the standard deviation map shows high uncertainty, corresponding to the high uncertainty region and uncertainty band in the prediction uncertainty map, which is used to indicate the potential risk of natural crack activation in this region. The prediction results are then verified in conjunction with microseismic monitoring data. The final output includes high-resolution fracture width maps, mean maps, standard deviation maps, and simulation results of uncertainty zones. These are used to compare the combination of fracturing parameters under injection flow rates of 15-24 m³ / min and viscosity of 5-25 mPa·s, and to analyze the fracture propagation path in conjunction with the geological uncertainties brought about by Young's modulus of 40-50 GPa and principal stress difference of 20-30 MPa.

[0168] Figure 7 This is a schematic diagram illustrating the quantification results of the crack width field uncertainty provided in an embodiment of this application. Figure 7 As shown, the figure contains two parts: (a) the average crack width field at different injection times; and (b) the standard deviation of crack width at different injection times. Each set of results, from top to bottom, consists of the cascaded model prediction, the fine-mesh simulator prediction, and the error distribution of both.

[0169] The comparison shows that the average width field predicted by the cascaded model is highly consistent with the predictions of the fine-grid simulator in terms of fracture morphology and magnitude. The standard deviation plot effectively identifies areas with low prediction confidence (such as fracture edges), thus visualizing uncertainty. Combined with geological data and subsequent microseismic monitoring results, it is confirmed that high uncertainty areas correspond to the activation locations of natural fractures, indicating that the uncertainty quantification information provided in this application can effectively assist in fracturing risk decision-making and has practical engineering guidance value.

[0170] This application embodiment can divide an electronic device or main control device into functional modules according to the above method examples. For example, each function can be divided into its own functional modules, or two or more functions can be integrated into one processing unit. The integrated unit can be implemented in hardware or as a software functional module. It should be noted that the module division in this embodiment is illustrative and only represents one logical functional division; in actual implementation, there may be other division methods.

[0171] Figure 8 This is a schematic diagram of a crack propagation simulation device based on a cascade model, provided as an embodiment of this application. Figure 8 As shown, the device includes: an acquisition module 810, a training module 820, a screening module 830, a cascade module 840, and a prediction module 850.

[0172] The acquisition module 810 is used to acquire multiple sets of crack propagation data. Each set of crack propagation data includes low-resolution crack propagation data and high-resolution crack propagation data corresponding to at least two time steps under the same physical constraint. The high-resolution crack propagation data is generated by simulation using a first simulation grid, and the low-resolution crack propagation data is generated by simulation using a second simulation grid. The spatial discretization accuracy of the first simulation grid is higher than that of the second simulation grid.

[0173] Training module 820 is used to train a preset time series prediction model based on low-resolution crack propagation data to obtain a pre-trained time series prediction model. The pre-trained time series prediction model is used to predict the low-resolution crack propagation data of the next time step based on the low-resolution crack propagation data of the previous time step and the physical constraints that match the current set of crack propagation data.

[0174] The filtering module 830 is used to analyze each candidate model in the preset super-resolution reconstruction model candidate pool based on high-resolution crack propagation data, and filter out the target super-resolution reconstruction model. The target super-resolution reconstruction model is used to map the low-resolution crack propagation data of the next time step into the reconstructed high-resolution crack propagation data.

[0175] The cascade module 840 is used to cascade the pre-trained temporal prediction model with the target super-resolution reconstruction model to obtain a cascaded model for crack propagation simulation.

[0176] The prediction module 850 is used to acquire the initial crack propagation data to be simulated and input the initial crack propagation data into the cascaded model to obtain the target crack propagation simulation results.

[0177] In one possible implementation, in the training module 820, the preset temporal prediction model adopts a U-shaped network architecture, which includes an encoder path, a decoder path, and a jump connection structure connecting the encoder path and the decoder path.

[0178] The encoder path is used to extract and downsample the low-resolution crack propagation data of the previous time step, while the decoder path is used to upsample and reconstruct the extracted features to output the low-resolution crack propagation data of the next time step.

[0179] In one possible implementation, the filtering module 830 is specifically used for:

[0180] Low-resolution crack propagation data is input into each candidate model in the candidate pool to obtain the corresponding reconstructed high-resolution crack propagation data.

[0181] Calculate the peak signal-to-noise ratio and structural similarity index between reconstructed high-resolution crack propagation data and high-resolution crack propagation data;

[0182] The peak signal-to-noise ratio and structural similarity index are weighted according to preset weights to obtain the scores of each candidate model;

[0183] The candidate model with the highest score is selected from the candidate pool as the target super-resolution reconstruction model.

[0184] In one possible implementation, the cascade module 840 is specifically used for:

[0185] The model parameters of the pre-trained temporal prediction model and the target super-resolution reconstruction model are fixed;

[0186] The output of the pre-trained temporal prediction model is directly connected to the input of the target super-resolution reconstruction model to build an end-to-end inference pipeline.

[0187] The inference pipeline is configured to: receive low-resolution crack propagation data at the current time step, output intermediate low-resolution crack propagation data for the next time step through a pre-trained time-series prediction model, and map the intermediate low-resolution crack propagation data to reconstructed high-resolution crack propagation data for the next time step through a target super-resolution reconstruction model.

[0188] In one possible implementation, the prediction module 850 is specifically used for:

[0189] Obtain the initial crack propagation data to be simulated. The initial crack propagation data includes the crack data at the initial moment and the target physical constraints.

[0190] The crack data and target physical constraints at the initial moment are used as the extended data at the current time step;

[0191] Input the current time step expansion data into the cascaded model to obtain the high-resolution crack propagation simulation results for the next time step;

[0192] If the preset simulation termination time has not been reached, a downsampling operation is performed on the high-resolution crack propagation simulation results of the next time step to obtain the downsampled crack propagation data of the next time step.

[0193] The steps are: using the downsampled crack propagation data of the next time step and the target physical constraints as the new current time step propagation data, and returning to input the current time step propagation data into the cascaded model to obtain the high-resolution crack propagation simulation results of the next time step.

[0194] When the preset simulation termination time is reached, the target crack propagation simulation result is obtained based on the high-resolution crack propagation simulation results of the next time step generated each time step.

[0195] In one possible implementation, the prediction module 850 is further configured to:

[0196] In the inference process of the cascaded model, a Monte Carlo dropout mechanism or an ensemble learning mechanism is introduced to perform multiple random forward propagations and obtain multiple sets of high-resolution crack propagation simulation results.

[0197] The results of multiple high-resolution crack propagation simulations are aggregated to calculate the average crack width and generate a crack width average map.

[0198] Based on the variance of multiple high-resolution crack propagation simulation results, a prediction uncertainty map is generated. The prediction uncertainty map is used to identify areas in the crack propagation path where the prediction confidence is lower than a preset threshold.

[0199] This embodiment provides a crack propagation simulation device based on a cascade model, which can execute a crack propagation simulation method based on a cascade model as described in the above embodiment. Its implementation principle and technical effect are similar, and will not be repeated here.

[0200] In the aforementioned specific implementation of a crack propagation simulation device based on a cascade model, each module can be implemented as a processor. The processor can execute computer execution instructions stored in the memory, thereby enabling the processor to execute the aforementioned crack propagation simulation method based on a cascade model.

[0201] Figure 9 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Figure 9 As shown, the electronic device includes at least one processor 910 and a memory 920. The electronic device also includes a communication component 930. The processor 910, memory 920, and communication component 930 are connected via a bus 940.

[0202] In the specific implementation process, at least one processor 910 executes computer execution instructions stored in memory 920, causing at least one processor 910 to execute a crack propagation simulation method based on a cascade model as executed on the electronic device side.

[0203] The specific implementation process of processor 910 can be found in the above method embodiments, and its implementation principle and technical effect are similar. It will not be repeated here.

[0204] In the above embodiments, it should be understood that the processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor.

[0205] The memory may include high-speed RAM, and may also include non-volatile storage (NVM), such as at least one disk storage.

[0206] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, the buses shown in the accompanying drawings are not limited to a single bus or a single type of bus.

[0207] The above description of the functions implemented by electronic devices and main control devices has introduced the solutions provided by the embodiments of the present invention. It is understood that, in order to implement the above functions, the electronic device or main control device includes hardware structures and / or software modules corresponding to the execution of each function. By combining the units and algorithm steps of the various examples described in the embodiments of the present invention, the embodiments of the present invention can be implemented in hardware or a combination of hardware and computer software. Whether a function is executed by hardware or by computer software driving hardware depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the technical solutions of the embodiments of the present invention.

[0208] This application also provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the crack propagation simulation method based on a cascade model as described above.

[0209] The aforementioned readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The readable storage medium can be any available medium accessible to a general-purpose or special-purpose computer.

[0210] An exemplary readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the readable storage medium. Of course, the readable storage medium can also be a component of the processor. The processor and the readable storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and the readable storage medium can exist as discrete components in an electronic device or a host device.

[0211] This application also provides a computer program product, which includes a computer program stored in a readable storage medium. At least one processor of an electronic device can read the computer program from the readable storage medium, and the at least one processor executes the computer program to cause the electronic device to perform the solution provided in the above embodiments.

[0212] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disk, or optical disk.

[0213] The technical solutions of this application have been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it is readily understood by those skilled in the art that the scope of protection of this application is obviously not limited to these specific embodiments. The above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. These modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A crack propagation simulation method based on a cascade model, characterized in that, include: Multiple sets of crack propagation data are acquired. Each set of crack propagation data includes low-resolution crack propagation data and high-resolution crack propagation data corresponding to at least two time steps under the same physical constraint. The high-resolution crack propagation data is generated by simulation using a first simulation mesh, and the low-resolution crack propagation data is generated by simulation using a second simulation mesh. The spatial discretization accuracy of the first simulation mesh is higher than that of the second simulation mesh. Based on the low-resolution crack propagation data, a preset time-series prediction model is trained to obtain a pre-trained time-series prediction model. The pre-trained time-series prediction model is used to predict the low-resolution crack propagation data of the next time step based on the low-resolution crack propagation data of the previous time step and the physical constraints that match the current set of crack propagation data. Based on the high-resolution crack propagation data, the candidate models in the preset super-resolution reconstruction model candidate pool are analyzed to select the target super-resolution reconstruction model. The target super-resolution reconstruction model is used to map the low-resolution crack propagation data of the next time step into reconstructed high-resolution crack propagation data. The pre-trained temporal prediction model is cascaded with the target super-resolution reconstruction model to obtain a cascaded model for crack propagation simulation. Acquire the initial crack propagation data to be simulated, and input the initial crack propagation data into the cascaded model to obtain the target crack propagation simulation results.

2. The method according to claim 1, characterized in that, The preset time-series prediction model adopts a U-shaped network architecture, which includes an encoder path, a decoder path, and a jump connection structure connecting the encoder path and the decoder path. The encoder path is used to extract and downsample the low-resolution crack propagation data of the previous time step, and the decoder path is used to upsample and reconstruct the extracted features to output the low-resolution crack propagation data of the next time step.

3. The method according to claim 1, characterized in that, The step of analyzing each candidate model in the preset super-resolution reconstruction model candidate pool based on the high-resolution crack propagation data and selecting the target super-resolution reconstruction model includes: The low-resolution crack propagation data is input into each candidate model in the candidate pool to obtain the corresponding reconstructed high-resolution crack propagation data. Calculate the peak signal-to-noise ratio and structural similarity index between the reconstructed high-resolution crack propagation data and the high-resolution crack propagation data; The peak signal-to-noise ratio and the structural similarity index are weighted according to preset weights to obtain the scores of each candidate model; The candidate model with the highest score is selected from the candidate pool as the target super-resolution reconstruction model.

4. The method according to claim 3, characterized in that, The step of cascading the pre-trained temporal prediction model with the target super-resolution reconstruction model to obtain a cascaded model for crack propagation simulation includes: The model parameters of the pre-trained temporal prediction model and the target super-resolution reconstruction model are fixed; The output of the pre-trained temporal prediction model is directly connected to the input of the target super-resolution reconstruction model to construct an end-to-end inference pipeline. The inference pipeline is configured to: receive low-resolution crack propagation data at the current time step, output intermediate low-resolution crack propagation data for the next time step through the pre-trained temporal prediction model, and map the intermediate low-resolution crack propagation data to the reconstructed high-resolution crack propagation data for the next time step through the target super-resolution reconstruction model.

5. The method according to claim 1, characterized in that, The process of acquiring initial crack propagation data to be simulated and inputting the initial crack propagation data into the cascaded model to obtain the target crack propagation simulation results includes: Acquire the initial crack propagation data to be simulated, which includes crack data at the initial moment and target physical constraints. The crack data at the initial moment and the target physical constraints are used as the extended data at the current time step; The current time step expansion data is input into the cascaded model to obtain the high-resolution crack propagation simulation results for the next time step; If the preset simulation termination time has not been reached, a downsampling operation is performed on the high-resolution crack propagation simulation results of the next time step to obtain downsampled crack propagation data for the next time step. The downsampled crack propagation data of the next time step and the target physical constraints are used as the new current time step propagation data, and the process of inputting the current time step propagation data into the cascaded model to obtain the high-resolution crack propagation simulation results of the next time step is returned. When the preset simulation termination time is reached, the target crack propagation simulation result is obtained based on the high-resolution crack propagation simulation result of the next time step generated each time.

6. The method according to any one of claims 1 to 5, characterized in that, The step of inputting the initial crack propagation data into the cascaded model to obtain the target crack propagation simulation results also includes: In the inference process of the cascaded model, a Monte Carlo dropout mechanism or an ensemble learning mechanism is introduced to perform multiple random forward propagations and obtain multiple sets of high-resolution crack propagation simulation results. The results of the multiple high-resolution crack propagation simulations are aggregated to calculate the average crack width and generate an average crack width map. Based on the variance of the set of multiple high-resolution crack propagation simulation results, a prediction uncertainty map is generated. The prediction uncertainty map is used to identify areas in the crack propagation path where the prediction confidence is lower than a preset threshold.

7. A crack propagation simulation device based on a cascade model, characterized in that, include: The acquisition module is used to acquire multiple sets of crack propagation data. Each set of crack propagation data includes low-resolution crack propagation data and high-resolution crack propagation data corresponding to at least two time steps under the same physical constraint. The high-resolution crack propagation data is generated by simulation using a first simulation grid, and the low-resolution crack propagation data is generated by simulation using a second simulation grid. The spatial discretization accuracy of the first simulation grid is higher than that of the second simulation grid. The training module is used to train a preset time series prediction model based on the low-resolution crack propagation data to obtain a pre-trained time series prediction model. The pre-trained time series prediction model is used to predict the low-resolution crack propagation data of the next time step based on the low-resolution crack propagation data of the previous time step and the physical constraints that match the current crack propagation data. The filtering module is used to analyze each candidate model in the preset super-resolution reconstruction model candidate pool based on the high-resolution crack propagation data, and filter out the target super-resolution reconstruction model. The target super-resolution reconstruction model is used to map the low-resolution crack propagation data of the next time step into reconstructed high-resolution crack propagation data. A cascade module is used to cascade the pre-trained temporal prediction model with the target super-resolution reconstruction model to obtain a cascaded model for crack propagation simulation. The prediction module is used to acquire the initial crack propagation data to be simulated and input the initial crack propagation data into the cascaded model to obtain the target crack propagation simulation results.

8. An electronic device, characterized in that, include: Memory, processor; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory, causing the processor to perform the method as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the method as described in any one of claims 1 to 6.

10. A computer program product, characterized in that, Includes a computer program that, when executed by a processor, implements the method as described in any one of claims 1 to 6.

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