Heterogeneous formation fracture pressure prediction and internal friction angle joint inversion method

Abstract

The invention discloses a fracture pressure prediction and internal friction angle joint inversion method for a heterogeneous stratum. The invention belongs to the technical field of petroleum engineering and artificial intelligence cross application, well depth is used as an independent variable, the minimum / maximum horizontal stress, pore pressure and cohesion are combined to construct well depth mixed input, only multi-scale periodic basis function transformation is carried out on the well depth, and a linear well depth channel is reserved; establishing a rupture pressure depth mapping model, introducing an augmented Lagrange physical constraint containing dual variables and a dynamic threshold, adaptively adjusting a physical weight according to a physical residual error and a threshold difference value, realizing dynamic balance of a rupture criterion and data fitting, and searching and optimizing a model topology by using a multi-target network structure; under a limited sample, a fracture pressure profile and a physically reasonable internal friction angle can be obtained at the same time, and the prediction precision and the physical consistency are improved.

Description

Technical Field

[0001] This invention belongs to the field of interdisciplinary application technology of petroleum engineering and artificial intelligence, and in particular relates to a method for predicting the fracture pressure and inverting the internal friction angle of heterogeneous strata. Background Technology

[0002] Formation fracture pressure (FFP) is a key safety boundary parameter in oil and gas well drilling engineering design and fracturing operations. Accurate prediction of fracture pressure is of great significance for determining a reasonable drilling fluid density window, ensuring wellbore stability, and optimizing hydraulic fracturing operation parameters. Currently, obtaining formation fracture pressure at engineering sites mainly relies on the following two methods: The first category is theoretical model calculation methods based on well logging data, such as the classic... Law, Law and Models; these methods are based on the effective stress principle and rock failure criteria (such as...) (Criteria); However, traditional theoretical models usually assume that the formation is a homogeneous and isotropic linear elastic body and are extremely dependent on the accurate selection of rock mechanical parameters (such as internal friction angle and Poisson's ratio). In reservoirs with strong heterogeneity and complex geological conditions, such as shale gas, the prediction accuracy of traditional models is often limited due to the failure to fully consider the nonlinear changes of parameters with depth and measurement errors, and it is difficult to apply a single formula to all well sections. The second category is purely data-driven machine learning methods. In recent years, algorithms such as BP neural networks, LSTM neural networks, and random forests have been widely used to establish nonlinear mappings between well logging parameters and fracture pressure. Although these methods have high fitting accuracy when there is sufficient data, they are essentially "black box" models, lacking physical mechanism constraints, resulting in poor interpretability of the models. More seriously, pure data models have weak generalization ability outside the coverage of training samples (such as extrapolation to deep formations), which can easily produce prediction results that violate physical common sense, posing a hidden danger to engineering safety. The emergence of Physical Information Neural Networks (PINNs) offers a new approach to solving the aforementioned problems. By embedding physical equations (partial differential equations or algebraic constraints) into a loss function, PINNs can simultaneously utilize monitoring data and physical laws. However, applying PINNs to formation fracture pressure prediction still faces three major technical bottlenecks: 1. Difficulty in multi-objective optimization: The loss function includes multiple components such as data residuals and physical residuals, with huge differences in magnitude between each component. Traditional methods rely on manual adjustment of weights, which is not only time-consuming and labor-intensive, but also easily leads to the network being biased towards a certain task and ignoring other constraints, resulting in unstable training. 2. Network architecture relies on experience: Existing PINN research mostly adopts a fixed fully connected network structure (such as a fixed number of layers and neurons). In fact, data with different geological features have drastically different requirements for network capacity and activation functions. Manual trial and error makes it difficult to find the optimal architecture, which limits the upper limit of prediction accuracy. Loss of high-frequency features: Formation logging data exhibits rich high-frequency fluctuations with depth, while conventional multilayer perceptrons (MLPs) suffer from "spectral bias," tending to learn low-frequency smooth functions and making it difficult to capture the details of local abrupt changes in fracture pressure with depth. In summary, there is a need for a new method for predicting fracture pressure that can adaptively balance physical constraint weights, automatically optimize network structure, and effectively capture high-frequency features of formations. This is the technical problem that this invention aims to solve. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of existing technologies in formation fracture pressure prediction models, such as poor physical consistency, difficulty in adjusting network hyperparameters, and difficulty in capturing high-frequency geological features. This invention provides a joint inversion method for fracture pressure prediction and internal friction angle in heterogeneous formations. This method integrates feature enhancement techniques, adaptive weight adjustment mechanisms, and automated architecture search strategies, achieving high-precision and highly physically interpretable fracture pressure prediction. To achieve the above objectives, this invention adopts the following technical solution: Step S10: Initialization of formation fracture pressure prediction process and setting of internal friction angle inversion parameters; select the target well section, based on well depth Using the minimum horizontal stress as the independent variable, obtain the minimum horizontal stress that varies along the well depth. Maximum horizontal stress pore pressure Cohesion and the corresponding measured burst pressure The above quantities are used as input physical quantities in subsequent methods; the internal friction angle of the rock is... These are considered as geomechanical parameters to be inverted and are not recorded as well logging inputs; only their physical feasible range is given. In the subsequent neural network training process, As learnable scalar parameters, they participate in backpropagation updates and are constrained by the Sigmoid activation function: ; in For the Sigmoid function, These are trainable parameters within the network, thus ensuring that the learned parameters are... It always stays within the preset effective range of rock physics and is output as the internal friction angle inversion result after training convergence; Step S20: Construction of well depth mixed features and establishment of fracture pressure depth mapping model; For the well depth D selected in step S10, multi-scale periodic basis function transformation is performed only on the independent variable of well depth to construct the well depth mixed feature vector: ; Where (D) is the original well depth component, ( ) is a preset or learnable frequency parameter, ( ) is the characteristic order, and the first component is always retained as the linear well depth (D); Will( ) and the minimum horizontal stress in step S10 ( ), maximum horizontal stress ( ), pore pressure and cohesion ( The features are concatenated to obtain hybrid input features for rupture pressure estimation: ; and with Construct a depth mapping model of fracture pressure for the independent variable: ; in, For parameterized vectors ( A multi-layer nonlinear mapping is used to approximate the formation fracture pressure field; in the mapping structure, the well depth mixing eigenvector is retained. The gradient propagation path between the linear well depth component D and the output layer in the calculation makes it possible to perform gradient propagation in subsequent calculations. When considering the second derivative with respect to well depth (D), this linear component is used as the dominant independent variable, thereby suppressing numerical divergence caused by high-frequency characteristics and ensuring the smoothness of the fracture pressure profile. Step S30: Adaptive and coordinated training of multi-source residuals under the constraint of the fracture criterion; Under the assumption of effective stress, construct a physical estimate of the fracture pressure including the internal friction angle parameter φ based on the formation fracture criterion: ; in Including the internal friction angle The differentiable function, at N selected well depth sampling points. At this point, the output of the rupture pressure depth mapping model in step S20 is denoted as... The observed rupture pressure is recorded as Define the following three evaluation functions: ; ; ; Used to measure data fitting error, relative to The degree of deviation of the physical model and the smoothness along the well depth direction; Based on this, an objective function for formation fracture pressure loss is constructed. ; in, For the weights of the physical constraint terms, To smooth the weights of regularization terms, These are the dual variables corresponding to the physical constraints. The physical residual dynamic threshold, This is the penalty coefficient; During network training, with To optimize the objective, the parameters of the rupture pressure-depth mapping model are adjusted. and internal friction angle parameters Perform gradient descent updates; at the end of each training round, record the mean physical residual of the current round as: ; The physics term weights and dynamic thresholds are adaptively updated according to the following rules: ; ; in, The moving average coefficients are between 0 and 1; simultaneously, the dual variables are updated according to the augmented Lagrange method. This causes the physical residual to remain above the threshold for an extended period. When the physical constraint strength is increased, the weight of the physical term is gradually reduced when the physical residual is stably below the threshold, thereby achieving an adaptive dynamic balance between data fitting accuracy and physical consistency throughout the training process. Step S40: Multi-objective search of network topology for heterogeneous formations; To adapt to the heterogeneity of formation parameters in the well depth direction, within the framework of the fracture pressure depth mapping model defined in steps S20 and S30, a structural search space is set, including the number of network layers, the number of neurons in each layer, the type of activation function, the residual or skip connection structure interval, and the order k of the well depth periodic basic feature; A sampling strategy based on tree-structured Bayesian optimization or tree-structured Pareto estimator is adopted to generate candidate network topologies in the search space. Each candidate structure is trained according to the adaptive physical constraints set in step S30, and the data error, physical residual index, and model complexity index are calculated on independent verification well sections. The three are used as joint evaluation targets, and the network topology at the Pareto front is selected as the preferred structure of the fracture pressure depth mapping model; Step S50: Formation fracture pressure profile generation and joint inversion with internal friction angle; using the network topology optimized in step S40 and its parameters after training convergence, point-by-point forward calculation is performed on the target well depth interval to obtain a predicted fracture pressure profile continuously distributed along the well depth. Simultaneously, the convergence value of the internal friction angle parameter defined in step S10 and updated during training is... The inversion result of the formation internal friction angle is output together with the fracture pressure profile for subsequent well completion design and geomechanical analysis.

[0004] Compared with the prior art, the present invention has the following beneficial effects: 1. Balancing high-frequency feature capture and computational stability, this invention effectively alleviates the 'spectral bias' problem of ordinary depth networks by introducing multi-scale well depth periodic basis feature enhancement technology while retaining the original well depth channel, enabling it to accurately capture the drastic fluctuations in formation fracture pressure with depth; at the same time, the retained linear well depth channel provides a stable gradient path for solving higher-order derivatives in the physical regularization term, avoiding numerical oscillations. 2. Adaptive balancing of physical constraint weights was achieved. By introducing the augmented Lagrangian (AL) mechanism, the weight ratio of data residuals and physical residuals was dynamically adjusted. This not only eliminated the burden of repeated manual trial and error parameter tuning, but also effectively prevented the model from getting stuck in local optima due to weight imbalance, significantly improving training convergence speed and physical consistency. 3. Automated adaptation to the optimal network architecture: This invention abandons the traditional manual trial and error and uses a Bayesian optimization algorithm to automatically search for the most suitable network topology structure (including the number of layers, width, activation function and jump connection method) for the target geological characteristics. Experiments show that the optimized specific architecture has stronger generalization ability and can more accurately extrapolate and predict the fracture pressure of unknown well sections. 4. To enhance the interpretability and reliability of the model, this invention explicitly embeds... The model uses physical criteria and internal friction angle as a learnable variable. While predicting the fracturing pressure, it can also invert rock mechanics parameters (such as internal friction angle) that conform to geological laws, so that the prediction results have clear physical meaning and provide a reliable safety boundary for drilling and fracturing operations. Attached Figure Description

[0005] Figure 1 The overall flowchart of the method (S10–S50) is shown below. Figure 2 This is a diagram showing the predicted formation fracture pressure results from the model. Detailed Implementation

[0006] To make the objectives, technical solutions, and beneficial effects of this invention clearer, a specific embodiment of the method of this invention will be described in detail below with reference to actual data from the Ning 227 shale gas well. The parameters and network configurations given in this embodiment are only used to illustrate one implementation of this invention and do not constitute a limitation on the scope of protection of this invention. 1. Data Source and Preprocessing (corresponding to step S10); In this embodiment, field measured data from a shale gas well, Ning 227, is selected as sample data. The collected physical quantities include: well depth. Minimum horizontal stress Maximum horizontal stress pore pressure Cohesion and the measured fracture pressure at the corresponding depth. The above physical quantities are continuously measured or tested at intervals along the well depth, forming a one-dimensional spatial coordinate system. The multi-physics field defined above: ; The above physical quantities are arranged into a discrete sample set according to well depth from shallowest to deepest: where Number the sampling points. For the first Measured fracture pressure at a depth point; well depth As the spatial independent variable, the other four quantities are used as input physical parameters, and the rupture pressure is used as the monitoring target of the network. For the few missing points in the measured well logging curves, the mean of the nearest interval is used to fill them in; obviously unreasonable extreme outliers (such as numerical overflow, infinity, etc.) are removed or backfilled with local statistics to improve the sample quality. Normalization and sample splitting: Standardize the input and target variables separately, for example, by: ; in , These are the mean and standard deviation of the corresponding variable across all samples, and these statistics are saved for subsequent inverse normalization of the network output to engineering units. Then, the samples are divided into training, validation, and test sets according to well depth; for example, the proportion can be taken as... It is used for model training, structure search, and final generalization ability evaluation; 2. Well Depth Hybrid Input Characterization and Fracture Pressure Mapping Model Construction (corresponding to step S20); To enhance the network's ability to represent high-frequency fluctuations in the well depth direction, and to ensure the numerical stability of subsequent calculations of the second derivative in the well depth direction, this embodiment only considers the well depth... Perform multi-scale periodic basis function transformation to construct a well depth hybrid eigenvector: ; The first dimension is the well depth component that retains its original dimensions. ,the remaining Each component is a periodic basis function; frequency parameter Sampling was performed from a random distribution with zero mean and adjustable variance to characterize the high-frequency fluctuations caused by stratigraphic heterogeneity at different spatial scales; For each depth sampling point Construct the input vector: ; The final input of the model is formed by concatenating the well depth hybrid features with four physical quantities. In this embodiment, a multilayer feedforward network (MLP) is used as the fracture pressure mapping model. The network includes an input layer, several hidden layers, and an output layer. Through automated structure search, a preferred structure is obtained: the hidden layer has 3 layers, each with approximately 128 neurons, and the activation function selected is SiLU, which performed well during the search process. The output layer is a single neuron used to predict the normalized fracture pressure. ; Internal friction angle parameterization and inversion: internal friction angle of rocks The internal friction angle is a key parameter in the fracture criterion, but it is difficult to measure accurately under field conditions. Therefore, in this embodiment, the internal friction angle is regarded as a trainable scalar in the network and reparameterized as follows: ; in For trainable parameters, For the Sigmoid function, This refers to a physically feasible range given based on core tests and empirical values; this approach ensures compatibility throughout the entire training process. Always falling within a reasonable physical range, obtained after training convergence. This is the inversion result of the friction angle within the target well section; 3. Physical Constraint Construction and Adaptive Weight Update (corresponding to step S30): Physical Estimation of Fracturing Pressure and Physical Residue: Under the assumption of effective stress, based on the rock failure criterion with embedded internal friction angle parameters, this embodiment constructs a physically estimated fracturing pressure to characterize the fracturing behavior: ; in , For the internal friction angle Differentiable functions, It is a differentiable combination function of pore pressure and cohesion; since the above expression is... Differentiable, obtainable within the framework of automatic differentiation. This allows for the simultaneous updating of network parameters and internal friction angle parameters during backpropagation. Based on this, the physical residual evaluation quantity is defined as: ; Data residuals and smoothness evaluation: Data residuals are used to measure the error between model predictions and measured rupture pressures. ; To suppress the severe oscillations in the predicted curve along the well depth direction that do not conform to engineering experience, the second derivative along the well depth direction is introduced as a smoothness evaluation term: ; The second derivative is obtained by automatically differentiating the network with respect to the well depth channel; Joint Objective Function and Augmented Lagrangian Form: Combining the above three evaluation metrics, a joint objective function is constructed: ; in For the weights of the physical constraint terms, The coefficients for the smoothness evaluation term; to avoid repeated manual adjustments. This embodiment introduces the augmented Lagrange concept, treating the physical residual as a threshold constraint term, and constructs: ; in As dual variables, The penalty coefficient is... This is a dynamic threshold used to characterize the currently acceptable level of physical residuals; Adaptive physical weight update based on residual threshold feedback: at the first... At the end of the iteration, calculate the physical constraint evaluation quantity for the current iteration: ; and the threshold of the previous round Compare; update the physics term weights based on the difference between the two: ; Simultaneously update the threshold using the moving average rule: ; in This is the moving average coefficient, for example, taken as 0.8 to 0.95; if the physical residual is consistently higher than the threshold, The physical constraints will be gradually increased and strengthened; if the physical residuals have already decreased to a low level... This will gradually decrease, allowing the model to focus more on data fitting, thereby achieving a dynamic balance between data accuracy and physical consistency during training; dual variables Synchronous updates are performed using the augmented Lagrange method to promote constraint convergence; 4. Network Topology Search and Optimization (corresponding to step S40): To obtain a network structure with good predictive performance in the target well section, this embodiment adopts an automated search strategy based on Bayesian optimization to jointly search for network topology-related hyperparameters; the search space includes: Number of hidden layers: ranges from 2 to 6; Number of neurons per layer: within... Select; Activation function type: In Select from the set; skip connection structure: for example, skip_every=0 (no skip connection), 2 or 3; well depth periodicity characteristic order. For example, in Select from; With the comprehensive objectives of validating the mean squared error of the validation set, the mean physical residual, and the number of model parameters, sampling algorithms such as a tree-structured Pareto estimator were used to conduct multiple rounds of trials and evaluations on the aforementioned space, automatically selecting a network configuration that strikes a good balance between accuracy and complexity. Experimental results show that a network configuration with 3 hidden layers, approximately 128 neurons per layer, and a selected activation function is optimal. The jump interval is once every 3 layers, and the characteristic order of the well depth period is... The network structure performed better in the data from well Ning 227. 5. Training Results and Effect Verification (corresponding to step S50): Under the above-mentioned optimized network structure and adaptive weight mechanism, the data of well Ning 227 were trained and tested, and the following typical results were obtained: (1) Convergence and Physical Consistency Verification: During the training process, the total objective function value decreased monotonically with the number of iterations and gradually tended to stabilize. The mean square error of both the training set and the validation set showed a trend of first decreasing rapidly and then converging slowly. The physical residual decreased significantly with the training iterations, and the dual variable With threshold Gradual convergence indicates that a relatively reasonable dynamic balance has been reached between the data terms and the physical terms; (2) Internal friction angle inversion results: the internal friction angle learned by the network convergence to approximately The range is basically consistent with the friction angle range of the shale gas reservoir in this region obtained by indoor rock mechanics tests, indicating that the method of the present invention can deduce rock mechanics parameters with reasonable physical meaning while predicting the fracture pressure; (3) Prediction effect of fracture pressure profile: Appendix Figure 2 The comparison between model predictions and well logging curves shows that: in terms of overall trend, the predicted curves and measured curves are highly consistent; in well sections with strong formation heterogeneity and local abrupt changes in fracture pressure, the predicted curves can still track measured fluctuations well; and compared with conventional wells without physical constraints... Neural networks Model and the basis without structure search Compared to the previous model, the adaptive physical information neural network in this embodiment performs better on the test set. The indicators were significantly improved, verifying the predictive ability and physical reliability of the proposed method; In summary, the fracture pressure prediction and internal friction angle joint inversion method for heterogeneous reservoirs described in this invention can simultaneously consider data fitting accuracy and physical rationality under limited sample conditions, and is applicable to fracture pressure assessment and wellbore stability analysis of heterogeneous reservoirs such as shale gas.

Claims

1. A method for fracture pressure prediction and joint inversion of internal friction angle of a heterogeneous formation, characterized in that, The method comprises the following steps: Step S10: Formation fracture pressure prediction process initialization and internal friction angle inversion parameter setting; selecting a target well section, the data including at least well depth ( ), minimum horizontal stress ( ), maximum horizontal stress ( ), pore pressure ( ), and cohesion ( ), and initializing an internal friction angle ( ) as a learnable network parameter, and using a Sigmoid function to constrain it within a preset physical range; Step S20: Well depth mixed feature construction and fracture pressure depth mapping model establishment; for the well depth D selected in step S10, only the well depth as the independent variable is subjected to multi-scale periodic basis function transformation to construct a well depth mixed feature vector: ； wherein D is the original well depth component, is a preset or learnable frequency parameter, is a characteristic order, and the first component is always kept as a linear well depth D; The minimum horizontal stress ( ), maximum horizontal stress ( ), pore pressure and cohesion in step S10 are concatenated to obtain the hybrid input features for fracture pressure estimation: ； And with A fracture pressure-depth mapping model is constructed as a function of wherein, is a multi-layer nonlinear mapping with parameter vector ) for approximating the formation fracture pressure field, in which the linear well depth component D in the well depth mixed feature vector is reserved between the gradient transmission path of the output layer and the mapping structure, so that when the second-order derivative of the subsequent calculation about the well depth (D) is calculated, the linear component is the dominant independent variable, thereby suppressing numerical divergence caused by high-frequency features and ensuring the smoothness of the fracture pressure profile. Step S30: Multi-source residual adaptive coordination training under the constraint of the rupture criterion; under the effective stress assumption, based on the criterion and the model construction physical constraint model, the physical estimated rupture pressure is calculated, and a composite loss function containing data residual , physical residual and smoothing regularization term is defined, in order to solve the weight balance problem in multi-objective optimization, the augmented Lagrange (AL) mechanism is introduced to introduce the dual variable and the dynamic threshold , and the weight of the physical term is adaptively updated according to the convergence of the physical residual in the training process, so as to realize the dynamic balance of data fitting and physical constraint; Step S40: Network topology multi-objective search for heterogeneous formation; to adapt to the heterogeneous characteristics of formation parameters in the well depth direction, within the framework of the fracture pressure depth mapping model defined in steps S20 and S30, a structure search space containing the number of network layers, the number of neurons of each layer, the type of activation function, the interval of residual or skip connection structure, and the order k of well depth periodic basis features is set; a sampling strategy based on tree structure Bayesian optimization or tree structure Pareto estimator is used to generate candidate network topologies in the search space; for each candidate structure, adaptive physical constraint training is performed according to the setting in step S30, and the data error, physical residual error index and model complexity index are calculated on the independent verification well section; the three are taken as joint evaluation objectives, and the network topology on the Pareto frontier is selected as the preferred structure of the fracture pressure depth mapping model; Step S50: Formation Fracture Pressure Profile Generation and Internal Friction Angle Joint Inversion; using the network topology and its trained and converged parameters obtained in step S40, point-by-point forward calculation is performed on the depth interval of the target well section to obtain the predicted fracture pressure profile continuously distributed along the depth ; at the same time, the converged value of the internal friction angle parameter defined in step S10 and updated during the training process is output as the inversion result of the internal friction angle of the formation, together with the fracture pressure profile, for subsequent well completion design and geomechanics analysis.

2. The method of claim 1, wherein, In the step S20, the well depth mixed input representation includes a well depth component maintaining original dimension and several nonlinear components transformed from the well depth by periodic basis functions, wherein the periodic basis functions are a set of bounded periodic functions, denoted as , and the independent variable is the product of the well depth and a frequency parameter drawn from a random distribution with zero mean and adjustable variance. The well depth related components obtained in this way are spliced with the minimum horizontal stress, the maximum horizontal stress, the pore pressure and the cohesion to form the input of the fracture pressure mapping model, which is used to represent the overall trend and the local fluctuation characteristics of the formation with the change of the well depth.​ 3. The method of claim 1, wherein, In step S30, the physical estimated fracture pressure for describing the fracture behavior of the formation is written in the form of explicitly containing the internal friction angle parameter, which satisfies: ； wherein with being a derivable function with respect to the internal friction angle , being a derivable combined function with respect to the pore pressure and the cohesion, such that the partial derivative of can be obtained automatically in a computational graph; during the network training process, using the partial derivative and the gradient of the physical constraint term, the internal friction angle parameter and the parameters of the fracture pressure mapping model are updated together, so as to identify the internal friction angle of the target stratum without the need to provide additional internal friction angle observation values.

4. The method of claim 1, wherein, In step S30, the formation fracture criterion is constructed to include the fracture pressure physical estimation value of the internal friction angle parameter: ； wherein is a differentiable function containing an internal friction angle at N selected well depth sampling points , the output of the fracture pressure depth mapping model in step S20 is denoted as , the observed fracture pressure is denoted as , and the following three evaluation functions are defined: ； ； ； Used to measure data fitting error, relative to The degree of deviation of the physical model and the smoothness along the well depth direction; On this basis, the objective function for the loss of the fracture pressure of the formation is constructed: ； wherein, is a physical constraint term weight, is a smoothing regular term weight, is a dual variable corresponding to the physical constraint, is a physical residual dynamic threshold, is a penalty coefficient; During network training, with To optimize the objective, the parameters of the rupture pressure-depth mapping model are adjusted. and internal friction angle parameters Perform gradient descent updates; at the end of each training round, record the mean physical residual of the current round as: And the physical item weight and dynamic threshold are adaptively updated according to the following rules: ； ； wherein, is a sliding average coefficient between 0 and 1; simultaneously updating the dual variables according to the augmented Lagrangian method so that when the physical residual is long-term higher than the threshold , the physical constraint strength is automatically increased, and when the physical residual is stably lower than the threshold, the weight of the physical term is gradually weakened, so as to realize the adaptive dynamic balance between the data fitting accuracy and the physical consistency in the whole training process.

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