A salt cavern storage prediction method based on physical constraint adaptation

Abstract

This invention discloses a physical constraint-based adaptive salt cavern storage prediction method. It constructs a long-term numerical simulation surrogate model PA-xLSTM based on xLSTM, employing a partitioned physical constraint mechanism to distinguish salt caverns and surrounding rock areas using spatial masks and applying different physical constraints. A dynamic gating network for physical loss is designed to adaptively adjust the weights of each physical equation according to the system state. A multi-task priority scheduling strategy is adopted to automatically allocate loss weights to different output tasks. The data fitting loss and physical constraint loss are jointly optimized to train the final surrogate model. By deeply integrating the physical mechanism with deep learning, a more accurate modeling and prediction of carbon dioxide salt cavern storage response is achieved.

Description

Technical Field

[0001] This invention relates to the field of salt cavern carbon dioxide storage and transportation, and specifically to a salt cavern storage prediction method based on physical constraints. Background Technology

[0002] Carbon dioxide geological storage is one of the core technologies for reducing greenhouse gas emissions. Its core principle is to achieve long-term storage of carbon dioxide by injecting it into deep geological structures. During storage, it is necessary to monitor the migration status of carbon dioxide, reservoir pressure changes, and potential leakage risks in real time to ensure the safety and effectiveness of the storage. The technology of using salt caverns for storing carbon dioxide or clean energy such as hydrogen / natural gas is becoming increasingly popular. Conventional salt cavern construction employs traditional numerical simulation methods, such as the finite element method or the finite volume method. However, these methods are computationally expensive and cannot meet the computational efficiency requirements of parameter optimization, real-time monitoring, and risk assessment in engineering design.

[0003] In existing technologies, deep learning-based surrogate models offer a new approach to salt cavern construction computation. Purely data-driven surrogate models learn the mapping relationship between input parameters and output results by training neural networks. Although they can achieve fast predictions, their predictions often violate physical laws and perform poorly in regions outside the training data distribution, requiring a large amount of simulated data as a training basis.

[0004] Physical Information Neural Networks (PINNs) improve physical consistency to some extent by incorporating the governing equations as regularization terms into the loss function. However, in the specific scenario of salt cavern storage, this invention directly applies the existing PINN method, which has certain shortcomings: directly applying the governing equations describing two-phase flow in porous media to the entire computational domain ignores the physical characteristics of salt caverns as free space; the constraint weights of multiple coupled physical equations need to be manually adjusted, making it difficult to balance the influence of different equations; and treating multiple outputs such as pressure, saturation, and permeability equally fails to reflect the different importance of each parameter in engineering applications. Therefore, there is an urgent need to comprehensively overcome the above shortcomings and develop a dedicated proxy model construction method that is compatible with computational efficiency, physical consistency, and engineering practicality, providing a new solution for the storage and transportation of carbon dioxide in salt caverns. Summary of the Invention

[0005] Purpose of the invention: To address the problems mentioned in the background art, this invention discloses a physical constraint-based adaptive salt cavern sealing prediction method. By designing a partitioned physical constraint module, a physical loss dynamic gating module, and a multi-task priority scheduling module after the xLSTM network, physical constraints are constructed through spatial partitioning and positioning, physical process control, and multi-task objective balancing and collaboration. An improved PA-xLSTM model, which is an improvement over the xLSTM model, is constructed, and the improved model is used to predict the physical properties of the sealing points.

[0006] Technical solution:

[0007] This invention discloses a physical constraint-adaptive method for predicting salt cavern storage, the method comprising the following steps:

[0008] S1: Simulate time-series data from multiple carbon dioxide sequestration sites as a dataset to obtain time-series geological data of the sequestration sites;

[0009] S2: Construct a physically enhanced long-term numerical simulation surrogate model xLSTM, whose inputs include time, spatial coordinates, geological parameters and operational parameters, and outputs include pressure field, gas saturation field and water production.

[0010] S3: After the xLSTM network, design a partitioned physical constraint module, a physical loss dynamic gating module, and a multi-task priority scheduling module. Construct physical constraints through spatial partitioning and localization, physical process control, and multi-task objective balancing and collaboration to build an improved PA-xLSTM model.

[0011] S4: Combining the data fitting loss and physical constraint loss, the network parameters are optimized using the gradient descent algorithm to obtain the final surrogate model. The preprocessed time series data is then input into the PA-xLSTM model for training. The trained PA-xLSTM model is then used to predict the physical properties of the sealing points.

[0012] Furthermore, the physically enhanced long-term numerical simulation surrogate model xLSTM described in S2 includes:

[0013] In the input layer, the geological data of the original archive points are constructed into time-series data. A sliding window technique is used to segment the time-series data into segments of length [length missing]. The sequence fragments are used to construct the input tensor. ,in For batch size, For feature dimensions.

[0014] Furthermore, the operational structure of the partition physical constraint module described in S3 is as follows:

[0015] The partitioned physical constraint mechanism module is a regularizer that embeds domain prior knowledge. It receives the predicted state field output by xLSTM and applies differentiated constraints based on spatial location, including the porosity field. Using the input feature, a binary porosity mask is generated. Using the binary porosity mask As a discriminant tensor Identify high-porosity salt cavern cavity regions. Identify the surrounding porous media rock area, calculate the residuals of the two areas separately, and perform weighted aggregation of the residuals of the two areas using a mask.

[0016] Furthermore, in the porous media surrounding rock region, a simplified governing equation for gas-water two-phase flow is adopted, and the residuals of the partial differential equations for mass conservation and Darcy's law are calculated using automatic differentiation technology:

[0017]

[0018]

[0019] in It's the viscosity of water. and These are the mass densities of water and gas (CO2), respectively. Operators are relative to spatial coordinates gradient, This indicates the inner product, where fluid properties such as density and viscosity are constant. For gas saturation, For penetration rate, For pressure, and These are the water output rate and the air injection rate, respectively. It is the acceleration due to gravity;

[0020] The fluid inside the high-porosity salt cavern region is in a freely connected state, and the pressure distribution is relatively uniform. The partitioned physical constraint mechanism module switches to simplified physical model constraints, and the residual calculation is as follows:

[0021]

[0022] in For mixed density.

[0023] Furthermore, the residuals of the two regions are weighted and aggregated using a mask, specifically as follows:

[0024] In the surrounding rock zone, the network is guided to learn complex seepage patterns; in the cavity zone, the network is guided to maintain numerical stability. The weighted aggregation result is as follows:

[0025] .

[0026] Furthermore, the operational structure of the physical loss dynamic gating module described in S3 is as follows:

[0027] A lightweight fully connected neural network is introduced as a gating network. The residual terms of each equation calculated by the partitioned physical constraint mechanism module are input, and the mean pressure is extracted from the current prediction field. Average gas saturation and the norm of the overall pressure gradient Global statistical features; the gated network outputs a weight vector normalized by Softmax. , respectively, correspond to the importance coefficients of the aqueous phase equation and the gas phase equation, and satisfy . Dynamic weighting is performed:

[0028]

[0029] in and These represent the residual losses of the aqueous and gas phase equations, respectively.

[0030] Furthermore, the multi-task priority scheduling module described in S3 has the following operational structure:

[0031] Introducing a Bayesian uncertainty weighting strategy, the multi-task priority scheduling module receives the computational pressure from the xLSTM output layer. Gas saturation and water production rate The original data loss for each task Introduce a learnable parameter , representing the inherent noise level or prediction uncertainty of the task, the total data loss function is reconstructed as:

[0032]

[0033] Weighted data loss output by the multi-task priority scheduling module The output loss of the physical loss dynamic gating module Add them together to form the global total loss function. The total loss is calculated using the backpropagation algorithm, which calculates the gradient with respect to the weights of the xLSTM network, thus completing one full parameter update iteration.

[0034] Furthermore, the present invention discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, implements any step of a physically constrained adaptive salt cavern sealing prediction method.

[0035] Beneficial effects:

[0036] 1. This invention introduces the xLSTM network as the backbone architecture, leveraging its matrix-level long-term memory capability and linear computational complexity to perform long-term geological evolution simulations, further improving the computation speed by 3-4 orders of magnitude (from hours to seconds), meeting the needs of real-time monitoring and large-scale parameter optimization. By embedding physical partial differential equation constraints, the model is forced to follow the laws of mass conservation and two-phase flow, effectively eliminating the non-physical prediction phenomena common in purely data-driven models, and further improving the model's generalization ability in the out-of-target (OOD) region.

[0037] 2. This invention designs a partitioned physical constraint mechanism. By constructing a spatial mask based on porosity, the computational domain is adaptively divided into a cavity region and a surrounding rock region: a two-phase flow equation constraint is strictly applied in the surrounding rock region to accurately capture the pressure diffusion front; a simplified physical model is applied in the cavity region to ensure the spatial uniformity of pressure. This solves the gradient conflict and numerical oscillation problem at the interface of different physical media, and achieves a full characterization of the complex flow field of salt caverns.

[0038] 3. This invention designs a dual intelligent adjustment mechanism, introducing dynamic gating of physical losses and multi-task priority scheduling. The dynamic gating network of physical losses can dynamically adjust the weights of each physical equation in real time according to the evolution of the flow field (such as pressure-dominated or saturation-dominated stages), solving the convergence imbalance caused by gradient competition. On the other hand, the multi-task scheduling strategy based on Bayesian uncertainty can automatically identify and reduce the weight interference of high-noise tasks (such as water production), ensuring that the model prioritizes fitting key safety indicators such as pressure and saturation. This further provides assurance for the site selection assessment, capacity optimization, and long-term safety monitoring of carbon sequestration projects, improving their engineering practicality. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the PA-xLSTM model architecture of the present invention;

[0040] Figure 2 This is a schematic diagram of the partitioned physical constraint module of the present invention;

[0041] Figure 3 This is a schematic diagram of the physical loss dynamic gating module of the present invention;

[0042] Figure 4 This is a schematic diagram of the multi-task priority scheduling module of the present invention;

[0043] Figure 5 This is a schematic diagram comparing the PA-xLSTM model of this invention with existing technologies. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] like Figure 1 As shown, this invention discloses a method for predicting salt cavern storage based on physical constraints, the steps of which are as follows:

[0046] Step 1: This invention uses CMG simulation software to simulate time-series data of 27 carbon dioxide sequestration sites as a dataset. Time-series geological data of the sequestration sites are obtained. First, the data is standardized to prevent the effects of gradient vanishing and gradient explosion, and also to help the optimization algorithm converge faster. As shown in Table 1, each independent data sample contains the following five sets of key physical characteristics, which together describe the dynamic process of carbon sequestration in salt caverns.

[0047] Table 1

[0048]

[0049] Step 1 includes the following:

[0050] Time-series geological data of 27 sealed points were acquired and input into the data preprocessing module.

[0051] Max-min standardization is applied to all attribute data in historical geological data to eliminate the influence of different units of measurement.

[0052]

[0053] in, For the various attribute data in the standardized geological data, These are the various attribute data in historical geological data. This represents the minimum value of the data. This represents the maximum value of the data.

[0054] After all modules of the model have completed their calculations, the output prediction data is inversely normalized to output the prediction results:

[0055]

[0056] in, These are the normalized physical prediction values ​​for the sealing points. This represents the actual physical prediction value after inverse normalization.

[0057] Step 2: Construct a Physically Enhanced xLSTM (PA-xLSTM) long-term numerical simulation surrogate model. Its inputs include time, spatial coordinates, geological parameters, and operational parameters, while its outputs include pressure field, gas saturation field, and water production. Three modules are added after the xLSTM network: these three modules, through a logical chain of "spatial partitioning and localization - physical process control - multi-task objective balancing," jointly construct a physical consistency constraint system for the PA-xLSTM model from local to global perspectives. First, the partitioned physical constraint module utilizes a spatial mask based on porosity. The complex salt cavern field is divided into two subdomains: "cavity" and "surrounding rock." Different physical constraints resolve the physical description conflicts caused by the non-homogeneous medium. Subsequently, the physical loss dynamic gating module acts as the "process commander," dynamically adjusting the weights of the gas and water phase equations based on system state characteristics such as average pressure and saturation using a lightweight gating network. This effectively resolves gradient competition and convergence imbalance issues in multi-physics coupling. Finally, the multi-task priority scheduling module introduces a Bayesian uncertainty weighting strategy. By automatically identifying and reducing the loss weights of high-noise tasks such as water production, it ensures that the model prioritizes core safety indicators such as pressure and saturation during training.

[0058] These three modules achieve synergy through deep interweaving at the loss function level: the partitioning module provides the "spatial boundaries" of physical constraints, the gating module assigns "temporally dynamic" weights to these constraints, and the scheduling module establishes the final balance between "data-driven metrics" and "adaptive physical constraints." The total global loss generated by all three is achieved through this process. By guiding the gradient flow in the direction that is most physically logically correct and has the highest engineering value, the surrogate model is ensured to maintain rigorous physical fidelity even under extremely rapid prediction.

[0059] Step 2 includes the following specific steps:

[0060] The input layer constructs time-series data from the original archived geological data. A sliding window technique is used to divide the decades-long time-series data into segments of length [missing information]. The sequence fragments are used to construct the input tensor. ,in For batch size, For feature dimensions.

[0061] This invention proposes a PA-xLSTM model consisting of three main modules. The xLSTM network aims to capture the temporal relationships in time-series data, reducing redundant information by gating key time-step features. A partitioning physical constraint module, a physical loss dynamic gating module, and a multi-task priority scheduling module are added after the xLSTM output.

[0062] xLSTM is one of the core components of the PA-xLSTM model. The extended long short-term memory network improves the forgetting aspect of LSTM for important information through exponential gating and modified memory structure. Two variants of the xLSTM architecture have been proposed, namely scalar LSTM with exponential gating and memory hybridization (sLSTM) and matrix LSTM with enhanced storage capacity (mLSTM).

[0063] Among them, the sLSTM block, as an advanced variant of the traditional LSTM architecture, significantly improves the model's effectiveness in storage decisions through innovative designs such as exponential gating, memory mixing, and stabilization mechanisms. The Matrix Long Short-Term Memory (mLSTM) model introduces a matrix memory unit along the covariance update mechanism for key-value pair storage, significantly increasing the model's memory capacity. In mLSTM, the gating mechanism works in conjunction with the covariance update rule to effectively manage memory updates. By removing hidden-to-hidden connections within the mLSTM model, the model's operations can be executed in parallel, thereby accelerating the training and inference processes. Finally, the xLSTM module is mapped to the predicted values ​​of the three physical fields through fully connected layers.

[0064] To enhance the predictive power of the model, the key lies in integrating domain knowledge into the model. The partitioned physical constraint mechanism module is a core component for achieving physically reliable predictions. This module acts as a regularizer embedded with prior domain knowledge, aiming to solve the problem that a single physical equation cannot simultaneously adapt to a binary medium of "cavity (free flow) - surrounding rock (seepage)". Figure 2 As shown, the module receives the predicted state field (pressure and saturation) output by the xLSTM and applies differentiated constraints based on spatial location. Porosity field ( This is a key control signal in the data stream. It serves not only as an input feature but is also used to generate binary geometric masks. The mask is defined as:

[0065]

[0066] Geometric Masking and Spatial Partitioning: Utilizing Binary Porosity Masks Generated in the Preprocessing Stage As a discriminant tensor. Among them, Identify high-porosity salt cavern cavity regions. The surrounding porous media rock area is marked. (Rock area) The simplified governing equations for gas-water two-phase flow are used, and the residuals of the partial differential equations for mass conservation and Darcy's law are calculated using automatic differentiation techniques.

[0067]

[0068]

[0069] in It's the viscosity of water. and These are the mass densities of water and gas (CO2), respectively. In these equations, Operators are relative to spatial coordinates gradient, The inner product is represented by the equation. These equations assume that the formation is isotropic and that fluid properties such as density and viscosity are constant. For gas saturation, For penetration rate, For pressure, and These are the water output rate and the air injection rate, respectively. This is the acceleration due to gravity.

[0070] Cavity region ( Given that the fluid inside the cavity is in a freely connected state, the pressure distribution is relatively uniform. In this region, the module switches to simplified physical model constraints:

[0071]

[0072] in For mixed density.

[0073] Residual Aggregation: The module ultimately performs weighted aggregation of the two residuals using a mask. This partitioned computation ensures the correct physical direction of gradient backpropagation: guiding the network to learn complex seepage patterns in the surrounding rock zone and maintaining numerical stability in the cavity zone. The weighted aggregation result is as follows:

[0074]

[0075] Then and Weighting is performed using a dynamic gating module for physical losses.

[0076] The Physical Loss Dynamic Gating Module is an intelligent regulator designed to address the common "gradient conflict" and "convergence imbalance" problems in training physical information neural networks. During salt cavern storage, the coupling between the gas phase equation and the aqueous phase equation is nonlinear, and their dominance varies at different time points. This module introduces a dynamic gating mechanism to adaptively adjust the equation weights. The input source is the physical residual values, derived from the residual terms of each equation calculated by the previous module. The specific operational structure is as follows:

[0077] like Figure 3 As shown, the global statistical features extracted from the current prediction field first include the average pressure. Average gas saturation and the norm of the overall pressure gradient These characteristics intuitively reflect the current fluid flow pattern; for example, a high-pressure gradient may indicate a strong seepage process, and high saturation may indicate a gas-driven process.

[0078] This module embeds a lightweight, fully connected neural network, acting as a "meta-controller." The gating network receives the system's state feature vector as input, sensing the current physical evolution stage. The network outputs a weight vector normalized by Softmax. , respectively, correspond to the importance coefficients of the aqueous phase equation and the gas phase equation, and satisfy . Then, dynamic weighting is performed:

[0079]

[0080] in and These represent the residual losses of the aqueous and gas phase equations, respectively.

[0081] Physical loss value after dynamic weighting This is combined with data-driven loss. Through this mechanism, the module replaces tedious manual hyperparameter tuning, significantly improving convergence stability and physical accuracy under multiphysics coupling.

[0082] Multi-task priority dynamic scheduling module: This module aims to solve the problem of mismatch between the importance and learning difficulty of different prediction objectives in engineering applications. For example... Figure 4 As shown, this module introduces a Bayesian uncertainty weighting strategy to automatically balance the multi-task learning process. The input source is the xLSTM output layer received by the module, which targets three tasks: stress, pressure, and weight. Gas saturation and water production rate The calculated loss on the raw data (e.g., mean squared error, MSE). The model is for each task. Introduce a learnable parameter , representing the inherent noise level or prediction uncertainty of the task. The total data loss function is reconstructed as:

[0083]

[0084] The role of the denominator ( For tasks with high noise and difficulty in fitting (such as water production), the model tends to increase its... value. Increasing the weight of the task's MSE decreases, thus reducing its contribution to the total gradient. This effectively achieves "automatic deweighting" or "soft ignoring" of noisy tasks, protecting the backbone network features from noise interference. (Logarithmic terms...) ) is a regularization penalty term.

[0085] Ultimately, the weighted data loss output by this module is... Compared with the aforementioned adaptive physical loss Add them together to form the global total loss function. The total loss is calculated using the backpropagation algorithm, which uses the gradient relative to the xLSTM network weights to complete one full parameter update iteration. This mechanism ensures that the final generated surrogate model is an intelligent system that "understands priorities" in engineering and "knows the laws of conservation" in physics.

[0086]

[0087] Output layer: The PA-xLSTM is trained. The final model output is obtained.

[0088] Step 3: Joint Training and Optimization. Combining data fitting loss and physical constraint loss, the network parameters are optimized using gradient descent to obtain the final surrogate model. Preprocessed time-series data is input into the PA-xLSTM model for training. During training, the model's performance is optimized by continuously adjusting parameters and using cross-validation. After training, the trained model is used to predict the physical properties of the sealed points.

[0089] Step 3 includes the following specific steps:

[0090] To ensure the practical application value of the experiment, this embodiment divides all samples into training set, validation set and test set in a 7:1:1 ratio and strictly follows the time sequence.

[0091] Set the key hyperparameters of the PA-xLSTM model. When predicting geological attributes, the input dimension depends on the sliding window size, as the input dimension is consistent with the number of nodes within the window; the output dimension can be set to 1 or longer, corresponding to predicting geological data at a single time point or several time points; here, to reduce the number of model parameters and prevent overfitting, the number of xLSTM layers is set to 2.

[0092] The optimizer for model training is set to the Adam optimizer, with a batch size of 64. The initial training parameters are as follows: two xLSTM layers (mLSTM block for the first layer and sLSTM block for the second, connected sequentially); hidden layer size is set to 64 for all layers; and the output headers are parallel fully connected layers that output the pressure field, gas saturation field, and water production, respectively. Learnable parameters... Set the parameter to 1.0, the number of training iterations to 500, and the learning rate to 0.0001. Further adjustments can be made based on the validation set prediction results to determine the parameters that best fit the prediction performance. Finally, use these parameters to predict the test set data.

[0093] In this implementation example, the mean absolute error and root mean square error are used to analyze the prediction error of the model, proving the accuracy of the model proposed in this invention.

[0094] Mean absolute error (MAE) is a metric used to measure the average prediction error of a forecasting model. It calculates the average absolute error between predicted and observed values ​​and is typically used to assess the accuracy and stability of a model.

[0095]

[0096] The root mean square error (RMSE) is the square root of the average of the squared differences between the predicted and actual values. It primarily measures the deviation between the two and is highly sensitive to outliers in the results.

[0097]

[0098] in, and These represent the true and predicted values ​​of the model on the test set, respectively. This indicates the size of the test set.

[0099] The invention will be further illustrated below with specific examples:

[0100] First, historical geological attribute data and multiple geological influencing factor variables were acquired to establish a time series dataset. Then, the original time series dataset underwent data preprocessing, and an extended Long Short-Term Memory (LSTM) network was used to capture short-term dependencies in the time series data. Simultaneously, the dynamic graph data was divided into training, validation, and test sets in an 8:1:1 ratio. The first part served as the training set for debugging model parameters; the middle part was used to check if the model training effect was deteriorating and participated in the training process for parameter selection and tuning; the last part was used to evaluate the model's effectiveness.

[0101] The prediction results show that this method performs well in assessing the importance of factors influencing geological attributes, with a good model fit and high prediction accuracy. The evaluation results of various indicators in the test set are shown in Table 1, further validating the accuracy and effectiveness of this method in reflecting the importance of factors influencing geological attributes.

[0102] Table 1

[0103] Models MSE-out1 MSE-out2 MSE-out3 RMSE MAE MLP 4.3033 0.0095 2.3714 0.0107 0.0052 LSTM 3.0471 0.0159 3.7333 0.0101 0.0050 PA-xLSTM 2.0521 0.0053 2.9233 0.0083 0.0039

[0104] As shown in Table 1 and Figure 5 As shown, the PA-xLSTM model has the smallest error and the highest fitting accuracy for each index, indicating that the method of using physical residuals as the loss function in this invention is feasible. At the same time, the local time series feature extraction and global dependency modeling of the time series data make this invention more advantageous and accurate in the geological response of carbon dioxide storage sites.

[0105] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent transformations or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting salt cavern storage based on physical constraints, characterized in that, The method includes the following steps: S1: Simulate time-series data from multiple carbon dioxide sequestration sites as a dataset to obtain time-series geological data of the sequestration sites; S2: Construct a physically enhanced long-term numerical simulation surrogate model xLSTM, whose inputs include time, spatial coordinates, geological parameters and operational parameters, and outputs include pressure field, gas saturation field and water production. S3: After the xLSTM network, design a partitioned physical constraint module, a physical loss dynamic gating module, and a multi-task priority scheduling module. Construct physical constraints through spatial partitioning and localization, physical process control, and multi-task objective balancing and collaboration to build an improved PA-xLSTM model. S4: Combining the data fitting loss and physical constraint loss, the network parameters are optimized using the gradient descent algorithm to obtain the final surrogate model. The preprocessed time series data is then input into the PA-xLSTM model for training. The trained PA-xLSTM model is then used to predict the physical properties of the sealing points.

2. The physical constraint-based adaptive salt cavern sealing prediction method according to claim 1, characterized in that, The physically enhanced long-term numerical simulation surrogate model xLSTM described in S2 includes: In the input layer, the geological data of the original archive points are constructed into time-series data. A sliding window technique is used to segment the time-series data into segments of length [length missing]. The sequence fragments are used to construct the input tensor. ,in For batch size, For feature dimensions.

3. The physical constraint-based adaptive salt cavern sealing prediction method according to claim 1, characterized in that, The operational structure of the partition physical constraint module described in S3 is as follows: The partitioned physical constraint mechanism module is a regularizer that embeds domain prior knowledge. It receives the predicted state field output by xLSTM and applies differentiated constraints based on spatial location, including the porosity field. Using the input feature, a binary porosity mask is generated. Using the binary porosity mask As a discriminant tensor Identify high-porosity salt cavern cavity regions. Identify the surrounding porous media rock area, calculate the residuals of the two areas separately, and perform weighted aggregation of the residuals of the two areas using a mask.

4. The physical constraint-based adaptive salt cavern sealing prediction method according to claim 3, characterized in that, The porous media surrounding rock region employs simplified governing equations for gas-water two-phase flow, and utilizes automatic differentiation techniques to calculate the residuals of the partial differential equations governing mass conservation and Darcy's law: ； ； in It's the viscosity of water. and These are the mass densities of water and gas (CO2), respectively. Operators are relative to spatial coordinates gradient, This indicates the inner product, where fluid properties such as density and viscosity are constant. For gas saturation, For penetration rate, For pressure, and These are the water output rate and the air injection rate, respectively. It is the acceleration due to gravity; The fluid inside the high-porosity salt cavern region is in a freely connected state, and the pressure distribution is relatively uniform. The partitioned physical constraint mechanism module switches to simplified physical model constraints, and the residual calculation is as follows: ； in For mixed density.

5. The physical constraint-based adaptive salt cavern sealing prediction method according to claim 4, characterized in that, The residuals of the two regions are weighted and aggregated using a mask, specifically as follows: In the surrounding rock zone, the network is guided to learn complex seepage patterns; in the cavity zone, the network is guided to maintain numerical stability. The weighted aggregation result is as follows: 。 6. The method for predicting salt cavern storage based on physical constraints according to claim 1, characterized in that, The operational structure of the physical loss dynamic gating module described in S3 is as follows: A lightweight fully connected neural network is introduced as a gating network. The residual terms of each equation calculated by the partitioned physical constraint mechanism module are input, and the mean pressure is extracted from the current prediction field. Average gas saturation and the norm of the overall pressure gradient Global statistical features; the gated network outputs a weight vector normalized by Softmax. , respectively, correspond to the importance coefficients of the aqueous phase equation and the gas phase equation, and satisfy . Dynamic weighting is performed: ； in and These represent the residual losses of the aqueous and gas phase equations, respectively.

7. The physical constraint-based adaptive salt cavern sealing prediction method according to claim 1, characterized in that, The multi-task priority scheduling module described in S3 operates as follows: Introducing a Bayesian uncertainty weighting strategy, the multi-task priority scheduling module receives the computational pressure from the xLSTM output layer. Gas saturation and water production rate The original data loss for each task Introduce a learnable parameter , representing the inherent noise level or prediction uncertainty of the task, the total data loss function is reconstructed as: ； Weighted data loss output by the multi-task priority scheduling module The output loss of the physical loss dynamic gating module Add them together to form the global total loss function. The total loss is calculated using the backpropagation algorithm, which calculates the gradient with respect to the weights of the xLSTM network, thus completing one full parameter update iteration.

8. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements any step of the physical constraint-based adaptive salt cavern sealing prediction method as described in claims 1-7.

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