Underground medium multi-scale forward and inverse method and system based on decoupled neural network

Abstract

The application discloses a decoupling neural network-based multi-scale forward and inverse method for underground medium, and belongs to the technical field of underground multi-physical field coupling. The decoupling neural network-based multi-scale forward and inverse method for underground medium comprises the following steps: generating a time-space evolution data set of multi-physical field variables; constructing a physical information neural network architecture for decoupling of physical fields, including three special sub-networks, each of which inputs based on a time-space coordinate and dynamically receives the output of other sub-networks as auxiliary input features, and realizes strong coupling modeling between physical fields through feature sharing and a joint loss function; executing a two-stage training strategy; and based on the trained neural network architecture, performing forward intelligent prediction or key physical property parameter inversion. The application constructs a unified neural network framework composed of multiple special sub-networks, realizes physical consistency and efficient data cross-scale modeling from a core scale to a site scale, and simultaneously supports forward simulation and parameter inversion.

Description

Technical Field

[0001] This invention belongs to the field of underground multiphysics coupling technology, specifically relating to a multi-scale forward and inverse modeling method and system for underground media based on decoupled neural networks. Background Technology

[0002] The statements herein provide only background information in relation to this invention and do not necessarily constitute prior art.

[0003] In deep energy engineering projects such as oil and gas extraction, high-level radioactive waste disposal, and carbon dioxide geological storage, the interaction of thermal, fluid, and solid multiphysics fields has a significant impact on system evolution. Accurately characterizing these processes requires not only reasonable mathematical models but also physical property parameters that can reflect the actual properties of the medium and their interrelationships.

[0004] Currently, numerical simulations are typically conducted at the site scale, employing the continuum assumption to describe multi-field coupling behavior. The constitutive relations and physical property parameters required for these models are often derived from core-scale experimental testing or empirical fitting. However, core samples only represent local medium characteristics, while actual sites exhibit significant spatial heterogeneity and structural diversity. Directly applying relations obtained at the core scale to the site scale easily overlooks the potential impact of microstructural differences on macroscopic responses, limiting the model's predictive ability under complex conditions. On the other hand, high-fidelity experiments or numerical simulations at the core scale can provide intuitive information on microscopic processes, revealing multi-field coupling mechanisms. However, there is a lack of effective connection between these microscopic data and engineering models.

[0005] In recent years, Physical Information Neural Networks (PINNs) have shown potential in multiphysics problems due to their ability to incorporate governing equations as constraints into data-driven modeling. However, existing applications often employ a unified network structure to handle all physical field variables, failing to fully consider the differences in evolutionary characteristics among different fields. More importantly, it is crucial to find a unified framework that organically combines core-scale microphysical information with site-scale monitoring data, and to achieve a reasonable transition from local mechanisms to regional predictions through neural networks. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a multi-scale forward and inverse modeling method and system for underground media based on decoupled neural networks. By constructing a unified neural network framework composed of multiple dedicated subnetworks, it achieves physical consistency and data-efficient cross-scale modeling from core scale to site scale, and simultaneously supports forward simulation and parameter inversion.

[0007] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0008] In a first aspect, the technical solution of the present invention provides a multi-scale forward and inverse modeling method for underground media based on decoupled neural networks, including:

[0009] Based on core-scale gas-water-rock interaction experiments and corresponding high-fidelity numerical simulations, a spatiotemporal evolution dataset of multi-physics variables is generated, and preprocessing and data augmentation are performed.

[0010] A physical information neural network architecture for decoupling physical fields is constructed, including a temperature field subnetwork, a seepage field subnetwork, and a stress field subnetwork. Each subnetwork takes spatiotemporal coordinates as its input and dynamically receives the outputs of other subnetworks as auxiliary input features. Strong coupling modeling between physical fields is achieved through feature sharing and joint loss function.

[0011] A two-stage training strategy is implemented for the physical information neural network architecture of physical field decoupling. In the first stage, the physical information neural network of physical field decoupling is pre-trained using core-scale datasets to internalize microscopic physical laws. In the second stage, the pre-trained physical information network of physical field decoupling is used as the initial model and fine-tuned by incorporating site-scale field monitoring data to realize the transfer from microscopic physical priors to macroscopic predictions.

[0012] Based on a trained physical information neural network architecture that decouples the physical field, it performs forward intelligent prediction or inversion of key physical property parameters.

[0013] In at least one embodiment, the temperature field subnetwork, the seepage field subnetwork, and the stress field subnetwork all adopt a deep multilayer perceptron architecture and use the Swish function as the activation function; the complete input vector of each subnetwork includes the basic spatiotemporal variables and the outputs of other subnetworks at the same spatiotemporal location.

[0014] In at least one embodiment, the joint loss function is specifically a weighted sum of temperature field loss, seepage field loss, stress field loss, and cross-coupling constraint loss.

[0015] In at least one embodiment, the temperature field loss is based on the energy conservation equation of the coupling effect of solid thermal conduction and fluid convection; the seepage field loss is based on the mass conservation equation of the influence of porous medium compressibility and skeleton deformation; the stress field loss is based on the quasi-static mechanical equilibrium equation that integrates the effective stress principle and thermoelastic effect; and the cross coupling constraint loss explicitly penalizes the inconsistency of physical variables between subnetworks.

[0016] In at least one embodiment, the cross-coupling constraint loss forces each constitutive relation to hold strictly at all sampling points; wherein the constitutive relations include Darcy's law, porosity-strain relation, and equation of state;

[0017] The cross-coupling constraint loss is specifically expressed as:

[0018]

[0019] In the formula, This represents the cross-coupling constraint loss; Represents the velocity vector; Indicates penetration rate; Indicates porosity; This represents the permeability function, which varies with porosity. And change; Indicates fluid viscosity; This represents the temperature output by the temperature field subnetwork; This represents the fluid viscosity function, which varies with the temperature output by the temperature field subnetwork. And change; Indicates the initial temperature; Indicates pore pressure; Indicates the pore pressure gradient; Indicates the initial pore pressure; Indicates initial porosity; Indicates the effective stress coefficient; This represents the displacement vector fed back from the stress field subnetwork. The displacement vector output by the stress field subnet The divergence; Indicates fluid density; Indicates the initial fluid density; Indicates the physical property coefficient; Indicates the initial fluid viscosity; Indicates the temperature dependence coefficient; express The square of the norm.

[0020] In at least one embodiment, the first stage is the microscopic pre-training stage, which uses a high-fidelity core-scale dataset as the only supervision signal and adopts an end-to-end approach to jointly optimize the temperature field subnetwork, seepage field subnetwork, and stress field subnetwork, with the goal of minimizing the joint loss function, thereby internalizing the complex physical relationships determined by the microscopic pore structure.

[0021] The second stage is the macro-integration and fine-tuning stage. The sub-networks that have been pre-trained in the micro-pre-training stage are used as the initial models with physical priors. The site-scale modeling task is connected, and the field monitoring data corresponding to the site-scale thermal-fluid-structure coupling numerical model is introduced to fine-tune the entire network end-to-end.

[0022] In at least one embodiment, the total loss function in the macro-fusion fine-tuning stage is a weighted combination of the joint loss and the observation loss, expressed as:

[0023]

[0024] In the formula, This represents the total loss during the macro-integration and fine-tuning phase; Indicates joint loss; This represents the actual observation value collected at the monitoring point location; The predicted output of the network at the same spatiotemporal location; The observation loss weight.

[0025] In at least one embodiment, forward intelligent prediction specifically includes: through a single forward propagation, based on the input target spatiotemporal location, boundary conditions, and initial field state, the temperature field subnetwork, seepage field subnetwork, and stress field subnetwork interact through a feature-sharing closed loop to jointly output predicted values ​​of temperature, pore pressure, and displacement.

[0026] In at least one embodiment, the key physical property parameter inversion specifically includes: modeling at least one physical property parameter among permeability, Biot coefficient, and thermal conductivity as a learnable field variable associated with spatial location, and forming a joint optimization vector together with all weights of the temperature field subnetwork, seepage field subnetwork, and stress field subnetwork; achieving parameter inversion by minimizing the difference between the predicted value and the field observation value, and synchronously updating the network parameters and physical property parameter distribution under the constraints of the multiphysics field control equation.

[0027] Secondly, the technical solution of the present invention also provides a multi-scale forward and inverse modeling system for underground media based on decoupled neural networks, including:

[0028] The data acquisition module is configured to generate a spatiotemporal evolution dataset of multi-physics variables based on core-scale gas-water-rock interaction experiments and corresponding high-fidelity numerical simulations, and to perform preprocessing and data augmentation.

[0029] The coupling modeling module is configured to: construct a physical information neural network architecture for decoupling physical fields, including a temperature field sub-network, a seepage field sub-network, and a stress field sub-network. Each sub-network takes spatiotemporal coordinates as its input and dynamically receives the outputs of other sub-networks as auxiliary input features. Strong coupling modeling between physical fields is achieved through feature sharing and joint loss function.

[0030] The training module is configured to execute a two-stage training strategy on the physical information neural network architecture decoupled from the physical field. In the first stage, the physical information neural network decoupled from the physical field is pre-trained using a core-scale dataset to internalize microscopic physical laws. In the second stage, the pre-trained physical information network decoupled from the physical field is used as the initial model and fine-tuned by incorporating site-scale field monitoring data to achieve the transfer from microscopic physical priors to macroscopic predictions.

[0031] The execution module is configured to perform forward intelligent prediction or key physical property parameter inversion based on a trained physical information neural network architecture that decouples the physical field.

[0032] The beneficial effects of the above-described technical solution of the present invention are as follows:

[0033] 1) The multi-scale forward and inverse modeling method for underground media based on decoupled neural networks in this invention achieves refined modeling of the evolution mechanisms of different physical fields by designing dedicated sub-neural networks for temperature field, seepage field, and stress field. Each sub-network focuses on learning the spatiotemporal variation law of its corresponding physical quantity, thereby improving the overall accuracy of multi-physics coupling simulation. It solves the problems of microscopic mechanisms being difficult to effectively integrate into macroscopic prediction and key physical parameters being difficult to accurately invert during the coupling of underground thermal-fluid-solid multi-physics fields, and avoids the dilution of characterization ability caused by the traditional single network structure due to taking into account multiple objectives.

[0034] 2) In the training process, this invention embeds the control equations and their coupling relationships of the thermal-fluid-solid fields as hard or soft constraints into the loss function, and realizes the dynamic transmission of physical information through the feature interaction mechanism between sub-networks. This mechanism ensures that the model strictly follows the basic physical principles throughout the solution domain, fundamentally guaranteeing the physical consistency and reliability of the prediction results.

[0035] 3) This invention proposes a two-stage training process: "core-scale microscopic pre-training – site-scale macroscopic fusion and fine-tuning," constructing a cross-scale modeling bridge from micro to macro. In the microscopic pre-training stage, the network learns the complex constitutive relationships determined by the microstructure using high-fidelity core experimental or simulated data. In the macroscopic fusion and fine-tuning stage, this pre-trained network serves as an initial model with physical priors, undergoing adaptive adjustments based on limited field monitoring data. This process allows microscopic mechanisms to be implicitly but transferably integrated into macroscopic predictions, without relying on empirical upscaling formulas.

[0036] 4) This invention has advantages in forward intelligent prediction and key physical property parameter inversion. In terms of forward intelligent prediction, it significantly improves computational efficiency. Once training is complete, the entire model can quickly output predicted values ​​of temperature, pressure, and displacement at any spatiotemporal location through a single forward inference, without the need for iterative solutions to large partial differential equation systems as in traditional numerical methods. In terms of parameter inversion, by setting key physical property parameters such as permeability and fluid viscosity as learnable variables in the neural network and optimizing them under the dual constraints of physical equations and microscopic priors, the spatial distribution of parameters obtained by inversion can not only fit the field observation data with high accuracy, but its changing trend is also highly consistent with the physical mechanism of the underground medium.

[0037] 5) This invention has a low dependence on field monitoring data. Thanks to the introduction of physical information constraints and core-scale prior knowledge, even under actual engineering conditions where monitoring points are sparse and data coverage is incomplete, the model can still make reasonable extrapolations based on physical laws and maintain good generalization ability and prediction stability. Attached Figure Description

[0038] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0039] Figure 1 This is a schematic diagram of the multi-scale forward and inverse modeling method for underground media based on decoupled neural networks disclosed in Embodiment 1 of the present invention;

[0040] Figure 2 This is a flowchart of the multi-scale forward and inverse modeling method for underground media based on decoupled neural networks disclosed in Embodiment 1 of the present invention;

[0041] Figure 3 This is a schematic diagram of parameter transfer in each sub-network of the physical information neural network architecture for physical field decoupling disclosed in Embodiment 1 of the present invention;

[0042] Figure 4 This is a schematic diagram of the two-stage training strategy disclosed in Embodiment 1 of the present invention. Detailed Implementation

[0043] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0044] As described in the background section, the purpose of this invention is to overcome the shortcomings of the prior art and provide a multi-scale forward and inverse modeling method and system for underground media based on decoupled neural networks. By constructing a unified neural network framework composed of multiple dedicated subnetworks, it achieves physical consistency and data-efficient cross-scale modeling from core scale to site scale, and simultaneously supports forward simulation and parameter inversion.

[0045] Example 1

[0046] In a typical embodiment of the present invention, such as Figures 1 to 4 As shown in the figure, this embodiment discloses a multi-scale forward and inverse modeling method for subsurface media based on a decoupled neural network, which specifically includes the following steps:

[0047] S1. Based on core-scale gas-water-rock interaction experiments and corresponding high-fidelity numerical simulations, a spatiotemporal evolution dataset of multi-physics variables is generated, and preprocessing and data augmentation are performed.

[0048] S2. Construct a physical information neural network architecture for decoupling physical fields, including a temperature field sub-network, a seepage field sub-network, and a stress field sub-network. Each sub-network takes spatiotemporal coordinates as its input and dynamically receives the outputs of other sub-networks as auxiliary input features. Strong coupling modeling between physical fields is achieved through feature sharing and joint loss function.

[0049] S3. A two-stage training strategy is implemented for the physical information neural network architecture decoupled from the physical field. In the first stage, the physical information neural network decoupled from the physical field is pre-trained using a core-scale dataset to internalize microscopic physical laws. In the second stage, the pre-trained network is used as the initial model and fine-tuned by incorporating site-scale field monitoring data to achieve the transfer from microscopic physical priors to macroscopic predictions.

[0050] S4. Based on the trained physical information neural network architecture with decoupled physical fields, perform forward intelligent prediction or key physical property parameter inversion.

[0051] The following detailed description of the above-mentioned multi-scale forward and inverse modeling method for underground media based on decoupled neural networks, with reference to specific implementation methods, is provided below.

[0052] S1. Based on core-scale gas-water-rock interaction experiments and corresponding high-fidelity numerical simulations, a spatiotemporal evolution dataset of multi-physics variables is generated, and preprocessing and data augmentation are performed.

[0053] In this step, based on core-scale gas-water-rock interaction experimental data and combined with high-fidelity core-scale numerical simulation results, a spatiotemporal evolution training dataset covering multiple physical field variables such as temperature, pressure (or hydraulic head), and displacement is generated. This dataset focuses on the more typical physical conditions of underground media in actual development scenarios: namely, under constant confining pressure constraints, multiphase flow, heat transfer, and micro-deformation response driven by fluid injection and temperature gradient. It can accurately reflect the influence of microscopic pore structure on the thermo-fluid-solid multiphysics coupling process, serving as the microscopic physical prior for subsequent neural network learning.

[0054] In this embodiment, the experimental platform employs a high-temperature, high-pressure core displacement system, including a constant-temperature oven, a confining pressure control unit, a horizontal flow pump, a back pressure regulating valve, a core holder, and a multi-channel sensor array. The core samples used in the experiment are representative cylindrical samples drilled from the target site, with a diameter of 50 mm and a length of 100 mm. Both ends are precision-machined and fitted with porous ceramic end caps to ensure uniform fluid distribution.

[0055] Specifically, after the core is loaded into the core holder, inert silicone oil is injected into the outer cavity of the core holder using a confining pressure pump to apply a hydrostatic confining pressure of 2-10 MPa to simulate the pressure of the overlying formation and maintain the structural integrity of the core. Under these conditions, deionized water or a CO2-water mixture is injected at a constant flow rate of 0.1-2.0 mL / min using a horizontal flow pump. Simultaneously, the core is heated to 60-120°C at the inlet and maintained at 25-40°C at the outlet, forming a stable axial thermal gradient. The outlet back pressure valve is set within the range of 5-15 MPa to ensure that the pore pressure is always higher than the saturated vapor pressure of the fluid, preventing phase transition interference. The entire displacement process lasts for 24 hours with a time resolution of 5 minutes, during which multiphysics response data is acquired simultaneously. During the acquisition of multiphysics response data, a distributed fiber optic temperature measurement system arranged along the core axis records the temperature profile in real time, inlet and outlet pressure sensors acquire the pressure difference evolution, a mass flow meter monitors the volume of the produced fluid, and a high-resolution laser displacement meter captures minute changes in the overall axial length of the core.

[0056] Since no active differential stress was applied in the experiment, the micro-strain observed in the core mainly originated from the thermal expansion effect and the adjustment of Biot effective stress caused by pore pressure fluctuations. Although these mechanisms are weak, they have clear physical significance and can serve as important constraint signals for stress field modeling.

[0057] To compensate for the limitation of the experiment's internal field variables not being directly observable, a corresponding numerical simulation was conducted simultaneously. First, the three-dimensional pore structure of the rock core was reconstructed using X-ray micro-CT scanning (5 μm resolution). Then, the coupled governing equations were solved on a simulation platform (such as COMSOL Multiphysics), and the simulated boundary and initial conditions replicated the experimental settings. Through parameter calibration, the simulated output inlet and outlet pressures, average temperature, and total axial deformation were made to closely approximate the experimental measurements. The relative error under the norm is controlled within 5%, thereby ensuring the physical reliability of the simulation results and obtaining high-fidelity core-scale numerical simulation results.

[0058] The calibrated model was used to "fill in" internal spatial points that the experiment could not cover, generating complete three-dimensional spatiotemporal field data, including arbitrary Temperature at location pore pressure and axial displacement Among them, any In position, For spatial location dimension, The time dimension.

[0059] Furthermore, this step enhances the generalization ability of the dataset through multi-condition data enhancement. By systematically changing the injected fluid type, temperature gradient amplitude, injection flow rate, and confining pressure level, several sets (e.g., 5-8 sets) of virtual experimental data under different physical scenarios are generated. Each set undergoes the aforementioned experiment-simulation co-calibration process, ultimately forming a comprehensive dataset containing approximately 800,000 spatiotemporal samples, with each sample being a seven-dimensional vector. , where displacement The axial component is mainly taken, while the radial component is derived through volumetric strain.

[0060] All data were spatiotemporally aligned in a unified coordinate system, and the spatial coordinates were normalized to [value missing]. Interval, time normalized to the proportion of total experiment duration, output variable , , Z-score standardization is used, and the standardized parameters are saved for use in the subsequent inversion stage. The standardization formula is specifically expressed as follows:

[0061]

[0062] In the formula, Represents the original variables in the dataset; Represents the standardized variables; This represents the mean of the dataset; This represents the standard deviation of the dataset.

[0063] The dataset is divided into training, validation and test sets in an 8:1:1 ratio to ensure a balanced distribution across all operating conditions.

[0064] S2. Construct a physical information neural network architecture for decoupling physical fields, including a temperature field subnetwork, a seepage field subnetwork, and a stress field subnetwork. Each subnetwork takes spatiotemporal coordinates as its input and dynamically receives the outputs of other subnetworks as auxiliary input features. Strong coupling modeling between physical fields is achieved through feature sharing and joint loss function.

[0065] The Decoupled Physical Information Neural Network (DPINN) constructed in this step is a unified modeling paradigm designed for the multi-physics coupling problem of underground media involving heat, fluid, and solid. Its core lies in the use of three specialized sub-neural networks—a temperature field sub-network—that are functionally specialized, structurally independent, but deeply collaborative in their training process. seepage field subnetwork With stress field subnetwork —Regarding temperature pore pressure and displacement vector Modeling is performed.

[0066] Based on the constructed physical information neural network architecture decoupled from the physical field, this step establishes an omnidirectional, dynamic, differentiable bidirectional feature interaction mechanism, such as... Figure 3 As shown, this allows any two physical fields to exchange state information in real time during forward inference and backward propagation.

[0067] Specifically, all three dedicated sub-networks adopt a deep multilayer perceptron (MLP) architecture, containing five fully connected hidden layers, each with 256 neurons, and uniformly using the Swish function as the activation function.

[0068]

[0069] This function combines the sparse activation properties of ReLU with the smoothness of Sigmoid, which is beneficial for maintaining gradient stability in complex nonlinear mappings.

[0070] All dedicated subnetworks share the same input preprocessing module, which processes the raw spatiotemporal coordinates. After normalization, it is mapped to Hypercube space is used to eliminate the interference of dimensional differences on the optimization process.

[0071] In this step, the input of each dedicated subnetwork not only includes basic spatiotemporal variables, but also dynamically embeds the current output of other subnetworks at the same spatiotemporal location as auxiliary features, forming a closed-loop, fully connected feature sharing graph.

[0072] Specifically, temperature field subnetwork The complete input vector is represented as:

[0073]

[0074] In the formula, For seepage field subnetwork In the The pressure value output during the second forward propagation; For stress field subnet The output displacement vector.

[0075] seepage field subnetwork The input vector is represented as:

[0076]

[0077] In the formula, a temperature field subnetwork is explicitly introduced. Output temperature To modify fluid properties and introduce stress field subnetworks. Output displacement vector To update the pore structure.

[0078] Stress field subnet The input vector is represented as:

[0079]

[0080] In the formula, For seepage field subnetwork In the The pressure value output during the second forward propagation; For temperature field subnetwork Output temperature. It simultaneously receives pressure and temperature signals to calculate the effective stress and thermal stress contribution.

[0081] This design enables the temperature field subnetwork seepage field subnetwork With stress field subnetwork The three constitute an implicitly coupled system that iterates synchronously: in a single forward propagation, the three dedicated subnetworks first calculate their respective physical fields based on the output (or initial guess) of the previous round, and then use the new output as the feature of the other's input in the next round. This process is repeated until convergence. The entire process can be embedded into the end-to-end training process through an automatic differentiation framework.

[0082] To ensure that this bidirectional interaction mechanism holds strictly at the physical level, this step explicitly encodes the governing equations of each physical field and their coupling relationships as differentiable constraint terms in the loss function. Total Loss Function It consists of four parts:

[0083]

[0084] In the formula, This indicates the loss of temperature field. Indicates the loss in the seepage field; Indicates stress field loss; This represents the cross-coupling constraint loss; Represents the weighting coefficients of each loss, where, The range of values ​​is , The range of values ​​is The performance of the validation set is dynamically adjusted to balance the magnitudes of various gradients.

[0085] Specifically, temperature field loss Based on the energy conservation equation, considering the coupling effect of solid heat conduction and fluid convection, It can be represented as:

[0086]

[0087] In the formula, Indicates divergence; Represents the gradient; This represents thermal conductivity, which is considered a constant or given a priori by lithology; Represents a spatial domain; Represents the time domain. Indicates the final state time; Represents the square of the norm; Represents the velocity vector; Indicates fluid density, Specific heat capacity can be expressed as:

[0088]

[0089]

[0090] In the formula, Indicates the initial fluid density; Indicates the initial pore pressure; Indicates the initial specific heat capacity; Indicates the initial temperature; , This is the physical property coefficient.

[0091] Flow velocity vector They are not independent variables, but are implicitly defined by Darcy's law, specifically expressed as:

[0092]

[0093] In the formula, Indicates penetration rate. This represents a permeability function that depends on porosity. With porosity And change, and And from the stress field subnetwork The output displacement is determined; Indicates the pore pressure gradient; Indicates fluid viscosity. Represents the fluid viscosity function, which varies with temperature field subnetwork Output temperature The changes are specifically represented as follows:

[0094]

[0095] In the formula, Indicates the initial fluid viscosity; This represents the temperature dependence coefficient.

[0096] Therefore, temperature field loss The calculation depends on the seepage field subnetwork Output pore pressure With stress field subnetwork Output displacement vector This forms a reverse physical dependency chain from the seepage field, stress field to the temperature field.

[0097] Seepage field loss Based on the mass conservation equation, the effects of porous media compressibility and skeleton deformation are considered. It can be represented as:

[0098]

[0099] In the formula, porosity It is no longer considered a constant, but a dynamic variable given by Biot's consolidation theory, expressed as:

[0100]

[0101] In the formula, Initial porosity; The effective stress (Biot-Willis) coefficient is usually... ; The displacement vector output by the stress field subnet The divergence of the displacement field. This expression explicitly defines the displacement field. Introducing the seepage control equation reduces the seepage field loss. The calculation must call the stress field subnet. The output of the stress field establishes a positive feedback path for the seepage field.

[0102] Stress field loss Based on the quasi-static mechanical equilibrium equations, and integrating the effective stress principle and thermoelastic effects, It can be represented as:

[0103]

[0104] In the formula, This represents the total stress tensor; it can be decomposed into elastic stress and pore pressure contributions, expressed as:

[0105]

[0106] In the formula, It is a fourth-order elastic tensor, which can be simplified to a function of Young's modulus and Poisson's ratio for isotropic media; Mechanical strain is defined as:

[0107]

[0108] In the formula, Thermal strain is defined as:

[0109]

[0110] In the formula, The coefficient of thermal expansion; Represents a unit tensor.

[0111] This shows that the stress field is simultaneously affected by pore pressure. With temperature Modulation must be achieved from the percolation field subnetwork. With temperature field subnetwork Input is acquired to form a dual-source driving mechanism.

[0112] To further enhance multi-field consistency, this step introduces a cross-coupling constraint loss term. Explicitly penalize the inconsistency of physical variables among subnetworks, specifically as follows:

[0113]

[0114] This forced Darcy's law, porosity-strain relationship, equation of state and other constitutive relations hold strictly at all sampling points, and can maintain physical consistency even in areas without observation data.

[0115] During training, the loss function described above is used to calculate gradients through automatic differentiation, and the Adam optimizer is used to synchronously update all parameters of the three dedicated sub-networks. Since the output of each dedicated sub-network serves as the input to other networks, its gradient propagation path naturally includes a flow of higher-order gradients across networks: for example, ( for Parameters) not only through In Transmission, also through China of Direct transmission forms multi-path gradient feedback, significantly improving the efficiency of coupled learning.

[0116] Furthermore, to avoid the coupling terms diverging due to excessive prediction bias in the early stages of training, a course learning strategy is adopted: in the initial stage, the prediction bias is reduced. Weights are applied preferentially to fit single-field equations; these weights are gradually increased as training progresses. This guides the model toward convergence towards strong coupling decoupling.

[0117] S3. A two-stage training strategy is implemented for the physical information neural network architecture decoupled from the physical field. In the first stage, the physical information neural network decoupled from the physical field is pre-trained using a core-scale dataset to internalize microscopic physical laws. In the second stage, the pre-trained network is used as the initial model and fine-tuned by incorporating site-scale field monitoring data to achieve the transfer from microscopic physical priors to macroscopic predictions.

[0118] To bridge the gap between core and site scales, this embodiment employs a two-stage training strategy for the physical information neural network architecture that decouples the physical fields. This aims to achieve intelligent transfer and cross-scale fusion of microscopic pore-scale physical mechanisms to macroscopic site-scale modeling tasks. The specific training process is as follows: Figure 4 As shown. The core idea of ​​the two-stage training strategy is: first, to fully pre-train the decoupled physical information neural network on a high-fidelity, high-resolution core-scale experimental-simulation joint dataset, so that it deeply internalizes the thermal-fluid-solid coupling law determined by the real pore structure; then, to use this network with microscopic physical priors as the initial model, and to transfer it to a more engineering-significant site-scale monitoring scenario for fine-tuning, so as to maintain physical consistency and prediction robustness under limited field data conditions.

[0119] Specifically, in the first stage, namely the microscopic pre-training stage, the physical information neural network decoupled from the physical field uses a high-fidelity spatiotemporal evolution training dataset as the sole supervision signal. This dataset is generated collaboratively from the aforementioned gas-water-rock displacement experiments and high-fidelity numerical simulations, containing approximately 800,000 spatiotemporal samples, each corresponding to a spatial location. With time The temperature below pore pressure and displacement Value. The input feature is the local coordinates of the core after spatiotemporal alignment and normalization (original spatial range). , ) and time The output is a joint prediction of the three variables.

[0120] The training process employs an end-to-end approach to jointly optimize three dedicated subnetworks, internalizing the complex physical relationships determined by the microporous structure. The goal is to minimize the total physical loss function (i.e., the joint loss function) embedded with the thermal-fluid-solid control equations and their cross-coupling constraints. The optimizer used was Adam, with an initial learning rate of 0.001. Cosine annealing was employed, and training continued for 1000 epochs until the loss converged. The core objective at this stage was not simply to fit the data, but to internalize the network's understanding of the mechanisms by which microscopic pore structures regulate multi-physics coupling behavior—for example, how local throat geometry determines permeability resistance, how mineral-fluid reactions influence thermal conductivity evolution, and how the Biot effect transforms pore pressure changes into micro-strain. After sufficient training, the network exhibited excellent generalization ability at the core scale, and its parameter space established a set of strong physical priors.

[0121] The second stage—macro-level fusion and fine-tuning—then proceeds, where the pre-trained network is directly deployed to the actual engineering site-scale modeling task. At this point, the input coordinate system is expanded to cover the entire site (where...). , , The time span has also been extended to several months or even several years.

[0122] The monitoring signals come from 500 sparsely distributed field monitoring points, including continuous temperature profiles provided by a distributed fiber optic temperature measurement system (DTS), pore pressure time series recorded by pressure sensors, and deformation fields obtained from InSAR remote sensing inversion. These data exhibit typical large-scale characteristics: wide spatial coverage but sparse sampling, temporal continuity but with instrument drift and environmental noise, and typically only containing partial physical fields. To effectively fuse these heterogeneous and incomplete observations, the total loss function is extended to a weighted combination of physical constraints and data fitting, i.e., physical loss (joint loss). With observation loss The weighted combination is specifically expressed as:

[0123]

[0124] In the formula, This represents the actual observation value collected at the monitoring point location; The predicted output of the network at the same spatiotemporal location; The observation loss weight ranges from 0.05 to 0.2. Its specific value is dynamically adjusted according to the signal-to-noise ratio of the observation data. Higher weights are assigned to high-precision DTS data, while the weights are appropriately reduced for InSAR displacements that are greatly affected by atmospheric interference.

[0125] Within this framework It is no longer just a regularization term, but serves as an implicit physical prior that continuously guides the entire optimization process: when the network attempts to fit sparse observation points, the physical loss term automatically constrains the evolution of field variables in the unobserved region to satisfy the basic laws of thermal-fluid-structure interaction, thereby effectively suppressing overfitting and non-physical solutions.

[0126] The fine-tuning process also uses end-to-end training, but the learning rate is reduced to 0.0001 to avoid destroying the learned microscopic physical laws. The training rounds are set to 500 rounds, and an early stopping mechanism is introduced to prevent overfitting.

[0127] Throughout the fine-tuning process, the mechanisms learned at the microscale, such as the porosity-permeability-thermal conductivity correlation, viscosity-temperature effect, and Biot consolidation response, are mapped onto the macroscopic geological body through continuous updates of network parameters.

[0128] S4. Based on the trained physical information neural network architecture with decoupled physical fields, perform forward intelligent prediction or key physical property parameter inversion.

[0129] After completing the two-stage training, the physical field decoupled physical information neural network constructed in this embodiment has evolved into a unified, efficient, and physically self-consistent multi-scale modeling paradigm. It can simultaneously support two core functions: high-precision forward intelligent prediction and automatic inversion of key physical property parameters. The two share the same network architecture and physical constraint mechanism, forming an integrated closed-loop intelligent system.

[0130] In the forward intelligent prediction mode, only the target spatiotemporal location, boundary conditions and initial field state need to be provided to obtain the complete thermal-fluid-structure interaction response at that point through a single forward propagation.

[0131] Specifically, the input features are first normalized and then fed into three dedicated sub-networks. The temperature field sub-network is one such sub-network. Receive the basic spatiotemporal coordinates and dynamically connect them to the seepage field subnetwork. Pore ​​pressure output at the same location As an auxiliary feature, it is used for real-time calculation of pressure-dependent fluid density and specific heat capacity; seepage field subnetwork Synchronous receiving temperature field subnetwork Output temperature To correct temperature-sensitive fluid viscosity And combined with stress field subnet Feedback displacement Update local porosity Stress field subnetwork Then the overall pore pressure With temperature Calculate effective stress and thermal stress, and output three-dimensional displacement vector. The three dedicated subnetworks achieve synchronous bidirectional interaction through the aforementioned closed-loop feature sharing channel, and ultimately jointly output the predicted values ​​of temperature, pore pressure, and displacement.

[0132] The entire positive intelligent prediction process does not require nonlinear iterative solutions or large matrix assembly in traditional numerical simulations. The computation time is reduced from hours to seconds, enabling real-time, high-resolution reconstruction of the site-scale THM coupled field and providing immediate support for engineering decisions.

[0133] In the parameter inversion mode, the penetration rate Biot coefficient Thermal conductivity Key physical property parameters are directly incorporated into the set of optimization variables of the pre-trained physical field decoupling physical information neural network, and the joint physical constraints output a parameter distribution that conforms to the law. These physical property parameters are modeled as learnable field variables associated with spatial location, and their spatial distribution is implicitly determined through joint optimization with the backbone network weights.

[0134] Specifically, in the site-scale coordinate system used in the macro-fusion and fine-tuning stage, the entire modeling region is divided into several control volumes. Each control volume is assigned a set of independent physical property parameter values, forming a globally trainable tensor. This tensor, together with all the weights of the temperature field sub-network, seepage field sub-network, and stress field sub-network, forms a joint optimization vector. .

[0135] The inversion process aims to minimize the difference between predicted and observed values, while being strictly controlled by the multiphysics governing equations embedded in the network loss function. The total loss function adopts the same form as the macroscopic fusion fine-tuning stage.

[0136] The inversion aims to minimize the discrepancy between in-situ observations and network predictions while maintaining strict adherence to the multiphysics governing equations. Since the physical property parameters are explicitly present in the physical residuals, their gradients can be derived from the physical loss through an automatic differentiation mechanism. and observation loss The backpropagation is performed naturally. During the optimization process, the physical property parameters and network weights are updated synchronously, so that the inversion results not only fit the measured data of the monitoring points, but also satisfy the inherent physical consistency of the thermal-fluid-structure interaction system.

[0137] Through the above process, the multi-scale forward and inverse modeling method for underground media based on decoupled neural networks disclosed in this embodiment ultimately forms a unified multi-scale modeling tool with dual functions: on the one hand, it can perform forward intelligent prediction, that is, given any spatiotemporal location, boundary conditions and initial state, it can quickly output the predicted values ​​of temperature, pressure and displacement at that location, thereby achieving high-precision reconstruction of the thermal-fluid-solid coupled field of the site; on the other hand, it can perform inverse modeling of key physical parameters, that is, setting physical parameters such as permeability, Young's modulus, and thermal conductivity, which are difficult to measure directly, as learnable variables in the neural network, minimizing the difference between model prediction and limited field observation, and automatically inverting the most likely spatial distribution of these parameters under the strict constraints of physical equations.

[0138] Example 2

[0139] In a typical embodiment of the present invention, this embodiment discloses a multi-scale forward and inverse modeling system for subsurface media based on a decoupled neural network, comprising:

[0140] The data acquisition module is configured to generate a spatiotemporal evolution dataset of multi-physics variables based on core-scale gas-water-rock interaction experiments and corresponding high-fidelity numerical simulations, and to perform preprocessing and data augmentation.

[0141] The coupling modeling module is configured to: construct a physical information neural network architecture for decoupling physical fields, including a temperature field sub-network, a seepage field sub-network, and a stress field sub-network. Each sub-network takes spatiotemporal coordinates as its input and dynamically receives the outputs of other sub-networks as auxiliary input features. Strong coupling modeling between physical fields is achieved through feature sharing and joint loss function.

[0142] The training module is configured to execute a two-stage training strategy on the physical information neural network architecture decoupled from the physical field. In the first stage, the physical information neural network decoupled from the physical field is pre-trained using a core-scale dataset to internalize microscopic physical laws. In the second stage, the pre-trained physical information network decoupled from the physical field is used as the initial model and fine-tuned by incorporating site-scale field monitoring data to achieve the transfer from microscopic physical priors to macroscopic predictions.

[0143] The execution module is configured to perform forward intelligent prediction or key physical property parameter inversion based on a trained physical information neural network architecture that decouples the physical field.

[0144] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-scale forward and inverse modeling method for subsurface media based on decoupled neural networks, characterized in that, include: Based on core-scale gas-water-rock interaction experiments and corresponding high-fidelity numerical simulations, a spatiotemporal evolution dataset of multi-physics variables is generated, and preprocessing and data augmentation are performed. A physical information neural network architecture for decoupling physical fields is constructed, including a temperature field subnetwork, a seepage field subnetwork, and a stress field subnetwork. Each subnetwork takes spatiotemporal coordinates as its input and dynamically receives the outputs of other subnetworks as auxiliary input features. Strong coupling modeling between physical fields is achieved through feature sharing and joint loss function. A two-stage training strategy is implemented for the physical information neural network architecture of physical field decoupling. In the first stage, the physical information neural network of physical field decoupling is pre-trained using core-scale datasets to internalize microscopic physical laws. In the second stage, the pre-trained physical information network of physical field decoupling is used as the initial model and fine-tuned by incorporating site-scale field monitoring data to realize the transfer from microscopic physical priors to macroscopic predictions. Based on a trained physical information neural network architecture that decouples the physical field, it performs forward intelligent prediction or inversion of key physical property parameters. The joint loss function is specifically a weighted sum of temperature field loss, seepage field loss, stress field loss, and cross-coupling constraint loss; The cross-coupling constraint loss forces all constitutive relations to hold strictly at all sampling points; these constitutive relations include Darcy's law, porosity-strain relationship, and equation of state. The cross-coupling constraint loss is specifically expressed as: In the formula, This represents the cross-coupling constraint loss; Represents the velocity vector; Indicates penetration rate; Indicates porosity; This represents the permeability function, which varies with porosity. And change; Indicates fluid viscosity; This represents the temperature output by the temperature field subnetwork; This represents the fluid viscosity function, which varies with the temperature output by the temperature field subnetwork. And change; Indicates the initial temperature; Indicates pore pressure; Indicates the pore pressure gradient; Indicates the initial pore pressure; Indicates initial porosity; Indicates the effective stress coefficient; This represents the displacement vector fed back from the stress field subnetwork. The displacement vector output by the stress field subnet The divergence; Indicates fluid density; Indicates the initial fluid density; Indicates the physical property coefficient; Indicates the initial fluid viscosity; Indicates the temperature dependence coefficient; express The square of the norm; The first stage is the microscopic pre-training stage, which uses a high-fidelity core-scale dataset as the only supervision signal. It adopts an end-to-end approach to jointly optimize the temperature field subnetwork, seepage field subnetwork, and stress field subnetwork, with the goal of minimizing the joint loss function, and internalizes the complex physical relationships determined by the microscopic pore structure. The second stage is the macro-integration and fine-tuning stage. The sub-networks that have been pre-trained in the micro-pre-training stage are used as the initial models with physical priors. The site-scale modeling task is connected, and the field monitoring data corresponding to the site-scale thermal-fluid-structure coupling numerical model is introduced to fine-tune the entire network end-to-end. The total loss function in the macro-fusion fine-tuning stage is a weighted combination of the joint loss and the observation loss, expressed as: In the formula, This represents the total loss during the macro-integration and fine-tuning phase; Indicates joint loss; This represents the actual observation value collected at the monitoring point location; The predicted output of the network at the same spatiotemporal location; The observation loss weight.

2. The multi-scale forward and inverse modeling method for subsurface media based on decoupled neural networks as described in claim 1, characterized in that, The temperature field subnetwork, seepage field subnetwork, and stress field subnetwork all adopt a deep multilayer perceptron architecture and use the Swish function as the activation function; the complete input vector of each subnetwork contains the basic spatiotemporal variables and the outputs of other subnetworks at the same spatiotemporal location.

3. The multi-scale forward and inverse modeling method for underground media based on decoupled neural networks as described in claim 1, characterized in that, Temperature field loss is based on the energy conservation equation of the coupling effect of solid thermal conduction and fluid convection; seepage field loss is based on the mass conservation equation of the influence of porous medium compressibility and skeleton deformation; stress field loss is based on the quasi-static mechanical equilibrium equation that integrates the effective stress principle and thermoelastic effect. Cross-coupling constraint loss explicitly penalizes inconsistencies in physical variables among subnetworks.

4. The multi-scale forward and inverse modeling method for subsurface media based on decoupled neural networks as described in claim 1, characterized in that, Forward intelligent prediction specifically includes: through a single forward propagation, based on the input target spatiotemporal location, boundary conditions, and initial field state, the temperature field subnetwork, seepage field subnetwork, and stress field subnetwork interact through a feature-sharing closed loop to jointly output predicted values ​​of temperature, pore pressure, and displacement.

5. The multi-scale forward and inverse modeling method for underground media based on decoupled neural networks as described in claim 1, characterized in that, The key physical property parameter inversion specifically includes: modeling at least one of the physical property parameters, such as permeability, Biot coefficient, and thermal conductivity, as a learnable field variable associated with spatial location, and forming a joint optimization vector together with all weights of the temperature field subnetwork, seepage field subnetwork, and stress field subnetwork; achieving parameter inversion by minimizing the difference between the predicted value and the field observation value, and synchronously updating the network parameters and physical property parameter distribution under the constraints of the multiphysics field control equation.

6. A multi-scale forward and inverse modeling system for underground media based on decoupled neural networks, characterized in that, include: The data acquisition module is configured to generate a spatiotemporal evolution dataset of multi-physics variables based on core-scale gas-water-rock interaction experiments and corresponding high-fidelity numerical simulations, and to perform preprocessing and data augmentation. The coupling modeling module is configured to: construct a physical information neural network architecture for decoupling physical fields, including a temperature field sub-network, a seepage field sub-network, and a stress field sub-network. Each sub-network takes spatiotemporal coordinates as its input and dynamically receives the outputs of other sub-networks as auxiliary input features. Strong coupling modeling between physical fields is achieved through feature sharing and joint loss function. The training module is configured to execute a two-stage training strategy on the physical information neural network architecture decoupled from the physical field. In the first stage, the physical information neural network decoupled from the physical field is pre-trained using a core-scale dataset to internalize microscopic physical laws. In the second stage, the pre-trained physical information network decoupled from the physical field is used as the initial model and fine-tuned by incorporating site-scale field monitoring data to achieve the transfer from microscopic physical priors to macroscopic predictions. The execution module is configured to perform forward intelligent prediction or key physical property parameter inversion based on a trained physical information neural network architecture that decouples the physical field. The joint loss function is specifically a weighted sum of temperature field loss, seepage field loss, stress field loss, and cross-coupling constraint loss; The cross-coupling constraint loss forces all constitutive relations to hold strictly at all sampling points; these constitutive relations include Darcy's law, porosity-strain relationship, and equation of state. The cross-coupling constraint loss is specifically expressed as: In the formula, This represents the cross-coupling constraint loss; Represents the velocity vector; Indicates penetration rate; Indicates porosity; This represents the permeability function, which varies with porosity. And change; Indicates fluid viscosity; This represents the temperature output by the temperature field subnetwork; This represents the fluid viscosity function, which varies with the temperature output by the temperature field subnetwork. And change; Indicates the initial temperature; Indicates pore pressure; Indicates the pore pressure gradient; Indicates the initial pore pressure; Indicates initial porosity; Indicates the effective stress coefficient; This represents the displacement vector fed back from the stress field subnetwork. The displacement vector output by the stress field subnet The divergence; Indicates fluid density; Indicates the initial fluid density; Indicates the physical property coefficient; Indicates the initial fluid viscosity; Indicates the temperature dependence coefficient; express The square of the norm; The first stage is the microscopic pre-training stage, which uses a high-fidelity core-scale dataset as the only supervision signal. It adopts an end-to-end approach to jointly optimize the temperature field subnetwork, seepage field subnetwork, and stress field subnetwork, with the goal of minimizing the joint loss function, and internalizes the complex physical relationships determined by the microscopic pore structure. The second stage is the macro-integration and fine-tuning stage. The sub-networks that have been pre-trained in the micro-pre-training stage are used as the initial models with physical priors. The site-scale modeling task is connected, and the field monitoring data corresponding to the site-scale thermal-fluid-structure coupling numerical model is introduced to fine-tune the entire network end-to-end. The total loss function in the macro-fusion fine-tuning stage is a weighted combination of the joint loss and the observation loss, expressed as: In the formula, This represents the total loss during the macro-integration and fine-tuning phase; Indicates joint loss; This represents the actual observation value collected at the monitoring point location; The predicted output of the network at the same spatiotemporal location; The observation loss weight.

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