Thermal conductivity field inversion method and device, system, storage medium

Abstract

The application discloses a thermal conductivity field inversion method and device, system and storage medium, and realizes thermal conductivity field inversion through manifold weight calculation, physical constraint prediction, RBF calibration and manifold fusion, uncertainty quantification and observation point recommendation. The technical scheme of the application significantly improves the accuracy, stability and physical credibility of thermal conductivity and temperature prediction in a sparse data scene.

Description

Technical Field

[0001] This invention belongs to the field of geothermal resource exploration technology, specifically relating to a method, apparatus, system, and storage medium for thermal conductivity field inversion. Background Technology

[0002] Thermal conductivity and temperature field are core parameters for evaluating the potential of geothermal resources, directly reflecting their development potential. Traditional thermal conductivity field inversion methods mainly suffer from the following problems: 1. Lack of physical consistency: Traditional Kriging or simple RBF interpolation methods are prone to producing physically inconsistent results in sparsely observed regions, failing to guarantee that the prediction results meet geological and thermal conductivity constraints. While purely data-driven neural networks can fit complex nonlinear relationships, they lack stratigraphic physical priors and boundary constraints, potentially leading to non-physical interpretations in areas without data.

[0003] 2. Inaccurate quantification of uncertainty: Traditional methods struggle to accurately quantify predicted uncertainty, which is crucial for risk assessment and decision support. The lack of complete uncertainty distribution information prevents the provision of a scientific basis for exploration decisions.

[0004] 3. Lack of proactive learning mechanism: Existing methods lack a variance-driven observation recommendation mechanism for exploration decision-making, which cannot guide field supplementary measurements, resulting in low observation efficiency and high exploration costs.

[0005] 4. Insufficient robustness with small samples: In scenarios with sparse observation points, the prediction accuracy of traditional methods drops significantly, failing to meet the needs of practical applications. The lack of an effective mechanism for utilizing prior knowledge makes it difficult to maintain high prediction accuracy under small sample conditions.

[0006] 5. Difficulty in fusing multi-source data: Thermal conductivity and temperature are affected by various factors, including lithology, porosity, and tectonic activity. Effectively fusing this multi-source data to improve prediction accuracy is a technical challenge.

[0007] 6. Lack of integrated tools: Current technologies have not yet formed an integrated tool that combines multi-layer stratigraphic modeling, physical constraint prediction, observation-based local calibration, uncertainty quantification and observation point recommendation, and 3D visualization, resulting in insufficient accuracy and interpretability of thermal conductivity field prediction and a high barrier to entry.

[0008] 7. Insufficient spatial correlation modeling: Existing methods typically use Euclidean distance to calculate spatial correlation, which fails to capture the inherent low-dimensional manifold structure of geological data. Geological features (lithology, porosity, structure) are often distributed on low-dimensional manifolds in high-dimensional space, and Euclidean distance cannot accurately reflect the true similarity between geological bodies, leading to unreasonable calculation of fusion weights. Summary of the Invention

[0009] To address the problems existing in the prior art, this invention provides a thermal conductivity field inversion method, device, system, and storage medium, which solves problems such as lack of physical consistency, insufficient spatial correlation modeling, inaccurate uncertainty quantification, lack of active learning mechanism, insufficient robustness for small samples, difficulty in multi-source data fusion, and lack of integrated tools in the prior art.

[0010] To achieve the above objectives, the present invention provides the following solution: A method for inverting thermal conductivity fields includes: Step S1: Obtain geological features; whereby geological features include: normalized coordinates, lithological proportions, and porosity; Step S2: Based on the geological characteristics, obtain the manifold distance and manifold regularization weight; Step S3: Use a lightweight Transformer model with geological features as input, and combine surface temperature, geothermal gradient and basement heat flow constraints to make real-time predictions of thermal conductivity and temperature, or use a rock physics baseline model to generate prior predictions when training data is lacking; wherein, the loss weights during Transformer model training include: physical constraint weights and manifold regularization weights. Step S4: Establish a thin plate spline interpolator based on the observation points, perform spatial calibration on the real-time prediction results or prior prediction results, and perform weighted fusion with the manifold distance weight and the Transformer model weight. Step S5: During the inference phase of the Transformer model, maintain Dropout activation and perform multiple forward propagations. After weighted fusion of each prediction with the RBF interpolation result, calculate the mean and standard deviation of thermal conductivity and temperature. Step S6: Select several high-uncertainty points as recommended observation points based on variance; select several high-uncertainty points as... Step S7: Display the mean / standard deviation field, observation points and recommended observation points in the 3D interface, and output the profile and result file.

[0011] The present invention also provides a thermal conductivity field inversion device, comprising: The first processing module is used to acquire geological features, which include: normalized coordinates, lithological proportions, and porosity. The second processing module is used to obtain the manifold distance and manifold regularization weight based on geological characteristics; The third processing module is used to use a lightweight Transformer model with geological features as input, combined with surface temperature, geothermal gradient and basement heat flow constraints to make real-time predictions of thermal conductivity and temperature, or to use a rock physics baseline model to generate prior predictions when training data is lacking; wherein, the loss weights during Transformer model training include: physical constraint weights and manifold regularization weights. The fourth processing module is used to establish a thin plate spline interpolator based on the observation points, perform spatial calibration on the real-time prediction results or prior prediction results, and perform weighted fusion with the manifold distance weight and the Transformer model weight. The fifth processing module is used to maintain Dropout activation during the inference phase of the Transformer model and perform multiple forward propagations. After weighted fusion of each prediction with the RBF interpolation result, the mean and standard deviation of thermal conductivity and temperature are calculated. The sixth processing module is used to select several high-uncertainty points as recommended observation points based on the standard deviation; The seventh processing module is used to display the mean / standard deviation field, observation points and recommended observation points in a 3D interface, and output profiles and result files.

[0012] The present invention also provides a thermal conductivity field inversion system, comprising: a memory and a processor, wherein the memory stores a computer program executed by the processor, and the computer program executes a thermal conductivity field inversion method when executed by the processor.

[0013] The present invention also provides a storage medium storing a computer program, which executes a thermal conductivity field inversion method when running.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention addresses the problems of low prediction accuracy and insufficient spatial correlation modeling in traditional methods under sparse observation conditions. By employing manifold distance calculation, manifold regularization loss, manifold distance fusion, dual-channel prediction mechanism, and rock physics baseline model, it achieves a deep integration of capturing the intrinsic structure of geological data and data-driven prediction, providing scientific and reliable technical support for geothermal resource evaluation. Attached Figure Description

[0015] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a flowchart of the thermal conductivity field inversion method according to an embodiment of the present invention. Detailed Implementation

[0017] 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.

[0018] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] Example 1 like Figure 1 As shown, the present invention provides a method for inverting thermal conductivity fields, comprising: Step S1: Obtain geological features; whereby geological features include: normalized coordinates, lithological proportions, and porosity; Step S2: Based on the geological characteristics, obtain the manifold distance and manifold regularization weight; Step S3: Use a lightweight Transformer model with geological features as input, and combine surface temperature, geothermal gradient and basement heat flow constraints to make real-time predictions of thermal conductivity and temperature, or use a rock physics baseline model to generate prior predictions when training data is lacking; wherein, the loss weights during Transformer model training include: physical constraint weights and manifold regularization weights. Step S4: Establish a thin plate spline interpolator based on the observation points, perform spatial calibration on the real-time prediction results or prior prediction results, and perform weighted fusion with the manifold distance weight and the Transformer model weight. Step S5: During the inference phase of the Transformer model, maintain Dropout activation and perform multiple forward propagations. After weighted fusion of each prediction with the RBF interpolation result, calculate the mean and standard deviation of thermal conductivity and temperature. Step S6: Select several high-uncertainty points as recommended observation points based on variance; select several high-uncertainty points as... Step S7: Display the mean / standard deviation field, observation points and recommended observation points in the 3D interface, and output the profile and result file.

[0020] As one embodiment of the present invention, step S2 includes: Step 2.1: Normalize the coordinates Lithology proportion and porosity are combined to form a high-dimensional feature vector. ;in, In three-dimensional space coordinates, The coordinates are horizontal east-west. The coordinates are in the horizontal north-south direction. For vertical depth coordinates, normalization refers to standardizing the coordinates to the appropriate values ​​based on the study area. interval; Represents the set of real numbers. express 3D real space; In this embodiment, the dimension of the feature vector is... ; Step 2.2: For each sampling point Find in feature space The nearest neighbors (default) Construct a k-nearest neighbor graph, that is, ; ; , ; in, This is a set of nodes containing all sample points; Let the set of edges connect each vertex to its k nearest neighbors; Step 2.3: Connect the nodes and Calculate the edge weights: (1) Calculate the Euclidean distance as the path weight of the edge for manifold distance calculation: ; (2) Calculate the heat kernel weights to construct the Laplace matrix: ; in, For the thermal core bandwidth; adaptive settings are used. ; For the edge The weights; , It is the first The and the first The geological feature vector of each sampling point is constructed by step 2.1 (normalized coordinates (x,y,z) + lithological proportion + porosity); For the first in the feature space The and the first Euclidean distance between sampling points; Step 2.4, based on Nearest neighbor graph, using Euclidean distance As edge weights, the manifold distance between any two points is calculated using either Dijkstra's algorithm or the Floyd-Warshall algorithm. That is, the sum of the edge weights along the shortest path in the graph; Step 2.5: Construct the normalized manifold Laplace matrix : ; in, The weight matrix has dimensions [missing information]. , element is ; The degree matrix is ​​a diagonal matrix with diagonal elements of 1. ; This is a combined Laplace matrix.

[0021] In one embodiment of the present invention, step S3 provides two prediction channels: a lightweight Transformer channel and a rock physics baseline channel, to achieve physically consistent predictions of thermal conductivity and temperature. The Transformer channel captures complex nonlinear relationships, while the rock physics baseline channel provides interpretable physical priors; the two are complementary. Based on a lithology-porosity combined physical model, a hybrid model is used to calculate the equivalent thermal conductivity: ; in, The thermal conductivity of the rock skeleton (e.g., 3.0 W / (m·K) for sandstone). The thermal conductivity of the pore fluid is taken as 0.6 W / (m·K) for water. Porosity.

[0022] This hybrid model provides interpretable physical priors for small-sample or unsupervised scenarios, addressing the generalization problem of deep learning methods in the face of sparse data. It automatically selects either the Transformer channel or the rock physics baseline channel based on the availability of training data, ensuring the system outputs reasonable results in any scenario.

[0023] Furthermore, during Transformer model training, the model's total loss function... for: ; in, For data fitting loss (MSE); This is due to temperature constraint loss; This is the heat flow constraint loss at the base boundary; For manifold regularization loss; The physical constraint weights are determined as follows: Initial settings ; Calculate the physical constraint violation rate for temperature and heat flux on the validation set; if the violation rate is >5%, multiply by 1.5 and iterate to adjust; Manifold regularization weights (default values) ).

[0024] For temperature constraint loss: ; in, The total number of training sampling points, For the first Predicted temperature (unit: °C or K) at each sampling point; The spatial gradient operator represents the gradient with respect to coordinates. The partial derivatives; For divergence operators, The heat generation rate (preset or set to 0 based on lithological characteristics).

[0025] For the thermal flow constraint loss at the base boundary: ; in, The number of basis boundary points. Given the known thermal flow boundary conditions at the base, For the first Thermal conductivity at the boundary point of the substrate; For the first Temperature at each base boundary point; This represents the temperature gradient along the depth z direction (unit: ℃ / m or K / m).

[0026] For manifold regularization loss; ; in, To predict the thermal conductivity vector, For predicting thermal conductivity vector The transpose of, with dimension ; This refers to the Laplace matrix of the manifold constructed in step 2.5; This is the symmetric edge set constructed in step 2.2, containing all pairs of nodes that are adjacent. To sum, traverse all pairs of nodes connected by an edge. ; For the first And the predicted thermal conductivity of the j-th sampling point (unit: W / (m·K)); For heat core weights.

[0027] In one embodiment of the present invention, in step S4, a thin plate spline radial basis function interpolator is constructed for the observation points to perform observation point interpolation calibration of the thermal conductivity. ; in, For position RBF interpolated thermal conductivity at the location; This represents the number of observation points; For the first Weighting coefficients for each observation point; These are linear polynomial terms used to ensure interpolation stability; For thin plate spline kernel functions, For prediction points To the Observation points The Euclidean distance; that is, ; The weighting coefficients of RBF interpolation are obtained by solving the following system of linear equations: ; in, The kernel function matrix has dimensions. ,element ; For smoothing coefficients; For identity matrix, dimension ; Let be a polynomial basis matrix, with dimension 1. Each line ; The weight coefficient vector has dimensions [not specified]. ; Let Lagrange multiplier vectors have dimensions [missing information]. , used to constrain polynomial terms; To observe the thermal conductivity vector, dimension .

[0028] The same RBF interpolation method is used for observation constraints at all temperature observation points: ; in, For position RBF interpolation temperature at the location; This represents the number of temperature observation points. These are the weighting coefficients for temperature interpolation; For the first Coordinates of the temperature observation points.

[0029] Next, to fuse the model predictions and RBF interpolation results, adaptive weights need to be calculated. First, the manifold distance from the predicted point x to the nearest observation point is calculated. : ; in, Represents the relationship between point x and the observation point The manifold distance (geodetic distance) between them.

[0030] Furthermore, to ensure the accuracy of the prediction points to be processed... manifold distance It can be calculated, and an approximate calculation method using the following extended graph can be used: for the predicted points Calculate its eigenvectors In the training sample node set Search for it in the middle The nearest neighbor set ;make With each nearest neighbor node Connect an edge whose weight is the Euclidean distance. Then the prediction point To any sample node The manifold distance can be defined as ; in, The geodesic distance pre-calculated on the training sample map in step 2.4. This definition is equivalent to... The result of finding the shortest path after creating a new node and connecting it with its nearest neighbors.

[0031] Based on this distance, calculate the RBF interpolation weights. With model prediction weights : ; in, The manifold feature decay scale is set to 0.5-2 times the median manifold distance between training samples, or it can be optimized through cross-validation to minimize the prediction error. To ensure that the weights are within a reasonable range and to avoid numerical instability or overfitting at observation points that are extremely close or far away, the following measures are taken: Perform cropping: ; in, This is a clipping function that takes the input value as a clipping function. z Limited to the range Inside.

[0032] Weighted fusion of model predictions and RBF interpolation: ; ; in, Predicting the thermal conductivity after fusion; Predicting the temperature after fusion; These are the predicted values ​​from the model (Transformer or Rock Physics). The predicted value is obtained through RBF interpolation.

[0033] As one embodiment of the present invention, in step S5, Dropout activation is maintained during the Transformer model inference phase, and... (Recommended) Forward propagation yields a predicted sample set of thermal conductivity and temperature; when training data is lacking and a rock physics baseline channel is used, the baseline model parameters (such as...) can be adjusted. Monte Carlo sampling is performed within a reasonable range to generate... A baseline prediction sample set is created, thus obtaining the samples needed for uncertainty estimation. For each prediction sample, it is weighted and fused with the RBF interpolation result according to the weights described in step S4, to obtain... Predicted field after group fusion: ; ; in, For the first Model predictions obtained from MC Dropout sampling.

[0034] based on Calculate the mean and variance of the sampling results: ; ; in, These are the predicted average values ​​for thermal conductivity and temperature. The predicted variances for thermal conductivity and temperature; This is Bessel correction, used for unbiased estimation.

[0035] Recommended observation points are selected based on the maximum variance criterion. ; in, The recommended coordinates for the new observation point; For the set of candidate prediction points; For position Uncertainty in the prediction of thermal conductivity and temperature at a given location.

[0036] The core innovations of this invention include: 1. Manifold distance calculation: Based on geological features, a k-nearest neighbor graph is constructed, and Dijkstra's algorithm is used to calculate manifold distance (geodetic distance) to replace the traditional Euclidean distance. This captures the inherent low-dimensional structure of geological data and more accurately reflects the true similarity between geological bodies. 2. Manifold Regularization Loss: Construct a normalized manifold Laplacian matrix and embed the manifold regularization term into the Transformer training loss function to constrain similar predicted values ​​for points close to each other on the manifold, thereby improving the smoothness and physical plausibility of the predictions. 3. Manifold distance fusion: Adaptive weights for RBF calibration are calculated using manifold distance (instead of Euclidean distance), which more reasonably achieves a continuous prediction field that closely matches near-field observations and smoothly transitions to the far-field. 4. Dual-channel prediction mechanism: The lightweight Transformer is combined with the rock physics baseline model to achieve dual-channel complementarity. When training data is available, the Transformer is used to capture complex nonlinear relationships, and when there is no training data, it automatically falls back to the rock physics model to ensure that the system can output reasonable results in any scenario. 5. Rock Physics Baseline Model: A physical model based on the combination of lithology and porosity, providing interpretable physical priors for small sample or unsupervised scenarios, complementing Transformer, and solving the generalization problem of deep learning methods when data is sparse.

[0037] Example 2 The present invention also provides a thermal conductivity field inversion device, comprising: The first processing module is used to acquire geological features, which include: normalized coordinates, lithological proportions, and porosity. The second processing module is used to obtain the manifold distance and manifold regularization weight based on geological characteristics; The third processing module is used to use a lightweight Transformer model with geological features as input, combined with surface temperature, geothermal gradient and basement heat flow constraints to make real-time predictions of thermal conductivity and temperature, or to use a rock physics baseline model to generate prior predictions when training data is lacking; wherein, the loss weights during Transformer model training include: physical constraint weights and manifold regularization weights. The fourth processing module is used to establish a thin plate spline interpolator based on the observation points, perform spatial calibration on the real-time prediction results or prior prediction results, and perform weighted fusion with the manifold distance weight and the Transformer model weight. The fifth processing module is used to maintain Dropout activation during multiple forward propagations in the weighted fusion Transformer model prediction to obtain the mean and variance of thermal conductivity and temperature. The sixth processing module is used to select several high-uncertainty points as recommended observation points based on variance; The seventh processing module is used to display the mean / variance field, observation points and recommended observation points in a 3D interface, and output profiles and result files.

[0038] Example 3 The present invention also provides a thermal conductivity field inversion system, comprising: a memory and a processor, wherein the memory stores a computer program executed by the processor, and the computer program executes a thermal conductivity field inversion method when executed by the processor.

[0039] Example 4 The present invention also provides a storage medium storing a computer program, which executes a thermal conductivity field inversion method when running.

[0040] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for inverting thermal conductivity fields, characterized in that, include: Step S1: Obtain geological features; whereby geological features include: normalized coordinates, lithological proportions, and porosity; Step S2: Based on the geological characteristics, obtain the manifold distance and manifold regularization weight; Step S3: Use a lightweight Transformer model with geological features as input, and combine surface temperature, geothermal gradient and basement heat flow constraints to make real-time predictions of thermal conductivity and temperature, or use a rock physics baseline model to generate prior predictions when training data is lacking; wherein, the loss weights during Transformer model training include: physical constraint weights and manifold regularization weights. Step S4: Establish a thin plate spline interpolator based on the observation points, perform spatial calibration on the real-time prediction results or prior prediction results, and perform weighted fusion with the manifold distance weight and the Transformer model weight. Step S5: During the inference phase of the Transformer model, maintain Dropout activation and perform multiple forward propagations. After weighted fusion of each prediction with the RBF interpolation result, calculate the mean and standard deviation of thermal conductivity and temperature. Step S6: Select several high-uncertainty points as recommended observation points based on variance; Step S7: Display the mean / standard deviation field, observation points and recommended observation points in the 3D interface, and output the profile and result file.

2. A thermal conductivity field inversion device, characterized in that, include: The first processing module is used to acquire geological features, which include: normalized coordinates, lithological proportions, and porosity. The second processing module is used to obtain the manifold distance and manifold regularization weight based on geological characteristics; The third processing module is used to use a lightweight Transformer model with geological features as input, combined with surface temperature, geothermal gradient and basement heat flow constraints to make real-time predictions of thermal conductivity and temperature, or to use a rock physics baseline model to generate prior predictions when training data is lacking; wherein, the loss weights during Transformer model training include: physical constraint weights and manifold regularization weights. The fourth processing module is used to establish a thin plate spline interpolator based on the observation points, perform spatial calibration on the real-time prediction results or prior prediction results, and perform weighted fusion with the manifold distance weight and the Transformer model weight. The fifth processing module is used to maintain Dropout activation during the inference phase of the Transformer model and perform multiple forward propagations. After weighted fusion of each prediction with the RBF interpolation result, the mean and standard deviation of thermal conductivity and temperature are calculated. The sixth processing module is used to select several high-uncertainty points as recommended observation points based on the standard deviation; The seventh processing module is used to display the mean / standard deviation field, observation points and recommended observation points in a 3D interface, and output profiles and result files.

3. A thermal conductivity field inversion system, characterized in that, include: A memory and a processor, wherein the memory stores a computer program executed by the processor, the computer program performing the thermal conductivity field inversion method as described in claim 1 when executed by the processor.

4. A storage medium, characterized in that, The storage medium stores a computer program, which executes the thermal conductivity field inversion method as described in claim 1 when it runs.

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