Probabilistic geothermal resource evaluation method and system based on weighted bayesian fusion and energy conservation constraint gaussian process

Abstract

The present application discloses a probabilistic geothermal resource evaluation method and system based on weighted Bayesian fusion and energy conservation constraint Gaussian process, belonging to the technical field of geothermal resource exploration and evaluation. The present application aims to solve the problems of lack of strict uncertainty quantification in data fusion, difficulty in balancing the physical constraints and precision of the proxy model, single extrapolation risk assessment method and large amount of calculation, and lack of intelligence in training sample selection in the early stage of exploration. The technical scheme includes the following points: using a weighted Bayesian framework to fuse and synthesize the measured temperature field to quantify the uncertainty; based on the physical coupling relationship, the parameter probabilistic sampling and verification are carried out; the training samples are selected adaptively according to the prediction uncertainty; the Gaussian process proxy model embedded with energy conservation constraint penalty term is trained; the double-index risk index is used for Monte Carlo simulation extrapolation protection; and the model is iteratively updated and version managed based on information gain.

Description

Technical Field

[0001] This invention belongs to the field of geothermal resource exploration and evaluation technology, and particularly relates to a probabilistic geothermal resource evaluation method and system based on weighted Bayesian fusion and energy conservation constrained Gaussian process. Background Technology

[0002] Geothermal resource assessment is a crucial step in geothermal project investment decisions. In the early stages of exploration, readily available direct data, such as drilling information, is often scarce, posing a significant challenge to resource assessment due to the difficulty of small-sample modeling. Currently, the probabilistic volumetric method combined with Monte Carlo simulation is the industry standard practice for handling parameter uncertainty. However, existing technologies have several significant shortcomings in practical applications, limiting the reliability, efficiency, and physical rationality of the assessment results. First, regarding data fusion, existing methods often employ heuristic weighting functions to fuse the synthetic temperature field generated by numerical simulation with limited field temperature measurement data, such as fixed weights or simple three-factor weighting functions. These methods lack a rigorous probabilistic statistical framework and cannot provide a complete posterior variance estimate of the fused temperature field. This leads to an underestimation or inaccurate estimation of uncertainty in data-sparse regions far from the measurement points, affecting the reliability of subsequent probabilistic analyses. Although methods such as depth adaptive fusion consider spatial distance, their uncertainty quantification remains insufficient. Second, surrogate models introduced to reduce computational costs, such as Gaussian process regression, face balancing difficulties when embedding physical constraints. Traditional methods introduce constraints such as heat flow balance through kernel functions, but the constraint strength is often fixed and difficult to adjust adaptively. Predictive accuracy is often sacrificed to ensure physical plausibility, and existing heat balance constraints fail to consider the formation heat generation rate, resulting in an incomplete physical description. Furthermore, when using surrogate models for large-scale extrapolation predictions, the risk assessment mechanism is relatively simplistic. Existing methods mostly rely on prediction variance or the boundaries of input parameters for judgment, lacking a systematic index that integrates model uncertainty, data distribution, and physical consistency. Some advanced methods, such as the ternary risk index, comprehensively consider statistical extrapolation, prediction uncertainty, and physical plausibility, but the high computational complexity of the Mahalanobis distance involved adds additional computational burden. Finally, in selecting training samples for constructing surrogate models, existing techniques generally employ fixed experimental designs, such as Latin hypercube sampling. This strategy does not consider the current learning state of the surrogate model and cannot adaptively select the most valuable high-fidelity simulation sample points for model improvement, resulting in wasted computational resources and requiring a large number of costly simulations to achieve the desired accuracy with small sample sizes. In recent years, while advanced methods such as variational inference and physical information neural networks have been introduced to improve scientific rigor, these methods often require complex optimization processes or training deep networks. In the small-sample scenarios of early exploration, their enormous computational costs and the resulting accuracy improvements are difficult to match the efficiency requirements of practical engineering applications. Therefore, the industry urgently needs an innovative solution that can balance physical reliability, prediction accuracy, and computational efficiency under small-sample conditions. Summary of the Invention

[0003] To address the aforementioned technical issues, this invention proposes a probabilistic geothermal resource evaluation method and system based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes. This method achieves efficient, physically sound, and risk-controllable probabilistic evaluation of geothermal resources, significantly improving prediction accuracy and computational efficiency under small sample conditions.

[0004] To achieve the above objectives, this invention provides a probabilistic geothermal resource evaluation method based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes, including: An enhanced temperature field that integrates synthetic and measured temperature fields is constructed, and its uncertainty is quantified. Based on physical constraints, probabilistic distribution modeling and sampling verification of evaluation parameters are performed. Based on the prediction uncertainty of the surrogate model, high-fidelity simulation training data is generated by adaptively selecting samples. Train a Gaussian process surrogate model with embedded physical constraint penalty terms to obtain a resource quantity prediction model; Monte Carlo simulations were performed using the resource quantity prediction model, and extrapolation results were based on the dual-indicator risk assessment. Based on the information gain from the new data, the resource quantity prediction model is iteratively updated and version managed.

[0005] Optionally, constructing an enhanced temperature field includes: Assume that both the synthesized temperature field data and the measured temperature data follow a Gaussian distribution; Using a weighted Bayesian inference framework, the synthetic temperature field data is fused with the measured temperature data to obtain the fused posterior mean and variance, which serve as the enhanced temperature field and its uncertainty quantification results.

[0006] Optionally, probabilistic distribution modeling and sampling verification of evaluation parameters based on physical constraints include: The coupling relationship between permeability and porosity was established based on the Kozeny-Carman equation; Establish the coupling relationship between temperature and depth based on the physical reasonable range of the geothermal gradient; During Monte Carlo sampling, each set of sampling parameters is validated according to the coupling relationship, and parameter combinations that violate the coupling relationship are rejected.

[0007] Optionally, adaptive selection of samples to generate high-fidelity simulated training data includes: A fixed experimental design method was used to select initial sample points and train the initial surrogate model. Based on the initial surrogate model, the prediction uncertainty of candidate sample points is calculated in the parameter space; The candidate sample points with the greatest prediction uncertainty are selected for high-fidelity simulation, and the results are added to the training set to update the surrogate model.

[0008] Optionally, training the Gaussian process proxy model includes: An energy conservation constraint penalty term is embedded in the standard radial basis kernel function to construct the constraint kernel function; The energy conservation constraint penalty term calculates the residual of the energy conservation equation based on the input parameters. As the residual increases, the value of the constraint kernel function decays.

[0009] Optional extrapolation results based on the dual-indicator risk assessment include: The risk index is defined as the weighted sum of the normalized prediction variance and the energy-conserving residual; Calculate the critical threshold of the risk index mentioned on the training set; In the Monte Carlo simulation, if the risk index of a sample exceeds the critical threshold, it is marked as a high-risk sample.

[0010] Optionally, iterative updates and version management of the resource quantity prediction model include: Calculate the key parameter distribution shifts and the proportion of new samples caused by the new data; When the distribution drift or the proportion of newly added samples exceeds a preset threshold, the full retraining of the resource quantity prediction model is triggered. Record the version information for each model update.

[0011] On the other hand, to achieve the above objectives, the present invention also provides a probabilistic geothermal resource evaluation system based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes, comprising: The temperature field fusion modeling module is used to construct an enhanced temperature field that integrates synthetic temperature field and measured data, and to quantify its uncertainty. The parameter probabilistic modeling module is used to perform probabilistic distribution modeling and sampling verification of evaluation parameters based on physical constraint relationships. An adaptive sampling module is used to adaptively select samples to generate high-fidelity simulation training data based on the prediction uncertainty of the surrogate model. The surrogate model training module is used to train a Gaussian process surrogate model with embedded physical constraint penalty terms to obtain a resource quantity prediction model. The risk assessment and simulation module is used to perform Monte Carlo simulation using the resource quantity prediction model and extrapolate the results based on the dual-indicator risk assessment. The iterative update management module is used to iteratively update and manage the version of the resource quantity prediction model based on the information gain of the new data.

[0012] An electronic device, the electronic device comprising: a processor and a memory storing computer program instructions; When the processor executes the computer program instructions, it implements the probabilistic geothermal resource evaluation method based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes.

[0013] A computer storage medium storing computer program instructions, which, when executed by a processor, implement the probabilistic geothermal resource evaluation method based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes.

[0014] Technical Advantages of this Invention: This invention discloses a probabilistic geothermal resource evaluation method and system based on weighted Bayesian fusion and energy-conservation-constrained Gaussian processes. Weighted Bayesian fusion provides rigorous and complete posterior uncertainty quantification, significantly improving the reliability of the fusion results. The energy-conservation-constrained Gaussian process surrogate model effectively ensures the physical consistency of the prediction results while maintaining high prediction accuracy and higher training efficiency. The proposed dual-index risk index avoids complex distance calculations, achieving efficient and reliable extrapolation risk identification and protection. The adaptive sampling strategy based on prediction uncertainty intelligently selects the most valuable training samples, thereby improving the utilization efficiency and modeling efficiency of high-fidelity simulation data. The overall technical solution reduces the computation time of large-scale probabilistic simulation from monthly to hourly using traditional methods, and can output complete probabilistic evaluation indicators and sensitivity analysis results. Its information gain-driven iterative update mechanism ensures continuous model optimization and version traceability, providing efficient, reliable, and physically reasonable quantitative basis for investment decisions in the early stages of geothermal resource exploration. Attached Figure Description

[0015] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart illustrating the probabilistic geothermal resource evaluation method based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes, as described in an embodiment of the present invention. Detailed Implementation

[0016] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0017] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0018] like Figure 1 As shown, this embodiment provides a probabilistic geothermal resource evaluation method based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes, including: This method is applicable to geothermal systems dominated by heat conduction, i.e., those with the Peckley number. (in The volumetric heat capacity of the fluid. For the Darcy flow velocity of groundwater, For characteristic length, (where is the thermal conductivity), at which point convective heat transfer is negligible, and the steady-state energy equation simplifies to: For convection-dominated systems ( ), which requires the introduction of convection terms to correct the energy conservation constraints; Step S1, Weighted Bayesian Physics Enhancement Modeling: A weighted Bayesian framework is used to fuse the synthesized temperature field with measured data to quantify uncertainty; wherein, the synthesized temperature field is assumed to be... and measured data All follow a Gaussian distribution, resulting in an enhanced temperature field after fusion. The posterior distribution is obtained through weighted Bayesian inference, providing complete posterior mean and variance quantification; Step S2, Probabilistic Coupling of Physical Coupled Parameters: Establish parameter coupling relationships based on the Kozeny-Carman equation and geothermal gradient constraints; wherein, the probability distribution of key evaluation parameters is defined, and physical coupling verification is performed on each set of sampled parameters during the Monte Carlo sampling stage, rejecting parameter combinations that violate the constraints; Step S3, Uncertainty-driven experimental design and high-fidelity simulation data generation: An uncertainty maximization strategy is used to adaptively select training samples; in the initial stage, a fixed experimental design is used to select initial sample points to train the initial surrogate model, and in subsequent iterations, new samples are selected based on the principle of maximizing prediction uncertainty to conduct high-fidelity simulations. Step S4: Training the Gaussian process surrogate model with energy conservation constraints: A Gaussian process kernel function with embedded energy conservation constraint penalty terms is used; where the energy conservation constraints are based on the complete energy conservation equation. Physical consistency is ensured through an energy residual penalty term; Step S5, Monte Carlo simulation and sensitivity analysis of dual-index risk protection: large-scale sampling from parameter distribution, calling the surrogate model to quickly predict resource quantity, and extrapolation protection through dual-index risk protection; wherein, the dual-index risk protection includes normalized prediction variance and energy conservation residual, without the need to calculate Mahalanobis distance; Step S6, Information Gain-Driven Iterative Updates and Version Management: When new data is input, calculate the information gain metric and trigger the corresponding update strategy, and record the version to support backtracking.

[0019] Furthermore, constructing an enhanced temperature field includes: Assume that both the synthesized temperature field data and the measured temperature data follow a Gaussian distribution; Using a weighted Bayesian inference framework, the synthetic temperature field data is fused with the measured temperature data to obtain the fused posterior mean and variance, which serve as the enhanced temperature field and its uncertainty quantification results.

[0020] Specifically, the implementation process of this embodiment includes: In step S1, the core of the weighted Bayesian physics-data fusion algorithm is the weighted Bayesian framework: assuming a synthesized temperature field and measured data All follow a Gaussian distribution: ; ; in , The mean, , Variance; mean of the synthesized temperature field and variance The sample statistics are obtained by sampling and solving the forward model of multiple sets of prior parameters (such as base heat flux, thermal conductivity, and heat generation rate), thereby propagating the uncertainty of the prior parameters to the temperature field. This method adopts a simplified strategy of independent fusion of depth points, that is, assuming that the errors between different depth points are independent of each other, in order to reduce computational complexity. This simplification may lead to an incomplete characterization of the depth-related error structure, but it can provide a reasonable first-order uncertainty estimate in engineering applications. Enhanced temperature field after fusion The posterior distribution is obtained through weighted Bayesian inference: ; The fusion mean and variance are: ; ; The weighting function is defined as follows: ; ; in This is the distance attenuation coefficient (unit: ℃² / m). The vertical distance to the nearest measured point (unit: m); in the weighting function The statistical significance of this item is as follows: as the predicted point moves further away from the measured point, the spatial representativeness of the measured data at that point decreases, which is equivalent to an increase in the effective observation variance of the measured data at that point, thereby reducing the weight of the measured data and increasing the weight of the synthetic model. This weighted Bayesian framework provides complete uncertainty quantification while maintaining computational efficiency, and the weight function automatically balances the uncertainty and spatial representativeness of different data sources.

[0021] Distance attenuation coefficient The following method was used to determine the optimal approach: leave-one-out cross-validation was performed at known measured points, with the objective of minimizing the root mean square error of the fused temperature field prediction at the leave-out points. Value; or based on the accuracy of the temperature measuring instrument. and regional geothermal gradient variability Using empirical formulas Confirmed, among which This is a calibration constant, with a typical value range of 0.5-2.0.

[0022] Furthermore, the probabilistic distribution modeling and sampling verification of the evaluation parameters based on physical constraints include: The coupling relationship between permeability and porosity was established based on the Kozeny-Carman equation; Establish the coupling relationship between temperature and depth based on the physical reasonable range of the geothermal gradient; During Monte Carlo sampling, each set of sampling parameters is validated according to the coupling relationship, and parameter combinations that violate the coupling relationship are rejected.

[0023] Specifically, the implementation process of this embodiment includes: In step S2, the physical coupling sampling of geothermal parameters includes: permeability-porosity coupling: for porous reservoirs (such as sandstone, conglomerate, and other sedimentary layers), based on the Kozeny-Carman equation... (180 is an empirical constant under the assumption of spherical particles) Establish permeability With porosity Equivalent particle diameter The equation relates to the constraints; it is applicable to pore flow in granular media, but for fracture-dominated reservoirs (such as fault zones and bedrock fractures), the fracture cubic law should be used instead. ( For crack aperture, (For fracture spacing) or equivalent fracture permeability model; samples are first extracted independently. (or , )and , then calculate Within the allowed range and extracting within that range; Temperature-depth coupling: based on geothermal gradient physical constraints ,in , The physically reasonable range of the regional geothermal gradient is typically 15-45℃ / km (this range is based on the statistical values ​​of typical geothermal gradients of the global continental crust, referencing Beardsmore & Cull, 2001; specific regions should be adjusted according to regional heat flow background and measured data); thermal conductivity-lithology coupling: the a priori distribution range of thermal conductivity is automatically constrained according to lithological type (granite, shale, sandstone, limestone, etc.), and the a priori parameters can refer to the rock thermal property database of Clauser & Huenges (1995); during the Monte Carlo sampling stage, physical coupling verification is performed on each group of sampling parameters, rejecting parameter combinations that violate the above constraints, rather than eliminating them afterward, which significantly improves the effective sample rate.

[0024] Furthermore, the adaptive selection of samples to generate high-fidelity simulated training data includes: A fixed experimental design method was used to select initial sample points and train the initial surrogate model. Based on the initial surrogate model, the prediction uncertainty of candidate sample points is calculated in the parameter space; The candidate sample points with the greatest prediction uncertainty are selected for high-fidelity simulation, and the results are added to the training set to update the surrogate model.

[0025] Specifically, the implementation process of this embodiment includes: In step S3, the uncertainty maximization strategy includes: initial agent model training: using a fixed experimental design (such as optimal Latin hypercube sampling) to select... We use 50 initial sample points to perform high-fidelity simulations to obtain initial training data and train the initial surrogate model; uncertainty index: for candidate sample points The prediction uncertainty is calculated using the current proxy model: ; in The surrogate model's prediction variance at that point. The target is the predicted mean; since the surrogate model predicts the amount of resources (positive value). The constant validity of this coefficient of variation indicates that the uncertainty index has good numerical stability; to enhance robustness, in practical implementation, it can be adjusted... Set lower limit truncation (e.g., the 1st percentile of the predicted mean), i.e. Sampling strategy: Select the candidate point with the greatest prediction uncertainty, i.e. ,in Candidate set; Iterative sampling: Generate a large number of candidate points from the parameter space (e.g., 10,000, and the generation process applies the physical coupling verification strategy described in step S2 to ensure that the candidate points are physically simulable), calculate the prediction uncertainty of each candidate point using the current surrogate model, and select the one with the highest uncertainty. Perform high-fidelity simulations on 20 points (e.g., 20 points) and add them to the training set. Retrain the surrogate model and repeat the above process until the target number of samples is reached or the convergence criterion is met (e.g., the prediction accuracy of the surrogate model). (When the target value or the number of samples reaches the upper limit); this strategy significantly reduces the computational cost compared to the information gain method (no need to calculate entropy and make multiple model predictions), and its effectiveness is comparable in practical applications.

[0026] Furthermore, training the Gaussian process surrogate model includes: An energy conservation constraint penalty term is embedded in the standard radial basis kernel function to construct the constraint kernel function; The energy conservation constraint penalty term calculates the residual of the energy conservation equation based on the input parameters. As the residual increases, the value of the constraint kernel function decays.

[0027] Specifically, the implementation process of this embodiment includes: In step S4, the kernel function for the energy conservation-constrained Gaussian process regression is: ; in For the standard radial basis kernel function: ; in For signal variance, For the first The feature length scale of the input dimension; an additional noise term is added when constructing the covariance matrix. ( For noise variance, (Kronecker symbol) Energy conservation constraint penalty term A function defined as an input parameter vector: ; Where the energy residual function Calculation based on input parameters: Energy conservation constraints are based on the complete energy conservation equation. ,in Thermal conductivity, For temperature field, For heat generation rate; For steady-state heat conduction ( Energy conservation equation This can be transformed into a heat flow balance relationship, that is, the conducted heat flow should be equal to the sum of the deep heat flow and the generated heat; The energy residual function is defined as ,in The base heat flux is expressed in mW / m². For heat generation rate (Unit: μW / m³) at reservoir thickness The cumulative heat flux generated within (unit: m) is converted to a unified unit (unit: mW / m²). Thermal conductivity (unit: W / (m·K)) Geothermal gradient (unit: °C / km); due to The unit is W / (m·K)×K / km = W / (m·km) = mW / m², and , The dimensions are consistent, requiring no additional conversion; The constraint strength coefficient (dimensionless); The difference between energy conservation constraints and thermal equilibrium constraints: Energy conservation constraints are based on the complete energy conservation equation. Compared to thermal equilibrium constraints (based solely on heat flow balance) The physical meaning is more comprehensive, taking into account the heat generation rate. The effects are applicable to a wider range of geothermal systems; Positive definiteness guarantee: due to ,in Always positive, therefore the product kernel exist It remains positive definite when the input parameter combination violates the law of conservation of energy. )hour, Increase, penalty item Approaching zero causes the kernel function value to decay, thereby suppressing the prediction weights of non-physical solutions; unlike the hard rejection in step S2, the soft constraint mechanism in S4 is mainly used to smooth the prediction behavior of the surrogate model at the boundary of the physically feasible domain, and serves as a secondary protection against potential missed anomalous samples in Monte Carlo simulations.

[0028] Constraint strength coefficient The initial setting is determined adaptively in the following manner: A small value (e.g., 0.1); during the training of the surrogate model, monitor the energy residual on the validation set. Distribution (unit: mW / m²); define energy violation rate as... Exceeding the physical reasonable threshold (e.g., 5 mW / m², corresponding to approximately 15% typical relative deviation in heat flux) sample proportion; if energy violation rate Then increase (e.g., multiply by 1.5); iteratively adjust until the energy violation rate drops below 5%, while maintaining the surrogate model's prediction accuracy. ;like If it drops below 0.90, it will revert. Up to the previous valid value.

[0029] Furthermore, the extrapolation results based on the dual-indicator risk assessment include: The risk index is defined as the weighted sum of the normalized prediction variance and the energy-conserving residual; Calculate the critical threshold of the risk index mentioned on the training set; In the Monte Carlo simulation, if the risk index of a sample exceeds the critical threshold, it is marked as a high-risk sample.

[0030] Specifically, the implementation process of this embodiment includes: The dual-indicator risk index is used for extrapolation risk assessment, and the dual-indicator risk index is defined as follows: ; in, This is the normalized prediction variance (coefficient of variation). The energy conservation residual (units are uniformly mW / m², where...) Convert μW / m² to mW / m². The unit is directly mW / m², calculated from the input parameters; weighting coefficients Determined by normalization using the inverse of variance: ; in, For the first The standard deviation of each indicator on the training set ensures that the contribution of each indicator to the risk index is consistent and relatively balanced. The design logic of the dual-indicator risk index is as follows: the first indicator (normalized prediction variance) captures the statistical uncertainty of the surrogate model. High variance usually means that the sample points are far from the dense area of ​​training data. The second indicator (energy conservation residual) captures the physical consistency of the parameter combination. High residual indicates that the parameter combination violates the energy balance relationship. The combination of the two can effectively identify high-risk samples of "statistical extrapolation + physical unreasonableness". For marginal cases of "statistically within the distribution but with high prediction uncertainty" or "physically reasonable but with insufficient training coverage", the dual-indicator mechanism provides complementary protection. Critical threshold Determined using the quantile method: Calculate on the training set... The 95th percentile as Alternatively, leave-one-out cross-validation can be used to plot the prediction error of the validation samples versus... The relationship curve is used to select the inflection point where the error increases sharply as... ;when When this occurs, a full-order simulation rollback is triggered or the system is marked as having low confidence, resulting in reduced weighting or removal in the sensitivity analysis.

[0031] In step S5, a multi-indicator convergence criterion combining quantiles, variance, and Sobol is used: Quantile convergence: ,in For the first The resource quantity at the next iteration percentile, Convergence thresholds corresponding to pessimistic, median, and optimistic estimates, respectively. , ; Variance convergence: ,in For the first The variance of resource quantity in each iteration ; Sobol convergence: ,in For the first During the nth iteration The Sobol total sensitivity index of the input parameters. ; Convergence is determined when all three indicators are met simultaneously. For high-risk samples ( Sensitivity results are marked with low confidence or removed from Sobol calculations.

[0032] Furthermore, the iterative updates and version management of the resource quantity prediction model include: Calculate the key parameter distribution shifts and the proportion of new samples caused by the new data; When the distribution drift or the proportion of newly added samples exceeds a preset threshold, the full retraining of the resource quantity prediction model is triggered. Record the version information for each model update.

[0033] Specifically, the implementation process of this embodiment includes: In step S6, the information gain-driven retraining strategy includes: calculating the information gain metric for the new data, including the drift in the distribution of key parameters. and the proportion of new samples ;when or When the performance on the validation set degrades to within a certain threshold (NLL increases), a full retraining of the surrogate model is triggered; when the performance on the validation set degrades to within a certain threshold (NLL increases), a full retraining of the surrogate model is triggered. , decline When only fine-tuning hyperparameters (e.g.) , , It records the version number, hyperparameters, verification metrics, sensitivity sorting, and data source for each update, and supports version rollback and rollback.

[0034] This embodiment provides a probabilistic geothermal resource evaluation system based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes, including: The temperature field fusion modeling module is used to construct an enhanced temperature field that integrates synthetic temperature field and measured data, and to quantify its uncertainty. The parameter probabilistic modeling module is used to perform probabilistic distribution modeling and sampling verification of evaluation parameters based on physical constraint relationships. An adaptive sampling module is used to adaptively select samples to generate high-fidelity simulation training data based on the prediction uncertainty of the surrogate model. The surrogate model training module is used to train a Gaussian process surrogate model with embedded physical constraint penalty terms to obtain a resource quantity prediction model. The risk assessment and simulation module is used to perform Monte Carlo simulation using the resource quantity prediction model and extrapolate the results based on the dual-indicator risk assessment. The iterative update management module is used to iteratively update and manage the version of the resource quantity prediction model based on the information gain of the new data.

[0035] An electronic device, the electronic device comprising: a processor and a memory storing computer program instructions; When the processor executes the computer program instructions, it implements the probabilistic geothermal resource evaluation method based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes.

[0036] A computer storage medium storing computer program instructions, which, when executed by a processor, implement the probabilistic geothermal resource evaluation method based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes.

[0037] Example 1 Taking the initial exploration of a hydrothermal geothermal target area in a sedimentary basin as an example, only two parameter wells and magnetotelluric data were available. The Peckley number for this target area... It belongs to the heat conduction-dominated type and falls within the scope of application of this invention.

[0038] like Figure 1 As shown, this invention provides a probabilistic geothermal resource evaluation method based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes, comprising: Step S1: Weighted Bayesian Physical Enhancement Modeling: Import geological maps, MT profiles, and logging and temperature measurement data from two wells. Set basement heat flow. mW / m² (reference regional geological background value), thermal conductivity W / (m·K) prior range, generating 5000 sets of Latin hypercubes. Solving the one-dimensional steady-state heat conduction equation yielded 5000 composite geothermal curves.

[0039] Weighted Bayesian fusion implementation: Calculating the mean and variance of the synthesized data at each depth: , The variance range is approximately 2-8℃²; the variance of the measured data is set according to the accuracy of the temperature measuring instrument. ℃²; Calculate the distance from each depth to the nearest temperature measurement point. Optimize by leave-one-out cross-validation ℃² / m, calculate the posterior distribution after fusion using a weighting function: , .

[0040] Result: Near the temperature measurement point ( m), with high weighting for measured data. Small (approximately 0.3℃²); in areas far from the temperature measurement point ( m), with increased weight in synthetic data. Increased (approximately 2-3℃²), fully quantifying uncertainty. Computation time: Weighted Bayesian fusion takes approximately 2 minutes, which is about 80% shorter than the variational Bayesian method (which requires optimization of ELBO and takes approximately 10 minutes) (within the 70-80% range).

[0041] Step S2, Probabilistic Approach to Physical Coupling Parameters: Area Extraction ,thickness ,temperature Penetration rate Porosity Parameters such as these.

[0042] Physical coupling sampling implementation: first extract porosity The range is [0.05, 0.35]; the equivalent particle diameter is set according to the lithology (mainly sandstone). (Corresponding to 0.01-0.1 mm); Allowable range calculated by the Kozeny-Carman equation. Range, extract within this range Verify if the temperature-depth combination meets the requirements. ℃ / km, reject samples that violate the constraints, and re-sample.

[0043] Results: The effective sample rate increased from approximately 65% ​​using traditional methods to 92%.

[0044] Step S3, Uncertainty-Driven Experimental Design and Full-Order Simulation: Initial Stage: Using the optimal LHS, 50 initial sample points are selected for high-fidelity simulation (TOUGH2, 30-year mining simulation) to obtain initial training data. Train the initial agent model (standard Gaussian process regression, without physical constraints).

[0045] Uncertainty Maximization Iteration: Round 1: Generate 10,000 candidate points from the parameter space (Physical coupling verification has been applied), the prediction uncertainty for each candidate point is calculated using the initial surrogate model. Select the 20 points with the highest uncertainty. Perform high-fidelity simulations to obtain new training data, add it to the training set (70 samples in total), and retrain the surrogate model (with energy conservation constraints added); Round 2: Use the updated surrogate model to generate 10,000 candidate points from the parameter space. The prediction uncertainty is calculated, and the 20 new sample points with the highest uncertainty are selected for high-fidelity simulation and added to the training set (90 samples in total) to retrain the surrogate model. From rounds 3 to 15, the above process is repeated, selecting 20 new samples each round. The quality of the surrogate model is gradually improved, the distribution of prediction uncertainty is continuously optimized, and the sampling strategy is adjusted accordingly. After 15 iterations, 350 high-fidelity training samples are finally obtained, and the prediction accuracy of the surrogate model is [data missing]. The convergence criterion was met when the value reached 0.92. Comparative experiments are shown in Table 1.

[0046] Table 1

[0047] Results: The uncertainty maximization strategy reduces the number of high-fidelity simulation samples required to achieve the same prediction accuracy by 20%, and shortens the sampling and computation time by 62.5% compared to the information gain method.

[0048] Step S4, Training the surrogate model of the energy conservation-constrained Gaussian process: Constructing an energy conservation-constrained Gaussian process: Standard RBF kernel: Length scale of each dimension Maximum likelihood estimation; energy conservation constraint penalty term: initial... Iterative adjustment : Monitoring and verification set energy violation rate ( (ratio of mW / m²); Round 1: The energy violation rate was 13.2%. Round 2: The energy violation rate was 8.8%. Round 3: The energy violation rate was 5.3%. Round 4: Energy violation rate 3.5%, (satisfying <5% and The comparative experiments are shown in Table 2.

[0049] Table 2

[0050] Results: The energy conservation constraint GPR, while ensuring physical plausibility (violation rate <5%), improves prediction accuracy. The energy violation rate (2.8%) is better than the thermal balance constraint (4.1%), and the training time is reduced by about 70% compared to MF-PINN (within the range of 60-70%). Compared to the thermal balance constraint, the energy conservation constraint takes into account the heat conduction equation more comprehensively.

[0051] Step S5, Monte Carlo simulation of dual-index risk protection: Extract 15,000 sets of parameters from the distribution in step S2 (physical coupling sampling), and call the agent to predict the amount of resources.

[0052] Implementation of the dual-indicator risk index: Obtaining the proxy forecast variance Training set standard deviation (Dimensionless after normalization); Calculate the energy conservation residual. (All items are uniformly expressed as mW / m², where) Convert μW / m² to mW / m². The unit is directly mW / m²), and the standard deviation of the training set after normalization. (Dimensionless); Reciprocal of variance normalized weights: , Determined by quantile method : Calculate on the training set The 95th percentile is obtained. .

[0053] Protection results: Of 15,000 samples, 1,123 (7.5%) triggered high-risk markers. (281 full-order backtracking simulations were used for validation). Validation showed that the mean surrogate prediction error for high-risk samples was 17.8%, significantly higher than the 3.1% for low-risk samples. The dual-index risk index successfully identified 85% of the high-error samples. Comparative experiments are shown in Table 3.

[0054] Table 3

[0055] Results: The dual-index risk index has an accuracy comparable to the ternary risk index (only 2% lower), but the computation time is reduced by 40%, and by 94% compared to the deep anomaly detection network.

[0056] Output: P10 = 45.2 PJ, P50 = 78.6 PJ, P90 = 134.5 PJ. Sensitivity ranking: Temperature ( =0.42)>penetration rate ( =0.28)>thickness( =0.18)>Area( =0.12).

[0057] Step S6, Closed-loop update: After adding data from one appraisal well: Calculate (<0.1), (<15%), validation set A decrease of 0.015 (<0.02) triggered hyperparameter fine-tuning instead of full retraining. After the update, the P50 was adjusted from 78.6 PJ to 82.3 PJ. The record version is v1.1, which supports backtracking.

[0058] This invention discloses a probabilistic geothermal resource evaluation method and system based on weighted Bayesian fusion and an energy-conservation-constrained Gaussian process. Weighted Bayesian fusion provides rigorous and complete posterior uncertainty quantification, significantly improving the reliability of the fusion results. The energy-conservation-constrained Gaussian process surrogate model effectively ensures the physical consistency of the prediction results while maintaining high prediction accuracy and higher training efficiency. The proposed dual-index risk index avoids complex distance calculations, achieving efficient and reliable extrapolation risk identification and protection. An adaptive sampling strategy based on prediction uncertainty intelligently selects the most valuable training samples, thereby improving the utilization efficiency and modeling efficiency of high-fidelity simulation data. The overall technical solution reduces the computation time of large-scale probabilistic simulation from months to hours using traditional methods and can output complete probabilistic evaluation indicators and sensitivity analysis results. Its information gain-driven iterative update mechanism ensures continuous model optimization and version traceability, providing an efficient, reliable, and physically reasonable quantitative basis for investment decisions in the early stages of geothermal resource exploration.

[0059] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A probabilistic geothermal resource evaluation method based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes, characterized in that, include: An enhanced temperature field that integrates synthetic and measured temperature fields is constructed, and its uncertainty is quantified. Based on physical constraints, probabilistic distribution modeling and sampling verification of evaluation parameters are performed. Based on the prediction uncertainty of the surrogate model, high-fidelity simulation training data is generated by adaptively selecting samples. Train a Gaussian process surrogate model with embedded physical constraint penalty terms to obtain a resource quantity prediction model; Training the Gaussian process surrogate model includes: embedding an energy conservation constraint penalty term into the standard radial basis kernel function to construct a constraint kernel function; the energy conservation constraint penalty term calculates the residual of the energy conservation equation based on the input parameters, and the value of the constraint kernel function decays as the residual increases; Monte Carlo simulations are performed using the resource quantity prediction model, and extrapolation results are based on the dual-indicator risk assessment. The extrapolation results based on the dual-indicator risk assessment include: defining the risk index as the weighted sum of the normalized prediction variance and the energy conservation residual; calculating the critical threshold of the risk index on the training set; in the Monte Carlo simulation, if the risk index of a sample exceeds the critical threshold, it is marked as a high-risk sample. Based on the information gain from the new data, the resource quantity prediction model is iteratively updated and version managed.

2. The probabilistic geothermal resource evaluation method based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes as described in claim 1, characterized in that, Constructing an enhanced temperature field includes: Assume that both the synthesized temperature field data and the measured temperature data follow a Gaussian distribution; Using a weighted Bayesian inference framework, the synthetic temperature field data is fused with the measured temperature data to obtain the fused posterior mean and variance, which serve as the enhanced temperature field and its uncertainty quantification results.

3. The probabilistic geothermal resource evaluation method based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes as described in claim 2, characterized in that, Probabilistic distribution modeling and sampling verification of evaluation parameters based on physical constraints include: The coupling relationship between permeability and porosity was established based on the Kozeny-Carman equation; Establish the coupling relationship between temperature and depth based on the physical reasonable range of the geothermal gradient; During Monte Carlo sampling, each set of sampling parameters is validated according to the coupling relationship, and parameter combinations that violate the coupling relationship are rejected.

4. The probabilistic geothermal resource evaluation method based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes as described in claim 3, characterized in that, Adaptive selection of samples to generate high-fidelity simulated training data includes: A fixed experimental design method was used to select initial sample points and train the initial surrogate model. Based on the initial surrogate model, the prediction uncertainty of candidate sample points is calculated in the parameter space; The candidate sample points with the greatest prediction uncertainty are selected for high-fidelity simulation, and the results are added to the training set to update the surrogate model.

5. The probabilistic geothermal resource evaluation method based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes as described in claim 1, characterized in that, Iterative updates and version management of the resource quantity prediction model include: Calculate the key parameter distribution shifts and the proportion of new samples caused by the new data; When the distribution drift or the proportion of newly added samples exceeds a preset threshold, the full retraining of the resource quantity prediction model is triggered. Record the version information for each model update.

6. A probabilistic geothermal resource evaluation system based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes, characterized in that, The system is used to implement the probabilistic geothermal resource assessment method based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes as described in any one of claims 1-5, the system comprising: The temperature field fusion modeling module is used to construct an enhanced temperature field that integrates synthetic temperature field and measured data, and to quantify its uncertainty. The parameter probabilistic modeling module is used to perform probabilistic distribution modeling and sampling verification of evaluation parameters based on physical constraint relationships. An adaptive sampling module is used to adaptively select samples to generate high-fidelity simulation training data based on the prediction uncertainty of the surrogate model. The surrogate model training module is used to train a Gaussian process surrogate model with embedded physical constraint penalty terms to obtain a resource quantity prediction model. The risk assessment and simulation module is used to perform Monte Carlo simulation using the resource quantity prediction model and extrapolate the results based on the dual-indicator risk assessment. The iterative update management module is used to iteratively update and manage the version of the resource quantity prediction model based on the information gain of the new data.

7. An electronic device, characterized in that, The electronic device includes: a processor and a memory storing computer program instructions; When the processor executes the computer program instructions, it implements the probabilistic geothermal resource evaluation method based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes as described in any one of claims 1-5.

8. A computer storage medium, characterized in that, The computer storage medium stores computer program instructions, which, when executed by a processor, implement the probabilistic geothermal resource evaluation method based on weighted Bayesian fusion and energy conservation-constrained Gaussian processes as described in any one of claims 1-5.

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