Mineral exploration prediction method based on piecewise linear function and PU hybrid expert network

Abstract

This invention relates to the fields of mineral resource prediction and machine learning technology, and provides a mineral exploration prediction method based on piecewise linear functions and a hybrid expert network (PU). The method includes the following steps: quantification of key ore-controlling elements; integration of geological and geochemical data; construction and training of a mineral exploration prediction model: constructing a hybrid expert network composed of an expert network and a gating network, and introducing non-negative risk estimation loss and load balancing loss from the PU learning strategy to train the hybrid expert network; and prediction of the mineralization potential of the target area. This invention transforms the spatial relationships of key ore-controlling elements into quantified functions with clear geological significance through piecewise linear functions, solving the problem of geological feature representation. Furthermore, this invention constructs a hybrid expert network based on the PU learning strategy, which overcomes the problem of missing negative samples while adaptively capturing the spatial heterogeneity of mineralization patterns using the expert network mechanism, thereby significantly improving the accuracy and reliability of mineral exploration prediction.

Description

Technical Field

[0001] This invention belongs to the field of mineral resource prediction and machine learning technology, and in particular relates to a mineral exploration prediction method based on piecewise linear functions and PU hybrid expert networks. Background Technology

[0002] Mineral Prospectivity Mapping (MPM) is an important method for delineating potential mineral exploration targets using multi-source data from geology, geophysics, geochemistry, and remote sensing. In recent years, with the rapid accumulation of these various types of data, MPM has entered the era of big data in earth sciences, and machine learning and deep learning algorithms have been widely applied in this field. Currently, the MPM process driven by geological and geochemical big data can be summarized as follows: First, ore-controlling elements (descriptive information) such as stratigraphy, structure, and igneous rocks are quantified and transformed into a form that can be processed by machine learning and deep learning. This data is then merged with numerical geochemical data to form a dataset of mineral exploration characteristic variables. Subsequently, a mineral exploration prediction model is constructed by selecting appropriate algorithms, and the dataset is processed and analyzed to extract the hidden mineral exploration information.

[0003] Currently, there are two main approaches to quantifying ore-controlling factors: one is to embed the ore-controlling factors into the model training process in an explicit mathematical form, such as constructing an empirical function between known ore deposits and ore-controlling factors based on singularity analysis or fractal theory, and then introducing this function as a loss function into the network training; the other is to explicitly transform the ore-controlling factors into input features that the model can learn, such as mapping geological attributes to spatial raster images or semantic features.

[0004] In constructing mineral exploration prediction models, commonly used algorithms include random forests, support vector machines, deep autoencoders, and graph neural networks. Among these, supervised algorithms such as random forests and support vector machines are limited by the scarcity of positive samples (anomalies) and the difficulty in reliably defining negative samples (background), resulting in low reliability of mineral exploration predictions. While algorithms such as deep autoencoders and graph neural networks can identify anomalies deviating from the background by calculating reconstruction errors, their high reconstruction errors do not necessarily correspond to mineralization anomalies, and there is still a lack of clear criteria to determine whether the results truly reflect the mineralization process. Furthermore, regardless of the type of model used, most are essentially global optimization models, implicitly assuming that the mineralization patterns are uniform across the entire area. However, under complex geological conditions, mineralization often exhibits significant spatial heterogeneity, making it difficult for a single model to adaptively adjust the weights of different ore-controlling elements spatially, thus limiting prediction accuracy.

[0005] In summary, the existing technology has the following three main shortcomings that need to be addressed:

[0006] 1. The quantification of ore-controlling factors is not reasonable enough. Embedding geological constraints into the model training process in an explicit mathematical form makes the prediction results heavily influenced by prior knowledge, which to some extent obscures the true mineralization information in the data and ignores the heterogeneity of mineralization processes. On the other hand, mapping geological attributes to spatial raster images or semantic feature expressions often fails to effectively distinguish between mineralization and non-mineralization geological processes, and may introduce spatial patterns that are irrelevant to mineralization or even misleading.

[0007] 2. For supervised learning algorithms such as random forests and support vector machines, selecting training samples is quite difficult, especially the selection of negative (background) samples. Inappropriate sample selection will severely impact the predictive ability of the mineral exploration prediction model.

[0008] 3. For unsupervised methods such as deep autoencoders and graph neural networks, there is still a lack of clear criteria for judging whether their results truly reflect the mineralization process. Furthermore, the global, single model built based on such algorithms is difficult to adapt to the spatial heterogeneity of mineralization, i.e., different regions are dominated by different geological factors. Mineralization is usually constrained by multiple ore-controlling factors, and the degree of dominance of each factor is unevenly distributed spatially. If this is not fully considered when constructing mineral exploration prediction models, it can easily lead to biased prediction results. Summary of the Invention

[0009] The purpose of this invention is to provide a mineral exploration prediction method based on piecewise linear functions and PU hybrid expert networks, aiming to solve the above-mentioned technical problems.

[0010] This invention is implemented as follows: a mineral exploration prediction method based on piecewise linear functions and a PU hybrid expert network, comprising the following steps:

[0011] Quantification of key ore-controlling elements: Obtain key ore-controlling elements of the target mineral in the target area. Based on the known spatial distance statistical relationship between the ore deposit and the ore-controlling elements, construct a piecewise linear function to convert the geometric distance from the sample point to the ore-controlling element into a quantitative value that reflects the decay of the mineralization probability, and generate ore-controlling element quantitative data.

[0012] Geological and geochemical data integration: Preprocessing the raw geochemical data to extract ore-forming element combination data related to the target mineral type; fusing and standardizing the ore-forming element combination data with the ore-controlling element quantitative data to generate a mineral exploration characteristic variable dataset;

[0013] Construct and train a mineral exploration prediction model: Construct a hybrid expert network consisting of an expert network and a gated network, introduce the non-negative risk estimation loss in the PU learning strategy and the load balancing loss of the hybrid expert network, and train the hybrid expert network based on a weighted random sampling strategy to obtain a mineral exploration prediction model;

[0014] Mineral potential prediction for the target area: Based on the trained mineral exploration prediction model, the mineral probability value of each sample point is predicted according to the mineral exploration feature variable dataset of the target area.

[0015] Furthermore, the steps for quantifying the key mineral control elements specifically include:

[0016] Based on the metallogenic regularity of the target mineral and the regional geological background, determine the key ore-controlling elements of the target mineral;

[0017] For each key ore-controlling element, calculate the Euclidean distance from each known ore deposit within the target area to the nearest ore-controlling element, forming a spatial distance set;

[0018] A survival function is constructed for the set of spatial distances; the value of the survival function decreases monotonically as the spatial distance independent variable increases, reflecting the nonlinear decay law of the ore-controlling effect with spatial distance;

[0019] The value of the survival function and the spatial distance independent variable are transformed into a double logarithmic coordinate system, and piecewise linear fitting is performed to obtain a piecewise linear function. The optimal number of segments and inflection points are automatically determined using the Bayesian information criterion.

[0020] For any sample point, measure its Euclidean distance to the ore-controlling element, select the parameters of the corresponding piecewise linear function according to the interval in which the Euclidean distance is located, calculate the basic quantified value, and perform normalization processing to generate quantified data of the ore-controlling element.

[0021] Furthermore, the expression for the survival function is: ;in, For the survival function value, Let be the cumulative distribution function. Let spatial distance be an arbitrarily set independent variable. Represents the set of spatial distances In the middle, the distance value is greater than The proportion of mineral deposit samples.

[0022] Furthermore, the expression for the piecewise linear function is: ;in, , All of these are parameters of the piecewise linear function, referring to the first... The slope and intercept of a piecewise linear function;

[0023] The formula for calculating the basic quantization value is: ;in, For the i-th sample point Basic quantization value, For the i-th sample point Euclidean distance to ore-controlling elements.

[0024] Furthermore, the steps for integrating the geological and geochemical data specifically include:

[0025] The original geochemical data were preprocessed using the central logarithmic ratio transformation method to obtain preprocessed geochemical data.

[0026] Multivariate statistical analysis was used to extract ore-forming elements and associated element combinations related to the target mineral from the preprocessed geochemical data, thus obtaining ore-forming element combination data;

[0027] The quantitative data of the ore-controlling elements and the combination data of the ore-forming elements are combined and merged to obtain a fused dataset.

[0028] The Z-score standardization method is used to standardize all variables in the fused dataset to generate a mineral exploration feature variable dataset.

[0029] Furthermore, the expert network consists of multiple multilayer perceptrons with identical structures, and its last layer outputs the mineralization probability value through the Sigmoid activation function;

[0030] The gated network is used to dynamically generate the weight coefficients of each expert network based on the input mineral exploration feature variable dataset.

[0031] Furthermore, the expression for the non-negative risk estimation loss in the PU learning strategy is as follows:

[0032] ;

[0033] in, Estimate losses for non-negative risk; This represents the prior probability of mineralization within the target area, reflecting the overall mineralization density of the area. This represents the sample mineralization probability value output by the mineral exploration prediction model; This represents the loss when a positive sample is correctly predicted as positive. This represents the loss when unlabeled samples are considered negative. This is a correction term used to offset the bias caused by treating potentially positive samples in unlabeled samples as negative samples;

[0034] The expression for the load balancing loss is as follows:

[0035] ;

[0036] in, For load balancing losses; The number of expert networks; It is the arithmetic mean of the probability weights of all samples in the current training batch assigned to the nth expert network in the gating network.

[0037] Furthermore, the weighted random sampling strategy is as follows: count the total number of unlabeled samples and positive samples in the whole region, fix the basic sampling weight of unlabeled samples to 1.0, and set the sampling weight of positive samples to the ratio of "the total number of unlabeled samples divided by the total number of positive samples". During the model training process, random sampling with replacement is performed according to this fixed weight to generate training batches.

[0038] Furthermore, the method for determining the mineralization prior probability is as follows: set a candidate interval, traverse the candidate interval with a fixed step size, train multiple mineral exploration prediction models, and count the total loss function value and AUC value of each mineral exploration prediction model on the validation set. Select the prior probability value corresponding to the stable AUC value and the minimum fluctuation of the total loss function value as the final mineralization prior probability.

[0039] The training process of the mineral exploration prediction model also includes: automatically optimizing the model hyperparameters using a Bayesian optimization algorithm based on tree-based Parzen estimation; and adopting an early termination strategy with dual-index joint verification to monitor the AUC value and total loss function value of the validation set in real time. If the AUC value no longer increases or the total loss function value no longer decreases during multiple consecutive training rounds, the training is terminated early, and the optimal mineral exploration prediction model is output.

[0040] Another objective of this invention is to provide a mineral exploration prediction system based on piecewise linear functions and a PU hybrid expert network, for implementing the aforementioned mineral exploration prediction method based on piecewise linear functions and a PU hybrid expert network, specifically including:

[0041] The mineral control element quantification module is used to obtain the key mineral control elements of the target mineral in the target area. Based on the known spatial distance statistical relationship between the mineral deposit and the mineral control element, a piecewise linear function is constructed to convert the geometric distance from the sample point to the mineral control element into a quantitative value that reflects the decay of the mineralization probability, and generate mineral control element quantification data.

[0042] The data integration module is used to preprocess the raw geochemical data and extract the ore-forming element combination data related to the target mineral type; and to fuse and standardize the ore-forming element combination data with the ore-controlling element quantitative data to generate a mineral exploration characteristic variable dataset.

[0043] The model building and training module is used to build a hybrid expert network consisting of an expert network and a gated network. It introduces the non-negative risk estimation loss in the PU learning strategy and the load balancing loss of the hybrid expert network. Based on the weighted random sampling strategy, the hybrid expert network is trained to obtain the mineral exploration prediction model.

[0044] The mineral potential prediction module is used to predict the mineralization probability value of each sample point based on the trained mineral exploration prediction model and the mineral exploration feature variable dataset of the target area.

[0045] The mineral exploration prediction method based on piecewise linear functions and a hybrid expert network (PU) provided by this invention uses piecewise linear functions to quantify key ore-controlling elements, which can accurately reflect the nonlinear decay law of ore-controlling effects with distance, giving the modeling data clear geological significance. The hybrid expert network architecture of this invention can adaptively identify the dominant ore-controlling elements at different locations within the target area, and the prediction results are more realistic compared to a single global model. In addition, this invention also introduces a PU learning strategy to avoid the bias caused by manually specifying negative samples. Especially in mineral exploration prediction under deep and complex geological conditions, it can effectively identify potential ore-causing anomalies that are misjudged as background. Attached Figure Description

[0046] Figure 1 This is a flowchart illustrating the mineral exploration prediction method based on piecewise linear functions and PU hybrid expert networks provided in an embodiment of the present invention.

[0047] Figure 2 The ROC curve is used to evaluate the model's performance.

[0048] Figure 3 A map showing the predicted mineralization potential calculated by the model. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0050] Currently, mineral prospect prediction methods driven by Earth science big data still have some problems in utilizing prior geological knowledge to constrain basic data and model construction. These problems mainly manifest in two aspects: unreasonable quantification of ore-controlling elements and insufficient theoretical basis for model construction. To address these issues, this invention proposes a mineral prospecting prediction method based on piecewise linear functions and a Positive-Unlabeled Mixture of Experts (PUMoE) network, aiming to improve the prediction results. This method first transforms the spatial relationships of ore-controlling elements into quantifiable functions with clear geological significance using piecewise linear functions, solving the problem of geological feature expression. Then, it constructs PUMoE, which overcomes the problem of missing negative samples while adaptively capturing the spatial heterogeneity of mineralization patterns using an expert network mechanism, thereby significantly improving the accuracy and reliability of mineral prospecting prediction.

[0051] Specifically, such as Figure 1 As shown, in one embodiment of the present invention, a mineral exploration prediction method based on a piecewise linear function and a PU hybrid expert network is provided, comprising the following steps:

[0052] S1. Quantification of key ore-controlling elements: Obtain key ore-controlling elements of the target mineral in the target area. Based on the known spatial distance statistical relationship between the ore deposit (i.e., mineral occurrence) and the ore-controlling elements, construct a piecewise linear function to convert the geometric distance from the sample point to the ore-controlling element into a quantitative value reflecting the decay of the mineralization probability, and generate ore-controlling element quantitative data. It should be noted that ore-controlling elements refer to the key geological factors that control the formation, location and distribution of ore deposits.

[0053] S2. Geological and Geochemical Data Integration: Preprocess the raw geochemical data to extract ore-forming element combination data related to the target mineral type; integrate and standardize the ore-forming element combination data with the ore-controlling element quantitative data to generate a mineral exploration characteristic variable dataset.

[0054] S3. Construct and train the mineral exploration prediction model: Construct a hybrid expert network (MoE) consisting of an expert network and a gated network, introduce the non-negative risk estimation loss in the PU learning strategy and the load balancing loss of the hybrid expert network, and train the hybrid expert network based on a weighted random sampling strategy to obtain the mineral exploration prediction model.

[0055] S4. Mineral potential prediction of the target area: Based on the trained mineral exploration prediction model, the mineralization probability value of each sample point is predicted according to the mineral exploration characteristic variable dataset of the target area; in addition, a mineral potential prediction map of the target area can be drawn according to the mineralization probability value.

[0056] In a preferred embodiment of the present invention, the step of quantifying the key mineral control elements specifically includes:

[0057] (1) Based on the metallogenic regularity of the target mineral and the regional geological background, determine the key ore-controlling elements of the target mineral;

[0058] Specifically, by conducting in-depth analysis of the metallogenic regularity and regional geological background of the target mineral in the target area, the key ore-controlling elements of the target mineral, such as faults, structures, and igneous rocks, can be identified.

[0059] (2) For each key ore-controlling element, calculate the Euclidean distance from each known ore deposit in the target area to the nearest ore-controlling element, and form a spatial distance set;

[0060] (3) Construct the survival function of the spatial distance set; the value of the survival function decreases monotonically as the spatial distance independent variable increases, reflecting the nonlinear decay law of the ore-controlling effect with spatial distance;

[0061] Specifically, the expression for the survival function is: ;in, For the survival function value, Let be the cumulative distribution function. Let spatial distance be an arbitrarily set independent variable. Represents the set of spatial distances In the middle, the distance value is greater than The proportion of mineral deposit samples; compared with the traditional cumulative distribution function In comparison, this survival function has a more intuitive geological interpretation: its value decreases monotonically with the increase of distance r, directly reflecting the geological law that "the closer to the ore-controlling element, the higher the probability of mineralization", and also reflecting the nonlinear decay law of the ore-controlling effect of geological ore-controlling elements with spatial distance.

[0062] (4) Transform the value of the survival function and the spatial distance independent variable to a double logarithmic coordinate system. In this process, piecewise linear fitting is performed to obtain piecewise linear functions, and the optimal number of segments and inflection points are automatically determined using the Bayesian Information Criterion (BIC) to avoid the subjectivity of manual segmentation. Different numbers of segmented inflection points are set, and piecewise linear fitting is performed under logarithmic coordinates. The BIC value of the corresponding fitted model is calculated, and the number of segments and inflection points corresponding to the model with the smallest BIC value are selected as the optimal parameters.

[0063] Specifically, for each segment of a linear function The expression for the fitted piecewise linear function is: ;in, , All of these are parameters of the piecewise linear function, referring to the first... The slope and intercept of a piecewise linear function.

[0064] (5) For any sample point Measure its Euclidean distance to the ore-controlling elements. The parameters of the corresponding piecewise linear function are selected based on the interval containing the Euclidean distance. , The value corresponding to the survival function is calculated as the basic quantification value and normalized to generate quantification data of ore-controlling elements.

[0065] Specifically, the formula for calculating the basic quantization value is as follows: ;in, This is the basic quantization value for the i-th sample point. For the i-th sample point The Euclidean distance to the ore-controlling element; the normalized formula is as follows:

[0066] ;

[0067] in, and These represent the minimum and maximum values ​​of the baseline quantized values ​​for all sample points, respectively. The normalized quantized values ​​for all sample points in the entire region. The collection constitutes the data of mineral control elements. .

[0068] In a preferred embodiment of the present invention, the step of integrating geological and geochemical data specifically includes:

[0069] (1) To eliminate the closure effect of geochemical data, the central logarithmic ratio transformation (clr) method was used to preprocess the original geochemical data to obtain preprocessed geochemical data; the specific formula of the central logarithmic ratio transformation method is as follows:

[0070] ;

[0071] in, ; Representing the The elemental content vector of each sample; For the first The first sample The content of each element; This represents the total number of sample points within the target area. The total number of elements involved in the calculation; It is the first All of the samples The geometric mean of the content of each element.

[0072] (2) Multivariate statistical analysis methods (such as factor analysis and cluster analysis) are used to extract the ore-forming elements and associated element combinations related to the target mineral from the preprocessed geochemical data to obtain ore-forming element combination data, which are used as input variables for geochemical characteristics. .

[0073] (3) The quantitative data of the ore-controlling elements and the combination data of the ore-forming elements are combined to obtain a fused dataset.

[0074] (4) The Z-score standardization method is used to standardize all variables in the fused dataset to generate a mineral exploration feature variable dataset;

[0075] Specifically, for any variable in the dataset, let its value at the i-th sample point be... The standardized formula is: , In the formula, The standardized feature value of this variable for the i-th sample point; and These represent the mean and standard deviation of the variable across all samples in the entire region, respectively. Using this standardization formula, all variables in the dataset are uniformly converted to a mean of 0 and a standard deviation of 1, eliminating dimensional differences between different data points and forming the final dataset of mineral exploration characteristic variables. , as input to the subsequent model.

[0076] In a preferred embodiment of the present invention, the mineral exploration prediction model is a hybrid expert network based on positive samples and unlabeled samples (PU), denoted as the PUMoE model. The hybrid expert network (MoE) consists of multiple expert networks and a gating network, with the specific architecture as follows:

[0077] Input layer: Receives a dataset of mineral exploration feature variables. ;

[0078] Expert Network: By It consists of three identical multilayer perceptrons (MLPs), whose last layer outputs a mineralization probability value through a sigmoid activation function, denoted as: The mapping relationship of each sub-region in the feature space is learned separately, that is, different mining control modes are captured;

[0079] Gated networks: Gated networks can adjust the input mineral exploration feature variables based on the given dataset. The system learns and determines which mineral-controlling factors primarily govern the region, thereby dynamically generating the weight coefficients for each expert network. The gating coefficients for each expert network are... ;

[0080] Output layer: The final output value P is the weighted sum of the outputs of all experts. ,in, This represents the mineralization probability value predicted by the nth expert network for sample point x belonging to a positive sample (known mineral deposit).

[0081] In a preferred embodiment of the present invention, to address the problem of scarce positive samples (anomalies) and a lack of reliable negative samples (background), this embodiment introduces a PU learning strategy, employing a non-negative risk estimate (nnPU Risk Estimator) as the basic loss function. Specifically, the expression for the non-negative risk estimation loss in the PU learning strategy is as follows:

[0082] ;

[0083] in, Estimate losses for non-negative risk; This represents the prior probability of mineralization within the target area, reflecting the overall mineralization density of the area. This represents the sample mineralization probability value output by the mineral exploration prediction model; This represents the loss when a positive sample is correctly predicted as positive. This represents the loss when unlabeled samples are considered negative. This is a correction term used to offset the bias caused by treating potentially positive samples in unlabeled samples as negative samples; in embodiments of the present invention, , , Both can be empirically estimated using binary cross-entropy loss.

[0084] Specifically, for example, the formula for calculating positive sample loss is: ;in, The number of positive samples. This represents the predicted probability of positive samples; the same applies to other loss terms. In actual model training, to avoid gradient vanishing, in... Introduce a small constant term (e.g., 10) into the term. -4 )prevent This item is 0.

[0085] It is worth noting that when only using When used as a loss function for a network, it can easily lead to a "winner-takes-all" phenomenon in hybrid expert networks during training (i.e., all samples are assigned to a single expert network, causing MoE to lose its ability to capture spatial heterogeneity). To address this, this embodiment of the invention also introduces load balancing loss to construct a joint training framework.

[0086] Specifically, the expression for load balancing loss is as follows:

[0087] ;

[0088] in, For load balancing losses; The number of expert networks; It is the arithmetic mean of the probability weights of all samples in the current training batch assigned to the nth expert network in the gating network; The target is a uniform distribution. This loss term forces the gating network to distribute samples evenly among the expert networks by minimizing the mean square error between the average weights of each expert and the target uniform distribution, ensuring that each expert is adequately trained.

[0089] Ultimately, the total loss function of the PUMoE model Defined as:

[0090] ;

[0091] in, The balancing coefficient ranges from 0.1 to 1.0 and can be optimized and determined based on the actual situation of the target area and the model validation effect; in this embodiment of the invention, the preferred value is... This ensures that the model accurately learns the mineralization patterns while effectively avoiding polarization in the expert network.

[0092] In a preferred embodiment of the present invention, the training process of the mineral exploration prediction model (i.e., the PUMoE model) specifically includes:

[0093] (1) Model input vector: The above mineral exploration feature variable dataset As input to the subsequent PUMoE model.

[0094] (2) Sample set construction and weighted random sampling: Known mineral deposits (points) within the target area and regional geochemical sample points within a set distance threshold range are defined as positive samples (P), labeled as y=1; at the same time, all regional geochemical sample points within the target area other than the positive sample area are regarded as unlabeled samples (U) and are not labeled. Given the extreme scarcity of positive samples in mineral exploration prediction, this embodiment of the invention adopts a weighted random sampling strategy when constructing the data loader: the total number of unlabeled samples and positive samples in the whole area is counted; the sampling base weight of unlabeled samples is fixed at 1.0, and the sampling weight of positive samples is set as the ratio of "the total number of unlabeled samples divided by the total number of positive samples". In the subsequent training process, the model performs random sampling with replacement according to this fixed weight to generate training batches. This weight allocation mechanism makes the expected occurrence frequency of positive samples and unlabeled samples in each training batch tend to be balanced, effectively solving the gradient shift problem caused by the scarcity of positive samples. Before network training, the constructed sample set is randomly divided into training set and validation set according to a set ratio (e.g., 8:2). The training set is used to update model parameters, while the validation set is used for sensitivity analysis of mineralization prior probabilities and evaluation of early termination strategies.

[0095] (3) Determination of prior probability of mineralization: Since PU learning is subject to prior probability The impact is significant. This embodiment of the invention employs a sensitivity analysis method based on the inflection point of the validation set performance to determine the prior probability of mineralization. First, set... The candidate interval (e.g., [0.01, 0.2]) is then traversed with a fixed step size (e.g., 0.01). Candidate intervals were identified, and multiple PUMoE models were trained. The loss function and AUC values ​​of each model on the validation set were then calculated. The model whose AUC value stabilized and whose loss function value fluctuated the least was selected. The value is used as the final prior probability of mineralization in the target area. This step ensures the model's adaptability to the scarcity of positive samples.

[0096] (4) Training and evaluation of the PUMoE model: The labeled sample set (P and U) is input into the PUMoE model. The gating network adaptively calculates the values ​​based on the features of each sample point x. The weight coefficients of each expert network During model training, a Bayesian optimization algorithm based on Tree-structured Parzen Estimator (TPE) is used to automatically optimize hyperparameters such as the number of network layers and nodes to obtain the optimal model structure. The total loss function, composed of non-negative risk estimation (nnPU) and load balancing loss, is used for model training. To prevent overfitting, this invention employs an early stopping strategy with dual-index joint validation: the area under the curve (AUC) of the validation set and the total loss function value are monitored in real time. If the AUC of the validation set no longer increases or the total loss of the validation set no longer decreases after 10 consecutive training rounds, training is terminated early, and the optimal model is output. After model training, the Receiver Operating Characteristic (ROC) curve and AUC value are used as core evaluation indicators to quantitatively assess the model's mineral exploration prediction performance. The closer the AUC value is to 1, the stronger the model's ability to distinguish between mineralized positive samples and unlabeled background samples, and the higher the mineral exploration prediction accuracy.

[0097] After the model training is completed, the mineral exploration characteristic variable dataset of all sample points in the target area will be generated. Input the trained mineral exploration prediction model (i.e., the PUMoE model), and the model outputs the predicted value for each sample point. This represents the probability that the point belongs to the "positive sample," i.e., the mineralization probability value. A mineralization potential prediction map is drawn based on the levels of these mineralization probability values.

[0098] Example 1: Taking the prospecting and prediction of skarn-type lead-zinc deposits in Guiyang area, Hunan Province as an example, the specific implementation process of the method provided in this embodiment of the invention is illustrated as follows:

[0099] I. Quantification of Lead-Zinc Ore-Controlling Elements: Collect basic geological data of the target area, including geological maps, exploration data of typical mineral deposits, and relevant academic papers and monographs.

[0100] Based on prior geological knowledge of skarn-type lead-zinc deposits in the target area, fault structures and the contact zone between intermediate-acidic magmatic rocks and carbonate rocks are identified as key ore-controlling elements.

[0101] The distances from known lead-zinc deposits (points) within the target area to the nearest fault and contact zone were calculated, and survival functions were constructed and fitted in a double logarithmic coordinate system. The results show that fault-controlled ore deposits exhibit a four-stage attenuation characteristic (the inflection points of the piecewise linear function are approximately 0.3 km, 2.4 km, and 3.9 km), reflecting different stages from direct ore control to secondary influences. Contact zone-controlled ore deposits exhibit a three-stage attenuation characteristic (the inflection points of the piecewise linear function are approximately 0.3 km and 1.3 km).

[0102] Using the piecewise linear function obtained by fitting, the basic quantitative values ​​of fracture and contact zone of 1863 sample points in the whole area were calculated and normalized to the [0,1] interval.

[0103] II. Data Integration of Characteristic Variables for Skarn-Type Lead-Zinc Deposits: 1:200,000 stream sediment geochemical data were collected for the target area. The central logarithmic ratio transformation method was used to process the regional geochemical data to eliminate the "closure effect." Factor analysis and cluster analysis identified Pb-Zn-Cu-Cd-Au-Bi-Mo as the main ore-forming element assemblage. The basic quantitative values ​​of fractures and contact zones from 1863 sample points in the target area were combined with the ore-forming element assemblage data to form a dataset of characteristic variables for skarn-type lead-zinc deposits. Z-score standardization was then performed to eliminate dimensional differences between variables.

[0104] III. Construction of the skarn-type lead-zinc deposit prospecting prediction model (i.e., the PUMoE model), as detailed below:

[0105] Input: The dataset of prospecting feature variables of skarn-type lead-zinc deposits is used as input.

[0106] Positive sample definition: 81 samples were selected from within a 1.5 km radius of the known ore deposit, and the remaining 1782 samples were unlabeled samples.

[0107] Model Training: A Bayesian optimization algorithm based on TPE was used to jointly search for key hyperparameters, including the number of expert networks (n_experts), the number of hidden layer neurons (hidden_dim), the number of network layers (MoE_layers), the batch size, the learning rate, and the dropout rate. The hyperparameter search range was set as follows: 2-5 expert networks, 16-128 hidden layer neurons, 2-5 network layers, 16-128 batch sizes, and a learning rate of 1×10⁻⁶. -5 -1×10 -2 The dropout rate is 0.1-0.4. The final network structure consists of 3 expert networks, each containing 4 hidden layers and 54 neurons. The dropout rate is 0.23, and the learning rate is 5×10⁻⁶.-4 The training batch size was 64. A total loss function weighted by nonnegative risk estimation (nnPU) and load balancing loss was used for model training. Sensitivity analysis was used to determine the prior probability of mineralization. .

[0108] Results: The trained model achieved an AUC of 0.93 on the validation set. The ROC curve for model performance evaluation is shown below. Figure 2 .

[0109] IV. Application of the Skarn-type Lead-Zinc Deposit Prospecting Prediction Model: After the model training is completed, the mineralization characteristic variable dataset of 1863 sample points in the target area is input into the model, and then the predicted lead-zinc mineralization value, i.e., the mineralization probability, is output for each sample point. Combined with the spatial coordinates of the sample points in the target area, a spatial visualization method is used to draw a predicted mineralization potential map of the entire area (see...). Figure 3 In the diagram, the color levels from low to high correspond to mineralization potential from weak to strong.

[0110] V. Model Performance Evaluation: The prediction results of lead-zinc mineralization potential in the target area show that the high mineralization probability zones identified by the method proposed in this invention have excellent spatial correspondence with known deposits (points). The vast majority of deposits (points) are located within the high probability zones, and there are relatively few meaningless anomalous areas (see...). Figure 3 This indicates that, under multiple constraints of geological and geochemical variables, the PUMoE framework can capture different dominant mineralization models through different expert networks, making the prediction results more instructive for exploration.

[0111] In another embodiment of the present invention, a mineral exploration prediction system based on piecewise linear functions and a PU hybrid expert network is also provided to implement the above-mentioned mineral exploration prediction method based on piecewise linear functions and a PU hybrid expert network, specifically including:

[0112] The mineral control element quantification module is used to obtain the key mineral control elements of the target mineral in the target area. Based on the known spatial distance statistical relationship between the mineral deposit and the mineral control element, a piecewise linear function is constructed to convert the geometric distance from the sample point to the mineral control element into a quantitative value that reflects the decay of the mineralization probability, and generate mineral control element quantification data.

[0113] The data integration module is used to preprocess the raw geochemical data and extract the ore-forming element combination data related to the target mineral type; and to fuse and standardize the ore-forming element combination data with the ore-controlling element quantitative data to generate a mineral exploration characteristic variable dataset.

[0114] The model building and training module is used to build a hybrid expert network consisting of an expert network and a gated network. It introduces the non-negative risk estimation loss in the PU learning strategy and the load balancing loss of the hybrid expert network. Based on the weighted random sampling strategy, the hybrid expert network is trained to obtain the mineral exploration prediction model.

[0115] The mineral potential prediction module is used to predict the mineralization probability value of each sample point based on the trained mineral exploration prediction model and the mineral exploration feature variable dataset of the target area.

[0116] It should be noted that each of the above modules can be implemented as a computer program, which can run on a computer device. The computer device's memory can store the computer program that makes up each module, enabling the processor to execute each step of the above method.

[0117] It should be understood that although the steps in the flowcharts of the various embodiments of the present invention are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the various embodiments may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps.

[0118] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory.

[0119] The above embodiments merely illustrate several implementation methods of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this patent should be determined by the appended claims.

Claims

1. A mineral exploration prediction method based on piecewise linear functions and a PU hybrid expert network, characterized in that, Includes the following steps: Quantification of key ore-controlling elements: Obtain key ore-controlling elements of the target mineral in the target area. Based on the known spatial distance statistical relationship between the ore deposit and the ore-controlling elements, construct a piecewise linear function to convert the geometric distance from the sample point to the ore-controlling element into a quantitative value that reflects the decay of the mineralization probability, and generate ore-controlling element quantitative data. Geological and geochemical data integration: Preprocessing the raw geochemical data to extract ore-forming element combination data related to the target mineral type; fusing and standardizing the ore-forming element combination data with the ore-controlling element quantitative data to generate a mineral exploration characteristic variable dataset; Construct and train a mineral exploration prediction model: Construct a hybrid expert network consisting of an expert network and a gated network, introduce the non-negative risk estimation loss in the PU learning strategy and the load balancing loss of the hybrid expert network, and train the hybrid expert network based on a weighted random sampling strategy to obtain a mineral exploration prediction model; Mineral potential prediction for the target area: Based on the trained mineral exploration prediction model, the mineral probability value of each sample point is predicted according to the mineral exploration feature variable dataset of the target area.

2. The mineral exploration prediction method based on piecewise linear functions and PU hybrid expert networks according to claim 1, characterized in that, The steps for quantifying the key mineral control elements specifically include: Based on the metallogenic regularity of the target mineral and the regional geological background, determine the key ore-controlling elements of the target mineral; For each key ore-controlling element, calculate the Euclidean distance from each known ore deposit within the target area to the nearest ore-controlling element, forming a spatial distance set; A survival function is constructed for the set of spatial distances; the value of the survival function decreases monotonically as the spatial distance independent variable increases, reflecting the nonlinear decay law of the ore-controlling effect with spatial distance; The value of the survival function and the spatial distance independent variable are transformed into a double logarithmic coordinate system, and piecewise linear fitting is performed to obtain a piecewise linear function. The optimal number of segments and inflection points are automatically determined using the Bayesian information criterion. For any sample point, measure its Euclidean distance to the ore-controlling element, select the parameters of the corresponding piecewise linear function according to the interval in which the Euclidean distance is located, calculate the basic quantified value, and perform normalization processing to generate quantified data of the ore-controlling element.

3. The mineral exploration prediction method based on piecewise linear functions and PU hybrid expert networks according to claim 2, characterized in that, The expression for the survival function is: ;in, For the survival function value, Let be the cumulative distribution function. Let spatial distance be an arbitrarily set independent variable. Represents the set of spatial distances In the middle, the distance value is greater than The proportion of mineral deposit samples.

4. The mineral exploration prediction method based on piecewise linear functions and PU hybrid expert networks according to claim 3, characterized in that, The expression for the piecewise linear function is: ;in, , All of these are parameters of the piecewise linear function, referring to the first... The slope and intercept of a piecewise linear function; The formula for calculating the basic quantization value is as follows: ;in, For the i-th sample point Basic quantization value, For the i-th sample point Euclidean distance to ore-controlling elements.

5. The mineral exploration prediction method based on piecewise linear functions and PU hybrid expert networks according to claim 1, characterized in that, The steps for integrating the geological and geochemical data specifically include: The original geochemical data were preprocessed using the central logarithmic ratio transformation method to obtain preprocessed geochemical data. Multivariate statistical analysis was used to extract ore-forming elements and associated element combinations related to the target mineral from the preprocessed geochemical data, thus obtaining ore-forming element combination data; The quantitative data of the ore-controlling elements and the combination data of the ore-forming elements are combined and merged to obtain a fused dataset. The Z-score standardization method is used to standardize all variables in the fused dataset to generate a mineral exploration feature variable dataset.

6. The mineral exploration prediction method based on piecewise linear functions and PU hybrid expert networks according to claim 1, characterized in that, The expert network consists of multiple multilayer perception mechanisms with the same structure, and its last layer outputs the mineralization probability value through the Sigmoid activation function. The gated network is used to dynamically generate the weight coefficients of each expert network based on the input mineral exploration feature variable dataset.

7. The mineral exploration prediction method based on piecewise linear functions and PU hybrid expert networks according to claim 1, characterized in that, The expression for the non-negative risk estimation loss in the PU learning strategy is as follows: ； in, Estimate losses for non-negative risk; This represents the prior probability of mineralization within the target area, reflecting the overall mineralization density of the area. This represents the sample mineralization probability value output by the mineral exploration prediction model; This represents the loss when a positive sample is correctly predicted as positive. This represents the loss when unlabeled samples are considered negative. This is a correction term used to offset the bias caused by treating potentially positive samples in unlabeled samples as negative samples; The expression for the load balancing loss is as follows: ； in, For load balancing losses; The number of expert networks; It is the arithmetic mean of the probability weights of all samples in the current training batch assigned to the nth expert network in the gating network.

8. The mineral exploration prediction method based on piecewise linear functions and PU hybrid expert networks according to claim 7, characterized in that, The weighted random sampling strategy is as follows: count the total number of unlabeled samples and positive samples in the whole region, fix the basic sampling weight of unlabeled samples to 1.0, and set the sampling weight of positive samples to the ratio of "total number of unlabeled samples divided by total number of positive samples". During the model training process, random sampling with replacement is performed according to this fixed weight to generate training batches.

9. The mineral exploration prediction method based on piecewise linear functions and PU hybrid expert networks according to claim 7, characterized in that, The method for determining the mineralization prior probability is as follows: set a candidate interval, traverse the candidate interval with a fixed step size, train multiple mineral exploration prediction models, and count the total loss function value and AUC value of each mineral exploration prediction model on the validation set. Select the prior probability value corresponding to the stable AUC value and the minimum fluctuation of the total loss function value as the final mineralization prior probability. The training process of the mineral exploration prediction model also includes: automatically optimizing the model hyperparameters using a Bayesian optimization algorithm based on tree-based Parzen estimation; An early termination strategy using dual-index joint validation is adopted. The AUC value and total loss function value of the validation set are monitored in real time. If the AUC value no longer increases or the total loss function value no longer decreases during multiple rounds of training, the training is terminated early, and the optimal mineral exploration prediction model is output.

10. A mineral exploration prediction system based on piecewise linear functions and a PU hybrid expert network, used to implement the mineral exploration prediction method based on piecewise linear functions and a PU hybrid expert network as described in any one of claims 1-9, characterized in that, include: The mineral control element quantification module is used to obtain the key mineral control elements of the target mineral in the target area. Based on the known spatial distance statistical relationship between the mineral deposit and the mineral control element, a piecewise linear function is constructed to convert the geometric distance from the sample point to the mineral control element into a quantitative value that reflects the decay of the mineralization probability, and generate mineral control element quantification data. The data integration module is used to preprocess the raw geochemical data and extract the ore-forming element combination data related to the target mineral type; and to fuse and standardize the ore-forming element combination data with the ore-controlling element quantitative data to generate a mineral exploration characteristic variable dataset. The model building and training module is used to build a hybrid expert network consisting of an expert network and a gated network. It introduces the non-negative risk estimation loss in the PU learning strategy and the load balancing loss of the hybrid expert network. Based on the weighted random sampling strategy, the hybrid expert network is trained to obtain the mineral exploration prediction model. The mineral potential prediction module is used to predict the mineralization probability value of each sample point based on the trained mineral exploration prediction model and the mineral exploration feature variable dataset of the target area.

Images