A spatiotemporal perception generative adversarial network-based in-situ leaching uranium mining simulation method

Abstract

The application provides a kind of spatiotemporal perception generative adversarial network's uranium in-situ leaching simulation method, comprising: obtaining the paired data set of "heterogeneous permeability coefficient field and well location map-uranium concentration spatiotemporal evolution sequence" for model training, and the paired data set is preprocessed and divided;Design a generative adversarial network model that fuses multi-scale cross attention and time perception mechanism, a generator containing a U-Net variant architecture and a conditional discriminator in the generative adversarial network model;In the training phase, the training set in the paired data set is input into the generative adversarial network model, and the generative adversarial network model is trained by minimizing a composite loss function;In the inference phase, the trained generative adversarial network model is deployed as a substitute simulator, a new heterogeneous permeability coefficient field and well location map are input, multiple target time points are batch input, and a complete uranium concentration spatiotemporal evolution prediction sequence is generated in parallel.

Description

Technical Field

[0001] This invention relates to the field of hydrogeological numerical simulation and deep learning interdisciplinary technology, and in particular to a method for simulating in-situ leaching uranium mining using a spatiotemporal-aware generative adversarial network. Background Technology

[0002] In-situ leaching (ISL) has become the mainstream mining method due to its minimal surface disturbance, controllable production costs, and low environmental footprint. This technology involves injecting a leaching agent into the ore-bearing aquifer to dissolve uranium minerals, and then recovering the uranium-bearing solution via pumping wells. However, the strong heterogeneity of the ore-bearing aquifer, especially the dramatic spatial variations in permeability, leads to complex leaching agent flow paths, forming dominant seepage channels and non-uniform propagation fronts. This directly restricts uranium recovery efficiency and ultimate recovery rate, and exacerbates environmental risks such as the excessive migration of leaching agents.

[0003] To assess and mitigate the impact of uncertainties in the permeability coefficient field, repeated simulations using numerical models for in-situ leaching of uranium are necessary. However, to accurately characterize the multiphysics coupling processes in heterogeneous media, these models often require extremely high spatiotemporal discretization precision, resulting in enormous computational costs. For example, related studies show that simulating the dynamic processes of a uranium deposit in Inner Mongolia can take up to 4.7 hours per run. When permeability coefficient field inversion or uncertainty quantification analysis is required, the thousands of simulation runs needed make traditional numerical methods virtually unusable in practice, severely hindering the refined development and risk management of this technology.

[0004] Therefore, researchers have turned to using efficient data-driven models to replace traditional model-based prediction processes. Among them, data-driven models based on Generative Adversarial Networks (GANs) have shown significant advantages in achieving image-to-image mapping from "permeability coefficient field to uranium concentration field," improving computational efficiency by several orders of magnitude while maintaining accuracy, providing a feasible solution for single-moment concentration spatial prediction. However, existing data-driven models still have inherent limitations when simulating full-cycle dynamic evolution processes: temporally, existing models typically treat time as a discrete condition input, severing the continuity and historical dependence of the physical process, leading to the accumulation of errors over time; spatially, the convolutional neural networks on which existing models rely, due to their local receptive field characteristics, struggle to capture long-distance global dependencies in the concentration field, limiting their ability to predict complex plume morphologies in long-term evolution.

[0005] Therefore, there is an urgent need to develop a data-driven model that can uniformly model spatiotemporal continuous processes and take into account both global spatial dependence and long-term accuracy stability, so as to achieve efficient and high-fidelity dynamic simulation of the entire process of uranium leaching in the earth. Summary of the Invention

[0006] To address the high computational costs of traditional reactive solute transport models and the technical bottlenecks of existing data-driven alternative models in long-term dynamic simulations due to spatiotemporal continuity disruptions and error accumulation, this invention provides an MCFT-GAN model construction method capable of efficiently and accurately simulating the long-term spatiotemporal evolution of uranium concentration. This model achieves deep fusion and global dependency modeling of geological conditions and transport processes in the spatiotemporal dimensions through a dual-path time-aware mechanism and a multi-scale cross-attention module in the generator. Furthermore, the dual image and time discrimination tasks in the conditional discriminator, along with the long-term consistency loss introduced during training, jointly ensure the spatial detail authenticity and temporal evolution rationality of the generated sequences.

[0007] The first aspect of this invention provides a method for simulating uranium mining in terrestrial leaching using a spatiotemporally aware generative adversarial network, comprising: S1. Obtain the paired dataset of "heterogeneous permeability coefficient field and well location map - spatiotemporal evolution sequence of uranium concentration" for model training, and preprocess and divide the paired dataset; wherein, the source of the paired dataset includes, but is not limited to, production data of the target mining area, production data of adjacent or similar mining areas, and numerical simulation data of the target mining area or similar mining areas. S2. Construct a generative adversarial network model that integrates multi-scale cross-attention and time-aware mechanisms, referred to as the MCFT-CAN model. The MCFT-CAN model includes a generator and a conditional discriminator. The generator uses U-Net as its backbone and introduces a multi-scale cross-attention module between the encoder and decoder to replace the traditional skip connections. It also integrates a dual-path time-aware mechanism to model global spatial dependencies and temporal continuity respectively. The conditional discriminator adopts the PatchGAN architecture and is constructed to perform a dual discrimination task of image authenticity and temporal authenticity. S3. Input the training set from the paired dataset into the MCFT-CAN model, and optimize the MCFT-CAN model by minimizing a composite loss function that includes adversarial loss and long-term consistency loss until the model converges. S4. Using the trained MCFT-CAN model as the forward prediction model, for a new heterogeneous permeability coefficient field and its corresponding well location map, forward propagation calculation is performed by inputting the target time point, and the uranium concentration field at the corresponding time point is directly output; or by inputting multiple target time points in batches, a complete spatiotemporal evolution prediction sequence of uranium concentration is generated in parallel.

[0008] Furthermore, step S1, which involves constructing a paired dataset through numerical simulation using a model, includes: A reaction solute transport model is established based on the geological and mining scheme parameters of the target mining area. Based on the geological and statistical characteristics of the target mining area, the spatial variation function model and parameters of the permeability coefficient field are determined. Based on the spatial variation function model and parameters, multiple sets of mutually independent heterogeneous permeability coefficient fields are generated using the geostatistical stochastic simulation method. Based on the mining scheme parameters and the preset well network scheme, the set of well locations in the model grid is determined, and the set of well locations is rasterized and encoded into a binary map of well locations consistent with the model grid. Each set of heterogeneous permeability coefficient fields and their corresponding well location binary maps are used as core variables to input into the reaction solute transport model for full-cycle dynamic simulation. A series of discrete time point full-field uranium concentration distribution data are extracted from the output of each simulation to form a set of paired data of "heterogeneous permeability coefficient field and well location map - uranium concentration spatiotemporal evolution sequence". All the paired data are combined to form a paired dataset for model training.

[0009] Furthermore, the multi-scale cross-attention module in the generator described in step S2 is connected between the encoder and the decoder. It is used to receive and process hierarchical feature maps of different scales extracted by the encoder, and to realize information interaction and aggregation between features of different scales through cross-scale cross-attention operation. The expression for cross-scale cross-attention operation is as follows: In the formula, N represents the number of scale sequences participating in the fusion; d represents the feature dimension. 、 、 They represent the first The original representations of the query sequence, key sequence, and value sequence corresponding to each scale feature sequence. Represents the linear projection operator. 、 、 Each represents a learnable parameter corresponding to the projection. Represents the normalization function. This represents feature concatenation along the sequence dimension; Intra-scale self-attention operations enhance the modeling of long-distance dependencies within feature maps at different scales. The expression for the intra-scale self-attention operation is as follows: In the formula, , , These represent the query matrix, key matrix, and value matrix after linear mapping of the input feature sequence, respectively. Represents the linear projection operator. 、 、 All represent learnable parameters; This indicates a pooling operation. This represents the learnable parameters related to pooling. Representing feature dimension, This represents the normalization function.

[0010] Furthermore, the dual-path time-aware mechanism integrated in the generator described in step S2 includes a first-path macroscopic time reference and a second-path deep time fusion; wherein, the first-path macroscopic time reference encodes discrete time points into spatial constant feature maps as macroscopic conditional inputs, providing a unified macroscopic time reference for the entire space; the second-path deep time fusion converts discrete time points into time embedding vectors through independent time embedding layers. and features of the generator bottleneck layer By fusing the data, we obtain global prior features under time constraints. The expression is: In the formula, and These respectively represent the transition from time embedding to... The channel-level scaling vector and bias vector generated by linear mapping are consistent with the number of bottleneck feature channels. ⊙ represents element-wise channel multiplication, and t represents the normalized time condition.

[0011] Furthermore, the conditional discriminator performs a dual discrimination task of image authenticity and temporal authenticity, including: Receive a conditional input tensor composed of the uranium concentration field image to be determined and its corresponding heterogeneous permeability field, well location map and time point information spliced ​​along the channel dimension; The conditional input tensor is input into the image authenticity discrimination branch, and a two-dimensional matrix representing the authenticity discrimination of the local region is output. At the same time, the time discrimination input tensor is received by splicing the uranium concentration field image to be judged and its corresponding heterogeneous permeability coefficient field and well location map along the channel dimension, and the time discrimination input tensor is input into the time authenticity discrimination branch, and the simulated time point prediction result corresponding to the uranium concentration field image is output. Based on the outputs of the image authenticity discrimination branch and the temporal authenticity discrimination branch, an adversarial signal is jointly generated to train the generator, so as to jointly constrain the consistency of the generated image in terms of spatial details and temporal evolution.

[0012] Furthermore, the adversarial loss described in step S3 consists of conditional least squares adversarial loss and temporal realism loss, which together drive the generator to simultaneously learn the accuracy of spatial distribution and the correctness of temporal evolution. The adversarial loss expression is as follows: In the formula, This represents the weighting coefficient for the time authenticity loss. This indicates a loss of time authenticity. Denote the conditional least - squares adversarial loss; where, It includes the loss of the discriminator on the image branch and the loss of the generator on the image branch. The loss expression of the discriminator on the image branch is: and the loss expression of the generator on the image branch is: In the formula, C represents the real concentration field sample, D

[0015] ,

[0014] , , , interp , , , , represents the image authenticity discrimination branch of the discriminator, E {} represents the mathematical expectation, represents the uranium concentration field at the corresponding moment; the time authenticity loss expression is: In the formula, represents the cross - entropy loss, E {} represents the mathematical expectation, C represents the real concentration field sample, D time represents the time authenticity discrimination branch of the discriminator.

[0013] Furthermore, the construction method of the long - term consistency loss in step S3 includes: Under the condition of the same heterogeneous permeability coefficient field input, each time the model iterates, a time triple satisfying t1 < t2 < t3 is randomly sampled from the training time set, and three predicted uranium concentration fields G1, G2, and G3 generated by the generator are obtained respectively; Use the endpoint concentration fields G1 and G3 for linear interpolation to construct the reference concentration field at t2 2; Construct the long - term consistency loss with the difference between G2 and 2, and the expression is: L c =E[w interp (t1,t3)×(‖G2 2‖1+(1 cos(G2, 2))], in the formula, cos(G2, 2) represents the cosine similarity between G2 and 2, represents the L1 norm, w interp ( ) represents the time - span weight.

[0014] The second aspect of the present invention provides a computer - readable storage medium, on which a computer program is stored. The computer program is executed by a processor to perform the steps of the above - mentioned uranium in - situ leaching simulation method of a spatio - temporal perception generative adversarial network.

[0015] A third aspect of the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described spatiotemporally aware generative adversarial network simulation method for uranium mining.

[0016] Compared with the prior art, the present invention has the following beneficial effects: 1) The generative adversarial network model proposed in this invention reduces the simulation time from hours in traditional numerical models to seconds, achieving an order-of-magnitude leap in computational efficiency and fundamentally breaking the core bottleneck of excessive time consumption and high computing power requirements in real-time simulation and large-scale analysis.

[0017] 2) To address the shortcomings of existing models that treat time as a discrete label input and thus sever the continuity of physical processes, this invention explicitly embeds spatiotemporal evolution constraints within a data-driven framework through a dual-path time-aware mechanism and a long-term consistency loss function. This ensures the smooth transition and physical rationality of the generated concentration field sequence in the time dimension and effectively suppresses the problem of error accumulation and divergence over time.

[0018] 3) To overcome the limitations of traditional convolutional neural networks in modeling long-distance spatial dependencies, a multi-scale cross-attention module was innovatively introduced to construct a cross-scale global spatial correlation between geological conditions and solute transport processes. This enables the model to more accurately characterize complex solute fronts and dominant transport paths under strong heterogeneity control, significantly improving the geometric realism and physical credibility of spatial predictions.

[0019] 4) It achieves end-to-end generation from static geological parameters to dynamic concentration field sequences: for any given time point, only one forward propagation is needed to output the corresponding concentration field; when multiple time points need to be covered, time points can be used as conditional batch inputs / cyclic inputs to obtain concentration field sequences, greatly simplifying the simulation process. The model architecture has good scalability, facilitates the integration of multi-source heterogeneous data, and provides a core simulation engine for building a digital twin system for in-situ leaching uranium mining.

[0020] 5) By designing a time-aware mechanism and long-term consistency loss, the physical prior knowledge of "continuous and smooth spatiotemporal evolution" is embedded into the deep learning model in the form of differentiable constraints. The fusion of physical information and data-driven approaches significantly enhances the stability of model interpolation predictions and the reliability of extrapolation, making its output more consistent with physical laws and improving the credibility and practical value of decision support under complex geological conditions. Attached Figure Description

[0021] Figure 1 A flowchart illustrating the steps of a spatiotemporally aware generative adversarial network-based simulation method for uranium mining in terrestrial leaching.

[0022] Figure 2This is a schematic diagram of the technical process for a generative adversarial network (MCFT-GAN) model that integrates multi-scale cross-attentional and fused temporal generative adversarial network mechanisms.

[0023] Figure 3 A schematic diagram of the generator structure for a generative adversarial network that integrates multi-scale cross-attention and time-aware mechanisms.

[0024] Figure 4 This is a schematic diagram of the conditional discriminator structure of the MCFT-GAN model. Detailed Implementation

[0025] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this specification, and not all embodiments. Based on the embodiments in this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this specification.

[0026] Please see Figure 1 , Figure 1 A flowchart illustrating the steps of a spatiotemporally aware generative adversarial network-based simulation method for uranium leaching in the earth, including the following steps: S1. Obtain the paired dataset of "heterogeneous permeability coefficient field and well location map - spatiotemporal evolution sequence of uranium concentration" for model training, and preprocess and divide the paired dataset; wherein, the source of the paired dataset includes, but is not limited to, production data of the target mining area, production data of adjacent or similar mining areas, and numerical simulation data of the target mining area or similar mining areas. S2. Construct a generative adversarial network model that integrates multi-scale cross-attention and time-aware mechanisms, referred to as the MCFT-CAN model. The MCFT-CAN model includes a generator and a conditional discriminator. The generator uses U-Net as its backbone and introduces a multi-scale cross-attention module between the encoder and decoder to replace the traditional skip connections. It also integrates a dual-path time-aware mechanism to model global spatial dependencies and temporal continuity respectively. The conditional discriminator adopts the PatchGAN architecture and is constructed to perform a dual discrimination task of image authenticity and temporal authenticity. S3. Input the training set from the paired dataset into the MCFT-CAN model, and optimize the MCFT-CAN model by minimizing a composite loss function that includes adversarial loss and long-term consistency loss until the model converges. S4. Using the trained MCFT-CAN model as the forward prediction model, for a new heterogeneous permeability coefficient field and its corresponding well location map, forward propagation calculation is performed by inputting the target time point, and the uranium concentration field at the corresponding time point is directly output; or by inputting multiple target time points in batches, a complete spatiotemporal evolution prediction sequence of uranium concentration is generated in parallel.

[0027] In one specific embodiment of this invention, the model training paired dataset sources include, but are not limited to, production data from the target mining area, production data from similar mining areas, and numerical simulation data from the model. This embodiment of the invention obtains the paired dataset for model training through conventional numerical simulation methods for solute transport models. The specific construction process of the paired dataset is as follows: This invention selects a sandstone-type uranium deposit in Inner Mongolia, China, as the research object. First, a reactive solute transport model (RTM) is constructed based on the geological and mining scheme parameters of the target mining area (hydraulic parameters, chemical and mineralogical parameters, well network parameters, injection-production regime, and total simulation control time and output time point). The ore-bearing aquifer of the target mining area is generalized into a three-dimensional model with dimensions of 500m×500m×20m. The following processes are coupled using the three-dimensional model (groundwater flow simulation based on Darcy's law, solute transport simulation based on convection-dispersion equations, and reaction kinetics simulation describing the dissolution of leaching agents (such as O2 / CO2) and pitchblende). All invariant engineering and chemical parameters (well network layout, injection-production regime, initial and boundary conditions, simulation duration) are fixed to form a consistent simulation scenario.

[0028] Based on borehole and geophysical data from the mining area, spatial structure parameters of the permeability coefficient field were obtained through variogram analysis. Using geostatistical software and a sequential Gaussian simulation method, 260 independent heterogeneous permeability coefficient fields satisfying the aforementioned statistical characteristics were randomly generated on the aforementioned RTM model grid. Each heterogeneous permeability coefficient field represents a possible spatial distribution scenario of subsurface permeability.

[0029] Twenty-sixty heterogeneous permeability coefficient fields were sequentially substituted into the established RTM model, and full-cycle dynamic simulations were conducted for 650 days under a fixed mining scheme. From the complete output of each simulation, uranium concentration distribution data for 13 discrete time points (t=50, 100, ..., 650 days) were extracted at fixed time intervals (e.g., every 50 days). Each heterogeneous permeability coefficient field precisely corresponds to a uranium concentration evolution sequence, ultimately resulting in a complete paired dataset of 260 sets of "heterogeneous permeability coefficient field-uranium concentration spatiotemporal evolution sequences".

[0030] Max-min normalization was performed on all 260 heterogeneous permeability coefficient fields and their corresponding uranium concentration fields, and they were linearly transformed to the [0,1] interval to accelerate network training convergence.

[0031] In one specific embodiment of this example, the purpose and innovation of the constructed MCFT-GAN model are analyzed as follows: In this embodiment, the construction of the Generative Adversarial Network (MCFT-GAN) model, which integrates multi-scale cross-attention and time-aware mechanisms, aims to systematically address two fundamental shortcomings of existing numerical simulation models in long-term dynamic simulation of uranium leaching in terrestrial mining: insufficient modeling of spatial global dependencies and the fragmentation of temporal continuity.

[0032] In practical applications (mineral mining), traditional generative adversarial network models based on CNN / U-Net / cGAN, with their inherent local receptive fields and simple skip connection mechanisms, struggle to capture the complex spatial structure of dominant channels and solute fronts with long-range dependencies induced by strongly heterogeneous permeability fields, often resulting in blurred plume boundaries in the prediction results. To address this, the MCFT-GAN model constructed in this invention innovatively improves upon traditional skip connections: the generator in the model abandons traditional skip connections and introduces a multi-scale cross-attention (MM-ViT) module between the encoder and decoder of U-Net. This module achieves global interaction between features of different resolutions through cross-scale cross-attention and establishes long-distance spatial correlations within each scale through intra-scale self-attention, thereby explicitly modeling the global spatial dependencies from geological conditions to concentration fields, laying the foundation for high-precision spatial reproduction.

[0033] Regarding time input, existing numerical simulation models often treat time as a discrete label input, lacking an intrinsic modeling of the continuity of physical processes. This leads to unstable predictions at unsupervised time points, discontinuous sequence evolution, and errors that easily accumulate over simulation time. To address this, this invention constructs a systematic time-awareness and constraint framework: within the model generator, time is deeply integrated through a dual-path approach. The first path, a macroscopic time reference, encodes discrete time points into spatial constant feature maps as macroscopic conditional inputs, providing a unified macroscopic time reference for the entire space. The second path, deep time fusion, converts discrete time points into time embedding vectors through an independent time embedding layer and fuses them with the features of the generator's bottleneck layer to obtain global prior features under time-constrained conditions.

[0034] In addition, the present invention innovatively adopts dual discrimination and introduces time variables in the model discriminator. In addition to performing image authenticity discrimination, the discriminator also constrains the generated results to correspond to the correct time points. The long-term consistency loss introduced during model training forces the generated sequence to satisfy physically reasonable smooth transitions between any adjacent time points.

[0035] The aforementioned innovations endow the trained MCFT-GAN model with a unique "time completion" capability, resolving a key cost contradiction in engineering simulations. Traditional RTM, to control computational overhead, can only output results for sparse moments (e.g., every 50 days). However, the MCFT-GAN model in this embodiment, during the inference phase, can accept arbitrarily dense sets of target time points within the training time window (e.g., any day from day 1 to 650) for the same permeability coefficient field, and instantaneously output the concentration fields for all corresponding moments through single or batch forward propagation. This makes it possible to obtain high temporal resolution evolution sequences without increasing the computational cost of the original RTM, providing an unprecedentedly efficient tool for fine dynamic analysis (e.g., calculating instantaneous frontal velocities and pinpointing peak times) and large-scale uncertainty quantification.

[0036] In one specific implementation of this embodiment, the composition and data processing of the Generative Adversarial Network (MCFT-GAN) model that integrates multi-scale cross-attention and time-aware mechanisms include: The MCFT-GAN model designed in this embodiment consists of a generator using a variant of the U-Net architecture and a conditional discriminator using the PatchGAN architecture. The technical process is as follows: Figure 2 As shown, the specific components and data processing procedures are as follows: (1) Specific components of the generator and data processing procedure: ①The network architecture of the generator is as follows Figure 3 As shown, the specific components are as follows: Multi-scale feature encoder: It consists of multiple levels of convolutional downsampling layers, which are used to downsample the input multi-channel conditional tensor to extract hierarchical feature maps with different spatial resolutions; wherein, the multi-channel conditional tensor is composed of a heterogeneous permeability coefficient field, well location information represented by a binary mask map, and encoded discrete time point information. Multi-scale cross-attention module: A multi-scale cross-attention module (MM-ViT, Multi-scale Mixing Vision Transformer) is set between the encoder and decoder to receive the hierarchical feature maps extracted by the encoder. Through cross-scale cross-attention operation, the features of each scale can aggregate relevant information from features of other scales. Through intra-scale self-attention operation, the modeling of long-distance dependencies within the feature maps of each scale is enhanced, and finally the modeling of global and long-distance spatial dependencies is realized to replace the traditional skip connections. Dual-path time-aware mechanism: The generator integrates a dual-path time-aware mechanism. The first path, macroscopic time reference, uses time information as part of the conditional input tensor to provide a macroscopic time reference for the entire space. The second path, deep time fusion, transforms time information into a high-dimensional feature vector through an independent time embedding layer, and fuses the high-dimensional feature vector with the network bottleneck layer features to apply fine-grained time guidance to the subsequent decoding process.

[0037] Upsampling decoder: It receives features that have been processed by the multi-scale cross-attention module and fused with time information. Through a series of upsampling-convolution operations modulated by time features, it gradually reconstructs a high-resolution spatial distribution map of uranium concentration corresponding to the input time point.

[0038] ② The generator data processing procedure is as follows: Input data integration: The heterogeneous permeability coefficient field representing geological conditions, the well location map represented by a binary raster, and discrete simulation time points (e.g., day 15) are stitched together along the channel dimension to form a 3×64×64 multi-channel integrated input tensor. The well location map and the permeability coefficient field have the same spatial resolution, with pixels in the well grid set to 1 and other pixels set to 0. For different simulation scenarios, the well location map varies with the set of well locations to characterize solute transport processes under different well location conditions. The time points are converted into constant feature maps with consistent spatial dimensions through an encoding layer (e.g., sinusoidal position encoding), providing a unified macroscopic benchmark for the entire spatial domain.

[0039] Encoder Feature Extraction: The synthesized input tensor is fed into a U-Net-based encoder for multi-scale feature extraction. This encoder consists of a series of convolutional downsampling modules. After five downsampling passes, the encoder generates five feature maps with different spatial resolutions, including feature maps corresponding to scales 1-4, with sizes of 32×32 (d1), 16×16 (d2), 8×8 (d3), and 4×4 (d4), respectively, as well as a bottleneck layer feature map with a size of 1×1.

[0040] Multi-scale cross-attention fusion: The multi-scale feature maps output by the encoder are input to the multi-scale cross-attention (MM-ViT) module, instead of being directly skipped. In the MM-ViT module, the four scale feature maps d1 to d4 from the encoder are used to achieve global integration of cross-scale information and extraction of information within each scale through a two-stage attention process.

[0041] The MM-ViT module achieves information interaction and aggregation between features of different scales in the first stage through cross-scale cross-attention operations. The expression for the cross-scale cross-attention operation is as follows: (1) In the formula, N represents the number of scale sequences participating in the fusion; d Representing feature dimension, 、 、 They represent the first The original representations of the query sequence, key sequence, and value sequence corresponding to each scale feature sequence. Represents the linear projection operator. 、 、 This represents the learnable parameters corresponding to the projection. Represents the normalization function. This represents feature concatenation along the sequence dimension; The second stage enhances the modeling of long-distance dependencies within feature maps at different scales through intra-scale self-attention operations. The expression for the intra-scale self-attention operation is as follows: (2) In the formula, 、 、 These represent the query matrix, key matrix, and value matrix used for attention calculation after the input feature sequence has undergone linear mapping; Represents the linear projection operator. 、 、 Indicates learnable parameters; This indicates a pooling operation. This represents the learnable parameters related to pooling. The feature dimension represents the attention computation. This represents the normalization function.

[0042] Simultaneously, a dual-path time-aware mechanism (a first-path macroscopic time reference and a second-path deep time fusion) is integrated between the encoder and decoder. The first-path macroscopic time reference encodes discrete time points into spatial constant feature maps as macroscopic conditional inputs, providing a unified macroscopic time reference for the entire space. The second-path deep time fusion maps discrete time points into time embedding vectors through an independent time embedding layer. and features of the generator bottleneck layer By fusing the data, we obtain global prior features under time constraints. The expression is shown in equation (3). The time-modulated bottleneck features are used as global priors to participate in subsequent fusion and reconstruction.

[0043] (3) In the formula, ⊙ represents element-wise multiplication of the channel. t This represents the normalized time condition. and These respectively represent the transition from time embedding to... The channel-level scaling vector and bias vector, generated by linear mapping, have the same number of bottleneck feature channels as the number of channels. The expression is shown in equation (4). The expression is shown in equation (5).

[0044] (4) (5) In the formula, Both represent learnable linear mapping parameters.

[0045] Image reconstruction: The decoder receives features fused by the MM-ViT module and injected with deep temporal information, and performs progressive upsampling through a series of transposed convolutional layers to restore the spatial resolution of the features to the original input size, and finally outputs a normalized uranium concentration spatial distribution prediction map with a size of 64×64 pixels in the range of [-1, 1].

[0046] (2) Conditional discriminators, such as Figure 4 As shown, the specific operation process is as follows: The system receives a conditional input tensor composed of a uranium concentration image to be determined and its corresponding conditional information; the corresponding conditional information includes the permeability field, well location information, and time point. Multiple convolutional layers are used to extract features from the conditional input tensor to obtain advanced semantic features; High-level semantic features are fed into two parallel output branches: the image authenticity discrimination branch and the temporal authenticity discrimination branch. The image authenticity discrimination branch outputs a two-dimensional discrimination matrix, where the value of each matrix element represents the confidence score that the corresponding local region in the input uranium concentration image is a true simulation result; the temporal authenticity discrimination branch extracts image features through a classification network and predicts the simulation time point corresponding to the uranium concentration image to be discriminated. The discrimination matrix output by the image authenticity discrimination branch and the time point prediction results output by the temporal authenticity discrimination branch are used together to generate an adversarial training signal, so as to constrain the image generated by the generator to simultaneously satisfy the authenticity of spatial details and the consistency of temporal evolution.

[0047] In one specific implementation of this embodiment, model training based on a deep learning framework can be performed on a GPU-accelerated computing device. The process of training and optimizing the Generative Adversarial Network (GAN) model includes: Training Environment Initialization and Data Loading: The training environment was set up using the PyTorch framework on a server equipped with an NVIDIA GeForce RTX 5070Ti GPU. The training set (200 data sets) was loaded from the preprocessed paired dataset, and the data was organized into mini-batches using a data loader, with a batch size of 16. Before each training cycle, the training set data was randomly shuffled to improve the model's generalization ability.

[0048] Define the loss function and set the optimizer: Use a composite loss function to guide model training, and employ the Adam optimization algorithm to optimize the generator and discriminator, with an initial learning rate set to 0.0002; The generator uses conditional input... x With time condition t as input, the condition input Includes heterogeneous permeability field and well location map, outputting uranium concentration field at corresponding time. (t)=G(x,t); The conditional discriminator D() performs dual discrimination of image authenticity and temporal authenticity on the input concentration field given (x,t): the image authenticity branch outputs a two-dimensional discrimination matrix, in which each element corresponds to the confidence score of the local region of the input concentration field as a real sample or a generated sample; the temporal authenticity branch outputs the prediction result of the simulated time point corresponding to the concentration field. Since the conditional discriminator adopts the PatchGAN architecture, the output of the image authenticity branch is a two-dimensional matrix, and the adversarial loss is calculated point by point for each element of the matrix and the mean (or mathematical expectation) is taken. The discriminator uses the conditional least squares adversarial loss (LSGAN), the definition of which is shown in Equation (6) and Equation (7) respectively: (6) (7) In the formula, C represents the true concentration field sample, and L adv_img (D) and L adv_img (G) represent the loss of the discriminator on the image branch and the loss of the generator on the image branch, respectively. img E represents the image authenticity discrimination branch of the discriminator. {} It represents the mathematical expectation.

[0049] To achieve supervised training of the temporal authenticity discrimination branch, a temporal authenticity loss L is introduced. time The expression is: (8) In the formula, L CE E represents the cross-entropy loss. {} Let C represent the mathematical expectation, and D represent the true concentration field sample. time This represents the time authenticity discrimination branch of the discriminator.

[0050] The discriminator adversarial loss consists of the conditional least squares adversarial loss and the temporal authenticity loss, and its expression is: (9) In the formula, represents the weight coefficient of the temporal authenticity loss, represents the temporal authenticity loss, represents the conditional least squares adversarial loss.

[0051] The long-term consistency loss ( L c ) is used to constrain the evolution consistency over a large time span: under the input conditions of the same heterogeneous permeability coefficient field, each time the model iterates, a time triple satisfying t1 < t2 < t3 is randomly selected from the training time set, and three predicted uranium concentration fields G1, G2, and G3 generated by the generator are obtained respectively. The reference concentration field at time t2 is constructed by linearly interpolating the endpoint concentration fields G1 and G3 2; To suppress the instability caused by the switching of time conditions, a time span weight is introduced, and its expression is shown in Equation (10), and the long-term consistency loss is constructed, and its expression is shown in Equation (11): w interp (t1,t3)=clip(|t3 t1| / (t max t min ),0,1) (10) L c =E {(x,t1,t2,t3)~p} [w interp (t1,t3)·(||G2 2||1+(1 cos(G2, 2)))] (11) In the formula, clip() represents the truncation function, which is used to limit the input value within the specified interval [0,1], and cos() represents the cosine similarity, represents the L1 norm (taking the absolute value of the pixel-by-pixel difference of the concentration field and summing or averaging).

[0052] The composite loss function (total training loss) is defined as: (12) In the formula, and respectively represent the weight coefficients corresponding to the adversarial loss and the long-term consistency loss, represents the long-term consistency loss, This indicates the discriminator's adversarial loss.

[0053] Adversarial training loop: Set the total number of training rounds to 150. In each training round, iteratively optimize the discriminator and generator in the model according to the following steps: Discriminator optimization: Real data (permeability coefficient field, corresponding real concentration field at the given time, and conditional information) is taken from the current mini-batch and input into the discriminator to obtain image authenticity branch output and temporal authenticity branch output. Simultaneously, the conditional input (x,t) from the same batch is input into the generator to obtain the generated concentration field G(x,t), which is then input into the discriminator to obtain the corresponding output. The adversarial loss Ladvance of the conditional LSGAN is calculated based on the image authenticity discrimination output of real and generated samples. adv_img (D), and calculate the cross-entropy loss L based on the time point prediction results of the time authenticity branch. time The total discriminant loss is obtained by weighting the two together. L adv The discriminator parameters are updated through backpropagation.

[0054] Generator optimization: With discriminator parameters fixed, input the same batch of generated data into the discriminator again. Calculate the generator's adversarial loss. (Including image realism adversarial terms and temporal realism constraints) and long-term consistency loss , and according to The total training loss of the generator is obtained by weighted summation, and the generator parameters are updated by backpropagation.

[0055] Training Monitoring and Validation: During training, the changing trends of the generator and discriminator losses are continuously monitored. Every 10 training epochs, the generator's prediction results on the validation set are saved for qualitative visualization evaluation. After each training epoch, the structural similarity index (SSIM) and root mean square error on the validation set are quantitatively calculated, and the best-performing model checkpoint is saved accordingly. If the validation set performance does not improve for 20 consecutive epochs, an early stopping mechanism is triggered. After training, the final model is evaluated using an independent test set (60 sets of data).

[0056] In one specific implementation of this embodiment, the trained MCFT-GAN model is used as an alternative simulator for the conventional reaction transport numerical model during the forward propagation process, including: After model training, a new heterogeneous permeability coefficient field is input into the trained MCFT-GAN model. For any given target time point, the model only needs one forward propagation to output the corresponding uranium concentration field. When multiple target time points need to be covered, multiple time points can be batch-input / cyclically-input as time conditions, thereby obtaining a uranium concentration spatiotemporal evolution prediction sequence covering a 650-day period (e.g., 14 representative time points). In practical implementation, for a given new permeability coefficient field, a traditional numerical model takes approximately 17 minutes (approximately 1020 seconds) to complete a simulation covering a 650-day period. In contrast, the MCFT-GAN model trained in this invention takes approximately 0.093 seconds for inference of 14 time points in a single scenario, achieving approximately 1.1 × 10⁻⁶ seconds compared to RTM. 4 The speedup is doubled. Furthermore, the results of this invention demonstrate that the constructed MCFT-GAN model exhibits high accuracy and stability throughout the 650-day simulation period, achieving a mean structural similarity (SSIM) of 0.971 and a mean root mean square error (RMSE) of 0.018 on the test set. At the sequence distribution level, the Fraser video distance (FVD) is 39.224, indicating that the generated sequence is statistically closer to the reference sequence of the reaction transport numerical model. These results also demonstrate that the dynamic evolution process of model generation exhibits high spatiotemporal consistency and stability with the actual simulation results.

[0057] This invention also provides a computer-readable storage medium storing a computer program thereon, the computer program being executed by a processor of the steps of a spatiotemporally aware generative adversarial network-based uranium leaching simulation method as described in any of the above embodiments.

[0058] This invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of a spatiotemporally aware generative adversarial network-based uranium leaching simulation method as described in any of the above embodiments.

[0059] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions conceived without inventive effort 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 defined in the claims.

[0060] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for simulating uranium mining by in-situ leaching using a spatiotemporally aware generative adversarial network, characterized in that, include: S1. Obtain the paired dataset of "heterogeneous permeability coefficient field and well location map - spatiotemporal evolution sequence of uranium concentration" for model training, and preprocess and divide the paired dataset; wherein, the source of the paired dataset includes, but is not limited to, production data of the target mining area, production data of adjacent or similar mining areas, and numerical simulation data of the target mining area or similar mining areas. S2. Construct a generative adversarial network model that integrates multi-scale cross-attention and time-aware mechanisms, referred to as the MCFT-CAN model. The MCFT-CAN model includes a generator and a conditional discriminator. The generator uses U-Net as its backbone and introduces a multi-scale cross-attention module between the encoder and decoder to replace the traditional skip connections. It also integrates a dual-path time-aware mechanism to model global spatial dependencies and temporal continuity respectively. The conditional discriminator adopts the PatchGAN architecture and is constructed to perform a dual discrimination task of image authenticity and temporal authenticity. S3. Input the training set from the paired dataset into the MCFT-CAN model, and optimize the MCFT-CAN model by minimizing a composite loss function that includes adversarial loss and long-term consistency loss until the model converges. S4. Using the trained MCFT-CAN model as the forward prediction model, for a new heterogeneous permeability coefficient field and its corresponding well location map, forward propagation calculation is performed by inputting the target time point, and the uranium concentration field at the corresponding time point is directly output; or by inputting multiple target time points in batches, a complete spatiotemporal evolution prediction sequence of uranium concentration is generated in parallel.

2. The method according to claim 1, characterized in that, Step S1, which involves constructing a paired dataset through numerical simulation, includes: A reaction solute transport model is established based on the geological and mining scheme parameters of the target mining area. Based on the geological and statistical characteristics of the target mining area, the spatial variation function model and parameters of the permeability coefficient field are determined. Based on the spatial variation function model and parameters, multiple sets of mutually independent heterogeneous permeability coefficient fields are generated using the geostatistical stochastic simulation method. Based on the mining scheme parameters and the preset well network scheme, the set of well locations in the model grid is determined, and the set of well locations is rasterized and encoded into a binary map of well locations consistent with the model grid. Each set of heterogeneous permeability coefficient fields and their corresponding well location binary maps are used as core variables to input into the reaction solute transport model for full-cycle dynamic simulation. A series of discrete time point full-field uranium concentration distribution data are extracted from the output of each simulation to form a set of paired data of "heterogeneous permeability coefficient field and well location map - uranium concentration spatiotemporal evolution sequence". All the paired data are combined to form a paired dataset for model training.

3. The method according to claim 1, characterized in that, The multi-scale cross-attention module in the generator described in step S2 is connected between the encoder and the decoder. It is used to receive and process hierarchical feature maps of different scales extracted by the encoder, and to realize information interaction and aggregation between features of different scales through cross-scale cross-attention operation. The expression for cross-scale cross-attention operation is as follows: In the formula, N represents the number of scale sequences participating in the fusion; d Representing feature dimension, 、 、 They represent the first The original representations of the query sequence, key sequence, and value sequence corresponding to each scale feature sequence. Represents the linear projection operator. 、 、 Each represents a learnable parameter corresponding to the projection. Represents the normalization function. This represents feature concatenation along the sequence dimension; Intra-scale self-attention operations enhance the modeling of long-distance dependencies within feature maps at different scales. The expression for the intra-scale self-attention operation is as follows: In the formula, , , These represent the query matrix, key matrix, and value matrix after linear mapping of the input feature sequence, respectively. Represents the linear projection operator. 、 、 All represent learnable parameters; This indicates a pooling operation. This represents the learnable parameters related to pooling. Representing feature dimension, This represents the normalization function.

4. The method according to claim 1, characterized in that, The dual-path time-aware mechanism integrated in the generator described in step S2 includes a first-path macroscopic time reference and a second-path deep time fusion. The first-path macroscopic time reference encodes discrete time points into spatial constant feature maps as macroscopic conditional inputs, providing a unified macroscopic time reference for the entire space. The second-path deep time fusion converts discrete time points into time embedding vectors through independent time embedding layers. and features of the generator bottleneck layer By fusing the data, we obtain global prior features under time constraints. The expression is: In the formula, and These respectively represent the transition from time embedding to... The channel-level scaling vector and bias vector generated by linear mapping are consistent with the number of bottleneck feature channels. ⊙ represents element-wise channel multiplication, and t represents the normalized time condition.

5. The method according to claim 1, characterized in that, The conditional discriminator performs a dual discrimination task of image authenticity and temporal authenticity, including: Receive a conditional input tensor composed of the uranium concentration field image to be determined and its corresponding heterogeneous permeability field, well location map and time point information spliced ​​along the channel dimension; Input the conditional input tensor into the image authenticity discrimination branch, and output a two-dimensional matrix representing the authenticity discrimination of the local area; at the same time, receive the time discrimination input tensor formed by splicing the uranium concentration field image to be discriminated, its corresponding heterogeneous permeability coefficient field and the well location map along the channel dimension, and input the time discrimination input tensor into the time authenticity discrimination branch, and output the predicted result of the simulation time point corresponding to the uranium concentration field image; Based on the output results of the image authenticity discrimination branch and the time authenticity discrimination branch, jointly generate an adversarial signal for training the generator to jointly constrain the consistency of the generated image in spatial details and time evolution.

6. The method according to claim 1, characterized in that, The adversarial loss described in step S3 consists of conditional least squares adversarial loss and temporal realism loss, which together drive the generator to simultaneously learn the accuracy of spatial distribution and the correctness of temporal evolution. The adversarial loss expression is as follows: In the formula, This represents the weighting coefficient for the time authenticity loss. This indicates a loss of time authenticity. This represents the conditional least squares adversarial loss; where, This includes the discriminator's loss on the image branch and the generator's loss on the image branch. The discriminator's loss on the image branch is expressed as follows: The loss expression for the generator on the image branch is: In the formula, C represents the true concentration field sample, and D img E represents the image authenticity discrimination branch of the discriminator. {} Represents the mathematical expectation. This represents the uranium concentration field at the corresponding time; the expression for the time accuracy loss is: In the formula, E represents the cross-entropy loss. {} Let C represent the mathematical expectation, and D represent the true concentration field sample. time This represents the time authenticity discrimination branch of the discriminator.

7. The method according to claim 1, characterized in that, The construction method of the long-term consistency loss described in step S3 includes: Under the condition of the same heterogeneous permeability coefficient field input, at each iteration of the model, randomly sample a time triple that satisfies t1 < t2 < t3 from the training time set, and respectively obtain three predicted uranium concentration fields G1, G2, and G3 generated by the generator; The reference concentration field at time t2 is constructed using linear interpolation of endpoint concentration fields G1 and G3. 2; With G2 and The difference between 2 and 3 constructs the long-term consistency loss, expressed as: L c =E[w interp (t1,t3)×(‖G2 2‖1+(1 cos(G2, 2)))],where, cos(G2, 2) indicates that G2 and Cosine similarity of 2 Let w represent the L1 norm. interp ( ) indicates the weight of the time span.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, the method described in any one of claims 1-7 is implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, the method described in any one of claims 1-7 is implemented.

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