Rare earth element migration prediction method and system

Abstract

Embodiments of the present application disclose a rare earth element migration prediction method and system; embodiments of the present application can obtain biological disturbance information and physicochemical state information corresponding to a target region; based on the biological disturbance information, interface interaction analysis and processing are performed on the surface attribute characteristics of natural colloids in the physicochemical state information, the interaction potential energy is calculated according to the effective surface potential of the natural colloids under biological mediation, and the dynamic migration information corresponding to the target colloidal carrier is obtained; according to a preset porous medium evolution relationship, physical conservation analysis and processing are performed on the dynamic migration information and the hydrodynamic characteristics in the physicochemical state information, the physical constraint characteristic information corresponding to the target region is obtained, the network parameter of an initial prediction network is updated through a preset joint loss function, and the spatiotemporal evolution prediction processing of the rare earth elements in the target region is performed. Thus, embodiments of the present application improve the accuracy of spatiotemporal evolution prediction of rare earth elements and the reliability of engineering application.

Description

Technical Field

[0001] This application relates to the interdisciplinary field of rare earth mining area environmental evolution and artificial intelligence, specifically to a method and system for predicting the migration of rare earth elements. Background Technology

[0002] The spatial migration of rare earth elements (REEs) in porous media refers to the spatial movement and morphological evolution of REEs within geological bodies with complex porous structures, such as soil and rock strata, carried by media such as pore water flow. Accurately understanding and predicting this process is of great significance for pollution prevention and control in mining areas and for the protection of groundwater.

[0003] Currently, predictions of this migration process are typically achieved by constructing traditional hydrodynamic numerical models or using conventional deep learning models. However, existing prediction methods have certain limitations: traditional numerical models often rely on idealized environmental assumptions and static empirical parameters, making it difficult to realistically reflect the nonlinear coupling effects within the complex and ever-changing geological environment; while conventional deep learning models, as purely data-driven "black boxes," have weak generalization capabilities when mining area monitoring data is limited or geological conditions are complex, and the prediction results lack mechanistic constraints and reliability, resulting in the final prediction accuracy and engineering practicality failing to meet actual needs. Summary of the Invention

[0004] This application provides a method and system for predicting the migration of rare earth elements. It can deeply integrate the microscopic interface dynamics mechanism mediated by biological disturbance with the physical conservation law of macroscopic porous media. The network parameter update process of the prediction network is constrained by the physical a priori mechanism, which effectively breaks through the limitations of traditional prediction methods that rely on static empirical parameters and conventional pure data-driven networks that lack physical boundary constraints. It enhances the generalization ability of the prediction network in complex geological conditions and sparse data scenarios, thereby improving the accuracy of rare earth element spatiotemporal evolution prediction and the reliability of engineering applications.

[0005] This application provides a method for predicting the migration of rare earth elements, the method comprising:

[0006] The multidimensional environmental media characteristics corresponding to the target area are obtained. The multidimensional environmental media characteristics include biological disturbance information and physicochemical state information. The biological disturbance information includes the concentration characteristics of microbial metabolic secretions, and the physicochemical state information includes the hydrodynamic characteristics of porous media and the surface property characteristics of natural colloids.

[0007] Based on bio-disturbance information, the surface property characteristics of natural colloids in the physicochemical state information are analyzed by interface interaction to obtain the effective surface potential of natural colloids under bio-mediated conditions. The interaction potential energy is calculated based on the effective surface potential to obtain the kinetic migration information of the target colloidal carrier. The kinetic migration information reflects the deposition and release state of the target colloidal carrier in the porous medium.

[0008] Based on the preset evolution relationship of porous media, the hydrodynamic characteristics in the dynamic migration information and physicochemical state information are subjected to physical conservation analysis to obtain the physical constraint characteristic information corresponding to the target region. The physical constraint characteristic information characterizes the residual constraint terms corresponding to the physical conservation equation.

[0009] Based on physical constraint feature information, the network parameters of the initial prediction network are updated through a preset joint loss function, and the spatiotemporal evolution prediction of rare earth elements in the target area is performed to obtain the migration prediction results of rare earth elements in the target area.

[0010] This application also provides a rare earth element migration prediction system, the system comprising:

[0011] The feature acquisition module is used to acquire the multidimensional environmental media features corresponding to the target area. The multidimensional environmental media features include biological disturbance information and physicochemical state information. The biological disturbance information includes the concentration features of microbial metabolic secretions, and the physicochemical state information includes the hydrodynamic features of porous media and the surface property features of natural colloids.

[0012] The interface interaction analysis module is used to perform interface interaction analysis on the surface property characteristics of natural colloids in the physicochemical state information based on bio-disturbance information, to obtain the effective surface potential of natural colloids under bio-mediated conditions, and to calculate the interaction potential energy based on the effective surface potential, thereby obtaining the kinetic migration information corresponding to the target colloidal carrier. The kinetic migration information reflects the deposition and release state of the target colloidal carrier in the porous medium.

[0013] The physical conservation analysis module is used to perform physical conservation analysis on the hydrodynamic characteristics in the dynamic migration information and physicochemical state information according to the preset porous media evolution relationship, so as to obtain the physical constraint characteristic information corresponding to the target area. The physical constraint characteristic information represents the residual constraint terms corresponding to the physical conservation equation.

[0014] The evolution prediction module is used to update the network parameters of the initial prediction network based on physical constraint feature information and through a preset joint loss function, and to perform spatiotemporal evolution prediction processing on rare earth elements in the target area to obtain the migration prediction results of rare earth elements in the target area.

[0015] This application also provides an electronic device, including a processor and a memory, wherein the memory stores multiple instructions; the processor loads instructions from the memory to execute the steps in any of the rare earth element migration prediction methods provided in this application.

[0016] This application also provides a computer-readable storage medium storing multiple instructions adapted for loading by a processor to execute steps in any of the rare earth element migration prediction methods provided in this application.

[0017] This application also provides a computer program product, including a computer program / instructions, which, when executed by a processor, implement the steps in any of the rare earth element migration prediction methods provided in this application.

[0018] In this application, after obtaining the multidimensional environmental media characteristics corresponding to the target area, interface interaction analysis is performed on the surface property characteristics of natural colloids in the physicochemical state information based on the bio-disturbance information therein, thereby obtaining the effective surface potential of natural colloids under bio-mediated conditions. Since the effective surface potential directly quantifies the charge distribution and electrostatic repulsion intensity of the colloid surface, it can not only accurately calculate the interaction potential energy to reveal the microscopic repulsion and attraction between the target colloidal carrier and the porous medium, but also derive the dynamic migration information that truly reflects the deposition and release state of the target colloidal carrier in the porous medium. This analysis provides a more effective basis for accurately grasping the nonlinear coupling law of rare earth elements in complex environments. Next, combining the dynamic migration information and the hydrodynamic characteristics in the physicochemical state information, physical conservation analysis is performed according to the preset porous medium evolution relationship to derive the physical constraint characteristic information characterizing the residual constraint term corresponding to the physical conservation equation. This physical constraint characteristic information is then introduced into the joint loss function to update the network parameters of the initial prediction network. This process of updating network parameters by dual constraints of microscopic dynamic parameters and macroscopic physical prior mechanisms effectively overcomes the limitations of traditional prediction methods that rely on static empirical parameters and the lack of physical boundary constraints in conventional pure data-driven networks. Based on this mechanism, spatiotemporal evolution prediction of rare earth elements within the target region is performed, resulting in rare earth element migration predictions that better conform to real physical laws. This makes the prediction process more reasonable and enhances the generalization ability of the prediction network under complex geological conditions and sparse data scenarios. Therefore, it improves the accuracy of rare earth element spatiotemporal evolution prediction and the reliability of engineering applications. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating the rare earth element migration prediction method provided in the embodiments of this application;

[0021] Figure 2 This is a schematic diagram of the structure of the rare earth element migration prediction system provided in the embodiments of this application. Detailed Implementation

[0022] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0023] This application provides a method and system for predicting the migration of rare earth elements.

[0024] Specifically, the rare earth element migration prediction system can be integrated into electronic devices, such as terminals or servers. Terminals can be mobile phones, tablets, smart Bluetooth devices, laptops, or personal computers (PCs); servers can be single servers or server clusters composed of multiple servers.

[0025] The following sections provide detailed descriptions of each example. It should be noted that the sequence numbers of the following embodiments are not intended to limit the preferred order of the embodiments.

[0026] In this embodiment, a method for predicting the migration of rare earth elements is provided, such as... Figure 1 The specific process of this rare earth element migration prediction method can be shown as follows:

[0027] S101. Obtain the multidimensional environmental media characteristics corresponding to the target area. The multidimensional environmental media characteristics include biological disturbance information and physicochemical state information. The biological disturbance information includes the concentration characteristics of microbial metabolic secretions. The physicochemical state information includes the hydrodynamic characteristics of porous media and the surface property characteristics of natural colloids.

[0028] In this application, the target area refers to a specific geographical or geological spatial range where the spatiotemporal evolution and pollution risk prediction of rare earth elements need to be carried out. For example, the target area may include the tailings pond and surrounding soil area of ​​a rare earth mine, the in-situ leaching mining operation area, the groundwater conservation area affected by mine leachate, or the environmental monitoring area where a geological seepage prevention layer project has been pre-constructed, etc. This application does not impose absolute restrictions on the specific geographical location and geological type of the target area.

[0029] Furthermore, the complex geological environment of the target area harbors abundant microbial activity, which significantly alters the microscopic state of the geological environment. Microbial metabolic secretions refer to various organic substances released into the external liquid phase by indigenous microorganisms during their metabolic and proliferative processes. For example, microbial metabolic secretions may include extracellular polymeric substances (EPS), low-molecular-weight organic acids (such as citric acid, oxalic acid, and acetic acid), and other bioactive macromolecules with complexing capabilities.

[0030] Concentration characteristics refer to the absolute quantity distribution of the aforementioned microbial metabolic secretions per unit volume of medium within a target area. In one specific embodiment, the acquisition of concentration characteristics may include: first, acquiring environmental fluid and medium samples by deploying a monitoring well array in the target area, and using physicochemical analysis equipment such as liquid chromatography-mass spectrometry (LC-MS) or three-dimensional fluorescence spectrometry to determine the measured concentration values ​​of extracellular polymers and low-molecular-weight organic acids in the samples at each discrete sampling point; subsequently, based on the acquired discrete point concentration values, using a spatial interpolation algorithm (such as Kriging interpolation or inverse distance weighting method) to reconstruct a three-dimensional spatial field, thereby obtaining a three-dimensional spatial concentration distribution matrix covering a continuous grid of the target area.

[0031] Based on the above parameters, bio-perturbation information comprehensively characterizes the degree of shift in the microscopic state of the environment within the target area caused by the life activities of the biological community. For example, bio-perturbation information can be a multi-channel dataset that integrates extracellular polymer concentration characteristics and low-molecular-weight organic acid concentration characteristics, providing basic data support for subsequent quantification of biological modification of the surface potential of colloids.

[0032] Furthermore, the background physical and chemical state of the target area is also a key factor determining migration patterns. Porous media refers to a solid geological framework within the target area that has interconnected pores and fissures, allowing fluid seepage. For example, porous media can include sandy soil layers, clay layers, tailings deposits, and rock aquifers with natural fissures.

[0033] Hydrodynamic characteristics refer to physical property parameters that describe the motion state of fluids and solute transport capabilities in porous media. In one specific embodiment, the acquisition of hydrodynamic characteristics may include: obtaining background data on porosity and physical permeability coefficients of the porous media in the target area through on-site hydrogeological surveys (e.g., pumping tests, tracer tests); further, combining groundwater level monitoring data of the target area, using groundwater flow numerical simulation tools (such as MODFLOW) to solve the background flow field in steady-state or transient states, thereby extracting the gridded actual groundwater velocity field, hydraulic gradient, and hydrodynamic dispersion coefficient matrix of the target area. In the liquid phase environment of porous media, a large number of natural colloids capable of adsorbing and carrying rare earth ions for co-migration are suspended, such as clay minerals or iron-aluminum oxides at the nanometer to micrometer scale.

[0034] Surface properties refer to the inherent physical and chemical properties of the surface of these natural colloidal particles before biological disturbance. In one specific embodiment, the acquisition of surface properties may include: performing ultrafiltration or high-speed centrifugation on the collected undisturbed porous media sample to obtain a natural colloidal suspension sample; subsequently, using a microelectrophoresis instrument (such as a Zeta potential analyzer) and a dynamic light scattering instrument (DLS), the initial surface Zeta potential background value and initial particle size distribution information of the colloid are measured, and the initial colloidal surface property matrix of the target region is constructed accordingly.

[0035] Based on the aforementioned properties of porous media and colloids, physicochemical state information comprehensively characterizes the background state of the target area environment under the influence of physical water flow and the interface of chemical substances. For example, physicochemical state information can be a composite feature map containing the groundwater velocity field matrix and the initial surface potential matrix of colloids.

[0036] Finally, by integrating the aforementioned biological and physicochemical data, the multidimensional environmental media characteristics corresponding to the target area can be obtained. These multidimensional environmental media characteristics represent a comprehensive underlying data structure that maps the real, complex biogeological-hydrological coupling state of the target area. For example, these characteristics can be represented as a three-dimensional multi-channel tensor input to the prediction network, with different channels carrying biological disturbance information and physicochemical state information, providing the most comprehensive and fundamental multidimensional data input for accurately inverting the dynamic migration state of the target colloidal carrier.

[0037] In some embodiments, in order to reduce on-site sampling costs while maximizing the representativeness of the collected data and the benefits of model training, thereby improving the prediction accuracy and generalization ability of the target prediction network under sparse samples, the method further includes the following before acquiring the multidimensional environmental media features of the target region:

[0038] The initial geological spatial model corresponding to the target area is obtained, and based on the initial geological spatial model and the preset prior prediction network, the information entropy distribution features corresponding to the candidate sampling grids in the target area are extracted. The information entropy distribution features characterize the degree of cognitive uncertainty of the prior prediction network in the initial evolution prediction state regarding the target area.

[0039] Extract the heterogeneity abrupt change features of the medium corresponding to the initial geological spatial model. The heterogeneity abrupt change features of the medium characterize the spatial gradient change distribution of the physical permeability properties within the target area.

[0040] Based on the information entropy distribution characteristics and the abrupt change characteristics of the heterogeneity of the medium, the candidate sampling grids are subjected to joint sampling benefit evaluation processing to obtain the target sampling benefit score matrix;

[0041] Based on the target sampling benefit scoring matrix, node optimization analysis is performed in the candidate sampling grid to determine the target sampling space nodes, so as to obtain multi-dimensional environmental medium characteristics at the target sampling space nodes.

[0042] The initial geological spatial model refers to a preliminary three-dimensional geological structure framework constructed based on historical exploration data or remote sensing data of the target area before conducting refined multi-dimensional environmental media characteristic sampling. For example, the initial geological spatial model can be a three-dimensional stratigraphic model generated by interpolation of historical borehole logging data, containing preliminary stratigraphic distribution boundaries and lithological classification information.

[0043] A pre-trained prior prediction network refers to a lightweight neural network model that has been pre-trained using historical data from similar mining areas or theoretical simulation data. Although this network has not been fine-tuned with detailed data from the current target area, it possesses a preliminary predictive ability regarding the migration patterns of rare earth elements. For example, the pre-trained prior prediction network can be a pre-trained graph neural network (GNN) or a basic physical embedded neural network (PINN).

[0044] A candidate sampling grid refers to a set of three-dimensional grids with potential sampling value formed after spatially discretizing the three-dimensional space of the target area according to a preset resolution. For example, a candidate sampling grid can be a three-dimensional voxel unit with a length, width, and height of 10 meters.

[0045] Information entropy distribution characteristics refer to the degree of dispersion or disorder of the prediction results at each candidate sampling grid, quantified by analyzing the output of the prior prediction network. The higher the information entropy, the more uncertain the model's prediction for that region. For example, when using a Bayesian neural network as the prior prediction network, the information entropy distribution characteristics can be a variance distribution map of the network's output concentration after multiple forward propagations or a three-dimensional spatial mapping of Shannon entropy.

[0046] The initial evolution prediction state refers to the baseline prediction capability or initial prediction baseline presented by the prior prediction network when the network parameters are updated based solely on the initial geological spatial model, without incorporating actual and detailed biological, physicochemical, and other multidimensional media characteristics of the current target area.

[0047] Cognitive uncertainty refers to the degree to which a prior prediction network "lacks sufficient information" about the evolution of rare earth elements at specific spatial nodes within a target region. For example, if a candidate sampling grid is located on the edge of a fault and has limited historical data, and the network provides a very wide confidence interval for predicted concentrations, it indicates that its cognitive uncertainty is extremely high.

[0048] The abrupt change in heterogeneity of a medium refers to the property boundaries or anomalous regions within a target area where the physicochemical properties of media such as soil or rock undergo drastic spatial changes. For example, the abrupt change in heterogeneity of a medium can be a region of maximum gradient of the permeability tensor in a spatial coordinate system, or a lithological abrupt boundary zone that spans from a sandstone layer to a clay water-blocking layer.

[0049] Physical permeability refers to the ability of a porous medium to allow fluids (such as groundwater and colloids carrying rare earth ions) to pass through it. For example, physical permeability can be hydraulic conductivity, porosity, or Darcy permeability.

[0050] The gradient distribution refers to the magnitude and direction of the rate of change of physical permeability properties along various directions (x, y, z) in three-dimensional space. For example, the gradient distribution can be a calculated three-dimensional permeability gradient field. The larger the gradient value, the more drastic the changes in geological conditions and the more complex the fluid dynamics.

[0051] Joint sampling benefit evaluation refers to coupling the "cognitive blind spot" (i.e., information entropy distribution characteristics) at the model algorithm level with the "complex region" (i.e., abrupt changes in media heterogeneity) at the physical and geological level to evaluate the overall information gain that sampling in a specific grid can bring. For example, this process can be achieved by constructing an acquisition function that weights and fuses the information entropy H with the permeability gradient ▽K: Score = α.H + β.||▽K||, where α and β are preset weight parameters.

[0052] The target sampling benefit score matrix is ​​a three-dimensional tensor or matrix that records the joint sampling benefit scores of all candidate sampling grids. The numerical values ​​in the matrix directly reflect the priority of the corresponding grid as the final sampling point; the higher the value, the greater the value of acquiring environmental medium features at that location.

[0053] Node optimization analysis refers to the process of selecting the optimal solution set based on the target sampling benefit score matrix, under certain physical and engineering constraints (such as maximum sampling quantity limit, spatial mutual exclusion distance of sampling points, etc.) through a search algorithm. For example, node optimization analysis can use the spatial Poisson disk sampling algorithm combined with Top-K sorting to select the grid nodes with the highest scores and relatively uniform spatial distribution, avoiding excessive clustering of sampling points.

[0054] Target sampling spatial nodes refer to the three-dimensional physical coordinate points in space that are ultimately determined after node optimization analysis and used for actual sensor deployment or borehole sampling. For example, a target sampling spatial node can be a specific coordinate set (x, y, z) that includes longitude, latitude, and underground depth. i ,y i ,z i The system will subsequently acquire multi-dimensional environmental media characteristics, such as biological disturbance information and physicochemical state information, at these coordinate points.

[0055] S102. Based on bio-disturbance information, the surface property characteristics of natural colloids in the physicochemical state information are analyzed by interface interaction to obtain the effective surface potential of natural colloids under bio-mediated conditions. The interaction potential energy is calculated based on the effective surface potential to obtain the kinetic migration information corresponding to the target colloidal carrier. The kinetic migration information reflects the deposition and release state of the target colloidal carrier in the porous medium.

[0056] Interfacial interaction analysis refers to the process of analyzing and calculating how microorganisms and their metabolites alter the physicochemical properties of the solid-liquid interface of natural colloids. For example, interfacial interaction analysis can utilize steric hindrance and charge compensation mechanisms to calculate the changes in the electric double layer thickness and the rearrangement of charge distribution caused by the attachment of extracellular polymers secreted by microorganisms to the surface of natural colloids.

[0057] Biological mediation refers to the mechanism by which the life activities and metabolic secretions of microorganisms in natural geological environments indirectly or directly affect the physicochemical properties of inorganic minerals or colloids, acting as an intermediary. For example, biological mediation can involve specific bacteria in groundwater environments secreting large amounts of low-molecular-weight organic acids and extracellular polymers. These substances coat the surface of colloids, thereby altering the original hydrophilicity, surface roughness, and electrostatic charge properties of the colloids.

[0058] Effective surface potential refers to the actual electrostatic repulsion or attraction value exhibited on the surface of a natural colloid after it has been disturbed by the adsorption and complexation of microorganisms and their secretions in the environment. For example, the effective surface potential can be an updated Zeta potential value obtained by correcting the theoretical formula after taking into account the increase in steric hindrance caused by the attachment of biomacromolecules and the partial neutralization of the original surface charge.

[0059] Interaction potential energy refers to the sum of the microscopic physical force fields existing between the target colloidal carrier and the porous medium (such as soil particles or rock pore walls), which determines the degree of repulsion or attraction when the colloid and the medium approach each other. For example, interaction potential energy can be the superposition of the short-range van der Waals gravitational potential energy between the target colloidal carrier and the porous medium, calculated based on the classical DLVO (Derjaguin-Landau-Verwey-Overbeek) theory, and the electrostatic repulsive potential energy calculated based on the effective surface potential.

[0060] Target colloidal carriers refer to tiny particles, typically ranging in size from nanometers to micrometers, in a porous liquid environment, whose surfaces can adsorb, bind, or complex rare earth elements. For example, target colloidal carriers can be natural organic colloids rich in humic substances, or iron oxide mineral particles with a particle size of around 100 nanometers and whose surfaces adsorb rare earth ions such as yttrium (Y) or lanthanum (La).

[0061] Kinetic migration information refers to a set of dynamic parameters characterizing the spatial movement and solid-liquid phase transition rate of a target colloidal carrier in a porous media flow field over time. For example, kinetic migration information can be a set of parameters including the critical deposition rate coefficient (Attachment Rate) and desorption release rate coefficient (Detachment Rate) of the colloid in a one-dimensional seepage field.

[0062] The deposition and release states refer to the microscopic existence forms of a target colloidal carrier within a porous medium, where it is fixed to the surface of the medium's framework or detaches from the framework and re-enters the fluid phase due to physicochemical forces. For example, the deposition and release states can be the "deposition state," where the target colloidal carrier irreversibly adheres to the surface of rock pores after overcoming the maximum interaction potential energy barrier; or the "free release state," where a sudden increase in fluid velocity causes the hydrodynamic shear force to exceed the interfacial adsorption force, resulting in the carrier detaching from the framework.

[0063] In some embodiments, to decouple the complex interference processes of microorganisms into physical spatial hindrance and chemical charge stripping, thereby accurately capturing the nonlinear interface evolution of natural colloids in complex biochemical environments and avoiding migration prediction distortion caused by the use of traditional static ideal parameters, specifically, based on bio-perturbation information, the surface property characteristics of natural colloids in the physicochemical state information are subjected to interface interaction analysis to obtain the effective surface potential of natural colloids under biological mediation, including:

[0064] Extract extracellular polymer concentration characteristics and low molecular weight organic acid concentration characteristics from biological disturbance information;

[0065] Based on the extracellular polymer concentration characteristics, the steric hindrance correction process is applied to the double layer thickness corresponding to the natural colloid to obtain the corrected double layer thickness.

[0066] Based on the concentration characteristics of low molecular weight organic acids, complexation competition analysis was performed on rare earth ions in the target area to obtain the charge correction offset corresponding to the natural colloid.

[0067] Based on the correction of the electric double layer thickness and the charge correction offset, the initial surface potential in the surface property characteristics is updated to obtain the effective surface potential of natural colloids under biological mediation.

[0068] Extracellular polymer concentration characteristics refer to the abundance or distribution of macromolecular polymers secreted by microorganisms during their growth and metabolism and distributed in the porous fluid of the target region. For example, extracellular polymer concentration characteristics can be the mass concentration values ​​(e.g., numerical characteristics in mg / L) of polysaccharides, proteins, or nucleic acids extracted from porous fluids.

[0069] Low molecular weight organic acid concentration characteristics refer to the liquid phase distribution of small molecular weight organic acids produced by microbial metabolism or organic matter degradation in the target area environment. For example, low molecular weight organic acid concentration characteristics can be the concentration values ​​(e.g., numerical characteristics in mmol / L) of organic acids with strong metal complexing ability, such as citric acid, oxalic acid, or acetic acid, in porous media water bodies.

[0070] The electric double layer thickness refers to the overall effective distance between the "closed layer and diffuse layer" formed by the surface charge of a natural colloid attracting anti-ion ions in a fluid medium. It is usually used to characterize the attenuation scale of the electrostatic field around the colloid. For example, the electric double layer thickness can be the theoretical Debye length, which is the distance at which the electrostatic potential of the colloid surface decays to one-half (1 / e) of the natural constant of the initial surface potential.

[0071] Spatial hindrance correction refers to the process of calculating, through physical or mathematical models, the outward expansion of the physical boundary when a macromolecular polymer (such as an extracellular polymer) adsorbs onto the surface of a natural colloid and forms an encapsulation layer, leading to the interaction between the colloid and its external environment. For example, spatial hindrance correction can be based on polymer brush theory, calculating the extension length of the polymer chain on the colloid surface, and using this extension length as a compensation for the outward displacement of the colloid's shear slip plane.

[0072] The corrected electric double layer thickness refers to the effective electrostatic field distance of a natural colloid in the current environment after the introduction of interference from the physical encapsulation of biomolecules. For example, the corrected electric double layer thickness can be the equivalent value of the sum of the initial Debye length (e.g., 10 nm) of the colloid when there is no biological disturbance and the thickness of the extracellular polymer bioadsorption layer (e.g., 15 nm) (i.e., 25 nm).

[0073] Rare earth ions refer to positively charged rare earth elements that exist in a free or ionized state in the liquid phase environment of porous media in the target area. For example, rare earth ions can be trivalent yttrium ions (Y³⁺) or trivalent lanthanum ions (La³⁺) that migrate with groundwater seepage.

[0074] Complexation competition analysis refers to the chemical equilibrium calculation process in which newly introduced strong complexing agents (low-molecular-weight organic acids) compete with existing coordination sites on the colloidal surface for metal ions, leading to the desorption and desorption of ions from the colloidal surface. For example, complexation competition analysis can use a surface complexation model to calculate the proportion of rare earth ions that are electrostatically adsorbed on the surface of a natural colloidal substance and forcibly coordinated and stripped away by a high concentration of citric acid, causing them to return to the liquid phase.

[0075] Charge correction offset refers to the relative change in the overall net charge quantity and polarity of a natural colloid surface due to changes in the chemisorption state (such as the desorption of a large number of positively charged ions). For example, charge correction offset can be the negative electrostatic equivalent change (such as a potential shift equivalent to -15mV) caused by the stripping of positively charged trivalent yttrium ions, resulting in a relative increase in the negative charge exposed on the surface of the natural mineral colloid.

[0076] Initial surface potential refers to the intrinsic electrostatic potential of a natural colloid in a pure background physical and geological environment before it is disturbed by microbial activity, extracellular polymers, or organic acids. For example, the initial surface potential can be the background zeta potential (e.g., -30 mV) of natural clay mineral particles measured in a standard background electrolyte solution.

[0077] In some embodiments, to accurately quantify the extension effect of macromolecular polymers on the colloidal physical boundary, a mathematical mapping between bio-perturbation and microscopic physical field distortion is established, thereby avoiding the prediction model from underestimating the frictional resistance and deposition probability of colloid transport in porous media due to neglecting the bio-encapsulation layer. Specifically, based on the extracellular polymer concentration characteristics, the steric hindrance correction process is applied to the double layer thickness corresponding to the natural colloid to obtain the corrected double layer thickness, including:

[0078] Based on the preset colloidal physical properties, the initial double layer thickness parameters corresponding to the natural colloid are determined. The initial double layer thickness parameters characterize the effective scale of the surface electrostatic field of the natural colloid in the porous medium liquid phase environment when it is not disturbed by biological activity.

[0079] Based on the extracellular polymer concentration characteristics, a steric hindrance correction function for natural colloids is constructed.

[0080] Based on the steric hindrance correction function, calculate the characteristic scale offset of the bioadsorption layer corresponding to the extracellular polymeric material to the effective action scale.

[0081] The feature scale offset is fused with the initial double layer thickness parameter to obtain the corrected double layer thickness corresponding to the natural colloid.

[0082] The preset colloidal physical properties refer to the inherent material, morphology, and microscopic electrical parameters of natural particles under a pure geological background without considering interference from exogenous biological macromolecules. For example, the preset colloidal physical properties can be the background equivalent spherical diameter (e.g., 100 nm), initial specific surface area, or background surface charge density of natural montmorillonite colloidal particles.

[0083] The initial electric double layer thickness parameter refers to the theoretical decay distance constant of the electric double layer formed by the interaction between the surface charge of a natural colloid and surrounding ions when it is not encapsulated by microbial extracellular polymers. For example, the initial electric double layer thickness parameter can be the Debye length κ calculated based on the standard background ion intensity. -1 It is typically a scalar value in the range of a few nanometers to tens of nanometers.

[0084] A surface electrostatic field refers to the potential energy distribution region generated in the surrounding microscopic space by natural colloidal particles due to their surface charge, which can exert a Coulomb force on surrounding charged particles. For example, a surface electrostatic field can be the radial potential gradient formed by the negative charge on the colloidal surface in water, the absolute value of which decreases exponentially with increasing distance from the colloidal surface.

[0085] A porous media liquid phase environment refers to a microscopic fluid space within the underground rock and soil mass of a target area, consisting of a network of interconnected or semi-connected pores and filled with water or aqueous solutions. For example, a porous media liquid phase environment could be a sandstone aquifer filled with groundwater pore fluid rich in various natural electrolyte ions (such as sodium ions and calcium ions).

[0086] The effective interaction scale refers to the critical physical distance at which the surface electrostatic field of a colloid can overcome the Brownian motion of fluid molecules and exert significant electrostatic repulsion or attraction on the walls of other colloidal particles or pore frameworks. For example, the effective interaction scale can be defined as the decay of the surface electrostatic potential to the thermal energy threshold k. B T / e (where k) B The radial distance in space corresponding to the time when (where is the Boltzmann constant, T is the absolute temperature, and e is the elementary charge).

[0087] A steric hindrance correction function is a mathematical expression or computational logic that uses the concentration characteristics of biomacromolecules as independent variables to fit or map the colloidal hydrodynamic boundary expansion effect caused by the physical adsorption of macromolecules. For example, the steric hindrance correction function can be an empirical formula based on polymer conformation theory (such as the polymer brush model) Δδ=α·ln(1+β·C EPS ), where C EPS The extracellular polymeric concentration characteristics are represented by α and β, which are pre-fitted scaling coefficients.

[0088] A biosorbent layer refers to a thin film of bio-organic polymers with a certain thickness and viscoelasticity, formed by the adhesion of extracellular polymers and other biological macromolecules in the environment to the surface of natural colloids through non-covalent bonding interactions such as van der Waals forces, hydrogen bonds, or electrostatic attraction. For example, a biosorbent layer can be a gel-like film with a thickness of 5 to 20 nm formed by the extracellular polysaccharides secreted by microorganisms in groundwater tightly wrapping the outer surface of quartz sand colloids.

[0089] The characteristic scale offset refers to the incremental distance by which the hydrodynamic shear plane or effective electrostatic boundary of natural colloids expands outward due to the physical presence of the bioadsorption layer during dynamic collisions or interfacial interactions. For example, the characteristic scale offset could be a distance correction scalar that requires shifting the equivalent distance origin outward by 15 nm when calculating the repulsive force between colloids because of a 15 nm thick biopolysaccharide adsorption layer.

[0090] In some embodiments, to accurately simulate the interfacial chemical competition behavior of multi-component ions coexisting in natural geological environments, and to avoid the model overestimating the retention of rare earth elements in solid colloids due to neglecting the strong complexing and elution effects of organic acids, thereby significantly improving the fidelity of rare earth element dynamic migration prediction in the target area, specifically, based on the concentration characteristics of low-molecular-weight organic acids, complexation competition analysis is performed on rare earth ions in the target area to obtain the charge correction offset corresponding to the natural colloid, including:

[0091] The concentration characteristics of competing mineral ions in porous media and the initial surface adsorption characteristics of rare earth ions on the surface of natural colloids were obtained. Competing mineral ions are ions that compete with rare earth ions for adsorption on the surface of natural colloids. The initial surface adsorption characteristics characterize the quantity and binding state of rare earth ions on the surface of natural colloids before the introduction of low molecular weight organic acids.

[0092] Based on the concentration characteristics of low-molecular-weight organic acids and competitive mineral ions, a competitive substitution function for rare earth ions is constructed. The competitive substitution function characterizes the probability mapping relationship of the stripping of rare earth ions on the surface of natural colloids by free ions in the environmental liquid phase.

[0093] Based on the competing substitution function, calculate the complexation-desorption ratio of low molecular weight organic acids on the initial surface adsorption characteristics;

[0094] Based on the complexation-desorption ratio, the effective charge distribution state of the natural colloid after desorption is determined, and the charge correction offset of the natural colloid is calculated based on the effective charge distribution state.

[0095] Among them, the concentration characteristics of competitive mineral ions refer to the background inorganic ion abundance that naturally exists in the porous liquid environment, has similar charge properties or coordination preferences to rare earth ions, and thus competes for limited adsorption sites on the colloidal surface. For example, the concentration characteristics of competitive mineral ions can be the molar concentration values ​​of calcium ions (Ca²⁺), magnesium ions (Mg²⁺), or aluminum ions (Al³⁺) extracted from groundwater chemical monitoring data.

[0096] Initial surface adsorption characteristics refer to the baseline chemical state in which rare earth ions are fixed on the surface of natural colloids by electrostatic attraction or endogenous complexation before microorganisms secrete low-molecular-weight organic acids with strong complexing capabilities. For example, initial surface adsorption characteristics can be the adsorption density (e.g., 1.5 mg / g) of trivalent yttrium ions (Y³⁺) attached to a unit mass of iron oxide colloid in adsorption equilibrium.

[0097] The quantitative binding state refers to the specific quantitative characterization of the strength and quantity of binding between rare earth ions and active sites (sites) on the surface of natural colloids. For example, the quantitative binding state can be the proportion of coordination sites on the colloidal surface that have been occupied by rare earth ions, or the number of moles of rare earth ions bound per square meter of colloidal surface.

[0098] A competitive substitution function is a mathematical-chemical equilibrium model used to calculate the resorption of rare earth ions originally adsorbed on the solid surface back into the liquid phase by newly introduced strong ligands (low-molecular-weight organic acids) and competing ions in the liquid phase (i.e., elution and desorption). For example, a competitive substitution function can be an equation based on a multicomponent extended Langmuir competitive adsorption isotherm, or a surface complexation reaction equation incorporating the law of mass action.

[0099] Free ions in the environmental liquid phase refer to combinations of charged particles that migrate freely in porous water media and are not bound by the solid-phase framework or colloidal surface. For example, free ions in the environmental liquid phase include both newly generated negatively charged citrate anions and pre-existing free sodium and calcium ions in the water.

[0100] The stripping probability mapping relationship refers to the quantitative mathematical correlation between the concentrations of competing ions and complexing agents in the liquid phase and the probability of desorption of rare earth ions originally adsorbed on the solid phase. For example, the stripping probability mapping relationship can be a response curve showing that as the concentration of acetic acid in the porous liquid phase increases logarithmically, the probability of lanthanide ions bound to the surface of natural clay colloids being stripped nonlinearly jumps from 5% to 85%.

[0101] The complexation-desorption ratio refers to the percentage or fraction of rare earth ions originally adsorbed on the colloidal surface that detach from the solid phase and re-enter the liquid phase as organic complexes under the strong complexing elution effect of low-molecular-weight organic acids. For example, the complexation-desorption ratio can be a dimensionless coefficient value (such as 0.45 or 45%) calculated using a competitive substitution function, representing that nearly half of the bound rare earth ions are eluted.

[0102] The effective charge distribution state refers to the equilibrium state of net charge polarity and density distribution that is re-achieved on the surface of a natural colloid after a large number of positively charged rare earth ions have been complexed and stripped by low-molecular-weight organic acids. For example, the effective charge distribution state can be a strong negative electrostatic distribution pattern that occurs when the colloid surface loses a large number of positive charges (rare earth cations), causing the originally neutralized negative charges to be re-exposed.

[0103] In some embodiments, to accurately map microscale interfacial physicochemical interactions to macroscopic kinetic migration parameters, avoiding prediction failures due to abrupt changes in the fluid environment caused by the use of traditional empirical constants, and thus significantly improving the prediction accuracy of the dynamic deposition and release process of the target colloidal carrier in complex porous media, specifically, the interaction potential energy is calculated based on the effective surface potential to obtain the kinetic migration information corresponding to the target colloidal carrier, including:

[0104] The size distribution characteristics of the target colloidal carrier and the ion background characteristics of the pore fluid in the porous medium are obtained. The ion background characteristics characterize the electrolyte strength of the liquid phase environment inside the porous medium.

[0105] Based on the size distribution characteristics, the short-range gravitational potential energy between the target colloidal carrier and the porous medium is calculated. The short-range gravitational potential energy characterizes the inherent attraction of the target colloidal carrier in the porous medium due to its own physical size.

[0106] Based on the effective surface potential and ion background characteristics, the electrostatic repulsion potential energy between the target colloidal carrier and the porous medium is calculated. The electrostatic repulsion potential energy characterizes the surface charge repulsion effect experienced by the target colloidal carrier under the current electrolyte strength.

[0107] By superimposing and analyzing the short-range gravitational potential energy and electrostatic repulsive potential energy, the total interaction potential energy characteristics of the target colloidal carrier are obtained.

[0108] The extreme potential energy feature is extracted from the total interaction potential energy feature as the target energy barrier height. The target energy barrier height characterizes the maximum potential energy threshold that the target colloidal carrier needs to overcome when it undergoes a state transition.

[0109] Thermodynamic probability conversion is performed based on the target energy barrier height to obtain the critical deposition rate parameter and desorption release rate parameter corresponding to the target colloidal carrier. The critical deposition rate parameter and desorption release rate parameter are used as kinetic migration information.

[0110] Size distribution characteristics refer to the geometric size and shape of colloidal particle groups in physical space and their statistical distribution patterns. For example, size distribution characteristics can be the hydrodynamic diameter of the target colloidal carrier determined by dynamic light scattering (DLS), such as a particle size distribution range mainly concentrated in the range of 50 to 200 nm.

[0111] Pore ​​fluids refer to natural aqueous solutions that fill the voids between the solid porous media such as soil, sand, or rock. For example, pore fluids can be groundwater rich in various dissolved minerals and organic matter beneath the surface of a mining area.

[0112] Ion background characteristics refer to the concentration and composition of background ions in porous fluids, excluding target rare earth ions. They are mainly used to measure the fluid's ability to shield against electric fields. For example, ion background characteristics can be a combined concentration matrix of background sodium ions (Na⁺) and chloride ions (Cl⁻) in groundwater solutions.

[0113] Electrolyte strength refers to the weighted sum of the concentrations of all ions in a solution, and is a key chemical indicator determining the degree of double-layer compression and the strength of electrostatic shielding effects on a colloidal surface. For example, electrolyte strength can be expressed using the formula I = 1 / 2∑c i z i 2 (where c) i Z represents the ion concentration. i The ionic strength is calculated from the ionic charge number, such as 0.05 mol / L.

[0114] Short-range gravitational potential energy refers to the physical attraction potential energy that plays a dominant role at microscopic distances, causing matter to move closer together. For example, short-range gravitational potential energy can be the van der Waals gravitational potential energy between the target colloidal carrier and the quartz sand medium wall, calculated based on the Hamaker constant. .

[0115] Intrinsic attraction refers to the spontaneous, purely physical tendency of substances to attract each other when they come close together due to their inherent physical properties such as intermolecular dipole moments or polarization. For example, intrinsic attraction can be the van der Waals attraction that exists independently of external charges and pH levels when colloidal particles approach the surface of a porous medium.

[0116] Electrostatic repulsive potential energy refers to the repulsive potential energy generated when particles with the same polarity of charge approach each other due to the overlap of their respective electric double layers. For example, electrostatic repulsive potential energy can be calculated by substituting the calculated effective surface potential into the Poisson-Boltzmann equation. .

[0117] Surface charge repulsion refers to the mechanical interaction at the solid-liquid interface where like charges repel each other, thus preventing particles from approaching each other. For example, surface charge repulsion can be the electrostatic repulsion between a negatively charged humic colloid and the surface of a similarly negatively charged clay mineral, preventing the colloid from colliding and depositing.

[0118] Superposition analysis refers to the process of algebraically adding forces or potential energies (such as gravitational and repulsive forces) from different physical sources at the same spatial distance scale. For example, superposition analysis can be based on the classical DLVO theory, where the calculated near-range gravitational potential energy and electrostatic repulsive potential energy are algebraically added point by point according to the distance function to obtain the resultant potential energy.

[0119] The total interaction potential energy characteristic refers to the shape and key characteristic values ​​of the combined force-energy curve between the target colloidal carrier and the porous medium as a function of distance. For example, the total interaction potential energy characteristic can be a curve showing the change of potential energy with distance. This includes geometric feature points such as the first minimum, the first maximum (potential barrier), and the second minimum.

[0120] The target energy barrier height refers to the peak value of the maximum positive potential energy on the total interaction potential energy curve. It is the energy "high wall" that particles must overcome to approach and deposit on the surface of a medium. For example, the target energy barrier height can be the absolute value of energy corresponding to the highest point on the potential energy curve (usually expressed in the unit of thermal energy, kJ / kb). B T indicates that the barrier height is 15k. B T).

[0121] Thermodynamic probability conversion refers to the mathematical transformation process that maps a potential energy barrier at the microscopic scale to the probability or rate constant of colloid deposition or desorption at the macroscopic scale, based on statistical thermodynamic laws. For example, thermodynamic probability conversion can be used to calculate the proportion of colloidal particles in a fluid that have sufficient kinetic energy to cross the target energy barrier height using the Maxwell-Boltzmann distribution law.

[0122] The critical deposition rate parameter refers to the kinetic rate constant at which the target colloidal carrier successfully overcomes the energy barrier and adheres to the surface of a porous medium per unit time. For example, the critical deposition rate parameter can be the colloidal deposition rate coefficient k defined based on the first-order kinetic equation. att (e.g., unit is s) -1 (constant).

[0123] The desorption release rate parameter refers to the rate constant at which a target colloidal carrier, already in a deposited state, re-enters the fluid from the porous medium surface due to increased fluid shear force or a change in the chemical environment. For example, the desorption release rate parameter could be the release rate coefficient k of deposited colloids re-entering the pore fluid due to elution by low-molecular-weight organic acids. det (e.g., unit is s) -1 (constant).

[0124] S103. Based on the preset porous media evolution relationship, perform physical conservation analysis on the hydrodynamic characteristics in the dynamic migration information and physicochemical state information to obtain the physical constraint characteristic information corresponding to the target region. The physical constraint characteristic information characterizes the residual constraint terms corresponding to the physical conservation equation.

[0125] The pre-defined porous media evolution relationship refers to the physical laws or mathematical governing equations that describe the migration, diffusion, and reaction of fluids and their carried solutes or colloids within the porous media space over time. For example, the pre-defined porous media evolution relationship can be the classic convection-diffusion-reaction equation, used to comprehensively express the convective motion with groundwater flow, molecular diffusion due to concentration gradients, and the physicochemical reaction processes between solid and liquid interfaces.

[0126] Physical conservation analysis refers to the detailed calculation process of substituting the dynamic parameters and hydrodynamic characteristics obtained from the preliminary calculations into the physical law equations to calculate the degree of error in the current predicted state deviating from the law of absolute mass conservation. For example, physical conservation analysis can be: first, based on hydrodynamic characteristics (such as pore water velocity ν, hydrodynamic dispersion coefficient D) and dynamic migration information (such as the critical deposition rate parameter k)... att and desorption release rate parameter k det Construct a partial differential equation characterizing the conservation of mass: ∂C / ∂t = ▽·(D▽C) - ▽·(νC) - k att C+k det S, where C is the concentration of free rare earth elements, S is the concentration of colloidal deposited rare earth elements, and ▽ is the Laplace operator; then, using the Automatic Differentiation (AD) technique in the deep learning framework, partial derivatives are obtained in the spatial dimension (x, y, z) and time dimension (t) for the concentration prediction value output by the prediction network; finally, the obtained partial derivatives and the above-mentioned characteristic parameters are substituted into the partial differential equation to calculate the difference (i.e., residual) between the two sides of the equation, thereby completing the quantitative analysis of the physical conservation state.

[0127] Physical constraint feature information refers to the specific numerical values ​​or feature matrices extracted after physical conservation analysis, reflecting the severity of the violation of known physical laws by the current output of the prediction model. For example, physical constraint feature information can be the partial differential equation residual matrix R at the spatial coordinate nodes and time nodes calculated based on the above partial differential equations. PDE (x,t), this residual term will subsequently be directly incorporated into the loss function of the neural network as a penalty term, forcing the network to optimize in a direction that conforms to the physical mechanism.

[0128] S104. Based on physical constraint feature information, the network parameters of the initial prediction network are updated through a preset joint loss function, and the spatiotemporal evolution prediction of rare earth elements in the target area is performed to obtain the migration prediction results of rare earth elements in the target area.

[0129] The initial prediction network refers to a deep learning model base that has been structurally built and assigned initial weights (such as random initialization or pre-training using historical mining data) before the current target area is trained with refined physical constraints. For example, the initial prediction network can be a fully connected neural network built on a multilayer perceptron (MLP), whose input receives spatial coordinates and timestamps, and whose output corresponds to the predicted concentration of various rare earth elements.

[0130] Network parameter update refers to the mathematical optimization process of iteratively adjusting the connection weight matrix and bias vector within a neural network using the backpropagation algorithm and the gradient calculated based on a pre-defined joint loss function. For example, network parameter update can employ the Adam optimizer or the L-BFGS quasi-Newton method, based on a joint loss function that includes physical constraint feature information (PDE residuals) and data mean square error, continuously fine-tuning the neuron weights of each hidden layer of the network at a certain learning rate until the joint loss function converges to a pre-defined minimum value.

[0131] Spatiotemporal evolution prediction processing refers to the detailed execution process of using a converged target prediction network, inputting continuous spatial coordinates and future time nodes, to deduce the dynamic distribution evolution of rare earth elements (REEs) in a target area over time in three-dimensional geological space. For example, spatiotemporal evolution prediction processing can be as follows: First, construct a three-dimensional spatial grid coordinate set (x, y, z) covering the target area and the sequence of future time nodes to be predicted, t, as a joint input tensor; then, input this joint input tensor (x, y, z, t) into the target prediction network after updating its network parameters for forward propagation calculation; during the calculation process, the network combines the known multidimensional environmental medium characteristics and hydrodynamic characteristics to continuously output the free-state REE concentration and colloidal-bound REE concentration at each spatial node under different time slices; finally, through tensor reconstruction and interpolation smoothing, continuous dynamic three-dimensional concentration field data is generated, thereby realizing continuous spatiotemporal dynamic simulation of the migration, diffusion, and deposition of REEs with groundwater flow.

[0132] Rare earth element migration prediction results refer to the qualitative and quantitative aggregate information that, after spatiotemporal evolution prediction processing, ultimately outputs qualitative and quantitative information reflecting the specific spatial distribution, occurrence form, and concentration gradient of rare earth elements in a target area at a future time or period. For example, rare earth element migration prediction results can be a set of three-dimensional isosurface point cloud data or a four-dimensional visualized concentration field (including length, width, depth, and time axis), intuitively showing the concentration of trivalent yttrium ions (Yttrium trioxide) in the groundwater surrounding the target deposit 180 days from now. 3+ The precise arrival location of the migrating front and the corresponding local peak concentration.

[0133] In some embodiments, to overcome the "black box" limitations of traditional neural networks, a multi-task learning framework is used to deeply integrate physical mechanisms with data-driven approaches. This effectively solves the network overfitting problem caused by the sparse groundwater monitoring samples and strictly ensures the conservation of microscopic mass when simultaneously predicting the extinction forms of multiple elements, thereby achieving high-precision spatiotemporal continuous evolution prediction. Based on physical constraint feature information, the network parameters of the initial prediction network are updated using a preset joint loss function. Spatiotemporal evolution prediction processing is performed on rare earth elements in the target area to obtain the migration prediction results of rare earth elements corresponding to the target area, including:

[0134] The multidimensional environmental medium features and the corresponding spatiotemporal coordinate features are input into the initial prediction network to obtain the first predicted concentration features and the second predicted concentration features corresponding to rare earth elements. The spatiotemporal coordinate features represent the three-dimensional spatial location and time evolution nodes corresponding to the multidimensional environmental medium features. The first predicted concentration features represent the concentration of free rare earth elements, and the second predicted concentration features represent the concentration of colloidal rare earth elements.

[0135] Based on the physical constraint feature information, the partial differential equation residual calculation is performed on the first predicted concentration feature and the second predicted concentration feature to obtain the first loss information. The first loss information characterizes the degree of deviation between the output result of the initial prediction network and the dynamic law of porous media.

[0136] Based on the first predicted concentration characteristics, the second predicted concentration characteristics, and the actual monitored concentration characteristics corresponding to the target area, data fitting analysis is performed to obtain the second loss information.

[0137] Based on the first predicted concentration feature, the second predicted concentration feature, and the total elemental concentration feature corresponding to the target region, morphological conservation verification is performed to obtain the third loss information. The third loss information represents the penalty amount for the sum of the first predicted concentration feature and the second predicted concentration feature violating the mass conservation boundary.

[0138] The first, second, and third loss information are weighted and fused to obtain a preset joint loss function. The network parameters of the initial prediction network are then updated based on the joint loss function to obtain the target prediction network, which is used to obtain the rare earth element migration prediction results.

[0139] In this context, three-dimensional spatial location refers to the specific physical location of the target area within a geographic or geological three-dimensional coordinate system. For example, three-dimensional spatial location can be a Cartesian coordinate coefficient value (x, y, z) that includes longitude, latitude, and underground depth.

[0140] A time evolution node refers to a discrete moment in time at which rare earth elements migrate and react in groundwater and porous media. For example, a time evolution node can be a time step characteristic t, such as the 10th day or the 20th day after the pollutant leak or injection.

[0141] Spatiotemporal coordinate features refer to the joint feature vector that combines spatial location information with temporal evolution information and is used as input to a prediction model. For example, a spatiotemporal coordinate feature can be a four-dimensional tensor (x, y, z, t).

[0142] The concentration of free rare earth elements refers to the abundance of rare earth elements in liquid media such as groundwater, which are not adsorbed by colloids and exist freely in ionic form. For example, the concentration of free rare earth elements can be the concentration of free trivalent yttrium ions (Yttrium) in porous water. 3+ The molar concentration of ).

[0143] The first predicted concentration feature refers to the network estimate of the free-state rare earth element concentration given by the initial prediction network at a specific output branch after forward propagation calculation. For example, the first predicted concentration feature can be a continuous variable in the network output. free (x,y,z,t).

[0144] Colloidal-bound rare earth element concentration refers to the abundance of rare earth elements that have been adsorbed or complexed by natural colloidal particles (such as iron oxide and clay colloids) and migrate along with the colloidal carrier. For example, the colloidal-bound rare earth element concentration can be the equivalent concentration of rare earth elements attached to a moving colloid.

[0145] The second predicted concentration feature refers to the network estimate of the concentration of colloidal rare earth elements given by the initial prediction network on its other output branch. For example, the second predicted concentration feature can be a continuous variable in the network output. colloid (x,y,z,t).

[0146] Partial differential equation residual calculation refers to the detailed calculation process of verifying whether the concentration prediction value output by the network strictly follows the fluid dynamics equations using the automatic differentiation mechanism of the deep learning framework. For example, partial differential equation residual calculation can be performed as follows: using the automatic differentiation (AutoDiff) technique, the first derivative (convection term) and second derivative (dispersion term) of the first and second predicted concentration features are calculated with respect to spatial coordinates, and the first derivative is calculated with respect to time coordinates; then, these derivative terms are substituted into the pre-constructed convection-dispersion-deposition dynamics partial differential equation; finally, the difference (i.e., the residual) between the two sides of the partial differential equation that cannot be absolutely balanced is calculated, thereby quantifying the degree to which the prediction result violates the physical laws.

[0147] The first loss information refers to the quantitative index of the basic physical error obtained after processing the residuals of the partial differential equation. For example, the first loss information can be the mean square error (MSE) of the PDE residuals at all spatiotemporal sampling points, i.e., the physical loss function L. phy .

[0148] The laws of porous media dynamics refer to the objective physical laws governing the transport of underground fluids and solutes within the pores of rock and soil. For example, the laws of porous media dynamics can be Darcy's Law and Fick's Law of Diffusion.

[0149] Actual monitored concentration characteristics refer to the rare earth element concentration data actually obtained through on-site sensors, sampling wells, or laboratory testing. For example, actual monitored concentration characteristics could be the true concentration value C obtained from a water sample collected from a monitoring well at a specific time point and analyzed by ICP-MS. true .

[0150] Data fitting analysis refers to the calculation process of evaluating the difference between the output value of the initial prediction network and the actual monitored value at spatiotemporal nodes with real data labels. For example, data fitting analysis may involve selecting a few anchor points in the target area that have actual monitored concentration characteristics, extracting the first and second predicted concentration features of the network under the corresponding spatiotemporal coordinates, and calculating the cross-entropy or mean square error (MSE) between the two and the actual monitored data.

[0151] The second loss information refers to the quantitative metric of the fitting deviation between the network's predicted values ​​and the actual monitoring data, and it is also the most common data-driven loss term in traditional deep learning. For example, the second loss information can be the data validation error L calculated from the data fitting analysis. data .

[0152] The total elemental concentration characteristic refers to the theoretical total amount or boundary constraint of all rare earth elements in a closed system or specific node, set according to the environmental background or pollution source strength. For example, the total elemental concentration characteristic could be the total mass of rare earth elements injected into an aquifer in a single operation, or the constant initial boundary concentration C in a laboratory soil column experiment. total .

[0153] In one specific implementation, the total elemental concentration characteristic C total The acquisition methods may include: based on the initial source strength information of the target area at the time of the pollution event (such as the total amount of leachate leakage from the tailings dam and the initial concentration at the leakage point), combined with the porosity of the porous medium and the volume of the aquifer, to calculate the initial total concentration distribution of rare earth elements in all forms (free state, colloidal bound state and sedimentary state) in the pore water per unit volume.

[0154] In another alternative implementation, when a persistent leakage source exists in the target area, the total elemental concentration characteristics can be calculated by time integration based on the leakage source intensity function Q(t) and the fundamental solution of the convection-dispersion equation, yielding the dynamic total concentration constraint C that varies with time. total (x,y,z,t).

[0155] Morphological conservation verification refers to the process of checking the mass conservation of a network to prevent it from making absurd predictions (such as high free state concentration but excessive total concentration) in order to force a fit to the data. For example, morphological conservation verification can be performed by algebraically adding the first predicted concentration feature (free state) and the second predicted concentration feature (bound state) output by a specific node, and then comparing the result with the total elemental concentration feature and taking the difference.

[0156] The third loss information refers to an additional error index derived from the morphological conservation verification process, specifically used to constrain the logical rationality of the concentration of each morphology. For example, the third loss information could be the morphological mass conservation loss function L. mass , .

[0157] The penalty for violating the mass conservation boundary refers to the numerical weight penalty imposed on the network to force it to correct when the sum of the first and second predicted concentration features exceeds (or is less than) the theoretical total concentration. For example, if the predicted total concentration is greater than the actual injected total concentration, the system will generate a very large gradient penalty, causing the network to reduce its output value in the next iteration.

[0158] A target prediction network refers to an optimal neural network model that has undergone extensive iterative training until the joint loss function (i.e., the weighted sum of the first, second, and third loss information) reaches convergence, at which point the network parameters are fixed and can be directly used for actual business prediction. For example, a target prediction network could be a fully trained PINN model that not only has extremely low error on the test set data but also whose output naturally satisfies the physical dynamics equations.

[0159] In some embodiments, to address the common "ill-conditioned gradient competition" problem in physically embedded neural networks coupled with complex biochemical dynamics models, and to prevent the network from ignoring actual monitoring data and getting trapped in local optima due to excessively large gradients in the residuals of the physical equations during the initial training phase, thereby ensuring smooth convergence of model training and significantly improving the final prediction accuracy, specifically, the first loss information, the second loss information, and the third loss information are weighted and fused to obtain a preset joint loss function, including:

[0160] Obtain the target network parameters corresponding to the initial prediction network in the current training stage, as well as the preset weight scheduling cycle characteristics. The weight scheduling cycle characteristics characterize the adaptive weight triggering interval of the initial prediction network during the network training process.

[0161] Based on the target network parameters, calculate the first gradient feature corresponding to the first loss information and the second gradient feature corresponding to the second loss information. The first gradient feature represents the degree to which the first loss information dominates the update of the target network parameters in the current training stage, and the second gradient feature represents the degree to which the second loss information dominates the update of the target network parameters in the current training stage.

[0162] Under the condition that the preset weight scheduling cycle characteristics are met in the current training phase, the balance difference analysis is performed based on the first gradient characteristics and the second gradient characteristics to obtain the target gradient balance coefficient.

[0163] Based on the target gradient balance coefficient, the preset physical constraint weight parameters of the initial prediction network are adaptively updated to obtain the target physical constraint weight parameters. The target physical constraint weight parameters are used to suppress the excessive dominance of the first loss information on the update of the target network parameters in the initial iteration stage when the second loss information has not reached the preset convergence condition.

[0164] Based on the target physical constraint weight parameters, the first loss information, the second loss information, and the third loss information are weighted and fused to obtain a preset joint loss function.

[0165] The current training phase refers to the specific round or time point in the iterative optimization process of the deep learning model. For example, the current training phase could be the 500th training batch that the network model is currently in.

[0166] The target network parameters refer to the real-time values ​​of the weight matrix and bias vectors between neurons in the initial prediction network during the current training phase. For example, the target network parameters could be the weight matrix and weight parameters θ of the last shared hidden layer in the initial prediction network.

[0167] The preset weight scheduling cycle feature refers to the step interval that is artificially set to trigger gradient penalty calculation and weight update in order to save computing resources. For example, the preset weight scheduling cycle feature can be a cycle identifier that sets an adaptive weight update judgment every 100 iterations.

[0168] The first gradient feature refers to the statistical representation of the gradient tensor obtained by differentiating the physical loss term (first loss information) with respect to the parameters of a specific layer in the network through backpropagation. For example, the first gradient feature could be the average of the absolute values ​​of the gradients of the first loss information with respect to the hidden layer weight matrix θ ||▽ θ L phy|| mean It reflects the magnitude of the force by which the physical equations attempt to change the network weights.

[0169] The second gradient feature refers to the statistical representation of the gradient tensor obtained by differentiating the data fitting loss term (second loss information) with respect to the parameters of the same network layer. For example, the second gradient feature can be the maximum absolute value of the gradient of the second loss information with respect to the weight matrix θ of the same hidden layer ||▽ θ L data || max It reflects the maximum pull of real data trying to change network weights.

[0170] Balanced difference analysis refers to the detailed numerical calculation process of comparing the gradients generated by the different loss terms to quantify the degree of imbalance in their magnitudes during backpropagation parameter updates. For example, balanced difference analysis might involve: first, using the automatic differentiation engine of a deep learning framework to extract the backpropagation gradient vectors of the first and second loss information with respect to the shared hidden layer weight matrix; then, calculating the statistical characteristics of these two gradient vectors (e.g., extracting the maximum absolute value of the second gradient feature and the mean absolute value of the first gradient feature); finally, dividing the two (i.e., dividing the maximum value of the second gradient by the mean value of the first gradient (||▽)). θ L data || max / ||▽ θ L phy || mean And by using the Exponential Moving Average (EMA) algorithm combined with the coefficient values ​​from the previous round for smoothing and filtering calculation, the difference in the ability of the two to dominate parameter updates can be accurately quantified.

[0171] The target gradient balance coefficient is a dynamic penalty or amplification multiplier calculated after balance difference analysis to smooth out the gradient magnitude gap between different loss terms. For example, the target gradient balance coefficient can be a calculated scalar value of 0.01, indicating that the gradient of the current physical loss is two orders of magnitude larger than the gradient of the data loss, and needs to be scaled and suppressed proportionally.

[0172] The physical constraint weight parameters refer to the initial or legacy hyperparameter multipliers assigned by the system to the physical loss item (first loss information) before this dynamic update. For example, the physical constraint weight parameters can be an initially preset fixed constant λ. phy =1.0.

[0173] The target physics constraint weight parameters refer to the latest weight hyperparameters for the physics loss term that are dynamically adjusted using the target gradient balancing coefficients and are actually effective in the following training cycles. For example, the target physics constraint weight parameters could be λ updated based on the aforementioned scalar. * phy =0.01, which forcibly reduces the proportion of physical losses in the total losses.

[0174] The pre-defined joint loss function refers to the total cost function, which is the linear weighted sum of various losses (physical loss, data loss, and mass conservation loss) after adaptive weight adjustment, and used as the sole optimization objective of the network's backpropagation. For example, the pre-defined joint loss function can be of the form Loss = λ * phy L phy +L data +λ mass L mass The comprehensive objective function is used by the network to calculate the total gradient and update the target network parameters of all layers, λ. mass These are the weighting parameters for the third loss information.

[0175] In some embodiments, in order to transform abstract concentration prediction data into intuitive engineering risk early warning signals, quantify in advance the probability of pollutants breaching artificial or natural geological seepage barriers, and accurately delineate high-risk leakage areas through three-dimensional visualization algorithms, thereby providing scientific decision support for emergency intervention and seepage prevention and repair of groundwater environment in mining areas, specifically, after obtaining the rare earth element migration prediction results corresponding to the target area, the method further includes:

[0176] The three-dimensional concentration field information of rare earth element migration prediction results in the target area is extracted, and the spatial change rate of the three-dimensional concentration field information is calculated to obtain the concentration gradient distribution characteristics.

[0177] Based on the gradient extreme value abrupt change information in the concentration gradient distribution characteristics, the target migration front characteristics are determined. The target migration front characteristics characterize the diffusion front boundary of rare earth elements in the target area.

[0178] Obtain a pre-constructed spatial model of the geological seepage barrier for the target area, and perform spatial intersection analysis on the target migration front characteristics and the geological seepage barrier spatial model to obtain the characteristics of the target intersection area;

[0179] Based on the hydrodynamic characteristics in the dynamic migration information and physicochemical state information, as well as the physical thickness characteristics corresponding to the spatial model of the geological seepage barrier, the penetration probability analysis is performed on the characteristics of the target intersection area to obtain the target penetration probability information. The target penetration probability information characterizes the risk probability of the target colloidal carrier carrying rare earth elements breaking through the spatial model of the geological seepage barrier.

[0180] Under the condition that the target penetration probability information meets the preset risk warning threshold, the minimum bounding box analysis is performed on the three-dimensional spatial discrete point set corresponding to the target intersection region features to generate risk convex hull annotation features, and three-dimensional visualization warning processing is performed based on the risk convex hull annotation features.

[0181] Among them, the three-dimensional concentration field information refers to the set of concentration values ​​of rare earth elements at various discrete nodes in the three-dimensional space of the target region. For example, the three-dimensional concentration field information can be a quadruple point cloud data volume containing a large number of (x,y,z) physical space coordinates and their corresponding predicted concentration values ​​C.

[0182] Spatial rate of change calculation refers to the numerical derivative process of calculating the rate and direction of change of the concentration field along each coordinate axis in three-dimensional space. For example, spatial rate of change calculation can be performed by using the central difference method or the finite volume method to obtain the partial derivative of concentration for each spatial grid node in the three-dimensional concentration field information, thereby calculating the concentration gradient vector ▽C=(∂C / ∂x,∂C / ∂y,∂C / ∂z) at that node.

[0183] Concentration gradient distribution characteristics refer to the distribution of a three-dimensional vector field showing the degree and direction of concentration changes throughout the target space. For example, concentration gradient distribution characteristics can be a set of concentration gradient vectors from various spatial nodes, with larger gradient magnitudes indicating steeper concentration changes in the spatial region.

[0184] Gradient extremum abrupt change information refers to the geometric location information in a gradient vector field where the value undergoes a discontinuous jump or reaches a local spatial maximum. For example, gradient extremum abrupt change information can be a three-dimensional spatial surface where the gradient value suddenly jumps from a background value close to zero to a maximum value, which physically usually corresponds to the leading edge of a plume.

[0185] Target migration front features refer to the geometric surface or contour model of the front edge that rare earth elements can reach by water flow or colloidal migration, extracted based on gradient mutation information. For example, target migration front features can be the outermost three-dimensional isosurface mesh that encloses all rare earth element concentrations greater than a preset safety threshold, extracted using the Moving Cubes algorithm.

[0186] The diffusion front boundary refers to the critical physical interface between an uncontaminated clean area and a contaminated area. For example, the diffusion front boundary can be a dynamic front line in a groundwater flow field where rare earth elements begin to accumulate on a large scale and permeate outwards.

[0187] A geological impermeable layer spatial model refers to a three-dimensional geometric solid model constructed in advance using exploration data, representing a natural, weakly permeable layer or artificial impermeable project at the bottom or periphery of a mining area used to prevent the migration of pollutants. For example, a geological impermeable layer spatial model can be a three-dimensional polygonal mesh model representing a high-density polyethylene (HDPE) geomembrane or a natural thick clay cushion layer, created using BIM (Building Information Modeling) software.

[0188] Spatial intersection analysis refers to the detailed computational process of using computational geometry algorithms to determine and extract the areas where a target migrating front and a geological impermeable layer collide or overlap in three-dimensional physical space. For example, spatial intersection analysis can be performed by using the Bounding Volume Hierarchy (BVH) algorithm for accelerated spatial collision detection and calculating the Boolean intersection between the three-dimensional isosurface representing the migrating front and the spatial model of the geological impermeable layer, thereby accurately cutting out the geometric spatial volume where physical contact occurs.

[0189] The target intersection region features refer to the geometric and topological properties of a specific region formed after the migrating front and the geological impermeable layer come into spatial contact. For example, the target intersection region features can be a set of three-dimensional polygonal patches generated by Boolean intersection operations, as well as the centroid coordinates and contact area of ​​the intersection region.

[0190] Physical thickness characteristics refer to the spatial geometric thickness parameters of a geological impermeable layer perpendicular to the main migration direction of pollutants. For example, physical thickness characteristics could be the effective water-blocking thickness of a natural clay impermeable layer, averaging 2.5 meters in the vertical direction (Z-axis).

[0191] Penetration probability analysis refers to the process of quantitatively calculating the probability that pollutants will completely penetrate the impermeable barrier by integrating fluid dynamics and boundary geometric parameters. For example, penetration probability analysis can be performed by combining hydrodynamic characteristics (such as pore velocity) and dynamic migration information, using a one-dimensional convection-dispersion analytical solution (such as the Ogata-Banks equation), considering the measurement uncertainties of each input parameter, and calculating the cumulative probability that, under the current hydraulic gradient, colloids containing rare earth elements will migrate a distance exceeding the physical thickness characteristic within a predetermined time period in the future.

[0192] Target penetration probability information refers to a specific numerical value or rating that quantifies the risk of pollutants penetrating seepage prevention facilities. For example, target penetration probability information could be a calculated probability of the seepage prevention layer breaking through being 85%, or a system-determined "Level 1 (extremely high) leakage penetration risk".

[0193] A three-dimensional discrete point set refers to a set of discretized points with spatial coordinates extracted from the interior and edges of the intersecting region of a target. For example, a three-dimensional discrete point set could be hundreds of points (x, y, ...) representing the frontal erosion impermeable layer region. i ,y i ,z i Risk touches coordinate points.

[0194] Minimum bounding box analysis refers to the geometric computation process of finding a convex polyhedron in three-dimensional space with the smallest volume that completely encloses all given discrete risk points. For example, minimum bounding box analysis can be performed as follows: input a set of discrete points in three-dimensional space, use a fast convex hull algorithm to recursively find the farthest point and construct new triangular patches, and finally generate a three-dimensional convex polyhedron with no surface depressions, the smallest volume, and complete enclosure.

[0195] Risk convex hull annotation features refer to the three-dimensional geometric bounding box or contour generated by the convex hull algorithm, used to strictly define the spatial extent of the maximum potential risk leakage range. For example, risk convex hull annotation features can be a three-dimensional geometric polyhedral mesh model that exactly wraps around all points that may be touched by the leakage.

[0196] 3D visualization early warning processing refers to the process of transforming abstract risk convex hull features into intuitive graphic image outputs and triggering system alarm actions through rendering and human-computer interaction. For example, 3D visualization early warning processing could involve: overlaying and importing the risk convex hull annotation features into a mining area digital twin system (such as a WebGIS platform), applying a red semi-transparent glowing and pulsed flashing rendering material to the convex hull area, and simultaneously generating a pop-up window containing "spatial coordinates, penetration probability 85%, and estimated breakdown time," which is then pushed to the front-end control screen for visual and audible alarms.

[0197] To better illustrate the technical solution of the embodiments of this application, the complete execution flow of this method is illustrated below with reference to the specific scenario of "groundwater pollution prediction of an ion-adsorption rare earth tailings dam": at the three-dimensional spatial node (x) of the target area i ,y i ,z i At this location, the system acquires multidimensional environmental media characteristics through sensors and a sampling network. Among these, bio-disturbance information indicates active microbial activity at this node, with an extracted extracellular polymeric substance (EPS) concentration of 15.5 mg / L and a low-molecular-weight organic acid (citric acid) concentration of 2.5 mmol / L. The pore water flow rate is 0.5 m / d, and the background electrolyte intensity is 0.02 mol / L.

[0198] The system performs interactive analysis and processing. The initial electric double layer thickness of the natural iron oxide colloid is 10 nm. Due to the encapsulation effect of 15.5 mg / L EPS, the steric hindrance correction function calculates a feature scale offset of 12 nm, resulting in a corrected electric double layer thickness of 22 nm after fusion. Simultaneously, due to the complexation competition from 2.5 mmol / L citric acid, the trivalent yttrium ions (Yttrium ions) originally adsorbed on the colloid surface... 3+ 45% of the colloid was desorbed and stripped, resulting in the exposure of negative charges on the colloidal surface. The charge correction offset was equivalent to -20mV, and the updated effective surface potential dropped to -45mV.

[0199] Based on the aforementioned effective surface potential and corrected double-layer thickness, the target energy barrier height ΔΦ is calculated by superimposing near-range attraction and electrostatic repulsion on the system. max 18k B T. The critical deposition rate parameter k is obtained through thermodynamic probability transformation. att The desorption release rate parameter k is 0.03. det It is 0.008.

[0200] Input the spatial coordinates and time nodes (x, y, z, t) into the initial prediction network, and the network outputs the free rare earth concentration C. free Concentration C of rare earth elements in colloidal form colloid The system will use the above k att k de Substituting t and water velocity into the convection-dispersion dynamics equations, the physical residual term (first loss information L) is calculated using automatic differentiation techniques. phy Simultaneously, the fitting error between the predicted values ​​and a small number of borehole measured values ​​(second loss information L) is calculated. data ), and the penalty for the sum of the two violating the total concentration mass conservation boundary (third loss information L) mass ).

[0201] During the 500th training iteration, the system extracted L data The second gradient feature is much smaller than L phy The first gradient feature. The system triggers weight scheduling, calculates the target gradient balance coefficient as 0.05, and sets the physical constraint weight parameter L. phy The value is automatically reduced to 0.05. This effectively suppresses gradient explosion caused by physical residuals in the early stages of training, allowing the network to converge smoothly and obtain the target prediction network.

[0202] The system utilizes a target prediction network to output three-dimensional concentration field information for the target area over the next 180 days. It calculates the spatial gradient extrema, accurately locating the rare earth element migration front above the HDPE geomembrane layer at a depth of 15 meters. Combined with hydrodynamic characteristic calculations, the penetration probability is as high as 88%, exceeding the 75% warning threshold. The system then executes a three-dimensional fast convex hull algorithm on the discrete point set of the leak contact surface, generating red risk convex hull annotation features, which are then highlighted and flashed on the digital twin platform as a warning.

[0203] It is important to note that the technical solution of this application is not a simple combination of known physicochemical models and neural networks. In existing technologies, when PINN is applied to predict solute migration in groundwater, the reaction kinetic parameters (such as the colloidal deposition rate coefficient and the desorption release rate coefficient) in the convection-dispersion-reaction equation are usually used as artificially calibrated static constants, which cannot reflect the dynamic influence of biological activity in the target area on the colloidal transport state. While research in environmental science on the influence of bio-disturbance on colloidal surface properties has revealed the qualitative influence of extracellular polymers and low-molecular-weight organic acids on colloidal potential and stability, it has failed to transform this microscopic interface effect into quantitative kinetic parameters that can be directly used in macroscopic migration prediction models.

[0204] This application constructs a complete computational chain: "Bio-perturbation information → Interface interaction analysis (spatial steric hindrance correction + complexation competition analysis) → Effective surface potential → DLVO potential energy calculation → Energy barrier height → Thermodynamic probability conversion → Kinetic migration parameters (katt, kdet)". This quantitatively maps the microscopic interface effects of bio-perturbation to kinetic parameters in the PINN physical constraint equations, allowing the PINN physical constraints to be dynamically driven by real-time environmental data, rather than relying on static empirical constants. There are strict upstream and downstream data flow dependencies between the various stages of this computational chain—the input parameters for subsequent stages must be provided by the calculation results of preceding stages; they cannot operate independently. Therefore, the technical solution of this application is an organic whole with inherent coupling relationships, rather than a simple combination of known technologies.

[0205] To verify the effectiveness and superiority of the rare earth element migration prediction method proposed in this application, the real historical monitoring data of the above-mentioned rare earth tailings dam (a total of 365 days, with the first 90 days of data as known input and the last 275 days of data as prediction validation set) were used for comparative evaluation.

[0206] Three prediction models were set up for comparative experiments: Comparative Model A (Traditional Pure Data-Driven Model): Employs a standard gated recurrent unit (GRU) network, relying solely on historical monitoring concentrations from the previous 90 days for time-series fitting and prediction, without incorporating any physical mechanisms. Comparative Model B (Conventional PINN Model): Embeds a neural network with the standard convection-diffusion equation, but does not introduce biologically mediated interface interaction analysis (no spatial steric hindrance or complexation correction), and does not employ adaptive gradient balancing techniques (physical loss and data loss weights are fixed at 1:1). The model in this application (Adaptive Mechanism-Data Dual-Driven Model): Employs the scheme described in the complete claims of this application, including biological perturbation interface analysis, mass conservation constraints, and a gradient-based adaptive joint loss function. The validation results are shown in the table below:

[0207]

[0208] Table 1: Comparison of Verification Results

[0209] Thus, it can be seen that, after being deprived of a large amount of training data, the NMAE of the long sequence prediction of the comparative model A is as high as 57.9%, and the mass conservation violation rate is as high as 35.8%, indicating that the pure data-driven model is difficult to capture the physical mechanism of rare earth element migration. Although the comparative model B introduces the convection-diffusion equation as a constraint, due to the failure to consider the biologically mediated interface interaction effect and the existence of ill-conditioned gradient oscillation, the RMSE is still 8.23 ​​mg / L, and it still does not fully converge after 4500 iterations of training. The model in this application, through the refined mechanism of "biologically mediated-interface interaction-dynamic transformation" and the adaptive gradient balancing strategy, reduces the RMSE to 2.15 mg / L and suppresses the mass conservation violation rate to 0.8%, and can converge smoothly in only 1500 iterations. It is significantly better than the comparative model in terms of prediction accuracy, physical consistency and training efficiency.

[0210] In summary, this application enhances the generalization ability of the prediction network under complex geological conditions and sparse data scenarios, thereby improving the accuracy of rare earth element spatiotemporal evolution prediction and the reliability of engineering applications.

[0211] To better implement the above methods, this embodiment will use the specific integration of a rare earth element migration prediction system into an electronic device as an example to provide a detailed description of the methods in this application embodiment. For example, as Figure 2 As shown, the rare earth element migration prediction system may include a feature acquisition module 201, an interface interaction analysis module 202, a physical conservation analysis module 203, and an evolution prediction module 204, as follows:

[0212] (I) Feature acquisition module 201.

[0213] The feature acquisition module 201 is used to acquire the multidimensional environmental media features corresponding to the target area. The multidimensional environmental media features include biological disturbance information and physicochemical state information. The biological disturbance information includes the concentration features of microbial metabolic secretions, and the physicochemical state information includes the hydrodynamic features of porous media and the surface property features of natural colloids.

[0214] (II) Interface Interaction Analysis Module 202.

[0215] The interface interaction analysis module 202 is used to perform interface interaction analysis on the surface property characteristics of natural colloids in the physicochemical state information based on bio-disturbance information, to obtain the effective surface potential of natural colloids under bio-mediated conditions, and to calculate the interaction potential energy based on the effective surface potential, thereby obtaining the kinetic migration information corresponding to the target colloidal carrier. The kinetic migration information reflects the deposition and release state of the target colloidal carrier in the porous medium.

[0216] (III) Physical Conservation Analysis Module 203.

[0217] The physical conservation analysis module 203 is used to perform physical conservation analysis on the hydrodynamic characteristics in the dynamic migration information and physicochemical state information according to the preset porous media evolution relationship, so as to obtain the physical constraint characteristic information corresponding to the target area. The physical constraint characteristic information represents the residual constraint term corresponding to the physical conservation equation.

[0218] (iv) Evolution Prediction Module 204.

[0219] The evolution prediction module 204 is used to update the network parameters of the initial prediction network based on physical constraint feature information and through a preset joint loss function, and to perform spatiotemporal evolution prediction processing on rare earth elements in the target area to obtain the migration prediction results of rare earth elements in the target area.

[0220] In practice, each of the above units can be implemented as an independent entity or can be arbitrarily combined to be implemented as the same or several entities. For the specific implementation of each of the above units, please refer to the previous method embodiments, which will not be repeated here.

[0221] Therefore, the embodiments of this application enhance the generalization ability of the prediction network under complex geological conditions and sparse data scenarios, thereby improving the accuracy of rare earth element spatiotemporal evolution prediction and the reliability of engineering applications.

[0222] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be performed by instructions, or by instructions controlling related hardware. These instructions can be stored in a computer-readable storage medium and loaded and executed by a processor.

[0223] Therefore, embodiments of this application provide a computer-readable storage medium storing a plurality of instructions that can be loaded by a processor to execute the steps in any of the rare earth element migration prediction methods provided in embodiments of this application.

[0224] The storage medium may include: read-only memory (ROM), random access memory (RAM), disk or optical disk, etc.

[0225] Since the instructions stored in the storage medium can execute the steps in any of the rare earth element migration prediction methods provided in the embodiments of this application, the beneficial effects that any of the rare earth element migration prediction methods provided in the embodiments of this application can achieve can be realized. For details, please refer to the previous embodiments, which will not be repeated here.

[0226] According to one aspect of this application, a computer program product or computer program is provided, comprising a computer program / instructions stored in a computer-readable storage medium. A processor of an electronic device reads the computer program / instructions from the computer-readable storage medium and executes the computer program / instructions, causing the electronic device to perform the method provided in the rare earth element migration prediction aspect of the above embodiments.

[0227] The above provides a detailed description of a rare earth element migration prediction method and system provided in the embodiments of this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The description of the above embodiments is only for the purpose of helping to understand the method and its core ideas. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for predicting the migration of rare earth elements, characterized in that, The method includes: The multidimensional environmental media characteristics corresponding to the target area are obtained. The multidimensional environmental media characteristics include biological disturbance information and physicochemical state information. The biological disturbance information includes the concentration characteristics of microbial metabolic secretions. The physicochemical state information includes the hydrodynamic characteristics of porous media and the surface property characteristics of natural colloids. Based on the bio-disturbance information, the surface property characteristics of the natural colloids in the physicochemical state information are analyzed by interface interaction to obtain the effective surface potential of the natural colloids under bio-mediated conditions. The interaction potential energy is calculated based on the effective surface potential to obtain the kinetic migration information corresponding to the target colloidal carrier. The kinetic migration information reflects the deposition and release state of the target colloidal carrier in the porous medium. The natural colloids can adsorb and carry rare earth ions for co-migration. The natural colloids are clay minerals or iron and aluminum oxides at the nanometer to micrometer scale. The target colloidal carrier refers to tiny particles with a size between nanometer and micrometer in the liquid phase environment of the porous medium, and whose surface can adsorb, bind, or complex rare earth elements. The target colloidal carrier includes natural organic colloids rich in humic substances and iron oxide mineral particles with rare earth ions adsorbed on their surface. Based on the preset porous media evolution relationship, the hydrodynamic characteristics in the dynamic migration information and the physicochemical state information are subjected to physical conservation analysis to obtain the physical constraint characteristic information corresponding to the target region. The physical constraint characteristic information characterizes the residual constraint terms corresponding to the physical conservation equation. Based on the physical constraint feature information, the network parameters of the initial prediction network are updated using a preset joint loss function. Spatiotemporal evolution prediction processing is then performed on rare earth elements within the target region to obtain the rare earth element migration prediction results corresponding to the target region, including: The multidimensional environmental medium features and the corresponding spatiotemporal coordinate features are input into the initial prediction network to obtain the first predicted concentration features and the second predicted concentration features corresponding to the rare earth elements. The spatiotemporal coordinate features represent the three-dimensional spatial position and time evolution node corresponding to the multidimensional environmental medium features. The first predicted concentration features represent the concentration of free rare earth elements, and the second predicted concentration features represent the concentration of colloidal rare earth elements. Based on the physical constraint feature information, partial differential equation residual calculation processing is performed on the first predicted concentration feature and the second predicted concentration feature to obtain the first loss information. The first loss information characterizes the degree of deviation between the output result of the initial prediction network and the dynamic law of porous media. Based on the first predicted concentration feature, the second predicted concentration feature, and the actual monitored concentration feature corresponding to the target area, data fitting analysis is performed to obtain the second loss information. Based on the first predicted concentration feature, the second predicted concentration feature, and the total elemental concentration feature corresponding to the target region, a morphological conservation verification process is performed to obtain third loss information. The third loss information represents the penalty amount for the sum of the first predicted concentration feature and the second predicted concentration feature violating the mass conservation boundary. The first loss information, the second loss information, and the third loss information are weighted and fused to obtain a preset joint loss function. The network parameters of the initial prediction network are updated based on the joint loss function to obtain the target prediction network, so as to obtain the rare earth element migration prediction result through the target prediction network.

2. The method as described in claim 1, characterized in that, The step of performing interface interaction analysis on the surface property characteristics of natural colloids in the physicochemical state information based on the bio-perturbation information to obtain the effective surface potential of the natural colloids under bio-mediated conditions includes: From the bio-disturbance information, extract the extracellular polymer concentration characteristics and low molecular weight organic acid concentration characteristics; Based on the extracellular polymer concentration characteristics, the steric hindrance correction process is applied to the double layer thickness corresponding to the natural colloid to obtain the corrected double layer thickness. Based on the concentration characteristics of the low molecular weight organic acids, the rare earth ions in the target region are subjected to complexation competition analysis to obtain the charge correction offset corresponding to the natural colloid. Based on the corrected double layer thickness and the charge correction offset, the initial surface potential in the surface property features is updated to obtain the effective surface potential of the natural colloid under biological mediation.

3. The method as described in claim 2, characterized in that, The step of performing steric hindrance correction processing on the electric double layer thickness corresponding to the natural colloid based on the extracellular polymer concentration characteristics to obtain the corrected electric double layer thickness includes: Based on the preset colloidal physical properties, the initial double layer thickness parameter corresponding to the natural colloid is determined. The initial double layer thickness parameter characterizes the effective scale of the surface electrostatic field of the natural colloid in the porous medium liquid phase environment when it is not disturbed by biological activity. Based on the extracellular polymer concentration characteristics, a steric hindrance correction function for the natural colloid is constructed. Based on the spatial steric hindrance correction function, calculate the characteristic scale offset of the bioadsorption layer corresponding to the extracellular polymer to the effective action scale; The feature scale offset is fused with the initial double layer thickness parameter to obtain the corrected double layer thickness corresponding to the natural colloid.

4. The method as described in claim 2, characterized in that, The step of performing complexation competition analysis on rare earth ions in the target region based on the concentration characteristics of the low-molecular-weight organic acids to obtain the charge correction offset corresponding to the natural colloid includes: The concentration characteristics of competing mineral ions in the porous medium and the initial surface adsorption characteristics of rare earth ions on the surface of the natural colloid are obtained. The competing mineral ions are ions that compete with the rare earth ions for adsorption on the surface of the natural colloid. The initial surface adsorption characteristics characterize the quantity and binding state of the rare earth ions on the surface of the natural colloid before the introduction of the low molecular weight organic acid. Based on the concentration characteristics of the low molecular weight organic acids and the concentration characteristics of the competing mineral ions, a competitive substitution function for the rare earth ions is constructed. The competitive substitution function characterizes the probability mapping relationship of the stripping of the rare earth ions on the surface of the natural colloid by free ions in the environmental liquid phase. Based on the competitive substitution function, calculate the complexation-desorption ratio of the low-molecular-weight organic acid on the initial surface adsorption characteristics; Based on the complexation-desorption ratio, the effective charge distribution state of the natural colloid after desorption is determined, and the charge correction offset corresponding to the natural colloid is calculated based on the effective charge distribution state.

5. The method as described in claim 1, characterized in that, The step of calculating the interaction potential energy based on the effective surface potential to obtain the kinetic migration information corresponding to the target colloidal carrier includes: The size distribution characteristics of the target colloidal carrier and the ion background characteristics of the pore fluid in the porous medium are obtained. The ion background characteristics characterize the electrolyte strength of the liquid phase environment inside the porous medium. Based on the size distribution characteristics, the short-range gravitational potential energy between the target colloidal carrier and the porous medium is calculated. The short-range gravitational potential energy characterizes the inherent attraction of the target colloidal carrier in the porous medium due to its own physical size. Based on the effective surface potential and the ion background characteristics, the electrostatic repulsion potential energy between the target colloidal carrier and the porous medium is calculated. The electrostatic repulsion potential energy characterizes the surface charge repulsion effect experienced by the target colloidal carrier under the current electrolyte strength. By superimposing and analyzing the near-range gravitational potential energy and the electrostatic repulsive potential energy, the total interaction potential energy characteristics corresponding to the target colloidal carrier are obtained. The potential energy extreme value feature is extracted from the total interaction potential energy feature as the target energy barrier height. The target energy barrier height characterizes the maximum potential energy threshold that the target colloidal carrier needs to overcome when a state transition occurs. Thermodynamic probability conversion is performed based on the target energy barrier height to obtain the critical deposition rate parameter and desorption release rate parameter corresponding to the target colloidal carrier. The critical deposition rate parameter and the desorption release rate parameter are used as the kinetic migration information.

6. The method as described in claim 1, characterized in that, The weighted fusion processing of the first loss information, the second loss information, and the third loss information to obtain a preset joint loss function includes: Obtain the target network parameters corresponding to the initial prediction network in the current training stage, as well as the preset weight scheduling cycle characteristics, wherein the weight scheduling cycle characteristics characterize the adaptive weight triggering interval of the initial prediction network during the network training process. Based on the target network parameters, a first gradient feature corresponding to the first loss information and a second gradient feature corresponding to the second loss information are calculated. The first gradient feature represents the degree to which the first loss information dominates the update of the target network parameters in the current training phase, and the second gradient feature represents the degree to which the second loss information dominates the update of the target network parameters in the current training phase. Under the condition that the preset weight scheduling cycle characteristics are met in the current training phase, balance difference analysis is performed based on the first gradient characteristics and the second gradient characteristics to obtain the target gradient balance coefficient. Based on the target gradient balance coefficient, the preset physical constraint weight parameters of the initial prediction network are adaptively updated to obtain the target physical constraint weight parameters. The target physical constraint weight parameters are used to suppress the excessive dominance of the first loss information on the update of the target network parameters in the initial iteration stage when the second loss information has not reached the preset convergence condition. Based on the target physical constraint weight parameters, the first loss information, the second loss information, and the third loss information are weighted and fused to obtain a preset joint loss function.

7. The method as described in claim 1, characterized in that, After obtaining the rare earth element migration prediction results corresponding to the target region, the method further includes: The three-dimensional concentration field information of the rare earth element migration prediction results in the target area is extracted, and the spatial change rate of the three-dimensional concentration field information is calculated to obtain the concentration gradient distribution characteristics. Based on the gradient extreme value abrupt change information in the concentration gradient distribution characteristics, the target migration front characteristics are determined, and the target migration front characteristics characterize the diffusion front boundary of the rare earth element in the target region; A pre-constructed spatial model of the geological impermeable layer for the target area is obtained, and spatial intersection analysis is performed on the target migration front characteristics and the geological impermeable layer spatial model to obtain the target intersection area characteristics; Based on the dynamic migration information, the hydrodynamic characteristics in the physicochemical state information, and the physical thickness characteristics corresponding to the geological seepage barrier spatial model, the penetration probability analysis is performed on the characteristics of the target intersection region to obtain target penetration probability information. The target penetration probability information characterizes the risk probability that the target colloidal carrier carrying the rare earth element will break through the geological seepage barrier spatial model. Under the condition that the target penetration probability information meets the preset risk warning threshold, the three-dimensional spatial discrete point set corresponding to the target intersection region feature is subjected to minimum bounding box analysis to generate risk convex hull annotation features, and three-dimensional visualization warning processing is performed based on the risk convex hull annotation features.

8. The method as described in claim 1, characterized in that, Before obtaining the multidimensional environmental media characteristics of the target area, the method further includes: An initial geological spatial model corresponding to the target area is obtained, and based on the initial geological spatial model and a preset prior prediction network, the information entropy distribution features corresponding to the candidate sampling grids in the target area are extracted. The information entropy distribution features characterize the degree of cognitive uncertainty of the prior prediction network regarding the target area in the initial evolution prediction state. Extract the heterogeneity abrupt change features of the medium corresponding to the initial geological spatial model. The heterogeneity abrupt change features of the medium characterize the spatial gradient change distribution of the physical permeability properties within the target area. Based on the information entropy distribution characteristics and the heterogeneous mutation characteristics of the medium, the candidate sampling grids are subjected to joint sampling benefit evaluation processing to obtain the target sampling benefit score matrix; Based on the target sampling benefit scoring matrix, node optimization analysis is performed in the candidate sampling grid to determine the target sampling space node, so as to obtain multi-dimensional environmental medium characteristics at the target sampling space node.

9. A rare earth element migration prediction system, characterized in that, The system includes: The feature acquisition module is used to acquire multidimensional environmental media features corresponding to the target area. The multidimensional environmental media features include biological disturbance information and physicochemical state information. The biological disturbance information includes the concentration features of microbial metabolic secretions. The physicochemical state information includes the hydrodynamic features of porous media and the surface property features of natural colloids. The interface interaction analysis module is used to perform interface interaction analysis on the surface property characteristics of natural colloids in the physicochemical state information based on the bio-disturbance information, to obtain the effective surface potential of the natural colloid under bio-mediated conditions, and to calculate the interaction potential energy based on the effective surface potential to obtain the kinetic migration information corresponding to the target colloidal carrier. The kinetic migration information reflects the deposition and release state of the target colloidal carrier in the porous medium. The natural colloid can adsorb and carry rare earth ions for co-migration. The natural colloid is a clay mineral and iron and aluminum oxide at the nanometer to micrometer scale. The target colloidal carrier refers to a tiny particulate matter with a size between nanometer and micrometer in the liquid phase environment of the porous medium, and whose surface can adsorb, bind or complex rare earth elements. The target colloidal carrier includes natural organic colloids rich in humic substances and iron oxide mineral particles with rare earth ions adsorbed on their surface. The physical conservation analysis module is used to perform physical conservation analysis on the hydrodynamic characteristics in the dynamic migration information and the physicochemical state information according to the preset porous media evolution relationship, so as to obtain the physical constraint characteristic information corresponding to the target region. The physical constraint characteristic information represents the residual constraint term corresponding to the physical conservation equation. The evolution prediction module is used to update the network parameters of the initial prediction network based on the physical constraint feature information and through a preset joint loss function, and to perform spatiotemporal evolution prediction processing on rare earth elements in the target region to obtain the rare earth element migration prediction results corresponding to the target region, including: The multidimensional environmental medium features and the corresponding spatiotemporal coordinate features are input into the initial prediction network to obtain the first predicted concentration features and the second predicted concentration features corresponding to the rare earth elements. The spatiotemporal coordinate features represent the three-dimensional spatial position and time evolution node corresponding to the multidimensional environmental medium features. The first predicted concentration features represent the concentration of free rare earth elements, and the second predicted concentration features represent the concentration of colloidal rare earth elements. Based on the physical constraint feature information, partial differential equation residual calculation processing is performed on the first predicted concentration feature and the second predicted concentration feature to obtain the first loss information. The first loss information characterizes the degree of deviation between the output result of the initial prediction network and the dynamic law of porous media. Based on the first predicted concentration feature, the second predicted concentration feature, and the actual monitored concentration feature corresponding to the target area, data fitting analysis is performed to obtain the second loss information. Based on the first predicted concentration feature, the second predicted concentration feature, and the total elemental concentration feature corresponding to the target region, a morphological conservation verification process is performed to obtain third loss information. The third loss information represents the penalty amount for the sum of the first predicted concentration feature and the second predicted concentration feature violating the mass conservation boundary. The first loss information, the second loss information, and the third loss information are weighted and fused to obtain a preset joint loss function. The network parameters of the initial prediction network are updated based on the joint loss function to obtain the target prediction network, so as to obtain the rare earth element migration prediction result through the target prediction network.

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