A method for generating materials with two-dimensional perception diffusion and physical relaxation optimization

Abstract

The application discloses a two-dimensional perception diffusion and physical relaxation optimization material generation method, and belongs to the field of computer technology and material design. The method comprises the following steps: constructing a high-quality two-dimensional material training dataset; decomposing a material structure into in-plane periodic fractional coordinates and out-of-plane aperiodic centralized coordinates, and constructing a two-dimensional perception structure representation; constructing a joint diffusion generation model containing continuous variable diffusion and discrete variable diffusion, and introducing conditional control information to support multi-objective constraint generation; introducing atomic distance, layer thickness, lattice distortion and symmetry consistency physical constraints in the model training and generation process; jointly training the diffusion generation model based on the training dataset; generating a candidate two-dimensional material structure through the trained diffusion model; adopting a relaxation optimization model based on a machine learning atomic potential to perform physical relaxation optimization and stability screening on the candidate structure, and outputting a target two-dimensional material structure.

Description

Technical Field

[0001] This invention relates to the fields of computer technology and materials design, and in particular to a two-dimensional material generation method and system based on a combination of artificial intelligence diffusion models and physical simulation. Background Technology

[0002] In the field of materials science, materials design and new materials development are crucial foundational steps for optimizing material performance and innovating functions. Traditional materials design methods typically rely on researchers' experience, theoretical analysis, and extensive experimental trial and error, continuously adjusting material composition, crystal structure, and preparation processes to obtain materials with target properties. These methods are characterized by long development cycles, high experimental costs, and difficulty in achieving rapid screening and optimization in high-dimensional material combinations. In recent years, with the development of artificial intelligence, machine learning and deep learning methods have been increasingly applied to materials design. By learning the mapping relationship between material structure and properties, they enable material performance prediction, structural optimization, and the automatic generation of new materials, thus providing a new technological path for new materials development.

[0003] However, existing technologies still have many shortcomings. For example, current material generation methods based on variational autoencoders or generative adversarial networks typically use fixed-dimensional feature vectors to represent crystal structures, making it difficult to maintain periodic boundary conditions between atoms. This leads to problems such as abnormal atomic spacing or lattice distortion in the generated structures. Furthermore, the application of existing diffusion models in the field of material generation is mostly concentrated on three-dimensional crystal materials, lacking dedicated modeling schemes for the coexistence of in-plane periodicity and out-of-plane aperiodicity in two-dimensional materials. At the same time, existing generation models generally lack physical constraint mechanisms, easily generating materials with unstable energy or unreasonable structures, and have weak ability to jointly control the generation of multiple performance parameters, lacking post-processing optimization processes that combine physical simulation.

[0004] Therefore, how to simultaneously ensure the accuracy of structural representation, the physical rationality of the generation process, and the controllability of multiple performance parameters during the generation of two-dimensional materials has become a pressing technical problem that needs to be solved. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a material generation method based on a two-dimensional perceptual diffusion model and physical relaxation optimization. This method solves the problems of insufficient structural expression ability, unstable generated structures, and lack of multi-condition control in existing material generation methods, thereby improving the accuracy and physical rationality of material generation.

[0006] To address the aforementioned technical problems, this invention provides the following technical solution: a material generation system based on a two-dimensional perceptual diffusion model and physical relaxation optimization. This system comprises: a data construction module, a structure representation module, a diffusion model module, a condition control module, a physical constraint module, a model training module, a generation module, and a relaxation optimization module, which are sequentially or interactively connected to respectively realize the acquisition and processing of two-dimensional material data, the construction of a two-dimensional perceptual structure representation, the establishment of a joint diffusion model, the introduction of condition control information, the application of physical constraints, model training, candidate structure generation, and relaxation optimization. The data construction module is used to acquire two-dimensional material data from multiple material databases, perform structural fingerprinting, deduplication, property calculation and quality screening, and build a high-quality two-dimensional material training dataset. The structure representation module is used to perform structure representation transformation on the two-dimensional material data, decompose the material structure into in-plane and out-of-plane directions, represent the in-plane coordinates as periodic fractional coordinates, and represent the out-of-plane coordinates as non-periodic Cartesian coordinates and perform centering processing to construct a two-dimensional perceptual structure representation. The diffusion model module is used to construct diffusion models for material structure generation, including graph structure modeling, structural feature extraction, continuous variable diffusion modeling, discrete variable diffusion modeling, joint generation mechanism and model coupling; The condition control module is used to acquire target condition information for controlling material generation, encode and generate condition embedding vectors, and input them into the diffusion generation model after fusing with material structural features. It supports multi-condition joint control and condition-guided generation. The physical constraint module is used to introduce physical constraint mechanisms during the material generation process, including at least one of the following: minimum interatomic distance constraint, layer thickness constraint and plane collapse constraint, in-plane lattice distortion constraint, and symmetry consistency constraint. The model training module is used to train the diffusion generation model based on the training data of the two-dimensional material, including applying noise perturbation to continuous variables and discrete variables respectively, inputting the perturbated variables and condition information into the model for joint modeling, constructing a training objective function and iteratively optimizing the model parameters; The generation module is used to generate candidate two-dimensional material structures based on the trained diffusion generation model under the guidance of target conditions. It includes generation initialization, progressive denoising sampling, condition guidance, legality check and candidate reordering. The relaxation optimization module is used to perform physical relaxation optimization on the generated candidate two-dimensional material structures, including fine-tuning of the potential energy model, prediction of physical quantities of candidate structures, relaxation update under two-dimensional boundary conditions, convergence determination, stability screening, and result output.

[0007] Furthermore, the specific implementation process of the data construction module is as follows: Two-dimensional material structure data are obtained from multiple two-dimensional material databases, including but not limited to C2DB database, JARVIS-DFT database, MC2D database and 2DMatpedia database; The acquired two-dimensional material structure data are characterized by structural fingerprints, and the similarity between material structures is identified through structural fingerprints. Based on the structural fingerprint similarity results, the material structures are deduplicated, duplicate or highly similar material structures are deleted, and unique two-dimensional material structures are retained to construct a redundancy-free two-dimensional material database. The physical properties of the deduplicated two-dimensional material structure are calculated using a material simulation model. The physical properties include one or more of energy, atomic force, stress, and magnetic moment. The calculated material data is subjected to quality screening, which includes removing data with missing key physical properties and outlier data to obtain a two-dimensional material training dataset.

[0008] Furthermore, the specific implementation process of the structure representation module includes: The material structure is divided into in-plane and out-of-plane directions; The atomic coordinates in the in-plane direction are represented as periodic fractional coordinates, as follows:

[0009] Describe the atomic coordinates in the out-of-plane direction as Cartesian coordinates. And by centralizing it, we get:

[0010] in, This represents the average value of all out-of-plane coordinates of the atoms; Calculate the layer thickness parameters based on the out-of-plane coordinates:

[0011] Based on in-plane fractional coordinates, out-of-plane centered coordinates, and layer thickness parameters, a two-dimensional material structure representation is constructed to serve as the input representation for subsequent models.

[0012] Furthermore, the construction process of the diffusion model module includes: The material structure is represented as a graph structure, where atoms are nodes and the interactions between atoms are edges. Construct a graph-based feature extraction model to extract spatial relationships and structural features between atoms; A continuous variable diffusion module is constructed to model atomic spatial coordinates and lattice parameters. The continuous variable diffusion process is represented as follows:

[0013] in, This represents continuous variables, including lattice parameters, in-plane coordinates, and out-of-plane coordinates. Indicates noise scheduling parameters; A discrete variable diffusion module is constructed to model material element types. The discrete diffusion process is represented as follows:

[0014] in, Represents a variable of discrete element type. Let be the transition probability matrix, and satisfy:

[0015] in, This represents the probability coefficient of element class retention during the t-th step of the discrete diffusion process. For reference element distribution; Represents the identity matrix Based on the graph structure feature extraction model, the continuous variable diffusion module and the discrete variable diffusion module are jointly modeled, and the structural information and element type information are collaboratively generated by sharing graph neural network features. The feature extraction model is coupled with the diffusion generation module, so that structural features are used as conditional inputs to the diffusion process, and participate in the modeling and prediction of the diffusion process.

[0016] Furthermore, the specific implementation process of the condition control module is as follows: Acquire target condition information for controlling the material generation process, the target condition information including material performance parameters and structural property parameters; The target condition information is encoded to obtain a condition embedding vector c; The conditional embedding vector is fused with the material structure features to generate a conditional enhanced feature representation, and the conditional enhanced feature is used as input to the diffusion generation model; During the diffusion generation process, the conditional embedding vector is introduced into the reverse diffusion process as conditional constraint information to constrain the gradual denoising process of the material structure, so that the generation result meets the constraint requirements corresponding to the target conditional information. By jointly encoding and fusing multi-source target condition information, joint constraints on material performance parameters and structural property parameters can be generated.

[0017] Furthermore, the specific implementation process of the physical constraint module is as follows: (1) Interatomic distance constraint The interatomic distance is calculated using the periodic minimum mirror rule in the inward direction. The interatomic distance is calculated using non-periodic Euclidean distance in the outward direction. The total distance between atoms is defined as:

[0018] When the interatomic distance satisfies When this is the case, a distance constraint term is introduced:

[0019] in, To calculate the in-plane and out-of-plane atomic distances using periodic boundary conditions, This is the preset minimum atomic spacing threshold.

[0020] (2) Layer thickness constraint A layer thickness constraint model is constructed to characterize the geometric distribution characteristics of two-dimensional materials in the out-of-plane direction.

[0021] Calculate layer thickness parameters based on the out-of-plane atomic distribution of two-dimensional materials:

[0022] in, Represents the set of out-of-plane coordinates of all atoms When the layer thickness parameter At that time, a layer thickness constraint term is introduced:

[0023] in, This indicates the preset minimum layer thickness threshold. This represents the layer thickness constraint loss term.

[0024] The training data provides the target layer thickness. In this case, a layer thickness deviation constraint term is further introduced:

[0025] in, This represents the target layer thickness parameter.

[0026] (3) Lattice distortion constraint A lattice distortion constraint model is constructed to limit excessive deviation in the ratio of the lengths of the two in-plane lattice basis vectors. First, the lattice aspect ratio parameter is calculated based on the lengths of the two in-plane lattice basis vectors:

[0027] Based on the aforementioned lattice aspect ratio parameter, the lattice distortion constraint is defined as:

[0028] in, , Represents the two in-plane lattice basis vectors of a two-dimensional material; , These represent the moduli of the lattice basis vectors, The preset lattice aspect ratio threshold, This is the lattice distortion constraint loss term. When the lattice aspect ratio parameter is not greater than the lattice aspect ratio threshold, the lattice distortion constraint loss is zero; when the lattice aspect ratio parameter is greater than the lattice aspect ratio threshold, a squared penalty is applied to the portion exceeding the lattice aspect ratio threshold.

[0029] (4) Symmetry constraints For training samples with symmetry labels, apply the corresponding set of space group symmetry operations to the denoised two-dimensional material structure. And calculate the matching error between the structure after symmetric transformation and the original structure:

[0030] in, This represents the total number of atoms in the material's structure. This indicates a predefined spatial group symmetry operation. Indicates the first Atoms undergo space group symmetry operations The corresponding symmetrical equivalent atoms of the same element type, Indicates the first The in-plane fractional coordinates of the i-th atom, representing the i-th atom's... The out-of-plane coordinates of an atom, This represents a distance metric that takes into account in-plane periodic boundary conditions. This represents the loss term for symmetric consistency constraints.

[0031] When the aspect ratio of the lattice exceeds the preset range, a symmetry consistency constraint penalty is applied to the corresponding structure.

[0032] (5) Energy stability constraints An energy stability constraint term is constructed based on the energy assessment results of the generated structure to constrain the thermodynamic stability of the generated structure.

[0033] The total energy of the generated structure was calculated using an energy assessment model. And energy constraint terms are defined based on structural energy:

[0034] in, This represents the total energy of the generated structure. This indicates the preset target energy threshold. This represents the energy stability constraint.

[0035] When the total energy of the generated structure exceeds the target energy threshold, an energy penalty constraint is applied to the corresponding structure to guide the generated structure toward a low-energy stable configuration.

[0036] Furthermore, the specific implementation process of the model training module includes: Noise perturbation is applied to continuous variables, including continuous diffusion noise applied to two-dimensional lattice parameters, in-plane atomic coordinates, and out-of-plane atomic coordinates.

[0037] For two-dimensional lattice parameters Its diffusion perturbation process is defined as:

[0038] in, Indicates the first The lattice parameters after diffusion are Indicates the parameters for scheduling diffused noise. This represents Gaussian noise.

[0039] For in-plane periodic fractional coordinates Apply periodic noise perturbation while maintaining periodic boundary conditions. The perturbation process is defined as follows:

[0040] in, Indicates the first Fractional coordinates within the plane after step diffusion. This indicates periodic disturbance noise. This represents the noise intensity parameter.

[0041] For out-of-plane coordinates Apply continuous noise perturbation in Euclidean space. The perturbation process is defined as follows:

[0042] in, Indicates the first Out-of-plane coordinates after step diffusion This represents Gaussian noise in the out-of-plane direction.

[0043] Applying discrete diffusion perturbations to discrete variables, including performing discrete diffusion processes on element categories, results in a transition probability matrix defined as follows:

[0044] in, Indicates the first Step-discrete diffusion transition probability matrix, Represents the discrete diffuse noise figure. Indicates the distribution of the reference element. Represents the identity matrix.

[0045] The perturbated two-dimensional lattice parameters, atomic coordinates, element types, and conditional information are jointly input into the diffusion generation model for joint modeling, and the denoised two-dimensional lattice parameters, in-plane coordinates, out-of-plane coordinates, and element types are predicted respectively.

[0046] Construct a training objective function based on the model prediction results:

[0047] in, This indicates the lattice parameter reconstruction loss; This represents the in-plane coordinate reconstruction loss; This indicates the loss in out-of-plane coordinate reconstruction; This represents the loss for predicting element categories; Indicates physical constraint loss; This represents the loss of symmetric consistency. and These are the weighting coefficients for physical constraint loss and symmetry consistency loss, respectively.

[0048] The lattice parameter reconstruction loss is defined as follows:

[0049] in, This represents the lattice parameters predicted by the model. Represents the actual lattice parameters.

[0050] The in-plane coordinate reconstruction loss is defined as:

[0051] in, Represents the predicted in-plane fractional coordinates. Represents the fractional coordinates within the true plane. This represents a periodic translation vector.

[0052] The out-of-plane coordinate reconstruction loss is defined as:

[0053] in, Indicates the predicted out-of-plane coordinates. Represents the actual out-of-plane coordinates.

[0054] The element class prediction loss is defined as:

[0055] in, Indicates the category label of the actual element. This represents the probability of the element class predicted by the model.

[0056] Based on the training objective function, the parameters of the diffusion generation model are iteratively optimized to achieve joint generative learning of two-dimensional material structure and elemental composition.

[0057] Furthermore, the specific implementation process of the generation module includes: Based on the trained diffusion generation model, candidate two-dimensional material structures are generated under the guidance of target condition information.

[0058] Generation initialization phase: Based on the statistical prior distribution of the training data or a preset initialization strategy, the two-dimensional lattice parameters, in-plane periodic fractional coordinates, out-of-plane coordinates, and element categories are initialized.

[0059] Continuous variable denoising generation stage: Stepwise denoising sampling is performed on the two-dimensional lattice parameters, in-plane coordinates, and out-of-plane coordinates. The continuous variable denoising process is expressed as follows:

[0060] in: Indicates the first Continuous variables in a step-diffusion state; Represents a continuous variable after denoising; Indicates the parameters for scheduling diffused noise; Represents the cumulative diffusion coefficient; This represents the noise term predicted by the diffusion model; Indicates conditional control information; This represents Gaussian random noise.

[0061] The continuous variables include two-dimensional lattice parameters, in-plane periodic coordinates, and out-of-plane coordinates.

[0062] Discrete variable denoising generation stage: Perform progressive discrete denoising sampling on the element type, based on the element probability distribution predicted by the model. Sampling by element category yields the first Step element type .

[0063] in, This represents the probability distribution of element categories predicted by the model. This represents the element category variable after denoising.

[0064] Condition-guided generation phase: During the stepwise sampling process, the denoising results of conditional and unconditional branches are combined to guide the diffusion generation process, thereby enhancing the consistency between the generated structure and the target conditions.

[0065] The conditional guidance method includes a classifier-guided method or a classifier-free guidance method.

[0066] Two-dimensional structure legality check stage: Perform structural validity checks on the generated candidate two-dimensional material structures, including layer thickness range checks and minimum atomic spacing checks.

[0067] When the layer thickness parameter satisfies Or there exists an interatomic distance that satisfies When this happens, the corresponding candidate structure will be judged as an unqualified structure.

[0068] in, This represents the layer thickness parameter of the generated structure. This indicates the preset minimum layer thickness threshold; Represents atoms With atoms The distance between them; This indicates the preset minimum atomic spacing threshold.

[0069] Symmetry post-processing and candidate reordering stage: Symmetry post-processing is performed on candidate structures that are detected as having low symmetry in order to obtain structural forms that meet the target symmetry requirements.

[0070] Based on the symmetry quality, structural stability, and condition matching degree of the candidate structures, multiple candidate two-dimensional material structures are reordered to output the final generated result.

[0071] Furthermore, the specific implementation process of the relaxation optimization module includes: A pre-trained machine learning atomic potential energy model is selected, and the pre-trained model is fine-tuned based on a two-dimensional material dataset to obtain a relaxation optimization model suitable for two-dimensional material systems.

[0072] The pre-trained machine learning atomic potential energy model includes an atomic potential energy model based on a graph neural network. The model can be a two-dimensional MatterSim model or a machine learning potential energy model for other material systems.

[0073] The generated candidate two-dimensional material structures are input into the fine-tuned relaxation optimization model to calculate the total energy of the system corresponding to the candidate structures. Atomic forces and stress tensors.

[0074] The force on an atom is defined as follows:

[0075] in, Represents atoms The forces acting on it; This represents the total energy of the system; Indicates the atom Gradient operator for coordinates.

[0076] While maintaining the in-plane periodic boundary conditions and the out-of-plane non-periodic boundary conditions, iterative relaxation optimization is performed on the candidate two-dimensional material structure.

[0077] The atomic coordinate update process is represented as follows:

[0078] in, Indicates the first Atomic coordinates of the next iteration; Indicates the step size for updating atomic coordinates; This represents the gradient of the system's energy with respect to the atomic coordinates.

[0079] Update the in-plane lattice parameters based on the stress tensor:

[0080] in, Indicates the first The lattice parameters for the next iteration; Indicates the lattice update step size; This represents the stress tensor corresponding to the structure.

[0081] The thickness of the vacuum layer in the out-of-plane direction remains fixed or is limited to a preset range.

[0082] The relaxation iteration terminates when the convergence condition is met, which is:

[0083] and:

[0084] in, This represents the force convergence threshold of an atom; Indicates the energy convergence threshold; and These represent the total energy of the system corresponding to adjacent iteration steps.

[0085] The stability of relaxed two-dimensional material structures is evaluated and candidates are screened. The screening indicators include at least system energy, minimum interatomic spacing, layer thickness parameters, and structural symmetry.

[0086] Based on the screening results, retain the two-dimensional material structures that meet the target requirements.

[0087] Output the target two-dimensional material structure after relaxation optimization and stability screening, along with the corresponding lattice parameters, atomic coordinates, elemental composition, and target performance prediction results.

[0088] By employing the above technical solutions, the present invention provides a material generation method, system, and terminal based on a two-dimensional sensing diffusion model and physical relaxation optimization, which has at least the following beneficial effects: This invention addresses the structural characteristics of two-dimensional materials, which exhibit periodicity in the in-plane direction and aperiodicity in the out-of-plane direction. It divides the structure of two-dimensional materials into in-plane periodic fractional coordinates and out-of-plane aperiodic coordinates, and constructs a two-dimensional perceptual structure representation method. This method can more accurately characterize the layered structural features and spatial distribution characteristics of two-dimensional materials, thereby improving the expressive power and structural preservation ability of two-dimensional material structure modeling.

[0089] This invention employs a joint modeling mechanism of continuous variable diffusion and discrete variable diffusion to achieve the coordinated generation of lattice parameters, atomic spatial coordinates, and elemental composition. Simultaneously, by introducing a conditional control mechanism, it achieves the joint constraint generation of various material performance parameters and structural property parameters, thereby improving the consistency and controllability between the generated two-dimensional material structure and the target performance.

[0090] This invention introduces multi-dimensional physical constraint mechanisms such as interatomic distance constraints, layer thickness constraints, lattice distortion constraints, and symmetry consistency constraints during the diffusion generation process, and applies these physical constraints simultaneously to the model training stage and the structure generation stage, thereby reducing the probability of generating non-physical or unstable structures and improving the physical rationality, thermodynamic stability, and structural reliability of the generated two-dimensional material structures.

[0091] This invention further combines a machine learning atomic potential energy model based on two-dimensional material data fine-tuning to perform structural relaxation optimization on the generated candidate structures, and iteratively optimizes atomic coordinates and lattice parameters under two-dimensional boundary conditions, thereby obtaining two-dimensional material structures with higher thermodynamic stability. At the same time, through stability assessment and candidate screening mechanisms, a complete two-dimensional material generation process from candidate generation, physical optimization to structure screening is realized, improving the applicability of the generation results in computational verification and experimental screening. Attached Figure Description

[0092] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is an overall flowchart of a material generation method based on a two-dimensional sensing diffusion model and physical relaxation optimization according to the present invention. Detailed Implementation

[0093] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the following embodiments are for illustrative purposes only and are not intended to limit the scope of protection of this invention.

[0094] This embodiment constructs a high-quality two-dimensional material dataset, designs a two-dimensional sensing structure representation method, establishes a joint diffusion generation model, introduces conditional control mechanisms and physical constraint mechanisms, generates candidate two-dimensional material structures after completing model training, and further obtains stable two-dimensional material structures through physical relaxation optimization.

[0095] like Figure 1 As shown, the system of the present invention includes: a data construction module, a structure representation module, a diffusion model module, a condition control module, a physical constraint module, a model training module, a generation module, and a relaxation optimization module. The following describes each module in detail with reference to specific embodiments.

[0096] Data building module Two-dimensional material data are obtained from multiple material databases, including but not limited to C2DB, JARVIS-DFT, MC2D, and 2DMatpedia database.

[0097] Structural fingerprinting is performed on the acquired material structures to identify the similarity between material structures; based on the structural fingerprint results, the materials are deduplicated to retain unique material structures, thereby constructing a non-redundant two-dimensional material database.

[0098] Material simulation models are used to calculate the properties of material structures, including physical properties such as system energy, atomic forces, stress tensors, and magnetic moments.

[0099] Data quality screening includes: (1) removing data with missing key physical attributes; and (2) filtering outlier data that exceeds the preset range.

[0100] Finally, a high-quality two-dimensional material training dataset was constructed.

[0101] Structure representation module: The structural representation transformation of the two-dimensional material data includes: The material structure is divided into in-plane and out-of-plane directions; The atomic coordinates in the in-plane direction are represented as periodic fractional coordinates:

[0102] in, and These represent the fractional coordinates of the atoms in the basis vector directions of the two-dimensional lattice.

[0103] The atomic coordinates in the out-of-plane direction are represented as aperiodic Cartesian coordinates. .

[0104] The external coordinates are centralized:

[0105] in, This represents the average value of all out-of-plane coordinates of the atoms.

[0106] Calculate layer thickness parameters based on out-of-plane coordinates:

[0107] in, This represents the layer thickness parameter of a two-dimensional material.

[0108] Based on in-plane periodic fractional coordinates, out-of-plane centered coordinates, and layer thickness parameters, a two-dimensional perceptual structure representation is constructed for use as input to the subsequent diffusion generation model.

[0109] Diffusion Model Module Construct a diffusion model for the generation of two-dimensional material structures.

[0110] First, the material structure is represented as a graph structure, where atoms are nodes and the interactions between atoms are edges.

[0111] A graph-based feature extraction model is constructed to extract spatial relationships and structural features between atoms.

[0112] Furthermore, a continuous-variable diffusion module is constructed to model lattice parameters, in-plane coordinates, and out-of-plane coordinates. Its continuous diffusion process is represented as follows:

[0113] in, Indicates the first The continuous variables in the step-diffusion state include lattice parameters, in-plane coordinates, and out-of-plane coordinates; Indicates the parameters for scheduling diffused noise; Represents the identity matrix.

[0114] Furthermore, a discrete variable diffusion module is constructed to model the element type, and its discrete diffusion process is represented as follows:

[0115] in, Indicates the first Element type variables in the step diffusion state; This represents the transition probability matrix.

[0116] The transition probability matrix satisfies:

[0117] in, Represents the discrete diffuse noise figure; Indicates the distribution of reference elements.

[0118] By jointly modeling the continuous variable diffusion module and the discrete variable diffusion module, the collaborative generation of two-dimensional material structure information and elemental composition information is achieved through shared graph neural network features.

[0119] The graph structure feature extraction model is coupled with the diffusion generation module, so that the structural features participate in the modeling and prediction of the diffusion process.

[0120] Condition control module Obtain target condition information for controlling the material generation process, including material performance parameters and structural property parameters.

[0121] The target condition information includes, but is not limited to, band gap, formation energy, space group, magnetic moment, and layer thickness parameters.

[0122] The target condition information is encoded to generate a conditional embedding vector. .

[0123] The conditional embedding vector is fused with the material structure features and then input into the diffusion generation model to conditionally guide the generation process.

[0124] During the diffusion generation process, the denoising process is constrained based on the conditional embedding vector, so that the generated two-dimensional material structure gradually approximates the information distribution that satisfies the target conditions.

[0125] It supports the joint input of multiple conditional information to achieve controllable generation of two-dimensional materials under multi-objective constraints.

[0126] Physical constraint module Introducing physical constraint mechanisms during the material generation process, including one or more of the following: (1) Minimum distance constraint between atoms: The interatomic distance is calculated using the periodic minimum mirror rule in the inward direction. The interatomic distance is calculated using non-periodic Euclidean distance in the outward direction. The total distance between atoms is defined as:

[0127] When the interatomic distance satisfies When this is the case, a distance constraint term is introduced:

[0128] in, This indicates the preset minimum interatomic distance threshold.

[0129] (2) Layer thickness constraint: Calculate layer thickness parameters based on the out-of-plane atomic distribution of two-dimensional materials:

[0130] in, This represents the set of out-of-plane coordinates of all atoms.

[0131] When the layer thickness parameter satisfies At that time, a layer thickness constraint term is introduced:

[0132] in, This indicates the preset minimum layer thickness threshold.

[0133] In the presence of target layer thickness In this case, a layer thickness deviation constraint term is further introduced:

[0134] (3) In-plane lattice distortion constraint: Calculate the lattice aspect ratio parameter based on the lengths of the two in-plane lattice basis vectors:

[0135] in, and These represent the lattice vector magnitudes, respectively. Based on the aforementioned lattice aspect ratio parameter, the lattice distortion constraint is defined as:

[0136] The aspect ratio parameter of the crystal lattice. The preset lattice aspect ratio threshold, This is the lattice distortion constraint loss term. When the lattice aspect ratio parameter is not greater than the lattice aspect ratio threshold, the lattice distortion constraint loss is zero; when the lattice aspect ratio parameter is greater than the lattice aspect ratio threshold, a squared penalty is applied to the portion exceeding the lattice aspect ratio threshold.

[0137] (4) Symmetric consistency constraint: For training samples with symmetric labels, apply a set of space group symmetric operations to the denoised structure. And calculate the matching error between the structures before and after the transformation:

[0138] in, This represents the total number of atoms in the material's structure. This indicates a predefined spatial group symmetry operation. Indicates the first Atoms undergo space group symmetry operations The corresponding symmetrical equivalent atoms of the same element type, Indicates the first The in-plane fractional coordinates of the i-th atom, representing the i-th atom's... The out-of-plane coordinates of an atom, This represents a distance metric that takes into account in-plane periodic boundary conditions. This represents the loss term for symmetric consistency constraints.

[0139] Physical constraint mechanisms can be used as part of the loss function in the model training phase for model optimization, or as candidate structure selection rules in the generation phase to improve the physical rationality and stability of the generated structures.

[0140] Model training module The diffusion generation model is trained based on the training data.

[0141] For continuous variables, including lattice parameters, in-plane coordinates, and out-of-plane coordinates, apply continuous diffusion noise perturbation.

[0142] The diffusion process of the two-dimensional lattice parameters is represented as follows:

[0143] in, .

[0144] The in-plane periodic fractional coordinate perturbation process is represented as:

[0145] in, .

[0146] The out-of-plane coordinate diffusion process is represented as:

[0147] in, .

[0148] For discrete variables, the transition probability matrix is ​​defined as follows: (The text is incomplete and requires further context.)

[0149] The perturbated variables and conditional information are input into the diffusion generation model to predict the denoised lattice parameters, atomic coordinates, and element categories.

[0150] The training objective function is defined as:

[0151] in:

[0152]

[0153]

[0154]

[0155] in, Represents the physical constraint loss term; Represents the symmetric consistency loss term; and This represents the weighting coefficient of the corresponding loss term.

[0156] The Adam optimizer is used to iteratively optimize the parameters of the diffusion generation model.

[0157] Generate module Candidate two-dimensional material structures are generated based on the trained diffusion generation model.

[0158] First, based on the statistical priors of the training data or a preset initialization strategy, the lattice parameters, in-plane coordinates, out-of-plane coordinates, and element categories are initialized.

[0159] For continuous variables, progressive denoising sampling is performed, and the sampling process is represented as follows:

[0160] in: Indicates the first Continuous variables in a step-diffusion state; Represents a continuous variable after denoising; Indicates the parameters for scheduling diffused noise; Represents the cumulative diffusion coefficient; This represents the noise term predicted by the diffusion model; Indicates conditional control information; This represents Gaussian random noise.

[0161] For discrete variables, based on the predicted probability distribution By sampling the element categories step by step, we can obtain .

[0162] During the sampling process, the prediction results of conditional branch and unconditional branch are combined to guide the diffusion generation process, so as to enhance the consistency between the generated structure and the target conditions.

[0163] Furthermore, a two-dimensional structure validity check is performed on the generated candidate structure, including layer thickness range check and minimum atomic spacing check.

[0164] When the layer thickness parameter satisfies Or there exists an interatomic distance that satisfies When this happens, the corresponding candidate structure will be judged as an unqualified structure.

[0165] Symmetry post-processing is performed on low-symmetry candidate structures, and multiple candidate structures are reordered based on structural symmetry quality.

[0166] Relaxation optimization module Physical relaxation optimization is performed on the generated candidate two-dimensional material structures.

[0167] A pre-trained machine learning atomic potential energy model was selected and fine-tuned based on two-dimensional material data to obtain a relaxation optimization model suitable for two-dimensional material systems.

[0168] The pre-trained machine learning atomic potential energy model includes the MatterSim model or other atomic potential energy models based on graph neural networks.

[0169] The candidate two-dimensional material structure is input into the relaxation optimization model to calculate the total energy of the system. Atomic forces and stress tensors.

[0170] The force on an atom is defined as follows:

[0171] While maintaining the in-plane periodic boundary conditions and the out-of-plane non-periodic boundary conditions, iterative relaxation optimization is performed on the candidate structure.

[0172] The atomic coordinate update process is represented as follows:

[0173] in, This indicates the step size for updating atomic coordinates.

[0174] Update the in-plane lattice parameters based on the stress tensor:

[0175] in, Indicates the lattice parameter update step size; This represents the stress tensor corresponding to the structure.

[0176] The thickness of the vacuum layer in the out-of-plane direction remains fixed or limited to a preset range.

[0177] Relaxation optimization terminates when the following convergence condition is met:

[0178] and:

[0179] The stability of relaxed two-dimensional material structures is evaluated and candidates are screened. The screening indicators include formation energy, minimum interatomic spacing, layer thickness parameter, structural symmetry, and phonon spectrum stability.

[0180] The final output is a two-dimensional material structure that meets the target requirements, along with the corresponding lattice parameters, atomic coordinates, elemental composition, and performance prediction results.

[0181] Those skilled in the art will understand that all or part of the processes in the embodiments of the present invention can be implemented by computer program instructions to related hardware devices. The computer program can be stored in a computer-readable storage medium and, when executed, implements the method steps described in the embodiments of the present invention. The computer-readable storage medium includes, but is not limited to, magnetic storage, optical storage, flash memory, solid-state drives, and other storage media capable of storing program code.

[0182] The embodiments of the present invention can also be implemented using a combination of software and hardware. The hardware component may include a processor, memory, graphics processor, server, or other computing devices used for model training and inference; the software component may include material data processing programs, diffusion generation model programs, structural optimization programs, and physical simulation programs, etc.

[0183] The embodiments in this specification are described in a progressive manner. The same or similar parts between the embodiments can be referred to each other. Each embodiment focuses on describing its distinguishing features from other embodiments.

[0184] It should be understood that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the present invention. For those skilled in the art, various modifications, substitutions and improvements can be made to the technical solutions of the present invention without departing from the technical concept of the present invention, and all such modifications, substitutions and improvements should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A material generation system for two-dimensional sensing diffusion and physical relaxation optimization, characterized in that, The system includes a data construction module, a structure representation module, a diffusion model module, a condition control module, a physical constraint module, a model training module, a generation module, and a relaxation optimization module, which are connected sequentially or interactively to realize the acquisition and processing of two-dimensional material data, the construction of two-dimensional sensing structure representation, the establishment of a joint diffusion model, the introduction of condition control information, the application of physical constraints, model training, candidate structure generation, and relaxation optimization, respectively. The data construction module is used to acquire two-dimensional material data from multiple material databases, perform structural fingerprinting, deduplication, property calculation and quality screening, and build a high-quality two-dimensional material training dataset. The structure representation module is used to perform structure representation transformation on the two-dimensional material data, decompose the material structure into in-plane and out-of-plane directions, represent the in-plane coordinates as periodic fractional coordinates, and represent the out-of-plane coordinates as non-periodic Cartesian coordinates and perform centering processing to construct a two-dimensional perceptual structure representation; The diffusion model module is used to construct diffusion models for material structure generation, including graph structure modeling, structural feature extraction, continuous variable diffusion modeling, discrete variable diffusion modeling, joint generation mechanism and model coupling; The condition control module is used to acquire target condition information for controlling material generation, encode and generate condition embedding vectors, and input them into the diffusion generation model after fusing with material structural features. It supports multi-condition joint control and condition-guided generation. The physical constraint module is used to introduce physical constraint mechanisms during the material generation process, including at least one of the following: minimum interatomic distance constraint, layer thickness constraint and plane collapse constraint, in-plane lattice distortion constraint, and symmetry consistency constraint. The model training module is used to train the diffusion generation model based on the training data of the two-dimensional material. It includes applying noise perturbation to continuous variables and discrete variables respectively, inputting the perturbated variables and condition information into the model for joint modeling, constructing a training objective function and iteratively optimizing the model parameters. The generation module is used to generate candidate two-dimensional material structures based on the trained diffusion generation model under the guidance of target conditions. It includes generation initialization, progressive denoising sampling, condition guidance, legality check and candidate reordering. The relaxation optimization module is used to perform physical relaxation optimization on the generated candidate two-dimensional material structures, including fine-tuning of the potential energy model, prediction of physical quantities of candidate structures, relaxation update under two-dimensional boundary conditions, convergence determination, stability screening, and result output.

2. The material generation system for two-dimensional sensing diffusion and physical relaxation optimization according to claim 1, characterized in that, The specific implementation process of the structure representation module includes: The material structure is divided into in-plane and out-of-plane directions; The atomic coordinates in the in-plane direction are represented as periodic fractional coordinates: Describe the atomic coordinates in the out-of-plane direction as Cartesian coordinates. And by centralizing it, we get: in This represents the average value of all out-of-plane coordinates of the atoms; Calculate the layer thickness parameters based on the out-of-plane coordinates: Based on in-plane fractional coordinates, out-of-plane centered coordinates, and layer thickness parameters, a two-dimensional perceptual structure representation is constructed to serve as the input representation for subsequent models.

3. The material generation system for two-dimensional sensing diffusion and physical relaxation optimization according to claim 1, characterized in that, The construction process of the diffusion model module includes: The material structure is represented as a graph structure, where atoms are nodes and the interactions between atoms are edges. Construct a graph-based feature extraction model to extract spatial relationships and structural features between atoms; A continuous variable diffusion module is constructed to model atomic spatial coordinates and lattice parameters. The continuous variable diffusion process is represented as follows: in Represents continuous variables, Indicates noise scheduling parameters; A discrete variable diffusion module is constructed to model material element types. The discrete diffusion process is represented as follows: in Represents a variable of discrete element type. The transition probability matrix; Based on the graph structure feature extraction model, the continuous variable diffusion module and the discrete variable diffusion module are jointly modeled, and the structural information and element type information are collaboratively generated by sharing graph neural network features.

4. The material generation system for two-dimensional sensing diffusion and physical relaxation optimization according to claim 1, characterized in that, In the physical constraint module: Interatomic distance constraints are defined as: in To calculate in-plane and out-of-plane atoms using periodic boundary conditions Inter-space distance, The minimum atomic spacing threshold is preset; Layer thickness constraint is defined as when the layer thickness parameter When this happens, a constraint term is introduced: in To preset the minimum layer thickness threshold, This represents the layer thickness constraint loss term; Lattice distortion constraints are used to limit excessive deviation in the ratio of in-plane lattice basis lengths. First, based on the in-plane lattice... The length of the basis vector is used to calculate the lattice aspect ratio parameter. Based on the aforementioned lattice aspect ratio parameter, the lattice distortion constraint is defined as: in Let A represent the two in-plane lattice basis vectors of the material structure. The aspect ratio parameter of the crystal lattice. The preset lattice aspect ratio threshold, This is the lattice distortion constraint loss term. When the lattice aspect ratio parameter is not greater than the lattice aspect ratio threshold, the lattice distortion constraint loss is zero; when the lattice aspect ratio parameter is greater than the lattice aspect ratio threshold, a squared penalty is applied to the portion exceeding the lattice aspect ratio threshold. The symmetry consistency constraint is defined as: in, This represents the total number of atoms in the material's structure. This indicates a predefined spatial group symmetry operation. Indicates the first Atoms undergo space group symmetry operations The corresponding symmetrical equivalent atoms of the same element type, Indicates the first The in-plane fractional coordinates of the i-th atom, representing the i-th atom's... The out-of-plane coordinates of an atom, This represents a distance metric that takes into account in-plane periodic boundary conditions. This represents the loss term for symmetric consistency constraints.

5. The material generation system for two-dimensional sensing diffusion and physical relaxation optimization according to claim 1, characterized in that, The training objective function of the model training module is: in, For lattice parameter reconstruction loss, For in-plane coordinate reconstruction loss, For out-of-plane coordinate reconstruction loss, Predict loss for element categories, For physical constraint loss, For symmetric consistency loss, and These are the weighting coefficients for physical constraint loss and symmetry consistency loss, respectively.

6. The material generation system for two-dimensional sensing diffusion and physical relaxation optimization according to claim 1, characterized in that, In the generation module, the stepwise denoising sampling process for continuous variables is represented as follows: in, For the first Continuous variables of the step, For the noise predicted by the model, For conditional control information, For the first Noise scheduling parameters for each step For cumulative noise scheduling parameters, It is Gaussian random noise; Furthermore, a validity check is performed on the generated candidate structures, when the layer thickness parameter... Or there may be interatomic distance If so, it is judged as an unqualified structure.

7. The material generation system for two-dimensional sensing diffusion and physical relaxation optimization according to claim 1, characterized in that, The relaxation optimization module employs a pre-trained machine learning atomic potential energy model, which is then fine-tuned based on a two-dimensional material dataset. The atomic coordinate update process is as follows: The in-plane lattice parameter update process is as follows: in Update the step size for atomic coordinates. The update coefficients are used to convert the stress tensor into in-plane lattice parameter updates. For energy gradient, It is the stress tensor; the out-of-plane lattice parameters remain unchanged during the in-plane lattice parameter update process; The relaxation convergence condition is: and: in For atoms to experience forces, The force convergence threshold of the atom. This is the convergence threshold for the energy change between two adjacent iterations.

8. The material generation system for two-dimensional sensing diffusion and physical relaxation optimization according to claim 1, characterized in that, In the condition control module, the target condition information includes material performance parameters and structural property parameters. The material performance parameters include band gap, formation energy, and magnetic moment, while the structural property parameters include space group and layer thickness parameters. By jointly encoding and fusing multi-source target condition information, joint constraints on material performance parameters and structural property parameters are generated.

9. The material generation system for two-dimensional sensing diffusion and physical relaxation optimization according to claim 1, characterized in that, The data construction module acquires two-dimensional material data from C2DB, JARVIS-DFT, MC2D, and 2DMatpedia databases; identifies the similarity between material structures through structural fingerprinting and performs deduplication; and uses a material simulation model to calculate the physical properties of energy, atomic force, stress, and magnetic moment. Remove missing key physical properties and outlier data that are outside the preset range to obtain a two-dimensional material training dataset.

10. A method for generating materials using two-dimensional sensing diffusion and physical relaxation optimization, characterized in that, Using the system of any one of claims 1 to 9, perform the following steps: Step 1: Construct a high-quality two-dimensional material training dataset using the data construction module; Step 2: Convert the material data into a two-dimensional perceptual structure representation using the structure representation module; Step 3: Construct and couple a joint diffusion generation model of continuous and discrete variables using the diffusion model module; Step 4: Introduce target condition information through the condition control module and fuse it with structural features; Step 5: Introduce physical constraints such as interatomic distance, layer thickness, lattice distortion, and symmetry through the physical constraint module; Step 6: Jointly train the diffusion generation model using the model training module; Step 7: Generate candidate two-dimensional material structures under the guidance of the target conditions using the generation module; Step 8: Perform physical relaxation optimization and stability screening on the candidate structures through the relaxation optimization module, and output the target two-dimensional material structure.

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