Disordered crystal structure generation method and apparatus, device, and storage medium

Abstract

The application provides a disordered crystal structure generation method, device and equipment and a storage medium, and relates to the technical field of material science and artificial intelligence. The method comprises the following steps: acquiring lattice parameters and site geometric information of a disordered crystal; constructing a substitutional disorder occupancy probability vector and a positional disorder weight probability vector for each site, and the vectors both satisfy simplex constraints of non-negativity and sum of 1; based on a flow matching generation process, taking the variables as joint generation variables to continuously evolve and jointly update along a time parameter from a prior distribution, and applying simplex constraints to the probability vectors during the whole updating process; and finally outputting a discrete disordered crystal structure through a voting discretization strategy. The application can uniformly depict substitutional disorder and positional disorder, stably generate a disordered crystal under probability constraints, and improve structure recoverability.

Description

Technical Field

[0001] This invention relates to the field of materials science and artificial intelligence, and in particular to a method, apparatus, device and storage medium for generating disordered crystal structures. Background Technology

[0002] The discovery and design of new materials are fundamental issues driving technological advancements in fields such as energy, electronics, and structural materials. Traditional materials discovery processes often rely on computational simulations and global searches (such as energy-based structure enumeration and phase stability searches). While reliable, these methods are typically computationally expensive and involve vast search spaces, making it difficult to efficiently cover large-scale material spaces. In recent years, deep generative models have been introduced into crystal structure generation / prediction tasks to directly learn the distribution of crystal data and rapidly generate candidate structures, thereby significantly improving the efficiency of materials discovery. Furthermore, these models make it easier to incorporate physical priors such as the periodicity of crystals into the modeling process.

[0003] Existing deep generation methods have made rapid progress on ordered crystals: some methods employ a two-stage strategy, first generating lattice parameters and then generating atomic positions and compositions; others jointly generate lattice, coordinates, and composition through diffusion / denoising processes; and still others learn distributions on Riemannian manifolds of crystal structures based on flow models of reversible mappings; recently, generation frameworks have also emerged that gradually refine structural parameters through iterative Bayesian inference. These methods generally rely on the fundamental assumption of "perfect periodicity," meaning that atomic types and precise coordinates repeat deterministically in three-dimensional space, thus enabling learning and sampling within a relatively well-defined representation space.

[0004] However, besides ordered crystals, there are a large number of disordered crystals that are crucial in applications, such as high-entropy alloys, solid electrolytes, and disordered superconducting systems. A key characteristic of disordered crystals is that their structure is not strictly deterministically repeating, but rather characterized probabilistically by variations in sites and positions. The paper emphasizes two typical types of disorder: substitutional disorder (SD), where different elements occupy the same lattice site with a certain probability; and positional disorder (PD), where atoms shift or split into multiple candidate sites relative to their ideal positions, distributed with probability weights at these sites. Characterizing these two types of disorder typically requires a "disorder weight" vector, whose components should be non-negative and sum to 1, thus forming a probability distribution (simplex constraint).

[0005] The probabilistic nature of disordered crystals makes existing generation models for ordered crystals difficult to apply directly. On the one hand, existing representations typically lack a unified, compact, and efficient method for characterizing the probabilistic occupancy of the sorted scalar (SD) and the multiple positions / offsets of the disordered scalar (PD). On the other hand, even when using continuous variables to represent disordered weights, the simplex constraint must be strictly satisfied, while many generation frameworks primarily model in Euclidean space or one-hot discrete spaces, making it difficult to stably generate physically effective probability distributions during training and sampling. Furthermore, due to the aforementioned difficulties in modeling and constraint handling, the field of disordered crystal generation lacks mature, unified public benchmarks and general technical routes.

[0006] In summary, existing technologies still have significant shortcomings in the end-to-end generation of disordered crystals: they lack a unified structural representation that can simultaneously cover both SD and PD, lack a mechanism for stably generating disordered weights under probabilistic simplex constraints, and lack an overall generative modeling framework that matches the disordered geometric structure. These problems form the practical basis for proposing the technical solution of this invention. Summary of the Invention

[0007] This invention provides a method, apparatus, device, and storage medium for generating disordered crystal structures. The technical problem it addresses is that existing crystal generation methods primarily target ordered crystals, typically employing one-hot element assignment and single-coordinate representation, which struggles to uniformly characterize and replace truly disordered structures such as disorder and positional disorder. Furthermore, disordered occupancy / positional weights are probabilistic variables that must satisfy the non-negative, sum-to-1 simplex constraint. Existing methods that generate in Euclidean space and then normalize are prone to numerical instability and physical inconsistencies. Moreover, existing methods lack an effective mechanism to reliably convert the disordered probability output into a discrete disordered crystal structure usable for subsequent structure optimization and property calculation. Therefore, this invention aims to provide a generation scheme that, while satisfying probabilistic constraints and crystal geometric consistency, can uniformly represent and generate disordered crystal structures end-to-end, achieving stable discretized output.

[0008] In a first aspect, the present invention provides a method for generating a disordered crystal structure, the method comprising: The lattice parameters and site geometry information of the target disordered crystal are obtained. The site geometry information includes the principal fractional coordinates of at least one symmetric independent site and at least one candidate fractional coordinate when there is site disorder. For each symmetric independent site, a replacement disorder occupancy probability vector and a site disorder weight probability vector are constructed. The components of the replacement disorder occupancy probability vector are non-negative and their sum is 1. The components of the site disorder weight probability vector are non-negative and their sum is 1. Based on the flow matching generation process, the lattice parameters, principal fraction coordinates, candidate fraction coordinates, substitution disorder occupancy probability vector, and position disorder weight probability vector are used as joint generation variables. Starting from a preset prior distribution, continuous evolution and joint updates are performed along the time parameter until the target data distribution is reached, resulting in a disordered crystal structure in continuous probability form. In each step of the continuous evolution and joint update, probabilistic simplex constraints are applied to the substitution disorder occupancy probability vector and the position disorder weight probability vector, such that the components of the updated substitution disorder occupancy probability vector remain non-negative and their sum is 1, and the components of the updated position disorder weight probability vector remain non-negative and their sum is 1. A voting discretization strategy is applied to the disordered crystal structure of the continuous probability form to output a discrete disordered crystal structure.

[0009] In one possible design, constructing a replacement disordered occupancy probability vector and a positional disordered weight probability vector for each of the symmetric independent sites includes: For each symmetrical independent site Let the probability vector of replacing disordered occupancy be denoted as The positional disorder weight probability vector is denoted as ; When this symmetrical independent site When replacing disorder, the probability vector of replacing disordered occupancy. Each component represents the probability or proportion of the corresponding element occupying that site; when this symmetric independent site When ordered, the probability vector of replacing disordered occupants It degenerates into a one-hot vector; When the location is unordered, the unordered weight probability vector Each component represents the probability or proportion of that site occupying the corresponding candidate score coordinate; when the site is unordered, the unordered position weight probability vector It degenerates into a deterministic weight vector.

[0010] In one possible design, based on the flow matching generation process, the lattice parameters, the principal fractional coordinates, the candidate fractional coordinates, the substitution disorder occupancy probability vector, and the position disorder weight probability vector are used as joint generation variables. Starting from a preset prior distribution, continuous evolution and joint updates are performed along the time parameters, including: Let the time parameter be denoted as The jointly generated variables in time The state is denoted as ,in Indicates lattice parameters, Represents the principal fraction coordinates. Represents the coordinates of the candidate scores. This represents the probability vector of replacing disordered occupants. This represents the positional unordered weight probability vector; Predicting the joint generative variables over time using neural networks velocity field ; According to the velocity field For the joint generated variables Update to obtain the state at the next time step. , where the probability vector of replacing disordered occupancy and the positional unordered weight probability vector The update employs a constraint update method consistent with probabilistic simplex geometry, ensuring that the updated replacement disordered occupancy probability vector... Each component is non-negative and their sum is 1, and the updated position is an unordered weight probability vector. Each component is non-negative and their sum is 1.

[0011] In one possible design, the use of neural networks to predict the joint generating variables over time... velocity field ,include: The lattice parameters of the current state, the principal fractional coordinates of each symmetric independent site, the candidate fractional coordinates, the substitution disorder occupancy probability vector, and the position disorder weight probability vector are input into the graph neural network, which models the interaction between sites. For sites with disordered positions, the geometric relationship is calculated simultaneously based on the principal fraction coordinates and the candidate fraction coordinates during the message passing process of the graph neural network to obtain distance and direction information of multiple position combinations. Based on the output of the graph neural network, the velocity field components corresponding to the lattice parameters, the principal fractional coordinates, the candidate fractional coordinates, the substitution disorder occupancy probability vector, and the position disorder weight probability vector are predicted respectively.

[0012] In one possible design, the implementation of a voting discretization strategy on the disordered crystal structure of continuous probability form to output a discrete disordered crystal structure includes: For each symmetric independent site, the probability vector of substitution disordered occupancy and the probability vector of position disordered weight are discretized in two stages: in the first stage, sites with highly concentrated probability distributions are determined as single-element occupancy or single-position occupancy; in the second stage, a candidate set is constructed for the remaining disordered sites. For the candidate set, candidate positions are selected from the replacement disordered position probability vector and candidate positions are selected from the position disordered weight probability vector according to multiple different candidate rules, resulting in multiple discrete candidate results; The multiple discrete candidate results are integrated and voted on, and the final multi-element occupancy scheme or multi-position occupancy scheme is output based on the voting results as the discrete disordered crystal structure.

[0013] In one possible design, the method further includes, before starting from a pre-defined prior distribution: Conditional initialization is performed based on at least one of the following conditional information: the chemical formula, element set, or number of sites of the target disordered crystal. An initial joint generation variable state matching the conditional information is sampled from the preset prior distribution.

[0014] In one possible design, the continuous evolution and joint update process also includes: After each update step, a crystal periodic constraint is applied to the principal fractional coordinates and the candidate fractional coordinates, and the fractional coordinates that exceed the unit cell range are mapped back to the standard unit cell range by translation. Based on the update of the lattice parameters, the periodic equivalent representations of the principal fractional coordinates and the candidate fractional coordinates are adjusted synchronously to ensure that the joint generation variables satisfy crystal geometric consistency throughout the update process.

[0015] In a second aspect, the present invention provides a disordered crystal structure generation apparatus, the apparatus comprising: A disordered crystal unified representation module is configured to acquire the lattice parameters and site geometry information of the target disordered crystal. The site geometry information includes principal fractional coordinates of at least one symmetric independent site and at least one candidate fractional coordinate when there is positional disorder. For each symmetric independent site, a replacement disorder occupancy probability vector and a positional disorder weight probability vector are constructed. The components of the replacement disorder occupancy probability vector are non-negative and their sum is 1. The components of the positional disorder weight probability vector are non-negative and their sum is 1. The disordered crystal generation module is configured to use a flow-matching generation process, taking the lattice parameters, principal fractional coordinates, candidate fractional coordinates, substitution disorder occupancy probability vector, and position disorder weight probability vector as joint generation variables. Starting from a preset prior distribution, it continuously evolves and jointly updates along the time parameter until it evolves to the target data distribution, thus obtaining a disordered crystal structure in continuous probability form. In each step of the continuous evolution and joint update, a probabilistic simplex constraint is applied to the substitution disorder occupancy probability vector and the position disorder weight probability vector, such that the components of the updated substitution disorder occupancy probability vector remain non-negative and their sum is 1, and the components of the updated position disorder weight probability vector remain non-negative and their sum is 1. The voting discretization module is configured to perform a voting discretization strategy on the disordered crystal structure of the continuous probability form and output a discrete disordered crystal structure.

[0016] Thirdly, embodiments of the present invention provide an electronic device, comprising: at least one processor and a memory; the memory storing computer execution instructions; the at least one processor executing the computer execution instructions stored in the memory, causing the at least one processor to perform the disordered crystal structure generation method as described in the first aspect and various possible designs of the first aspect.

[0017] Fourthly, embodiments of the present invention provide a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the disordered crystal structure generation method described in the first aspect and various possible designs of the first aspect.

[0018] Fifthly, embodiments of the present invention provide a computer program product, including a computer program that, when executed by a processor, implements the disordered crystal structure generation method described in the first aspect and various possible designs of the first aspect.

[0019] The method, apparatus, device, and storage medium for generating disordered crystal structures provided by this invention have at least the following beneficial effects: This invention constructs a replacement disordered occupancy probability vector and a position disordered weight probability vector for each symmetric independent site, and ensures that each component strictly satisfies the simplex constraint that is non-negative and sums to 1. At the same time, it applies a constraint update method consistent with simplex geometry to the probability vector during the flow matching generation process. This avoids the boundary numerical instability and physical inconsistency problems caused by normalization alone after generation in traditional Euclidean space. It ensures that the probability output of the entire generation process is within the legal physical range, thereby solving the modeling problem that ordered crystal generation models are difficult to directly transfer to disordered systems. Building upon this foundation, by coupling lattice parameters, principal fractional coordinates, candidate fractional coordinates, and two types of probability vectors as joint generation variables for continuous evolution, and simultaneously calculating geometric relationships based on principal and candidate fractional coordinates during the update process, the generation process can fully integrate distance and orientation information from multiple positional combinations. This significantly improves the structural recoverability in cases of mixed substitution disorder and positional disorder. Experimental data show that this invention improves the matching rate by 12.21 percentage points on the COD-SPD-20 benchmark and by 10.39 percentage points on the more challenging COD-SPD-50 benchmark, while maintaining the same order of magnitude in matching accuracy, verifying its effectiveness in complex disordered systems. Furthermore, through a two-stage deterministic and multi-rule integrated voting discretization strategy, the continuous probability output is transformed into a discrete disordered crystal structure that satisfies stoichiometry and site consistency. This effectively reduces the randomness and uncertainty of a single discretization path, enabling the generation results to reliably connect to subsequent structure optimization and property calculation processes, thereby improving the engineering usability and implementation efficiency of disordered crystal structure prediction tasks. Attached Figure Description

[0020] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0021] Figure 1 A flowchart of a method for generating a disordered crystal structure provided in an embodiment of the present invention; Figure 2 This is a flowchart of the disordered crystal generation process provided in an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the working principle of the voting discretization strategy provided in this embodiment of the invention. Figure 4 This is a structural diagram of the disordered crystal structure generation device provided in an embodiment of the present invention.

[0022] The accompanying drawings have illustrated specific embodiments of the invention, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the invention in any way, but rather to illustrate the concept of the invention to those skilled in the art through reference to specific embodiments. Detailed Implementation

[0023] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of apparatuses and methods consistent with some aspects of the invention as detailed in the appended claims.

[0024] In the technical solution of this invention, the collection, storage, use, processing, transmission, provision and disclosure of relevant data and information comply with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0025] It should be noted that in the embodiments of the present invention, certain software, components, models and other existing solutions in the industry may be mentioned. These should be regarded as exemplary and are only intended to illustrate the feasibility of implementing the technical solution of the present invention. However, they do not mean that the inventor has used or necessarily used the solution.

[0026] The technical solution of the present invention and how the technical solution of the present invention solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of the present invention will now be described with reference to the accompanying drawings.

[0027] This invention provides a method for generating disordered crystal structures. It solves the problems of existing technologies, such as difficulty in uniformly characterizing SD / PD, difficulty in stably satisfying probabilistic constraints, and difficulty in discretizing and implementing the generated results, by working together through three technical measures: unified representation of disordered crystals, consistent generation process, and voting discretization from probability to discrete structure.

[0028] Before describing the specific implementation methods, the technical principles involved in this invention will first be explained to enable those skilled in the art to understand the theoretical basis of this invention. Flow matching is a generative modeling method based on Continuous Normalizing Flow (CNF). Its core idea is to construct a probability path that evolves over time, smoothly transforming a simple prior distribution (such as a standard normal distribution) into a target data distribution. Specifically, flow matching learns a vector field parameterized by a neural network, which defines the instantaneous direction and magnitude of the probability density change during the time evolution process. By solving the Ordinary Differential Equation (ODE), samples from the prior distribution can be pushed to the target distribution along the time dimension, thereby generating new samples. The advantage of flow matching over the traditional diffusion model is that its probability path can be directly constructed from the optimal transport scheme between the target distribution and the prior distribution, thus obtaining a more stable and efficient training signal, and the number of sampling steps can be flexibly configured. However, when the generated variables include probability vectors (such as the substitution disordered occupancy probability vector and the position disordered weight probability vector in this invention), these variables must remain within the probability simplex throughout the entire generation process, meaning that each component is non-negative and their sum is 1. The standard flow matching framework operates in Euclidean space and cannot naturally guarantee this constraint; if normalization is only performed after generation, negative values ​​or numerical overflows are easily generated in intermediate states, leading to physically invalid structural intermediate states and thus affecting the final generation quality. Therefore, this invention, based on the flow matching framework, introduces a constraint update method consistent with simplex geometry to ensure that the probability variables satisfy the probability simplex constraint at every step of the ODE solution, thereby guaranteeing the physical legitimacy of the structure at the generation source. The technical solution of this invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0029] like Figure 1 As shown, the disordered crystal structure generation method specifically includes the following steps S10-S30, where the three steps correspond to the three technical measures mentioned above: unified representation of disordered crystals, consistent generation process of constraints, and voting discretization from probability to discrete structure.

[0030] S10: Obtain the lattice parameters and site geometry information of the target disordered crystal; construct a replacement disorder occupancy probability vector and a position disorder weight probability vector for each symmetric independent site, wherein each component of the replacement disorder occupancy probability vector is non-negative and its sum is 1, and each component of the position disorder weight probability vector is non-negative and its sum is 1.

[0031] In step S10, lattice parameters can be obtained from X-ray diffraction (XRD) experimental data or density functional theory (DFT), or read from known crystal structure databases (such as the Inorganic Crystal Structure Database (ICSD) and the Materials Project). Site geometry information can be determined based on crystallographic symmetry analysis. By using space group information recorded in the International Tables for Crystallography, inequivalent crystallographic sites (Wyckoff sites) are identified to determine the number, coordinates, and multiplicity of symmetry-independent sites. When obtained from experimental data, the XRD pattern is refined using Rietveld to obtain the lattice constant and atomic fraction coordinates; when read from a database, cell parameters and atomic position information are directly extracted.

[0032] In this embodiment, the site geometry information includes the principal fractional coordinates of at least one symmetric independent site and at least one candidate fractional coordinate when there is positional disorder.

[0033] It should be noted that fractional coordinates are a coordinate representation based on the unit cell basis vectors, and their values ​​typically range from [0,1). Any fractional coordinate plus any integer vector describes the same position within the unit cell, which is the core of the periodicity constraint of crystals. The principal fractional coordinate represents the symmetric position of the site in an ideal crystal structure, while the candidate fractional coordinates represent the deviated positions that the site might occupy when positional disorder occurs. For the same symmetric independent site, the number of candidate fractional coordinates can be 2, 3, or more, depending on the actual physical situation of positional disorder at that site. For example, in solid electrolyte materials, some sites can split into 2 to 4 candidate positions, each corresponding to atomic vibrations or migration paths at different temperatures.

[0034] In some embodiments, step S10 can be specifically constructed by the following steps S101-S103 for each symmetric independent site to construct a replacement disordered occupancy probability vector and a position disordered weight probability vector.

[0035] S101: For each symmetrical independent site Let the probability vector of replacing disordered occupancy be denoted as The position-disordered weight probability vector is denoted as .

[0036] S102: When this symmetrical independent site When replacing disorder, the probability vector of replacing disordered occupants. Each component represents the probability or proportion of the corresponding element occupying that site; when this symmetric independent site When ordered, replace the disordered occupancy probability vector. It degenerates into a one-hot vector.

[0037] S103: When the site is out of order, the positional disorder weight probability vector Each component represents the probability or proportion of that site occupying the corresponding candidate score coordinate; when the site is unordered, the unordered position weight probability vector... It degenerates into a deterministic weight vector.

[0038] In another embodiment, an exemplary unified representation scheme for disordered crystals is provided. Specifically, this embodiment first constructs a unified data representation suitable for disordered crystals to simultaneously characterize substitution disorder (SD) and positional disorder (PD), while being compatible with ordered crystals as a special case. For each symmetric independent site in the crystal... Its state is defined by the following elements: 1) Lattice parameters / cell matrix , used to describe periodic crystal lattices; 2) A set of fractional coordinates used to describe the geometric location of a point: containing principal fractional coordinates. and (when there is positional disorder) at least one candidate fractional coordinate When there is no position and no order, it can degenerate into using only ; 3) Replace disordered placeholder vectors This describes the probability / proportion of a site being occupied by a mixture of multiple elements. Each component is non-negative and their sum is 1; in the ordered case Degenerates into one-hot; 4) Position-unordered weight vector This describes the occupancy weight of the site among multiple candidate locations. Each component is non-negative and its sum is 1; when there is no position and no order. It degenerates into deterministic weights.

[0039] The above representation allows the same structure to be geometrically ( ) and disorder probability ( The representation is uniformly expressed in the form of a probability vector, thus providing a trainable, sampleable, and physically valid parameterization space for the subsequent generation process. The role of this representation scheme in the method of this invention is to replace the traditional one-hot / single-coordinate description with a probability vector, explicitly expressing the statistical occupancy rules of disordered materials, and providing a direct interface for the generation and discretization of probability constraints.

[0040] As an alternative implementation of step S10, for characterizing positional disorder, in addition to using explicit multiple candidate fractional coordinates... Alternatively, a site offset distribution parameterization method can be used as an alternative representation. Specifically, this can be represented using a principal fractional coordinate system. The positional dispersion of a point is described by an offset distribution parameter (e.g., the mean and variance of an isotropic or anisotropic Gaussian distribution), in which case the positional unordered weight vector is used. Each component corresponds to a probability weight for each offset direction. This alternative method also requires matching probability weights to characterize the occupancy distribution, and these probability weights must also satisfy the simplex constraint that is non-negative and sums to 1.

[0041] S20: Based on the flow matching generation process, the lattice parameters, principal fraction coordinates, candidate fraction coordinates, substitution disorder occupancy probability vector and position disorder weight probability vector are used as joint generation variables. Starting from the preset prior distribution, the process is continuously evolved and jointly updated along the time parameter until it evolves to the target data distribution, thus obtaining a disordered crystal structure in continuous probability form.

[0042] In step S20, the preset prior distribution can be a standard normal distribution or a uniform distribution, with its dimension consistent with the total dimension of the joint generating variables. When conditional initialization is used, the preset prior distribution can be sampled within a subspace of given conditional information (e.g., stoichiometry) to accelerate the convergence of the generation process. The time parameters of the flow-matching generation process are also considered. t The typical value range is: ,in t =0 corresponds to the prior distribution. t =1 corresponds to the target data distribution; in numerical solutions, the time interval can be discretized into several steps (e.g., 100 steps, 200 steps, or 500 steps), and the ODE can be numerically integrated using the Euler Method or the Runge-Kutta Method. For each step of the generation process, the velocity field predicted by the neural network... The current state is encoded. In time The instantaneous changing trend of each variable can be observed by linearly superimposing the current values ​​of each variable with their corresponding velocity field components, thus obtaining the state estimate for the next moment. This process is repeated iteratively until... Reaching the preset endpoint means completing the evolution from the prior distribution to the target data distribution.

[0043] In this embodiment, in each step of continuous evolution and joint update, a probabilistic simplex constraint is applied to the substitution disorder occupancy probability vector and the position disorder weight probability vector, such that each component of the updated substitution disorder occupancy probability vector remains non-negative and its sum is 1, and each component of the updated position disorder weight probability vector remains non-negative and its sum is 1.

[0044] In some embodiments, in step S20, continuous evolution and joint update along the time parameter can be performed through the following steps S201-S203.

[0045] S201: Record the time parameter as Jointly generated variables in time The state is denoted as ,in Indicates lattice parameters, Represents the principal fraction coordinates. Represents the coordinates of the candidate scores. This represents the probability vector of replacing disordered occupants. This represents the positional unordered weight probability vector.

[0046] S202: Using neural networks to predict joint generator variables over time velocity field .

[0047] In some embodiments, step S202 can specifically be achieved by using a neural network to predict the joint generator variable over time through the following steps S2021-S2023. velocity field .

[0048] S2021: The lattice parameters of the current state, the principal fractional coordinates of each symmetric independent site, the candidate fractional coordinates, the substitution disorder occupancy probability vector, and the position disorder weight probability vector are input into the graph neural network, which models the interactions between sites.

[0049] As an illustrative example of a graph neural network structure, a variant based on the Crystal Graph Convolutional Neural Network (CGCNN) architecture can be used. Specifically, each symmetric independent site is treated as a node in the graph, and the node feature vector is composed of the probability vector of disordered occupancy at that site. Position-disordered weight probability vector and principal fraction coordinates The graph is constructed by concatenating encoded data. The edges of the graph are determined by the distance between points; a connection is established when the Euclidean distance between two points is less than a preset threshold (e.g., 6.0 Å), indicating an interatomic interaction between them. Each layer of the graph neural network performs the following message passing operations: for nodes... Aggregate all neighboring nodes The message that was delivered ,in By node The current features and edge features (including the principal fractional coordinate difference vector between two nodes and the corresponding distance value) are calculated through linear transformation and nonlinear activation functions (such as ReLU or SiLU); the aggregation method can be summation aggregation or mean aggregation; after multi-layer (e.g., 3~6 layers) message passing, the global representation of the entire cell is obtained through global pooling, and then mapped to the velocity field components corresponding to each variable through multi-head fully connected layers. The trainable parameters of the graph neural network include the weight matrix and bias terms of each linear layer, and the total number of parameters can be adjusted between hundreds of thousands and millions depending on the actual application scale.

[0050] S2022: For sites with unordered locations, geometric relationships are calculated simultaneously based on the principal fraction coordinates and candidate fraction coordinates during the message passing process of the graph neural network to obtain distance and direction information for multiple location combinations.

[0051] In step S2022, the distance and orientation information of the multi-location combination are obtained in the following manner. For a site with disordered location... Its candidate score coordinate set is The corresponding positional unordered weight probability vector is ,in During message passing, for two sites and Calculation of the geometric relationship between the sites, if the sites If the positions are unordered, calculate them separately. with site Principal fraction coordinates Periodic distance between The 'round' directive indicates rounding to the nearest integer, used to handle periodic boundary conditions, and is combined with positional unordered weights. Weighted summation of distances, i.e. To obtain the site and Weighted effective distance between The processing of directional information is similar to that of distance. Each candidate location has a directional vector that exists between it and its neighboring locations. A weighted average of these directional vectors is then performed using unordered position weights to obtain the location information. and The effective direction vector between them. If both sites are out of order, then the distance and direction are calculated for each pair of candidate sites, and the corresponding weights are multiplied as weights for weighted summation. This method enables the graph neural network to consider the geometric contributions of the main position and multiple candidate positions simultaneously in message passing, thereby accurately capturing the structural information brought about by multi-positional disorder.

[0052] S2023: Based on the output of the graph neural network, predict the velocity field components corresponding to the lattice parameters, principal fractional coordinates, candidate fractional coordinates, substitution disorder occupancy probability vector, and position disorder weight probability vector, respectively.

[0053] In step S2023, the output of the graph neural network is a high-dimensional feature vector, which is mapped to five velocity field components through five independent output heads. Each output head can be implemented using a two- or three-layer fully connected network, with the last layer not using an activation function to allow arbitrary real values ​​to be output. For the velocity field components of lattice parameters, principal fractional coordinates, and candidate fractional coordinates, their output dimensions are consistent with the dimensions of their respective variables. For the velocity field components of the replacement disordered occupancy probability vector and the position disordered weight probability vector, their output dimensions are also consistent with the dimensions of their respective probability vectors, but the output values ​​are not subject to non-negativity or summation constraints, because the probability constraints will be applied through a projection operation in the update stage of step S203, rather than being directly restricted in the velocity field prediction stage.

[0054] S203: According to the velocity field For joint generating variables Update to obtain the state at the next time step. The probability vector of replacing disordered occupants and positional disordered weight probability vector The update employs a constraint update method consistent with probabilistic simplex geometry, ensuring that the updated replacement disordered occupancy probability vector... Each component is non-negative and their sum is 1, and the updated position is an unordered weight probability vector. Each component is non-negative and their sum is 1.

[0055] The following exemplary approach is provided for the specific implementation of probabilistic simplex constraints.

[0056] In step S203, the probability vector of replacing disordered occupancy is... and positional disordered weight probability vector The update employs a constraint update method consistent with probabilistic simplex geometry. This method achieves probability vector constraint updates by designing a projected gradient on the right side (velocity field) of the flow-matched ODE, replacing the disordered occupancy probability vector. For example, let the velocity field component predicted by the neural network be... The standard Euclidean update formula is: This result is likely to exceed the range of the probability simplex, therefore the updated result needs to be projected onto the probability simplex, and the following optimization problem needs to be solved: The domain of the probability simplex Represented as: This projection can be efficiently solved using a sorting-based analytical algorithm, with a time complexity of O(log n). ( (Probability vector dimension). Position-unordered weighted probability vector. Constraint application method and Completely consistent, with independent projection operations. This method guarantees the validity of all probability variables throughout the numerical solution process and is fully compatible with the flow matching ODE framework.

[0057] As an alternative to the probabilistic simplex constraint in step S203, the penalty method or barrier method can be used to softly introduce the constraint into the optimization objective. That is, by adding a penalty term to the loss function for the non-negativity and summation of each component of the probability vector, the neural network gradually learns to output a velocity field that satisfies the constraint during training. However, this alternative method may result in constraint violations in the early stages of the generation process. To pursue higher physical rigor, the aforementioned projection method is preferred.

[0058] In some embodiments, after step S203, step S20 further includes the following steps S204 and S205 during the continuous evolution and joint update process.

[0059] S204: After each update step, apply crystal periodicity constraints to the principal fractional coordinates and candidate fractional coordinates, and map fractional coordinates that are outside the unit cell range back into the standard unit cell range by translation.

[0060] In this embodiment, the standard unit cell interval is [0,1) or (-0.5,0.5], which can be selected according to usage habits. Taking the [0,1) interval as an example, for the updated fractional coordinates... f ,pass f ← f -⌊ f ⌋ maps it back to the interval [0,1), where ⌊⌋ represents the floor function. This operation is physically equivalent to translating an atom from its original unit cell to an equivalent position in an adjacent unit cell, without changing the physical structure of the crystal. For candidate fractional coordinates They also independently apply the same periodic mapping operation.

[0061] S205: Based on the update of the lattice parameters, the periodic equivalent representations of the principal fractional coordinates and candidate fractional coordinates are adjusted synchronously to ensure that the joint generation variables satisfy the crystal geometric consistency throughout the update process.

[0062] In this embodiment, when the lattice parameter Updated to Since the fractional coordinates are relative coordinates referenced to the unit cell basis vectors, their values ​​themselves do not change with lattice variations, but the absolute distances between atoms do change with lattice variations. To achieve crystal geometric consistency, this embodiment does not change the values ​​of the fractional coordinates, but rather updates the unit cell matrix. Defined metric tensor All subsequent distance and angle calculations are based on the updated metric tensor. That is, crystal geometric consistency is reflected in the fact that any module that relies on unit cell parameters for geometric calculations (such as the distance threshold determination in the neural network) uses the lattice parameters at the current moment. The absolute distance is recalculated to ensure that the pairing of fractional coordinates and lattice parameters remains physically consistent. Furthermore, if an asymmetric representation of the lattice parameters is used, such as using cell edges... a , b , c and angle α , β ,γ replaces the complete unit cell matrix After the update, it is necessary to ensure that the cell parameters satisfy the positive definiteness condition (i.e., the cell volume is positive). This can be specifically achieved by checking the Gram matrix. G The eigenvalues ​​are determined by whether all of them are positive. If a non-positive definite case occurs, the cell matrix is ​​projected onto a positive definite matrix cone.

[0063] In some embodiments, before starting from a preset prior distribution, step S20 further includes: performing conditional initialization based on at least one of the conditional information of the chemical formula, element set, or number of sites of the target disordered crystal, and sampling an initial joint generation variable state that matches the conditional information from the preset prior distribution.

[0064] As a specific example of conditional initialization, when the chemical formula of the given target disordered crystal is A x B y C z When A, B, and C represent different elements, and x, y, and z represent the stoichiometric ratios of the corresponding elements, the total number of sites can be determined. And the global proportion of each element. During initialization, the probability vector of substitution disorder occupancy for each site is... This is achieved by sampling from the Dirichlet distribution and calibrating the sampling results according to the global elemental proportions to match the expected value with the target chemical formula. Given a certain number of sites... At that time, just follow Construct the dimensions of the site-related variables in the joint generation variables. Given a set of elements, limit the dimension of each probability vector to the number of categories of elements in the set, and exclude elements outside the set. Through the above conditional initialization, the generation process can be guaranteed to start from a physically reasonable initial state, thereby improving generation efficiency.

[0065] In another embodiment, an exemplary process for generating a disordered crystal is provided, such as... Figure 2 As shown, based on the unified representation obtained in step S10, this embodiment adopts a generation process based on the flow matching idea for the lattice. Geometric coordinates ( ) and disordered probability variables ( Joint generation / update can be summarized through the following steps: S2-1, Overview of the generation process: Initialize the crystal state from a preset simple prior distribution. Starting with the lattice, coordinates, and disorder probability variables, conditional initialization is performed, and the crystal state is interpolated to the real data. Simultaneously, the velocity field at each time step It can be calculated using ordinary differential equations; S2-2, Data Flow: The crystal lattice is a 3×3 matrix located in Euclidean space. For coordinates, this method uses fractional coordinates, which are periodic (period 1), and the data are distributed on a torus. For unordered probability variables, the constraints of non-negativity and summation to 1 must be satisfied, thus placing them on a simplex. Considering numerical stability, this method maps them to a sphere, which is equivalent to the former.

[0066] S2-3, Velocity Field Prediction: In the time parameter Driven by this approach, this embodiment first encodes the crystal's lattice length and angle, number of atoms, substitution disorder, and positional disorder (considering the geometric relationships related to primary / secondary positions). Then, it models and updates the interactions between points using an isotropic graph neural network. Finally, it outputs the velocity field corresponding to each physical quantity through different output heads. During the update process, crystal periodicity and geometric consistency constraints are introduced, enabling the model to learn the distance and direction information brought about by multi-positional combinations, thereby improving the local rationality of the generated structure.

[0067] The role of the above generation process in the method of this invention is to achieve the coupled generation of lattice, coordinates and disorder weights within the same framework, and to ensure that the disorder probability variable satisfies the physical probability constraints throughout the generation process, thereby reducing illegal structures and numerical instability from the source.

[0068] S30: Perform a voting discretization strategy on the disordered crystal structure in continuous probability form, and output a discrete disordered crystal structure.

[0069] In this embodiment, the disordered crystal structure in the form of continuous probability refers to the probability vector of each substitution disordered site after the flow matching generation process in step S20. and the unordered weight probability vector at each position The probability vector form is maintained (each component is between [0,1] and the sum is 1), while the lattice parameters and fractional coordinates are fixed values. This continuous probability form can be directly used for subsequent statistical property calculations (such as configuration entropy, average magnetic moment, etc.), but for applications that require a clear atomic occupancy configuration, such as first-principles DFT structure optimization, phonon spectrum calculation, elastic constant calculation, etc., the continuous probability needs to be converted into a discrete occupancy scheme, which is the function to be achieved in step S30.

[0070] In some embodiments, step S30 specifically includes the following steps S301-S303.

[0071] S301: Perform two-stage discretization on the substitution disorder occupancy probability vector and the position disorder weight probability vector for each symmetric independent site: In the first stage, determine the sites with highly concentrated probability distributions as single-element occupancy or single-position occupancy; in the second stage, construct a candidate set for the remaining disordered sites.

[0072] In step S301, the threshold for determining a highly concentrated probability distribution can be set by those skilled in the art based on the actual application. As an optional implementation, when the maximum component of the probability vector exceeds a preset threshold (e.g., 0.85 or 0.90), the site is considered a near-deterministic site. At this point, the site is discretized into the element or position corresponding to the maximum component, i.e., the position is... The element corresponding to the largest component is taken as the final placeholder element for that site, or... The candidate score coordinates corresponding to the largest component are taken as the final position of the site. This is for the replacement of the disordered occupancy probability vector. If the maximum component is less than a preset threshold (i.e., there is no obviously dominant element), the site is included in the unordered site candidate set, and its probability distribution is preserved for the second stage of processing. For the positional unordered weight probability vector... The judgment method and They are exactly the same. The purpose of the first stage of deterministic processing is to reduce the size of the subsequent candidate set construction and improve discretization efficiency.

[0073] S302: For the candidate set, candidate positions are selected from the replacement disordered position probability vector and candidate positions are selected from the position disordered weight probability vector according to multiple different candidate rules, resulting in multiple discrete candidate results.

[0074] As a specific example of multiple candidate rules in step S302, the following four rules can be used simultaneously: Rule 1 (Top-k): Select the highest probability from the probability vector. k One component is selected as a candidate, among which k The value is determined based on the expected number of element types or the number of candidate locations at the site, for example... k =2 or k =3; Rule 2 (Probability Threshold): Select a probability value greater than a preset threshold. τ (For example τ =0.2 or τ All components with a value of 0.3 are considered as candidates; Rule 3 (quantiles): Select components with probability values ​​higher than the upper quartile (75th percentile) as candidates; Rule 4 (Entropy-Driven Adaptation): Calculate the Shannon entropy of the probability vector. When the entropy value is higher than a preset entropy threshold (e.g.) When the entropy value is greater than 1.0 (corresponding to a higher degree of uniformity), the size of the candidate set is increased (e.g., selecting Top-3). When the entropy value is lower than the preset entropy threshold, the size of the candidate set is reduced (e.g., selecting Top-1 or Top-2).

[0075] The four rules described above independently select candidates for the same probability vector, thus yielding four discrete candidate results for a single site. When the number of sites is large, applying the above rules to all sites separately results in multiple sets of complete discrete structure candidates.

[0076] S303: Integrate and vote on multiple discrete candidate results, and output the final multi-element occupancy scheme or multi-position occupancy scheme based on the voting results as a discrete disordered crystal structure.

[0077] In step S303, the integrated voting can be implemented as follows: For each unordered site, the frequency of that site being selected as a placeholder element or candidate position under each candidate rule is counted, and the element or position with the highest frequency is selected as the final discrete placeholder for that site. For example, if a certain unordered site is selected by 3 out of 4 candidate rules, element A is selected by 2 out of 4 rules, element B is selected by 2 out of 1, and element C is selected by 1 out of 4 rules, then element A receives 3 votes, element B receives 2 votes, and element C receives 1 vote. Element A is then selected as the placeholder element for that site. If there is a tie for the highest number of votes (e.g., 2 votes to 2 votes), the candidate with the higher probability value in the original probability vector can be selected as the final output, or one can be randomly selected and its uncertainty recorded. The advantage of integrated voting is that it combines the perspectives of multiple candidate strategies, effectively smoothing the unstable decision-making of a single strategy in boundary cases.

[0078] In another embodiment, an exemplary voting discretization strategy for probabilistic to discrete disordered structures is provided. To enable the generated results to be used for subsequent structure optimization and property calculations, this embodiment provides a discretization strategy from continuous probability output to discrete disordered crystal structures after generation, such as... Figure 3 As shown, its core is two-stage processing and integrated voting.

[0079] Two-stage discretization: First, deterministic processing is performed on near-deterministic sites (e.g., when the probability distribution is highly concentrated, it is discretized into single-element occupants or single-position occupants), transforming them into ordered / near-ordered parts; then, candidate sets are constructed and discretized for the remaining disordered sites.

[0080] Multi-strategy candidate selection and ensemble voting: For disordered sites, candidate occupants / positions are selected from the probability vector based on different candidate rules (e.g., Top-k, probability threshold, quantile, entropy / uncertainty driven adaptive rules, etc.) to obtain multiple discrete candidates; then, the candidate results are ensembled and voted to output the final multi-element occupancy (multi-hot) or multi-position occupancy scheme, so as to improve the robustness of discrete results to noise and uncertainty, and better meet the requirements of stoichiometry and occupancy consistency.

[0081] The role of this voting discretization strategy in the method of this invention is to stably convert the probability distribution output by the generative model into a usable discrete structure representation, thereby reducing the randomness and instability caused by single threshold / single path discretization.

[0082] As an alternative implementation of step S30, besides the integrated voting strategy described above, constrained optimization discretization can also be employed. Specifically, the discretization problem is formulated as an integer programming problem: using the final occupant elements or positions of all sites as decision variables, the objective function maximizes overall probability consistency (i.e., the sum of probability values ​​corresponding to each decision variable), while using stoichiometry (the proportion of total atoms of each element) and occupancy constraints (the total number of occupants at each site is 1) as constraints to solve for the optimal discrete configuration. This optimization problem can be solved within an acceptable time using combinatorial optimization algorithms such as branch and bound or simulated annealing. Alternatively, sampling discretization can be used, i.e., random sampling is performed based on the multinomial distribution defined by each probability vector to generate multiple sets of discrete structures, and then the optimal structure is selected through energy screening or consistency screening after structural relaxation. All of the above alternatives can achieve the same discretization objective without departing from the core idea of ​​this invention.

[0083] To further ensure that those skilled in the art can implement this invention, a complete parameter configuration example in a specific application scenario is provided below. However, it should be noted that this example is merely a specific choice for implementing this invention and does not constitute any limitation on the scope of protection of this invention. In an exemplary embodiment, the preset prior distribution is selected as a standard normal distribution. Time parameters t The value range is [0,1], the step count is set to 200 steps, and the Euler method is used for numerical integration of the ordinary differential equation. The graph neural network uses 4 layers of message passing, the hidden dimension of each node feature is 256, and the global pooling after message passing uses attention pooling. The output head uses a two-layer fully connected network with a hidden layer dimension of 128 and the activation function is SiLU. The probabilistic simplex projection uses a ranking-based projection algorithm (its implementation is as described above). In the discretization stage, the deterministic threshold is determined. τ det Set to 0.85, the top-k candidate rules k The value is set to 2, which is the probability threshold. τ The value is set to 0.25, which is the entropy threshold. H threshold When set to 1.2, the integrated voting process selects the candidate with the higher probability value in the parallel processing.

[0084] It should be noted that the above parameter configuration is merely an example and does not constitute a limitation of the present invention. Those skilled in the art can adjust the above parameters accordingly based on the actual task scale and accuracy requirements.

[0085] To further illustrate the feasibility and advancement of the method of this invention, this embodiment compares and evaluates the method of this invention with DiffCSP on the disordered crystal structure prediction (CSP) task. The evaluation benchmark includes four datasets: COD-SD-20, COD-SPD-20, COD-SD-50, and COD-SPD-50, where SD indicates that it only contains substitution disorder, SPD indicates that it contains both substitution disorder and position disorder, and "-20 / -50" represents different scale / difficulty settings. The evaluation metrics used are the matching rate MR (the proportion of generated structures that can match the target structure, the higher the better) and RMSE (the structural error calculated only for successfully matched samples, the lower the better), which are used to measure the recoverability of the generated structure and the geometric accuracy after matching, respectively.

[0086] Table 1 CSP Results (-20)

[0087] Table 2 CSP Results (-50)

[0088] As shown in Tables 1 and 2, the present invention significantly improves MR across all four benchmarks: at the -20 setting, COD-SD-20 improves by 6.65 percentage points (70.57 vs 63.92), and COD-SPD-20 improves by 12.21 percentage points (65.30 vs 53.09); at the more challenging -50 setting, COD-SD-50 improves by 4.07 percentage points (49.12 vs 45.05), and COD-SPD-50 improves by 10.39 percentage points (45.87 vs 35.48). The improvement is more pronounced on the SPD dataset, indicating that the present invention has stronger structural recoverability in mixed cases of "displacement disorder + positional disorder". In terms of RMSE, this invention performs slightly better on COD-SPD-20 (0.0533 vs 0.0548), while the RMSE of other datasets is slightly higher. Considering the definition that RMSE is only calculated on successfully matched samples, this indicates that this invention mainly brings higher effective matching coverage and generation availability (more samples can be successfully matched), while maintaining the same order of magnitude in terms of accuracy after matching. This is more conducive to the engineering implementation of CSP scenarios and the subsequent property calculation process.

[0089] This invention also provides a disordered crystal structure generation apparatus for implementing the methods described in any of the above embodiments, such as... Figure 4 As shown, the device includes: The disordered crystal unified representation module 401 is configured to acquire the lattice parameters and site geometry information of the target disordered crystal. The site geometry information includes the principal fractional coordinates of at least one symmetric independent site and at least one candidate fractional coordinate when there is positional disorder. For each of the symmetric independent sites, a replacement disorder occupancy probability vector and a positional disorder weight probability vector are constructed. The components of the replacement disorder occupancy probability vector are non-negative and their sum is 1. The components of the positional disorder weight probability vector are non-negative and their sum is 1. The disordered crystal generation module 402 is configured to use a flow-matching generation process, taking the lattice parameters, the principal fractional coordinates, the candidate fractional coordinates, the substitution disorder occupancy probability vector, and the position disorder weight probability vector as joint generation variables, and continuously evolving and jointly updating along the time parameter from a preset prior distribution until the target data distribution is reached, thus obtaining a disordered crystal structure in continuous probability form; wherein, in each step of the continuous evolution and joint update, a probabilistic simplex constraint is applied to the substitution disorder occupancy probability vector and the position disorder weight probability vector, such that each component of the updated substitution disorder occupancy probability vector remains non-negative and its sum is 1, and each component of the updated position disorder weight probability vector remains non-negative and its sum is 1; The voting discretization module 403 is configured to perform a voting discretization strategy on the disordered crystal structure of the continuous probability form and output a discrete disordered crystal structure.

[0090] This invention provides an electronic device. The electronic device may include a processor and a memory, wherein the processor and the memory can communicate; exemplarily, the processor and the memory communicate via a communication bus.

[0091] The processor executes computer execution instructions stored in memory, causing the processor to perform the scheme in the above embodiments. The processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0092] The communication bus can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The system bus can be divided into address bus, data bus, control bus, etc. Transceivers are used to enable communication between database access devices and other computers (e.g., clients, read-write libraries, and read-only libraries). Memory may include random access memory (RAM) and may also include non-volatile memory.

[0093] The electronic device provided in this embodiment of the invention can be the terminal device described in the above embodiments.

[0094] This invention also provides a computer-readable storage medium storing computer instructions that, when executed on a computer, cause the computer to perform the technical solution of the disordered crystal structure generation method described above.

[0095] This invention also provides a computer program product, which includes a computer program stored in a computer-readable storage medium. At least one processor can read the computer program from the computer-readable storage medium, and when the at least one processor executes the computer program, it can implement the technical solution of the disordered crystal structure generation method described in the above embodiments.

[0096] In the several embodiments provided by this invention, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or modules, and may be electrical, mechanical, or other forms.

[0097] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to implement the solution of this embodiment according to actual needs.

[0098] Furthermore, the functional modules in the various embodiments of the present invention can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The unit composed of the above modules can be implemented in hardware or in the form of hardware plus software functional units.

[0099] The integrated modules described above, implemented as software functional modules, can be stored in a computer-readable storage medium. These software functional modules, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute certain steps of the methods of the various embodiments of the present invention.

[0100] It should be understood that the aforementioned processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. A general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly manifested as execution by a hardware processor, or execution by a combination of hardware and software modules within the processor.

[0101] The memory may include high-speed RAM, and may also include non-volatile storage (NVM), such as at least one disk storage device, and may also be a USB flash drive, external hard drive, read-only memory, disk or optical disc, etc.

[0102] Buses can be Industry Standard Architecture (ISA) buses, Peripheral Component Interconnect (PCI) buses, or Extended Industry Standard Architecture (EISA) buses, etc. Buses can be categorized into address buses, data buses, control buses, etc.

[0103] The aforementioned storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The storage medium can be any available medium that can be accessed by a general-purpose or special-purpose computer.

[0104] An exemplary storage medium is coupled to a processor, enabling the processor to read information from and write information to the storage medium. Alternatively, the storage medium can be an integral part of the processor. The processor and storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and storage medium can exist as discrete components in an electronic control unit or main control device.

[0105] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0106] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for generating a disordered crystal structure, characterized in that, The method includes: The lattice parameters and site geometry information of the target disordered crystal are obtained. The site geometry information includes the principal fractional coordinates of at least one symmetric independent site and at least one candidate fractional coordinate when there is site disorder. For each symmetric independent site, a replacement disorder occupancy probability vector and a site disorder weight probability vector are constructed. The components of the replacement disorder occupancy probability vector are non-negative and their sum is 1. The components of the site disorder weight probability vector are non-negative and their sum is 1. Based on the flow matching generation process, the lattice parameters, principal fraction coordinates, candidate fraction coordinates, substitution disorder occupancy probability vector, and position disorder weight probability vector are used as joint generation variables. Starting from a preset prior distribution, continuous evolution and joint updates are performed along the time parameter until the target data distribution is reached, resulting in a disordered crystal structure in continuous probability form. In each step of the continuous evolution and joint update, probabilistic simplex constraints are applied to the substitution disorder occupancy probability vector and the position disorder weight probability vector, such that the components of the updated substitution disorder occupancy probability vector remain non-negative and their sum is 1, and the components of the updated position disorder weight probability vector remain non-negative and their sum is 1. A voting discretization strategy is applied to the disordered crystal structure of the continuous probability form to output a discrete disordered crystal structure.

2. The method for generating a disordered crystal structure according to claim 1, characterized in that, The construction of a replacement disordered occupancy probability vector and a positional disordered weighted probability vector for each of the symmetric independent sites includes: For each symmetrical independent site Let the probability vector of replacing disordered occupancy be denoted as The positional disorder weight probability vector is denoted as ; When this symmetrical independent site When replacing disorder, the probability vector of replacing disordered occupancy. Each component represents the probability or proportion of the corresponding element occupying that site; when this symmetric independent site When ordered, the probability vector of replacing disordered occupants It degenerates into a one-hot vector; When the location is unordered, the unordered weight probability vector Each component represents the probability or proportion of that location occupying the corresponding candidate score coordinate; when the location is unordered, the unordered position weight probability vector It degenerates into a deterministic weight vector.

3. The method for generating a disordered crystal structure according to claim 1, characterized in that, Based on the flow matching generation process, the lattice parameters, principal fractional coordinates, candidate fractional coordinates, substitution disorder occupancy probability vector, and position disorder weight probability vector are used as joint generation variables. Starting from a preset prior distribution, continuous evolution and joint updates are performed along the time parameters, including: Let the time parameter be denoted as The jointly generated variables in time The state is denoted as ,in Indicates lattice parameters, Represents the principal fraction coordinates. Represents the coordinates of the candidate scores. This represents the probability vector of replacing disordered occupants. This represents the position-disordered weight probability vector; Predicting the joint generative variables over time using neural networks velocity field ; According to the velocity field For the joint generated variables Update to obtain the state at the next time step. , where the probability vector of replacing disordered occupancy and the positional unordered weight probability vector The update employs a constraint update method consistent with probabilistic simplex geometry, ensuring that the updated replacement disordered occupancy probability vector... Each component is non-negative and their sum is 1, and the updated position is an unordered weight probability vector. Each component is non-negative and their sum is 1.

4. The method for generating a disordered crystal structure according to claim 3, characterized in that, The method of using neural networks to predict the joint generated variables over time... velocity field ,include: The lattice parameters of the current state, the principal fractional coordinates of each symmetric independent site, the candidate fractional coordinates, the substitution disorder occupancy probability vector, and the position disorder weight probability vector are input into the graph neural network, which models the interaction between sites. For sites with disordered positions, the geometric relationship is calculated simultaneously based on the principal fraction coordinates and the candidate fraction coordinates during the message passing process of the graph neural network to obtain distance and direction information of multiple position combinations. Based on the output of the graph neural network, the velocity field components corresponding to the lattice parameters, the principal fractional coordinates, the candidate fractional coordinates, the substitution disorder occupancy probability vector, and the position disorder weight probability vector are predicted respectively.

5. The method for generating a disordered crystal structure according to claim 1, characterized in that, The step of performing a voting discretization strategy on the disordered crystal structure of the continuous probability form to output a discrete disordered crystal structure includes: For each symmetric independent site, the probability vector of substitution disordered occupancy and the probability vector of position disordered weight are discretized in two stages: in the first stage, sites with highly concentrated probability distributions are determined as single-element occupancy or single-position occupancy; in the second stage, a candidate set is constructed for the remaining disordered sites. For the candidate set, candidate positions are selected from the replacement disordered position probability vector and candidate positions are selected from the position disordered weight probability vector according to multiple different candidate rules, resulting in multiple discrete candidate results; The multiple discrete candidate results are integrated and voted on, and the final multi-element occupancy scheme or multi-position occupancy scheme is output based on the voting results as the discrete disordered crystal structure.

6. The method for generating a disordered crystal structure according to claim 1, characterized in that, Before starting from a preset prior distribution, the method further includes: Conditional initialization is performed based on at least one of the following conditional information: the chemical formula, element set, or number of sites of the target disordered crystal. An initial joint generation variable state matching the conditional information is sampled from the preset prior distribution.

7. The method for generating a disordered crystal structure according to claim 1, characterized in that, The continuous evolution and joint update process also includes: After each update step, a crystal periodic constraint is applied to the principal fractional coordinates and the candidate fractional coordinates, and the fractional coordinates that exceed the unit cell range are mapped back to the standard unit cell range by translation. Based on the update of the lattice parameters, the periodic equivalent representations of the principal fractional coordinates and the candidate fractional coordinates are adjusted synchronously to ensure that the joint generation variables satisfy crystal geometric consistency throughout the update process.

8. A device for generating disordered crystal structures, characterized in that, The device includes: A disordered crystal unified representation module is configured to acquire the lattice parameters and site geometry information of the target disordered crystal. The site geometry information includes principal fractional coordinates of at least one symmetric independent site and at least one candidate fractional coordinate when there is positional disorder. For each symmetric independent site, a replacement disorder occupancy probability vector and a positional disorder weight probability vector are constructed. The components of the replacement disorder occupancy probability vector are non-negative and their sum is 1. The components of the positional disorder weight probability vector are non-negative and their sum is 1. The disordered crystal generation module is configured to use a flow-matching generation process, taking the lattice parameters, principal fractional coordinates, candidate fractional coordinates, substitution disorder occupancy probability vector, and position disorder weight probability vector as joint generation variables. Starting from a preset prior distribution, it continuously evolves and jointly updates along the time parameter until it evolves to the target data distribution, thus obtaining a disordered crystal structure in continuous probability form. In each step of the continuous evolution and joint update, a probabilistic simplex constraint is applied to the substitution disorder occupancy probability vector and the position disorder weight probability vector, such that the components of the updated substitution disorder occupancy probability vector remain non-negative and their sum is 1, and the components of the updated position disorder weight probability vector remain non-negative and their sum is 1. The voting discretization module is configured to perform a voting discretization strategy on the disordered crystal structure of the continuous probability form and output a discrete disordered crystal structure.

9. An electronic device, characterized in that, include: A processor, and a memory communicatively connected to the processor; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory to implement the disordered crystal structure generation method as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the disordered crystal structure generation method as described in any one of claims 1-7.

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