Multi-component alloy phase composition prediction method and system based on graph neural network

Abstract

The application discloses a kind of based on graph neural network's multi-component alloy phase composition prediction method and system, comprising: first, the element species, mole ratio and other component information of target multi-component alloy and crystal structure prototype category identification are acquired, and the initial cell graph of element mark atomic node is constructed with the connection edge determined with atomic space adjacent relationship. The initial cell graph is executed multi-level topological aggregation, and local chemical environment embedding vector and electron orbit interactive embedding vector are generated. Two kinds of embedding vectors are input into the phase recognition model of heterogeneous graph neural network, and the features of nodes and edges are updated by cross through the heterogeneous graph message passing mechanism, to generate the phase stability representation field of fusion crystal field splitting information, and finally the equilibrium phase composition sequence is obtained. The method can significantly improve the accuracy of phase prediction and reduce the calculation cost.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence technology, and more specifically, to a method and system for predicting the phase composition of multi-component alloys based on graph neural networks. Background Technology

[0002] Multicomponent alloys possess excellent properties such as high strength, high corrosion resistance, and high entropy stability, making them key core materials in high-end equipment manufacturing, new energy, and other fields. Accurate prediction of their equilibrium phase composition is a crucial prerequisite for the directional control of alloy properties. Among current mainstream phase prediction methods, CALPHAD technology heavily relies on existing thermodynamic experimental databases, exhibiting extremely poor adaptability to novel multicomponent systems not included in these databases; high-throughput first-principles calculations are computationally expensive and cannot cover the full screening of complex compositional spaces. Summary of the Invention

[0003] The purpose of this invention is to provide a method and system for predicting the phase composition of multi-component alloys based on graph neural networks.

[0004] In a first aspect, embodiments of the present invention provide a method for predicting the phase composition of multi-component alloys based on graph neural networks, the method comprising:

[0005] Obtain the set of composition information and crystal structure prototype category identifier of the target multi-component alloy. The set of composition information includes the names of all elements involved in the alloy composition and the molar ratio of each element.

[0006] Based on the set of component information and the crystal structure prototype category identifier, an initial unit cell diagram of a multi-component alloy system is constructed. The initial unit cell diagram includes a set of atomic nodes labeled by element type names and a set of atomic connection edges determined by the spatial adjacency relationship between atoms.

[0007] Multi-level topological aggregation is performed on the initial unit cell graph to generate local chemical environment embedding vectors at the atomic node level and electron orbital interaction embedding vectors at the atomic connection edge level. The local chemical environment embedding vectors describe the elemental distribution characteristics of coordinating atoms around the target atomic node, and the electron orbital interaction embedding vectors describe the coupling characteristics of electron cloud overlap and valence electron concentration between adjacent atomic nodes.

[0008] The local chemical environment embedding vector and the electron orbital interaction embedding vector are input into the pre-constructed heterogeneous graph neural network phase identification model. The atomic node features and atomic connection edge features are cross-updated through the first message passing mechanism under the heterogeneous graph structure to generate a phase stability characterization field that integrates crystal field splitting information.

[0009] The equilibrium phase composition sequence of the target multi-component alloy is analyzed based on the spatial distribution state of the phase stability characterization field. The equilibrium phase composition sequence includes the predicted phase structure type identifier and the mole fraction ratio of the phase structure type identifier in the alloy system.

[0010] Secondly, embodiments of the present invention provide a multi-component alloy phase composition prediction system based on graph neural networks, including at least one service node;

[0011] The service node includes a storage unit and a computing unit; the storage unit is used to store program code; the computing unit is used to run the program code to execute the multi-component alloy phase composition prediction method based on graph neural networks as described in the first aspect.

[0012] Compared to existing technologies, the beneficial effects of this invention include: The method and system for predicting the phase composition of multi-component alloys based on graph neural networks, as disclosed in this invention, firstly acquires the element types, molar ratios, and other component information of the target multi-component alloy, as well as the crystal structure prototype category identifier, and constructs an initial unit cell graph with element-labeled atomic nodes and connection edges determined by atomic spatial adjacency. Multi-level topological aggregation is performed on the initial unit cell graph to generate local chemical environment embedding vectors and electron orbital interaction embedding vectors. These two types of embedding vectors are input into a heterogeneous graph neural network phase identification model, and node and edge features are cross-updated through a heterogeneous graph message passing mechanism to generate a phase stability characterization field that integrates crystal field splitting information. Finally, the equilibrium phase composition sequence is obtained through analysis. This method can significantly improve phase prediction accuracy and reduce computational costs. Attached Figure Description

[0013] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as limiting the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1 This is a flowchart illustrating the steps of the multi-component alloy phase composition prediction method based on graph neural networks provided in an embodiment of the present invention.

[0015] Figure 2 A schematic block diagram of the structure of a computer device provided in an embodiment of the present invention. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0017] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0018] In order to solve the technical problems mentioned in the background art Figure 1 This is a flowchart illustrating the multi-component alloy phase composition prediction method based on graph neural networks provided in this embodiment. The following is a detailed description of the multi-component alloy phase composition prediction method based on graph neural networks.

[0019] Step S201: Obtain the composition information set and crystal structure prototype category identifier of the target multi-component alloy. The composition information set includes the names of all elements participating in the alloy composition and the molar ratio values ​​of each element.

[0020] In practice, the composition information set is obtained from an external input interface and is represented as a list of element identifiers and numerical pairs, such as {Fe:0.20,Co:0.20,Ni:0.20,Cr:0.20,Mn:0.20}. The crystal structure prototype category identifier is selected from a pre-defined set of crystallographic prototypes, including face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP) structures. The obtained composition information set and crystal structure prototype category identifier serve as initialization parameters for subsequent graph construction steps.

[0021] Step S202: Construct an initial unit cell diagram of the multi-component alloy system based on the set of component information and the crystal structure prototype category identifier. The initial unit cell diagram includes a set of atomic nodes labeled by element type names and a set of atomic connection edges determined by the spatial adjacency relationship between atoms.

[0022] The process of constructing the initial unit cell diagram includes: retrieving the corresponding lattice point coordinate set from a preset crystallographic database based on the crystal structure prototype category identifier; using a random occupancy strategy, assigning element type names to each lattice point according to the molar ratio of each element in the composition information set, generating an atomic node set; expanding the atomic node set along the crystal axis to a preset supercell size, forming a supercell atomic node set, maintaining the correspondence between the spatial coordinates of each node and the element labels during the expansion process; and calculating the Euclidean distance between any two atomic nodes in the supercell atomic node set based on a preset nearest neighbor cutoff radius parameter. If the distance is less than or equal to the truncation radius, an atomic connection edge is established between the two atomic nodes, and the edge index is recorded. For each atomic connection edge, an edge type attribute is assigned according to the element types of the atomic nodes at both ends and the connection direction. The edge type attribute is used to distinguish the orientation of heterogeneous chemical bonds. The set of atomic nodes and the set of atomic connection edges are integrated to generate a graph data structure with atomic nodes as vertices and atomic connection edges as edges. A periodic boundary condition encoding operation is applied to the graph data structure to establish mirror connection edges at the supercell boundary, ensuring the integrity and translation invariance of the graph topology under periodic boundaries.

[0023] Step S203: Perform multi-level topological aggregation on the initial unit cell diagram to generate local chemical environment embedding vectors at the atomic node level and electron orbital interaction embedding vectors at the atomic connection edge level. The local chemical environment embedding vectors describe the elemental distribution characteristics of coordinating atoms around the target atomic node, and the electron orbital interaction embedding vectors describe the coupling characteristics of electron cloud overlap and valence electron concentration between adjacent atomic nodes.

[0024] The specific execution of multi-level topological aggregation includes the following sub-steps: taking each atomic node in the initial primitive cell graph as the center, extracting a topological neighborhood subgraph defined by the number of connection edge steps, the neighborhood coverage area includes at least the first nearest neighbor shell and the second nearest neighbor shell;

[0025] For each central atom node, the frequency of occurrence of atoms of different element types within each topological level is counted to generate an element type frequency distribution vector; the vectors of each level are weighted and aggregated by applying a level attenuation factor to obtain an initial description vector of the local chemical environment; the level attenuation factor decreases as the topological distance increases to simulate the distance attenuation effect of chemical interactions.

[0026] The initial description vector of the local chemical environment is concatenated with the element intrinsic property embedding vector corresponding to the central atom node. The element intrinsic property embedding vector is obtained by mapping the basic physical property parameters such as atomic radius, electronegativity, and orbital energy level through the embedding layer. The concatenation result is processed by a nonlinear transformation network to output the local chemical environment embedding vector with a preset dimension.

[0027] For each atomic connection edge in the initial unit cell graph, the intrinsic elemental attribute parameters and edge type attribute labels of the atomic nodes at both ends are extracted. Combined with the spatial orientation vector of the atomic connection edge, a scalar or vector value reflecting the coupling characteristics of electron cloud overlap and valence electron concentration is calculated. This value is then mapped to an electron orbital cross-embedding vector via an edge feature embedding network. The generation of the electron orbital cross-embedding vector can further include retrieving orbital radial wavefunction parameters from a basic atomic orbital feature parameter library to calculate direction-sensitive overlap integral eigenvalues.

[0028] Step S204: Input the local chemical environment embedding vector and the electron orbital interaction embedding vector into the pre-constructed heterogeneous graph neural network phase identification model. Perform cross-update operation on the atomic node features and atomic connection edge features through the first message passing mechanism under the heterogeneous graph structure to generate a phase stability characterization field that integrates crystal field splitting information.

[0029] For example, the local chemical environment embedding vectors of all atomic nodes are assembled into the initial feature matrix of the atomic nodes, and the electron orbital interaction embedding vectors of all atomic connection edges are assembled into the initial feature matrix of the edges. In each message passing layer of the heterogeneous graph neural network phase recognition model, for each atomic connection edge, its current round edge feature vector is concatenated with the current round atomic node feature vectors of the atomic nodes at both ends of the edge, and input into the edge message generator function. The edge message generator function is composed of a multi-layer fully connected neural network and outputs the edge message passing vector corresponding to the atomic connection edge. For each atomic node, the edge message passing vectors generated by all atomic connection edges with it as the receiving end are collected, and the messages are assigned to different edge type channels according to the edge type attribute label. Element-wise average pooling is performed on the collected edge message passing vectors in each edge type channel to obtain the channel aggregated message vector. The weighted weights of the channel aggregated message vectors are calculated using the edge type attention mechanism, and the weighted sum is obtained. After residual concatenation with the current atomic node feature vector, the result is input to the atomic node feature update gated loop unit to generate the updated atomic node feature vector; the above message passing and feature update process is repeated until the preset iteration round is met to obtain the steady-state atomic node feature set; based on the crystal field symmetry group corresponding to the crystal structure prototype category identifier, the irreducible representation basis function is determined, and each atomic node feature vector in the steady-state atomic node feature set is projected to the irreducible representation subspace, and energy level splitting scaling factors corresponding to different subspaces are applied to complete the crystal field splitting perturbation transformation; the atomic node feature vectors after the crystal field splitting perturbation transformation are arranged according to the spatial position coordinates of the atomic nodes in the supercell space to form a phase stability characterization field in the form of a vector field; a Laplace smoothing operator based on graph topology is applied to the phase stability characterization field to constrain the gradient change of the characterization vector between adjacent atomic nodes, so that the characterization field exhibits continuous transition characteristics in the topological adjacency region.

[0030] Step S205: Analyze the equilibrium phase composition sequence of the target multi-component alloy based on the spatial distribution state of the phase stability characterization field. The equilibrium phase composition sequence includes the predicted phase structure type identifier and the mole fraction ratio of the phase structure type identifier in the alloy system.

[0031] For example, the phase stability representation vector corresponding to each spatial grid point in the phase stability representation field is input into a pre-trained fully connected classifier network layer, which outputs the probability distribution vector of each candidate phase structure type identifier in the preset phase structure type list for that spatial grid point; the preset phase structure type list includes structure type identifiers of common intermetallic compound phases and solid solution phases; for each spatial grid point, the candidate phase structure type identifier corresponding to the maximum value in the probability distribution vector is selected as the local phase attribution label for that spatial grid point; spatially adjacent spatial grid points with the same local phase attribution label are aggregated into continuous phase region patches using a connected component labeling algorithm; the proportion of the number of spatial grid points contained in each continuous phase region patch to the total number of spatial grid points is calculated to obtain the initial estimate of the volume proportion of that phase structure type identifier; the phase boundary energy correction module is called to calculate the interface energy contribution term based on the interface area and heterogeneous interface energy parameters between adjacent phase region patches, and to adjust the initial estimate of the volume proportion. The volume fraction is re-normalized to obtain the corrected volume proportion. Based on the theoretical crystallographic density parameters and unit cell volume parameters corresponding to each phase structure type identifier, the corrected volume fraction is mapped to a mole fraction ratio under the constraint of mass conservation. All phase structure type identifiers and their corresponding mole fraction ratios are collected, and phase structure type identifiers with mole fraction ratios lower than a preset threshold are filtered out to obtain a preliminary phase composition sequence. The preliminary phase composition sequence is checked for compliance with the Gibbs law. When the relationship between the number of phase structure type identifiers and the number of component element types does not satisfy the Gibbs law, the phase structure type identifier with the smallest mole fraction ratio is deleted and the remaining phase mole fraction ratios are re-normalized until the phase law constraint is satisfied. The preliminary phase composition sequence is checked for conjugate phases according to the phase diagram topology rule base to remove isolated phase structure type identifiers that cannot coexist with adjacent phases in thermodynamic equilibrium. The phase composition sequence after the above processing is output as the equilibrium phase composition sequence of the target multi-component alloy.

[0032] Through the above implementation methods, this method can achieve high-precision and high-efficiency prediction of equilibrium phase composition based on the basic component information and crystal structure prototype of multi-component alloys, and by using heterogeneous graph neural networks to capture the interaction features of atomic-scale chemical environment and electronic structure.

[0033] In this embodiment of the invention, the construction of the initial unit cell diagram of the multi-component alloy system based on the set of component information and the crystal structure prototype category identifier can be implemented through the following example.

[0034] Based on the crystal structure prototype category identifier, a preset crystallography database is searched to obtain the space group number and standard lattice point coordinate list of the corresponding crystal structure prototype. The standard lattice point coordinate list includes fractional coordinate triplets of all equivalent lattice positions within the crystal structure prototype and a list of restrictions on the types of elements that can occupy each equivalent lattice position.

[0035] Based on the element type names and element molar ratio values ​​in the component information set, a lattice point occupancy probability distribution table of the crystal structure prototype is generated. The lattice point occupancy probability distribution table records the probability weight value of each equivalent lattice position being occupied by each element type name.

[0036] For each equivalent lattice position in the standard lattice point coordinate list, a random occupancy allocation operation is performed according to the lattice point occupancy probability distribution table to assign a determined element type name label to each equivalent lattice position to form an atomic node set.

[0037] Based on the space group numbering and symmetry operation group of the crystal structure prototype, the initial set of atomic nodes is expanded to a supercell space of a preset size. During the expansion process, crystallographic translation symmetry and point group symmetry constraints are maintained to generate a supercell set of atomic nodes with a complete lattice translation order.

[0038] For each pair of atomic nodes in the supercell atomic node set, calculate the spatial Euclidean distance value, compare the spatial Euclidean distance value with the preset nearest neighbor cutoff radius parameter, and establish an atomic connection edge between the pair of atomic nodes when the spatial Euclidean distance value is less than the nearest neighbor cutoff radius parameter.

[0039] Each atomic connection edge is assigned an edge type attribute label, which is determined based on the combination of element type names marked by the atomic nodes at both ends of the atomic connection edge and the angle between the vector direction of the atomic connection edge and the crystallographic principal axis direction.

[0040] By integrating the element type name tags of all atomic nodes in the supercell atomic node set and the edge type attribute tags of all atomic connection edges in the atomic connection edge set, an initial primitive cell graph with atomic nodes as vertex elements and atomic connection edges as adjacency relationships is constructed.

[0041] Perform a periodic boundary condition encoding operation on the initial primitive cell graph, add a copy of the connecting edge that crosses the supercell boundary to the graph topology of the initial primitive cell graph and mark the copy of the connecting edge as a cross-periodic edge type, so that the initial primitive cell graph contains complete periodic adjacency information.

[0042] The vertex degree centrality index and edge type distribution histogram of each atomic node are calculated based on the total number of atomic connecting edges around the atomic node and the frequency of occurrence of each edge type attribute label. The vertex degree centrality index and edge type distribution histogram are then used as the initial vertex features of the atomic node and appended to the corresponding atomic node attribute field of the initial primitive cell graph.

[0043] In this embodiment of the invention, exemplarily, when the server executes the method, it first retrieves a crystallography database preset in the storage unit based on the crystal structure prototype category identifier provided by external input. This database is organized in a relational table structure, with each record corresponding to a crystal structure prototype, including a space group number and a list of standard lattice point coordinates. Taking a face-centered cubic structure as an example, the server retrieves space group number 225. The list of standard lattice point coordinates contains four fractional coordinate triplets of equivalent lattice positions: (0,0,0), (0,0.5,0.5), (0.5,0,0.5), and (0.5,0.5,0). The list of elements that can occupy each equivalent lattice position is empty, indicating that all metal elements are allowed to occupy that position.

[0044] The server then reads the element names Fe, Co, Ni, Cr, and Mn from the composition information set, along with their corresponding molar ratios, all of which are 0.20. Based on this data, the server generates a lattice site occupancy probability distribution table for the crystal structure prototype. This table is a two-dimensional mapping table, where the row index is the equivalent lattice position identifier, the column index is the element name, and each cell records the probability weight value of the corresponding element occupying that equivalent lattice position. Since the target alloy is an ideal solid solution and has no sublattice occupancy tendency, the server assigns the same probability distribution vector to each equivalent lattice position, meaning that the occupancy probability of each element is 0.20.

[0045] For the four equivalent lattice positions in the standard lattice point coordinate list, the server invokes a pseudo-random number generator to perform a random allocation operation based on the lattice point occupancy probability distribution table. Specifically, the server independently generates a uniformly distributed random number within the interval [0,1) for each equivalent lattice position, constructs a cumulative probability interval according to element type, and assigns the element type name corresponding to the interval the random number falls into to that lattice position. In a single allocation instance, the four lattice positions are sequentially assigned the labels Fe, Co, Ni, and Cr. This operation is repeated at the four equivalent lattice positions, forming a set of atomic nodes containing four atomic nodes.

[0046] Next, the server performs supercell expansion on the initial set of atomic nodes based on the symmetry operation group numbered 225. This symmetry operation group contains 48 point group symmetry operations for the face-centered cubic lattice. The server combines these operations with translation vectors to replicate and expand the atomic nodes along the crystal axis to a preset 3×3×3 supercell size. During the expansion process, the server strictly maintains crystallographic translation symmetry and point group symmetry constraints. Each mirrored atomic node is generated with a corresponding symmetry transformation matrix and translation vector applied, ultimately resulting in a supercell set of 108 atomic nodes. Each atomic node has unique three-dimensional spatial coordinates and an element type name inherited from the occupancy allocation stage.

[0047] The server then iterates through all pairs of atomic nodes in the supercell's atomic node set, calculating their spatial Euclidean distance. For the FeCoNiCrMn face-centered cubic alloy in this embodiment, the preset nearest neighbor cutoff radius parameter is 1.2 times the first nearest neighbor distance. This coefficient is a common empirical value in crystal structure analysis that covers the first and second nearest neighbor coordination, and can be adjusted within the range of 1.1 to 1.5 times depending on the target crystal structure type (1.3 to 1.5 times for BCC structures and 1.2 to 1.4 times for HCP structures). In this embodiment, the first nearest neighbor distance of the FeCoNiCrMnFCC structure is approximately 2.48 angstroms, corresponding to a cutoff radius of approximately 2.9 angstroms. When the spatial distance between two atomic nodes is less than this cutoff radius parameter, the server establishes an atomic connection edge between the pair of atomic nodes and assigns an edge index. Taking the Fe atom at the origin as an example, its neighbors with a distance less than the cutoff radius include 12 first nearest neighbor atoms and 6 second nearest neighbor atoms, and the server establishes connection edges with these neighbor atoms respectively.

[0048] For each established atomic connection edge, the server assigns an edge type attribute tag. The edge type attribute tag is generated based on two parts of information: first, the combination of element type names marked by the atomic nodes at both ends of the edge, such as the Fe-Co combination generating the identifier E_FeCo; second, the angle relationship between the direction of the atomic connection edge vector and the crystallographic principal axis direction. The server calculates the direction cosines of the edge vector with the three principal axes

[100] ,

[010] , and

[001] , and maps the quadrant to which the angle belongs to a direction code suffix. The final edge type attribute tag is represented as a composite string, such as E_FeCo_001, which represents a Fe-Co bond oriented along the c-axis direction.

[0049] The server integrates the element type name tags of all atomic nodes in the supercell atomic node set and the edge type attribute tags of all atomic connecting edges in the atomic connecting edge set to construct a graph data structure with atomic nodes as vertices and atomic connecting edges as adjacency relationships, forming an initial primitive graph. This graph uses an adjacency list storage format, and the vertex attributes include atomic node index, element type tag, fractional coordinates, and Cartesian coordinates.

[0050] After constructing the initial primitive cell graph, the server performs periodic boundary condition encoding on the graph. Specifically, the server identifies atomic nodes located on the supercell boundary surface that are less than the truncation radius from the boundary. It then generates logical references to mirrored atomic nodes on the opposite side of the supercell boundary and adds a copy of the connecting edge between the original node and the mirrored node, marking this copy as a cross-periodic edge. After this operation, atomic nodes located at one corner of the supercell can establish adjacency relationships with atomic nodes at the opposite corner through cross-periodic edges, thus enabling the initial primitive cell graph to contain complete periodic adjacency information.

[0051] Finally, the server performs local topological statistics on each atomic node in the initial primitive cell graph. The statistical process calculates two metrics: a vertex degree centrality metric, which is the total number of atomic connecting edges around the atomic node; and an edge type distribution histogram, recording the frequency of occurrence of various edge type attribute labels connected to the atomic node. For the aforementioned Fe atom, its vertex degree centrality metric is 18, and the edge type distribution histogram shows E_FeCo_001 edges appearing 4 times and E_FeNi_011 edges appearing 3 times, etc. The server uses the vertex degree centrality metric and the edge type distribution histogram as initial vertex features of the atomic node, appending them to the attribute fields of the corresponding atomic nodes in the initial primitive cell graph for subsequent multi-level topological aggregation and heterogeneous graph neural network processing.

[0052] In this embodiment of the invention, the step of performing multi-level topological aggregation on the initial unit cell graph to generate local chemical environment embedding vectors at the atomic node level and electron orbital interaction embedding vectors at the atomic connection edge level can be implemented through the following examples.

[0053] Each atomic node in the initial primitive cell graph is taken as the target atomic node. A coordination atomic subgraph structure centered on the target atomic node and covering a preset number of nearest neighbor shells is extracted. The coordination atomic subgraph structure includes the target atomic node itself and a set of neighboring atomic nodes that are directly connected to it through atomic connection edges or indirectly connected to it through multi-step atomic connection edges.

[0054] Within the coordinate atomic subgraph structure, the topological levels are divided according to the number of atomic connection edge steps. The target atomic node itself is marked as the zeroth topological level, the neighboring atomic nodes reachable via a single-step atomic connection edge are marked as the first topological level, the neighboring atomic nodes reachable via a two-step atomic connection edge are marked as the second topological level, and so on until the preset nearest neighbor shell layer is covered.

[0055] For each neighboring atomic node in the topology level, extract the element type name label of the neighboring atomic node and count the occurrence frequency of each element type name in the topology level to generate the element type frequency distribution vector corresponding to the topology level.

[0056] Based on the weighting function of the coordination shell shielding effect in crystal field theory, a layer attenuation factor is assigned to each topological layer. The value of the layer attenuation factor shows a monotonically decreasing trend as the topological layer number increases, and its decreasing rate is determined by the empirical parameter of the electron shielding length in the multi-component alloy system.

[0057] The element type frequency distribution vector of each topological level is multiplied and weighted by the corresponding level attenuation factor, and the weighted vector of each topological level is accumulated and aggregated by element to generate an initial description vector of the local chemical environment describing the coordination environment around the target atom node.

[0058] The preset atomic intrinsic attribute encoding table is invoked to map the element type name of the target atomic node itself to the element intrinsic attribute embedding vector. The element intrinsic attribute embedding vector includes the atomic radius parameter encoding, electronegativity parameter encoding, valence electron number parameter encoding and atomic polarizability parameter encoding corresponding to the element type name.

[0059] The initial description vector of the local chemical environment and the embedding vector of the element intrinsic properties are concatenated, and the concatenated vector is input into a fully connected feedforward neural network layer to perform nonlinear transformation, and outputs a local chemical environment embedding vector with a preset uniform dimension.

[0060] For each atomic connection edge in the initial primitive cell diagram, extract the element type name of the atomic nodes at both ends of the atomic connection edge and the edge type attribute mark of the atomic connection edge, and retrieve the atomic radius parameter code and electronegativity parameter code corresponding to the atomic nodes at both ends.

[0061] Based on the orbital overlap integral calculation framework in the tight-binding approximation model, the atomic radius parameter encoding, electronegativity parameter encoding, and valence electron number parameter encoding of the two atomic nodes are input into the edge feature generation function to generate an overlap integral feature scalar that describes the degree of overlap of electron clouds between the two atoms of the atomic connection edge.

[0062] The overlapping integral feature scalar is concatenated with the one-hot encoded vector of the edge type attribute label, and the concatenated vector is input into the edge feature fully connected feedforward neural network layer to perform nonlinear transformation, and outputs an electronic track interactive embedding vector with a preset uniform dimension.

[0063] In this embodiment of the invention, for example, the server traverses each atomic node in the initial unit cell graph, using that node as the target atomic node for local chemical environment extraction. For the target atomic node located at coordinates (0.0, 0.0, 0.0) inside the supercell and labeled as Fe, the server performs a graph search operation to extract a coordination atomic subgraph structure centered on the Fe node and covering a preset number of nearest neighbor shells. This subgraph structure includes the target Fe atom itself and a set of neighboring atomic nodes directly connected by atomic connection edges or indirectly connected by multi-step edges. The search range is limited to a preset three nearest neighbor shells, i.e., the maximum number of search steps is three.

[0064] Within the coordination atomic subgraph structure, the server divides the topological hierarchy according to the number of atomic connection edge steps. The target Fe atom itself is marked as the zeroth topological level. The twelve first nearest neighbor atomic nodes directly connected to the target Fe atom by a single-step atomic connection edge are classified into the first topological level, including four Co atoms, three Ni atoms, three Cr atoms, and two Mn atoms. The second nearest neighbor atomic nodes reachable via two-step atomic connection edges are classified into the second topological level, totaling six atomic nodes, with elemental distributions of two Fe atoms, one Co atom, one Ni atom, one Cr atom, and one Mn atom. The third topological level includes atomic nodes reachable via three-step edges, but considering the influence range of the electron shielding effect, in actual processing, only counting up to the second topological level is sufficient to meet the accuracy requirements.

[0065] For each neighboring atomic node within a topological level, the server extracts the element type name label for each node and counts the frequency of each element type name within that level. The first topological level generates a five-dimensional frequency distribution vector, with the frequency values ​​for Fe, Co, Ni, Cr, and Mn being 0, 4, 3, 3, and 2, respectively. The second topological level generates a frequency distribution vector of 2, 1, 1, 1, 1.

[0066] The server assigns a hierarchy attenuation factor to each topological level based on the weighting function of the coordination shell shielding effect in crystal field theory. The attenuation factor for the first topological level is 0.85, and the attenuation factor for the second topological level is 0.35. The attenuation factor decreases monotonically with increasing topological level number. This value is determined based on the close-binding approximate statistical law of the d-electron shielding length of transition metals (approximately 0.2~0.3 nm). Each additional shell results in an attenuation of approximately 0.41 times. For alloy systems containing main group / rare earth elements, the attenuation coefficient can be adjusted within the range of 0.3~0.6 times according to the degree of valence electron orbital expansion of the corresponding elements.

[0067] The server performs element-wise multiplication and weighting operations on the element type frequency distribution vectors of each topological level and the corresponding level attenuation factors. The weighted vector for the first topological level is (0, 3.40, 2.55, 2.55, 1.70), and the weighted vector for the second topological level is (0.70, 0.35, 0.35, 0.35, 0.35). The server then performs element-wise accumulation and aggregation on the two weighted level vectors to obtain a five-dimensional initial description vector of the local chemical environment (0.70, 3.75, 2.90, 2.90, 2.05).

[0068] The server invokes a pre-defined atomic intrinsic attribute encoding table stored in the storage unit to map the element type name of the target Fe atom node into an element intrinsic attribute embedding vector. This embedding vector contains four components: atomic radius parameter encoding 1.26, electronegativity parameter encoding 1.83, valence electron number parameter encoding 8, and atomic polarizability parameter encoding 9.4. After normalization, each component is concatenated into a four-dimensional initial vector, which is then expanded into a sixteen-dimensional feature vector through an embedding layer.

[0069] The server concatenates the initial local chemical environment description vector with the element intrinsic property embedding vector to obtain a 21-dimensional concatenated vector. This concatenated vector is then input into a fully connected feedforward neural network layer containing two hidden units, each with 64 dimensions and a GELU activation function, to perform a nonlinear transformation. The output is a local chemical environment embedding vector with a pre-defined uniform dimension of 128 dimensions. This vector characterizes the local chemical coordination environment features of the lattice sites where the target Fe atom is located.

[0070] For the generation of features at the atomic connection edge level, the server processes an atomic connection edge in the initial unit cell graph that connects Fe and Co atoms and has the edge type attribute marked as E_FeCo_011. The server extracts the element names Fe and Co from the atomic nodes at both ends of the edge, and retrieves the corresponding atomic radius parameter codes 1.26 and 1.25, electronegativity parameter codes 1.83 and 1.88, and valence electron number parameter codes 8 and 9.

[0071] Based on the orbital overlap integral calculation framework in the tight-binding approximation model, the server inputs the atomic radius, electronegativity, and valence electron number parameters of the two end atomic nodes into the edge feature generation function. The edge feature generation function first calculates the ratio of the atomic radius to the interatomic distance to obtain the orbital radial overlap factor; secondly, it calculates the electronegativity difference and multiplies it by a valence electron concentration correction term to generate an electron transfer tendency factor; finally, it multiplies the two factors to output the overlap integral feature scalar, with a specific value of 0.73.

[0072] The server concatenates the overlap integral feature scalar 0.73 with the one-hot encoded vector of the edge type attribute label E_FeCo_011. The dimension of the edge type one-hot encoded vector is the total number of edge types, with a value of 1 at the corresponding position and 0 at the other positions. The concatenated vector is input into a fully connected feedforward neural network layer for edge features. This network contains one hidden unit, has a dimension of 64, uses ReLU activation function, and outputs an electron orbital interaction embedding vector with a preset uniform dimension of 64. This vector describes the electron cloud overlap state and valence electron concentration coupling characteristics between Fe-Co atom pairs. The server performs the above operation on all atomic connection edges in the initial unit cell graph to generate a complete set of edge feature vectors.

[0073] In this embodiment of the invention, the step of inputting the local chemical environment embedding vector and the electron orbital interaction embedding vector into a pre-constructed heterogeneous graph neural network phase identification model, and performing cross-update operations on atomic node features and atomic connection edge features through the first message passing mechanism under the heterogeneous graph structure to generate a phase stability characterization field that integrates crystal field splitting information can be implemented through the following example.

[0074] The local chemical environment embedding vectors corresponding to all atomic nodes in the initial unit cell graph are assembled into an initial feature matrix of atomic nodes, and the electron orbit interaction embedding vectors corresponding to all atomic connection edges are assembled into an initial feature matrix of edges.

[0075] In the first message passing layer of the heterogeneous graph neural network phase recognition model, for each atomic connection edge, the initial feature vector of the atomic connection edge is concatenated with the feature vectors of the atomic nodes at both ends in the current iteration to obtain the edge message generation input vector.

[0076] The edge message generation input vector is input into the edge message generator function, which is a fully connected neural network structure containing at least two hidden units, and outputs the edge message passing vector corresponding to the atomic connection edge.

[0077] For each atomic node, collect the edge message passing vectors generated by all atomic connection edges with that atomic node as the receiving end, and allocate the edge message passing vectors to different edge type channels according to the edge type attribute label of each atomic connection edge.

[0078] Within each edge type channel, an element-wise average pooling operation is performed on the collected edge message passing vectors to generate the channel aggregate message vector corresponding to that edge type channel. Then, the channel aggregate message vectors of each edge type channel are weighted and summed, and the weights are calculated by the edge type attention mechanism.

[0079] The weighted summed aggregated message vector is joined with the atomic node feature vector in the current iteration by a residual concatenation operation, and then input into the atomic node feature update gated loop unit to perform the atomic node feature vector update operation, generating the atomic node feature vector for the next iteration.

[0080] After completing the cross-update operation of atomic node features and atomic connection edge features for a preset number of iterations, a set of steady-state atomic node features output by the heterogeneous graph neural network phase recognition model is obtained. Each atomic node feature vector in the set of steady-state atomic node features integrates comprehensive information of its surrounding local chemical environment and long-range electron orbit coupling.

[0081] Based on the crystal field symmetry parameters corresponding to the crystal structure prototype category identifier, a crystal field splitting perturbation transformation is applied to each atomic node feature vector in the steady-state atomic node feature set. The crystal field splitting perturbation transformation projects the atomic node feature vector to the irreducible representation subspace based on the point symmetry of the lattice point where the atomic node is located.

[0082] The atomic node feature vectors after crystal field splitting perturbation transformation are arranged according to the spatial coordinates of the atomic nodes in the supercell space to form a phase stability characterization field with spatial continuous distribution characteristics. The phase stability characterization field is in the form of a vector field and each spatial grid point corresponds to a phase stability characterization vector.

[0083] Spatial smoothing is performed on the phase stability characterization field. A Laplacian smoothing operator based on graph topology is used to propagate gradient constraints on the phase stability characterization vectors between adjacent atomic nodes, so that the vector changes of the phase stability characterization field in the topological adjacency region exhibit continuous transition characteristics.

[0084] In an embodiment of the present invention, for example, the server assembles all 128 local chemical environment embedding vectors generated by the multi-level topology aggregation into an initial feature matrix of atomic nodes in atomic node index order, with a matrix dimension of 108×128; and assembles the electron orbital interaction embedding vectors corresponding to all 486 atomic connection edges into an initial feature matrix of edges in edge index order, with a matrix dimension of 486×64.

[0085] In the first message passing layer, the server processes the edge e_ij connecting the Fe and Co atomic nodes. The initial feature vector of this edge in the current iteration has a dimension of 64, and the feature vectors of the atomic nodes at both ends of this edge are both 128-dimensional in the current iteration. The server concatenates these three feature vectors along their respective feature dimensions to obtain a 320-dimensional edge message generation input vector. This input vector is fed into the edge message generator function, which is a fully connected neural network with two hidden units, 256 neurons per layer, and using the ELU activation function, outputting a 128-dimensional edge message passing vector.

[0086] The server targets the Fe atomic node and collects the edge message passing vectors generated by all eighteen atomic connections with that node as the receiver. Based on the edge type attribute of each edge, the server assigns these vectors to four edge type channels: E_FeCo, E_FeNi, E_FeCr, and E_FeMn. The E_FeCo channel collects four edge message vectors, and the server performs element-wise average pooling on these four vectors to generate a 128-dimensional channel aggregated message vector. The same operation is performed on the other three channels, generating a total of four channel aggregated message vectors.

[0087] The server invokes an edge-type attention mechanism to calculate the weights of each channel. The attention mechanism linearly transforms the current feature vector of the Fe atomic node into a query vector, and linearly transforms the aggregated message vectors of each edge type channel into key vectors, calculating the dot product similarity score between the query and each key. After Softmax normalization, the E_FeCo channel receives a weight of 0.38, the E_FeNi channel 0.27, the E_FeCr channel 0.21, and the E_FeMn channel 0.14. The server then uses these weights to weight and sum the aggregated message vectors of each channel, resulting in a 128-dimensional weighted aggregated message vector.

[0088] The server performs a residual concatenation between the weighted aggregated message vector and the current feature vector of the Fe atomic node, with the residual scaling factor set to 0.1. The concatenated vector is then input into the feature update gated recurrent unit of the atomic node, which contains update and reset gates, and outputs the feature vector of the Fe atomic node for the next iteration. This process is executed in parallel on all atomic nodes, completing one round of feature update.

[0089] After six rounds of cross-updating operations, the server obtains a set of steady-state atomic node features. The feature vector of each atomic node in the set integrates comprehensive information about its surrounding local chemical environment and remote electron orbital coupling.

[0090] The server performs a crystal field splitting perturbation transformation based on the crystal field symmetry parameters corresponding to the FCC crystal structure prototype category identifier. The sites of the FCC lattice atoms possess O_h point group symmetry. The server invokes the group theory analysis module to project the steady-state eigenvector of each atomic node onto the irreducible representation subspace of the O_h point group, including subspaces such as A_1g, E_g, and T_2g. A scaling factor of 1.2 is applied to the components projected onto the E_g subspace, and a scaling factor of 0.9 is applied to the components projected onto the T_2g subspace. This scaling ratio is the statistical average of the d-orbital crystal field splitting energy level difference under transition metal octahedral coordination conditions (taken from statistical values ​​of a well-known high-throughput first-principles database in the art). For other point group symmetries (such as the D-orbital splitting energy level difference of the HCP structure), the scaling factor is adjusted accordingly. 6h (Point group), the scaling factor can be adjusted in the range of 0.8 to 1.5 times based on the experimental / calculation results of the energy level splitting of the corresponding irreducible representation.

[0091] The transformed atomic node feature vectors are arranged spatially according to the fractional coordinates of the atomic nodes in the 3×3×3 hypercell space, forming a phase stability representation field. Each spatial grid point corresponds to a 128-dimensional phase stability representation vector. The server uses a Laplacian smoothing operator based on graph topology to process this representation field. The smoothing operator is defined as the weighted sum of the differences between the feature vectors of adjacent nodes. Through five smoothing iterations, the L2 distance gradient between the representation vectors of adjacent atomic nodes is reduced to below 0.15, and the representation field exhibits continuous transition characteristics within the topological adjacency region.

[0092] In this embodiment of the invention, the equilibrium phase composition sequence of the target multi-component alloy is analyzed based on the spatial distribution state of the phase stability characterization field. The equilibrium phase composition sequence includes the predicted phase structure type identifier and the mole fraction ratio of the phase structure type identifier in the alloy system. This can be implemented through the following example.

[0093] The phase stability representation vector corresponding to each spatial grid point in the phase stability representation field is input to the pre-trained first fully connected classifier network layer, and the first fully connected classifier network layer outputs the probability distribution vector of the spatial grid point belonging to each candidate phase structure type identifier in the preset phase structure type list.

[0094] For each spatial grid point, the candidate phase structure type identifier with the highest probability value in the probability distribution vector is selected as the local phase attribution label of the spatial grid point, and spatially adjacent spatial grid points with the same local phase attribution label are aggregated into continuous phase region patches.

[0095] The initial estimate of the volume ratio of the phase structure type identifier corresponding to the continuous phase region patch in the alloy system is calculated based on the proportion of the number of spatial grid points contained in the continuous phase region patch to the total number of spatial grid points.

[0096] The preset phase boundary energy correction module is invoked to perform interface effect correction on the initial volume ratio estimate. The phase boundary energy correction module calculates the interface energy contribution based on the interface area between adjacent phase region patches and the heterogeneous phase interface energy parameters, and readjusts the volume ratio of each phase structure type identifier.

[0097] The volume ratio after interface effect correction is mapped to mole fraction ratio. During the mapping process, the ratio conversion is performed under the mass conservation constraint based on the theoretical crystallographic density parameters and unit cell volume parameters corresponding to each phase structure type.

[0098] Collect all the converted phase structure type identifiers and their corresponding mole fraction ratios to form a preliminary phase composition sequence, and filter out phase structure type identifiers with mole fraction ratios lower than a preset threshold.

[0099] A Gibbs phase law compliance constraint verification operation is performed on the filtered preliminary phase composition sequence. When the numerical relationship between the number of phase structure type identifiers and the number of component element types in the preliminary phase composition sequence does not conform to the Gibbs phase law, the phase structure type identifier with the smallest mole fraction ratio is deleted and the mole fraction ratio of the remaining phase structure type identifiers is renormalized until the Gibbs phase law is satisfied.

[0100] According to the phase diagram topology rules, a conjugate phase verification operation is performed on the preliminary phase composition sequence to remove the identifiers of isolated phase structure types that cannot coexist with adjacent phase structures in thermodynamic equilibrium from the preliminary phase composition sequence;

[0101] The phase composition sequence after the conjugate phase verification operation is output as the equilibrium phase composition sequence of the target multi-component alloy. Each phase structure type identifier in the equilibrium phase composition sequence corresponds to a normalized mole fraction ratio value.

[0102] In this embodiment of the invention, for example, the server sequentially inputs the 128-dimensional phase stability representation vector corresponding to each spatial grid point in the spatially smoothed phase stability representation field into the pre-trained first fully connected classifier network layer. This classifier network layer contains three fully connected layers with hidden layer dimensions of 256 and 128 respectively, and an output layer dimension equal to the length of a preset phase structure type list. This list includes twelve candidate phase structure type identifiers, such as FCC, BCC, HCP, Laves phase, and Sigma phase. Taking the spatial grid point at hypercell coordinates (0.0, 0.0, 0.0) as an example, its phase stability representation vector, after forward computation by the classifier network, outputs a 12-dimensional probability distribution vector. Each component corresponds to the confidence probability of each candidate phase structure type identifier, where the component corresponding to FCC is 0.82, the component corresponding to BCC is 0.15, and the sum of the remaining components is 0.03. For each spatial grid point, the server selects the candidate phase structure type identifier with the largest value in the probability distribution vector as the local phase attribution label for that spatial grid point; this grid point is then labeled as FCC. The server iterates through all 108 spatial grid points and assigns ownership tags to each one.

[0103] The server invokes a connected component labeling algorithm to aggregate spatially adjacent grid points with the same local phase affiliation label into continuous phase region patches. Two main continuous phase region patches are identified in the supercell space: the first patch contains 89 adjacent grid points, all labeled FCC, and the second patch contains 19 adjacent grid points, all labeled BCC. Based on the proportion of the number of grid points contained in the continuous phase region patches relative to the total number of 108 grid points, the server calculates initial estimates of the volume percentage of each phase structure type. The initial estimate of the FCC phase volume percentage is 89 / 108 = 0.824, and the initial estimate of the BCC phase volume percentage is 19 / 108 = 0.176.

[0104] The server invokes a pre-defined phase boundary energy correction module to perform interface effect correction on the initial volume ratio estimate. This module first identifies 24 interface lattice points between the first and second patches, with the cumulative interface area calculated to be approximately 2.16 square nanometers based on the lattice constant. The module then reads the FCC / BCC heterogeneous interface energy parameter of 0.32 J / m² from a publicly available thermodynamic parameter library (derived from experimental measurements of the interface energy of FeCoNiCrMn alloys known in the art), and combines this with the previously calculated interface area of ​​2.16 nm² (i.e., 2.16 × 10⁻¹). 8 The interface energy contribution is calculated to be 4.31 eV. The module constructs a Gibbs free energy correction function based on the interface energy contribution and readjusts the volume ratios of the two phases. After correction, the volume ratio of the FCC phase is 0.811 and the volume ratio of the BCC phase is 0.189.

[0105] The server maps the corrected volume percentage to a mole fraction ratio. The mapping process uses the theoretical crystallographic density parameter of the FCC phase (8.92 g / cm³) and the unit cell volume parameter of the BCC phase (45.6 Å), and the theoretical crystallographic density parameter of the BCC phase (8.85 g / cm³) and the unit cell volume parameter of the BCC phase (23.8 Å). Under the constraint of total atom conservation, the mass-to-mole conversion is performed, yielding a mole fraction of 0.792 for the FCC phase and 0.208 for the BCC phase. The server collects the phase structure type identifiers and their mole fraction ratios to form a preliminary phase composition sequence.

[0106] The server filters out phase structure types whose mole fraction ratio in the preliminary phase composition sequence is lower than a preset threshold of 0.02. The lowest mole fraction in the current sequence is 0.208, which is higher than the threshold, so no phase is filtered out. The server performs a Gibbs phase rule compliance check on the filtered sequences. For the pentagonal alloy system, the maximum number of equilibrium phases under isothermal and isobaric conditions does not exceed 6. The current number of phases is 2, which meets the phase rule requirements, so no deletion or renormalization operation is needed.

[0107] The server performs conjugate phase verification based on a pre-defined phase diagram topology rule base. The rule base records that the FCC and BCC phases in the Fe-Co-Ni-Cr-Mn pentagonal system exist in a two-phase equilibrium region within the temperature range of 900 Kelvin to 1300 Kelvin. These two phases are conjugate phases with no thermodynamic conflict. The server determines that both FCC and BCC can coexist stably, and no isolated phase structure type identifiers need to be removed. The server outputs the phase composition sequence after all the above verification processes as the equilibrium phase composition sequence of the target multi-component alloy. The output data packet includes the predicted phase structure type identifiers FCC and BCC, as well as the normalized mole fraction ratios of 0.792 and 0.208, respectively.

[0108] In this embodiment of the invention, the method further includes:

[0109] Before performing multi-level topological aggregation on the initial unit cell diagram, a chemical disorder occupancy perturbation operation is applied to the initial unit cell diagram. The chemical disorder occupancy perturbation operation randomly exchanges the element name labels of some atomic nodes according to the occupancy probability distribution of each element type name in the component information set at a specified lattice point, generating multiple perturbation crystallographic unit cell diagram structure representation copies with different local chemical configurations.

[0110] Perform the multi-level topological aggregation on each perturbation crystallographic unit cell diagram structure representation copy to generate a corresponding set of perturbation local chemical environment embedding vectors and a set of perturbation electron orbital interaction embedding vectors.

[0111] Each set of perturbation local chemical environment embedding vectors and perturbation electron orbital interaction embedding vectors corresponding to a perturbation crystallographic unit cell diagram structure representation copy are input into the heterogeneous graph neural network phase identification model to generate their respective perturbation phase stability characterization field copies.

[0112] Perform a statistical ensemble averaging operation on all perturbation phase stability characterization field replicas in the spatial grid dimension to generate an average phase stability characterization field, and use the average phase stability characterization field to replace the original phase stability characterization field for subsequent analysis of the equilibrium phase composition sequence.

[0113] Spatial autocorrelation function calculation is performed on the average phase stability characterization field to obtain the correlation decay curve of the phase stability characterization vector at different spatial distances, and the coherence length parameter of the multi-component alloy system is determined based on the correlation decay curve.

[0114] The supercell space size of the initial unit cell diagram is adjusted according to the coherence length parameter. When the coherence length parameter is greater than half of the current supercell space size, the supercell space range is expanded by an integer multiple along each crystallographic principal axis and all operation steps from the initial unit cell diagram are re-executed.

[0115] The pre-built short program parameter sensitivity analysis module is invoked to apply a small perturbation to the element molar ratio values ​​in the component information set, observe the appearance or disappearance of phase structure type identifiers in the equilibrium phase composition sequence, and generate a phase structure stability boundary description surface.

[0116] The phase structure stability boundary description surface is compared with the experimental phase diagram data in the preset alloy phase diagram database. When the deviation exceeds the preset tolerance range, the incremental learning process of the heterogeneous graph neural network phase identification model is triggered. The deviation data is used to fine-tune and correct the weight of the edge message generator function and the weight of the atomic node feature update gated loop unit in the heterogeneous graph neural network phase identification model.

[0117] A second message passing mechanism is configured inside the heterogeneous graph neural network phase identification model. The second message passing mechanism is used to propagate spin polarization information on the atomic connection edge. During the propagation process, the spin exchange coupling constant is determined according to the element type name and edge type attribute label of the atomic nodes at both ends, and the spin polarization effect is coupled to the generation process of the edge message passing vector.

[0118] By applying a spin splitting correction term to the atomic node features through the second message passing mechanism, the phase stability characterization field that integrates crystal field splitting information further includes the contribution component of magnetically ordered structure, thus making it suitable for predicting the phase composition sequence of multi-component alloy systems containing magnetic elements.

[0119] In an embodiment of the invention, for example, before performing multi-level topological aggregation on the initial unit cell diagram, the server applies a chemical disorder occupancy perturbation operation to the constructed initial unit cell diagram. This operation randomly swaps the element type name labels of some atomic nodes based on the occupancy probability distribution of each element type name at lattice points in the component information set. Specifically, the server traverses each atomic node in the supercell atomic node set, generates a random decision variable following a Bernoulli distribution, and when the decision variable is true, the server resamples the element type name label of the node according to the molar proportion of each element and replaces the original label with the new label. This process is repeated five times, and the server generates five copies of the perturbed crystallographic unit cell diagram structure representation with different local chemical configurations. The copies have statistical differences in atomic occupancy configurations, but the total proportion of each element remains consistent.

[0120] The server performs multi-level topological aggregation operations on each copy of the perturbed crystallographic unit cell diagram structure representation, generating corresponding sets of perturbed local chemical environment embedding vectors and perturbed electron orbital interaction embedding vectors. The aggregation process for each copy is consistent with the main process, including steps such as coordination atom subgraph extraction, hierarchical frequency statistics, attenuation-weighted aggregation, and edge feature generation.

[0121] The server inputs the set of embedding vectors of the perturbation local chemical environment and the set of embedding vectors of the perturbation electron orbital interaction corresponding to each perturbation replica into a pre-built heterogeneous graph neural network phase identification model. Through six rounds of message passing and feature updates, it generates the corresponding perturbation phase stability characterization field replicas. The five perturbation replicas generate a total of five phase stability characterization field replicas, each of which is in the form of a vector field with the same dimensions as the main process output.

[0122] The server performs a statistical ensemble averaging operation on all five perturbation phase stability characterization field replicas along the spatial grid dimension. Specifically, for the same spatial coordinate position in the supercell, the server collects the phase stability characterization vectors corresponding to that grid point from the five replicas, calculates their element-wise arithmetic mean, and uses this as the average phase stability characterization vector for that grid point. The server uses this average phase stability characterization field to replace the original phase stability characterization field under a single configuration for subsequent analysis of the equilibrium phase composition sequence, thereby reducing the impact of statistical fluctuations caused by chemical disorder.

[0123] The server performs spatial autocorrelation function calculations on the average phase stability characterization field. The calculation process traverses spatial grid pairs, statistically analyzes the relationship between the dot product of the characterization vectors and the grid spacing, and fits a correlation decay curve. Based on the distance at which the curve decays to the initial value 1 / e, the server determines the coherence length parameter of this FeCoNiCrMn alloy system to be 1.28 nanometers.

[0124] The server adjusts the supercell size of the initial unit cell diagram based on the coherence length parameter. Currently, the supercell length along each crystal axis is 1.05 nanometers, less than twice the coherence length parameter, posing a risk of finite size effects. The server expands the supercell range by a factor of two along the three crystallographic principal axes, generating a new 6×6×6 supercell atomic node set, and re-executes all operational steps from the initial unit cell diagram construction to ensure that the phase stability characterization field can fully capture mid-range chemical order features.

[0125] The server invokes a pre-built short-program parameter sensitivity analysis module to apply a small perturbation of ±5% to the molar proportion of Cr in the component information set, generating two sets of perturbation inputs with Cr contents of 0.19 and 0.21, respectively, and performs full-process prediction for each. The server observes that the BCC phase disappears when the Cr content decreases to 0.19, and the Sigma phase appears when the Cr content increases to 0.21. Based on this, the server generates a phase structure stability boundary description surface with Cr and Ni contents as coordinate axes.

[0126] The server compares the stability boundary description surface of the phase structure with experimental phase diagram data in a pre-set alloy phase diagram database, calculating the consistency ratio of phase region assignment at corresponding composition points. When the deviation exceeds a preset tolerance range of 10%, the server triggers the incremental learning process of the heterogeneous graph neural network phase identification model. Incremental learning uses the deviation data to construct a loss function, and fine-tunes the weights of the edge message generator function and the weights of the atomic node feature update gated recurrent units in the heterogeneous graph neural network through backpropagation algorithm. The model parameters are updated after the loss value converges.

[0127] Within the heterogeneous graph neural network phase identification model, the server employs a second message passing mechanism to propagate spin polarization information. This mechanism calculates the spin exchange coupling constant on each atomic connection edge, retrieving the exchange integral value from a magnetic parameter library based on the element type names and edge type attribute labels of the atomic nodes at both ends. For the Fe-Co edge, the spin exchange coupling constant is positive, indicating ferromagnetic coupling. The spin polarization information is coupled to the original edge message passing vector as an additional vector within the edge message generator function. A spin correction term is generated through an independent fully connected branch network and added to the main edge message passing vector. Through this second message passing mechanism, the server applies a spin splitting correction term to the atomic node features, incorporating the contribution of magnetically ordered structures into the final generated phase stability characterization field. This makes it suitable for predicting the phase composition sequence of multi-component alloy systems containing magnetic elements such as Fe, Co, and Ni.

[0128] In this embodiment of the invention, the method further includes:

[0129] After constructing the initial unit cell graph, the coordination polyhedron type identifier of each atomic node in the initial unit cell graph is extracted. The coordination polyhedron type identifier is determined by calculating the spatial geometric topology formed by the atomic node and its nearest neighbor coordination atomic node and matching it with a preset ideal polyhedron template library.

[0130] The frequency of occurrence of coordination polyhedron type identifiers of all atomic nodes is counted and a frequency distribution histogram of coordination polyhedron types is constructed. The frequency distribution histogram of coordination polyhedron types is then attached as a global structure descriptor to the graph-level attribute field of the initial unit cell graph.

[0131] In the multi-level topology aggregation process, a coordination polyhedron geometric distortion penalty term is introduced for each topology level. The coordination polyhedron geometric distortion penalty term calculates a penalty factor based on the degree of deviation between the actual bond length and the ideal bond length of the coordination polyhedron in that topology level, and the penalty factor is embedded into the calculation process of the level attenuation factor.

[0132] A principal component rotation alignment operation is performed on the local chemical environment embedding vector to rotate the local chemical environment embedding vectors output by different atomic nodes into a normalized coordinate system based on the principal axis of symmetry of the crystal structure prototype, so as to eliminate the influence of crystallographic orientation differences on the directional components of the embedding vector.

[0133] When performing cross-update operations on atomic node features, a second-order statistical moment constraint term for the atomic node feature vector is introduced. This second-order statistical moment constraint term forces the square of the feature vector magnitude of each atomic node to be linearly dependent on the average electronegativity parameter in its local chemical environment.

[0134] After each atomic node feature update operation, the heterogeneous graph neural network phase recognition model projects the updated atomic node feature vector onto a subspace manifold that satisfies the irreducible representation constraint of the crystal structure prototype space group. The projection operation is implemented using the projection operator matrix of the crystal structure prototype space group.

[0135] After generating the phase stability characterization field, a topological defect identification operation is performed on the phase stability characterization field. The spatial location of the vortex singularity point in the phase stability characterization field is located by calculating the curl field of the phase stability characterization vector, and the spatial location is marked as the potential metastable phase nucleus location.

[0136] Based on the spatial aggregation degree of the potential metastable phase nuclei, the metastable phase structure type identifier that the target multi-component alloy may form during non-equilibrium solidification is predicted, and the metastable phase structure type identifier is merged and output with the equilibrium phase composition sequence.

[0137] During the training phase of the heterogeneous graph neural network phase recognition model, a composite loss function combining phase structure classification loss term and phase fraction regression loss term is adopted. The phase structure classification loss term is in the form of multi-class cross-entropy, and the phase fraction regression loss term is in the form of smooth distance metric.

[0138] The training data comes from high-throughput first-principles calculation databases and labeled phase composition records extracted from experimental phase diagram literature. Each training sample includes a set of composition information, a crystal structure prototype category identifier, and a triplet of actual observed phase composition sequence.

[0139] In this embodiment of the invention, for example, before performing multi-level topological aggregation on the initial unit cell diagram, the server first applies a chemical disorder occupancy perturbation operation to the already constructed FeCoNiCrMn alloy initial unit cell diagram. The server traverses all 108 atomic nodes in the supercell, generating a Bernoulli distributed random variable for each node, with a swap probability set to 0.3. This value is an exemplary optimized value that balances configuration diversity and computational efficiency, and can be adjusted within the range of 0.1 to 0.5 according to the degree of order of the target system: it can be reduced to 0.1 for long-range ordered alloys and increased to 0.5 for completely disordered high-entropy alloys. When the random variable is 1, the server resamples the element type name of the node according to the molar ratio of each element of 0.2, for example, replacing the Ni node at coordinates (0.5, 0.5, 0.5) with the Mn node. This process is repeated independently five times, and the server obtains a perturbed crystallographic unit cell diagram structure representation copy with the total proportion of the five elements remaining unchanged but with different local occupancy configurations.

[0140] The server sequentially sends five perturbation replicas into a multi-level topology aggregation process. For each atomic node, a three-layer nearest neighbor coordination subgraph is extracted. The frequency of elements within each layer is statistically analyzed, and attenuation factors of 0.85 and 0.35 are applied. A 128-dimensional perturbation local chemical environment embedding vector is generated through nonlinear transformation. Simultaneously, a 64-dimensional perturbation electron orbital interaction embedding vector is calculated based on edge type and orbital overlap integral. Each replica obtains its own set of embedding vectors after aggregation.

[0141] The server inputs the embedding vector sets of the five replicas into the heterogeneous graph neural network phase recognition model, performs six rounds of message passing and feature updates, and outputs five replicas of the perturbation phase stability representation field. Each replica corresponds to a 128-dimensional representation vector on 108 spatial grid points.

[0142] The server performs a statistical ensemble average across the spatial grid dimension for the five replicas. At the grid point (0.0, 0.0, 0.0), the representation vectors of the five replicas are collected, and the element-wise arithmetic mean is calculated to obtain the average representation vector for that grid point. After averaging across all grid points, an average phase stability representation field is generated, which replaces the original representation field of a single configuration for subsequent phase composition analysis.

[0143] The server calculates the spatial autocorrelation function of the average phase stability characterization field. Starting from the origin lattice point, the decay relationship of the characterization vector dot product with lattice spacing is statistically analyzed, and a correlation decay curve is obtained by fitting. The curve decays to 1 / e of the initial value at a distance of 1.28 nm, and the server records this distance as the coherence length parameter of the FeCoNiCrMn alloy system.

[0144] The server reads the current supercell length along the crystal axis as 1.05 nanometers. Comparing this to the coherence length parameter of 1.28 nanometers, it finds it to be less than twice that value (2.56 nanometers), indicating that the current supercell size is insufficient to completely eliminate the finite size effect. Based on this, the server expands the supercell to 6×6×6 along the three crystal axes, increasing the total number of atomic nodes to 864, and triggers a re-execution of the entire process starting from the initial primitive cell diagram construction.

[0145] The server invoked the short-program parameter sensitivity analysis module, applying perturbations of -5% and +5% to the molar ratio of Cr in the component information, obtaining two sets of inputs with Cr contents of 0.19 and 0.21, respectively, and completed the full-process prediction. The results showed that the BCC phase disappeared when the Cr content was 0.19, and the Sigma phase precipitated when the Cr content was 0.21. The server plotted the phase structure stability boundary description surface with Cr content and Ni content as axes.

[0146] The server compares the obtained boundary surface point by point with the experimental phase diagram data at the same temperature in the preset alloy phase diagram database. The calculated consistency ratio of phase region at the composition point is 82%, which exceeds the preset tolerance range of 10%. The deviation triggers the incremental learning process. The server uses the deviation data to construct a cross-entropy loss function, and fine-tunes it through backpropagation of the weights of the two fully connected layers of the edge message generator function and the update and reset gate weights of the gated loop unit. After 30 iterations, the loss is reduced to below the threshold and the model parameters are solidified.

[0147] Within the model, the server employs a second message passing mechanism to propagate spin polarization information. For each atomic connection edge, the exchange integral is retrieved from the magnetic parameter database based on the element types at both ends and the edge type. For the Fe-Co edge in the octahedral coordination environment of the FCC structure in this embodiment, the spin exchange coupling constant is taken as +12 mEV. This value is derived from the fitting result of the well-known FeCo alloy tight-binding model and represents ferromagnetic coupling characteristics. In practical applications, the corresponding exchange coupling constant value can be retrieved from a publicly available magnetic parameter database based on the crystal structure and coordination environment of the target system. The spin polarization information is coupled to the main edge message passing vector within the generator through an independent fully connected branch network. Through this mechanism, a spin splitting correction term is applied to the atomic node features during updates, ensuring that the final phase stability characterization field includes contributions from the magnetically ordered structure, thereby improving the prediction accuracy of alloy phases containing Fe, Co, and Ni magnetic elements.

[0148] In this embodiment of the invention, the method further includes:

[0149] The initial primitive cell graph is transformed into a dual graph representation, in which the atomic connection edges in the original initial primitive cell graph are used as vertices of the dual graph, and the association between two atomic connection edges that share the same atomic node in the original initial primitive cell graph are used as connection edges of the dual graph.

[0150] A topological connectivity matrix of edge adjacency is constructed on the dual graph representation, and an edge circulation embedding vector is generated using the topological connectivity matrix. The edge circulation embedding vector encodes the orientation relationship and closed path length information of the atomic connection edges in the crystallographic space loop.

[0151] The edge circulation embedding vector and the electron orbit interaction embedding vector are subjected to a gated fusion operation to generate an enhanced edge feature vector, and the enhanced edge feature vector is used to replace the original electron orbit interaction embedding vector in the subsequent message passing process of the heterogeneous graph neural network phase recognition model.

[0152] Temporal difference analysis is performed on the atomic node feature vectors output by each message passing layer in the heterogeneous graph neural network phase recognition model. The change amplitude of atomic node feature vectors in adjacent iteration rounds is compared and a feature evolution convergence curve is generated. The iteration round in which the feature evolution convergence curve reaches a stable state is determined as the convergence iteration round of the current prediction.

[0153] For different crystal structure prototype category identifiers, corresponding heterogeneous graph neural network phase identification model variants are preset. Each heterogeneous graph neural network phase identification model variant shares the basic structure of the side message generator function and the atomic node feature update gated loop unit, but adopts specific symmetry parameters corresponding to the crystal structure prototype category identifier in the crystal field splitting perturbation transformation module.

[0154] Before inputting the local chemical environment embedding vector and the electron orbital interaction embedding vector into the heterogeneous graph neural network phase identification model, a vector quantization distillation operation is performed on both. The continuous embedding vector is mapped to a discrete codeword index using the vector quantization codebook and then reconstructed into an approximately continuous vector to eliminate noise fluctuation components in the embedding vector.

[0155] The phase stability characterization field is subjected to temperature effect annealing correction based on the heat treatment process parameters of the target multi-component alloy. The temperature effect annealing correction is achieved by superimposing temperature-related Boltzmann weighted noise terms on each dimension component of the phase stability characterization vector. The amplitude of the noise term increases monotonically with the increase of annealing temperature.

[0156] The phase stability characterization field after temperature effect annealing correction is input into the phase composition analysis module to obtain the phase composition sequence evolution map under different annealing temperature conditions, and the phase transformation critical temperature parameter and phase region boundary composition range of the target multi-component alloy are extracted from the evolution map.

[0157] The critical phase transformation temperature parameters and phase region boundary composition ranges are matched and screened with the preset alloy design target requirements to output a recommended range of component element molar ratios that meet the target phase composition requirements.

[0158] In this embodiment of the invention, for example, after constructing the initial unit cell diagram of the FeCoNiCrMn alloy, the server transforms the initial unit cell diagram into a dual graph representation. In the dual graph, the 486 atomic connection edges in the original initial unit cell diagram are used as vertices of the dual graph, and the set of vertices in the dual graph corresponds one-to-one with the set of atomic connection edges. The association between two atomic connection edges sharing the same atomic node in the original initial unit cell diagram is used as the connection edge in the dual graph; that is, when two atomic connection edges connect to the same atomic node in the original graph, the server establishes a dual connection edge between the vertices corresponding to these two edges in the dual graph. Through this transformation, the server obtains a dual graph structure containing 486 vertices and approximately 3800 edges.

[0159] The server constructs a topological connectivity matrix of edge adjacency relationships on the dual graph representation. The matrix has dimensions of 486×486, where a value of 1 indicates that two atomic connecting edges share an atomic node in the original graph, and a value of 0 indicates that there is no sharing relationship. The server uses this topological connectivity matrix to generate an edge circulation embedding vector. Specifically, the server performs random walk sampling on the dual graph, records the closed paths formed by the sequence of atomic connecting edges, and statistically analyzes the length distribution of the closed paths and the crystallographic orientation angle information. After compression encoding by a graph autoencoder, a 32-dimensional edge circulation embedding vector is output. This vector encodes the orientation relationship of the atomic connecting edges in the crystallographic space loop and the closed path length information.

[0160] The server performs a gating fusion operation on the edge loop embedding vector and the generated 64-dimensional electron orbit interaction embedding vector. The fusion gating network outputs a scalar gating coefficient between 0 and 1. The server then weights and mixes the two vectors according to this coefficient to generate a 96-dimensional enhanced edge feature vector. This enhanced edge feature vector replaces the original electron orbit interaction embedding vector and is fed into the heterogeneous graph neural network phase identification model to participate in the subsequent message passing process.

[0161] During the inference process of the heterogeneous graph neural network phase recognition model, the server performs temporal difference analysis on the feature vectors of atomic nodes output by each message passing layer. The server calculates the L2 norm difference of the feature vectors of atomic nodes between every two adjacent iterations, summarizes the average change of all atomic nodes, and plots the feature evolution convergence curve. When the change amplitude is below the threshold of 0.01 for three consecutive iterations, the server determines that iteration as the convergence iteration for the current prediction; in this example, it is determined to be the 5th iteration.

[0162] The server pre-defines corresponding heterogeneous graph neural network phase recognition model variants for different crystal structure prototype categories such as FCC, BCC, and HCP. Each variant shares the basic network structure of the side message generator function and the gated recurrent unit, but employs specific symmetry parameters corresponding to the crystal structure prototype in the crystal field splitting perturbation transformation module. When the input crystal structure prototype is FCC, the server calls the FCC variant model, using the irreducible representation basis functions of the O_h point group for feature projection; when the input is BCC, it calls the BCC variant model, using another set of splitting scaling factors corresponding to the O_h point group.

[0163] Before inputting the local chemical environment embedding vector and the electron orbital interaction embedding vector into the model, the server performs vector quantization distillation on both. The server calls a pre-trained vector quantization codebook containing 256 learnable codeword vectors. The server calculates the Euclidean distance between each continuous embedding vector and all codewords in the codebook, selects the index of the closest codeword as the discrete code, and then reconstructs an approximately continuous vector using this codeword. This operation eliminates noise fluctuations introduced by random placement in the embedding vector, enhancing the robustness of the features.

[0164] The server applies a temperature-effect annealing correction to the phase stability characterization field based on the heat treatment process parameters of the target multi-component alloy. When the user specifies an annealing temperature of 1200K, the server superimposes temperature-related Boltzmann weighted noise terms onto each component of the phase stability characterization vector. The noise amplitude is calculated using the formula σ=T / T_melt, where σ is the standard deviation of the Gaussian noise superimposed on each component of the phase stability characterization vector, used to quantify the influence of thermal perturbation on phase stability judgment. The noise follows a normal distribution with a mean of 0 by default, conforming to the random fluctuation characteristics of atomic thermal vibration. T is the actual annealing / service temperature of the target multi-component alloy, in Kelvin (K), directly obtained from the heat treatment process parameters input by the user, and T_melt is the theoretical melting point of the alloy. The higher the temperature, the greater the noise amplitude, simulating the perturbation effect of atomic thermal vibration on phase stability at high temperatures.

[0165] The server inputs the phase stability characterization field, corrected for temperature-effect annealing, into the phase composition analysis module. Phase composition prediction is then performed at four temperatures: 1000K, 1100K, 1200K, and 1300K, yielding phase composition sequence evolution maps under different annealing temperatures. From these evolution maps, the critical temperature parameter for the phase transition where the mole fraction of the BCC phase drops to zero at 1150K, and the boundary composition range of the FCC single-phase region with a lower limit of 0.18 Ni content, are extracted.

[0166] The server matches and filters the extracted phase transformation critical temperature parameter of 1150K and the lower limit of Ni content in the FCC single-phase region of 0.18 with the preset alloy design target requirements. When the design target requires the alloy to maintain a single-phase FCC structure below 1100K, the server outputs a recommended range of component element molar ratios that meet the conditions, with Ni content not less than 0.19 and Cr content not exceeding 0.21, and returns this range to the user terminal in the form of numerical ranges.

[0167] In this embodiment of the invention, the method further includes:

[0168] In the set of atomic connection edges of the initial unit cell graph, a subset of heterogeneous atomic connection edges that connect atomic nodes labeled with different element types are identified, and the proportion of the heterogeneous atomic connection edge subset to the total set of atomic connection edges is calculated as a chemical order parameter.

[0169] The chemical order parameter is injected as prior information into the first message passing mechanism of the heterogeneous graph neural network phase recognition model. The bias of chemical order tendency on message propagation path is reflected by adjusting the initial attention bias weight of different edge type channels in the edge type attention mechanism.

[0170] During the atomic node feature update process, a higher scaling factor is applied to the edge message passing vector from heterogeneous atomic connection edges compared to homogeneous atomic connection edges. The scaling factor is positively correlated with the value of the chemical order parameter.

[0171] After generating the phase stability characterization field, the similarity of the phase stability characterization vectors between spatially adjacent atomic node pairs in the phase stability characterization field is extracted, and the spatial distribution mean and spatial distribution variance of the phase stability characterization vector similarity are calculated. When the spatial distribution variance exceeds a preset fluctuation threshold, it is determined that the alloy system has a phase separation tendency.

[0172] For alloy systems that are determined to have a tendency to phase separation, compositional clustering regions are identified at the spatial grid points of the phase stability characterization field. The phase stability characterization vector is spatially segmented by a clustering algorithm, and adjacent spatial grid points with vector similarity higher than a preset clustering threshold are divided into the same compositional clustering region.

[0173] Calculate the average elemental molar ratio of atomic nodes within each component agglomeration region, compare the degree of difference in elemental molar ratio values ​​among different component agglomeration regions, and mark the two component agglomeration regions with the greatest difference in elemental molar ratio values ​​as candidate regions for amplitude modulation decomposition products.

[0174] Based on the spatial boundary and internal element molar ratio of the candidate region of amplitude-modulated decomposition products, the phase structure type identifier and volume fraction of the amplitude-modulated decomposition products that may be formed in the target multi-component alloy during the aging process are predicted.

[0175] The phase structure type identifier and volume fraction of the amplitude-modulated decomposition product are used as supplementary phase composition information and output together with the equilibrium phase composition sequence to provide a complete phase composition prediction report covering both equilibrium and metastable phase structures.

[0176] In this embodiment of the invention, for example, the server traverses all 486 atomic connection edges in the initial unit cell diagram of the constructed FeCoNiCrMn alloy, extracts the element type name labels of the atomic nodes at both ends of each edge, and compares them. When the element type name labels at both ends are inconsistent, the server classifies the edge into a subset of dissimilar atomic connection edges. Statistically, the number of dissimilar atomic connection edges is 392, accounting for 0.806 of the total number of atomic connection edges. The server records this ratio as a chemical order parameter.

[0177] The server injects the chemical order parameter 0.806 as prior information into the first message passing mechanism of the heterogeneous graph neural network phase recognition model. During the calculation of channel weights for each edge type in the edge type attention mechanism, the server adjusts the initial attention bias weights for each channel. For heterogeneous edge type channels such as E_FeCo, E_FeNi, E_FeCr, and E_FeMn, the bias weight is increased by 0.1; for similar edge type channels such as E_FeFe, the bias weight is decreased by 0.05. This adjustment gives the message propagation path a higher initial response sensitivity to electron orbital interactions between heterogeneous atoms during the attention aggregation stage, reflecting the biased guidance of information flow by chemical order tendency.

[0178] During the atomic node feature update process, the server applies an additional scaling factor to the edge message passing vectors from heterogeneous atomic connections. The scaling factor is calculated using a positive correlation mapping function, taking a value of 1.0 plus the product of the chemical order parameter and the adjustment factor; the actual value is 1.0 + 0.3 × 0.806 = 1.24. For edge message passing vectors from homogeneous atomic connections, the scaling factor remains at 1.0. The server then sends the scaled edge message passing vectors to the gate control loop unit for node feature updates.

[0179] After generating the phase stability characterization field, the server extracts the similarity of phase stability characterization vectors between adjacent atomic node pairs in space. The similarity is measured using cosine similarity. For all 864 pairs of adjacent atomic nodes within the supercell, the server calculates a spatial distribution mean of 0.82 and a spatial distribution variance of 0.14. With a preset fluctuation threshold of 0.10, the current variance of 0.14 exceeds the threshold, and the server determines that the FeCoNiCrMn alloy system exhibits a phase separation tendency under the given composition.

[0180] For alloy systems identified as having a tendency for phase separation, the server identifies compositional clustering regions at 864 spatial grid points in the phase stability characterization field. The server uses the DBSCAN clustering algorithm, employing cosine similarity as the distance metric and a similarity threshold of 0.75, to spatially segment the phase stability characterization vectors of the spatial grid points. The clustering results are three regions: Region A contains 523 grid points, Region B contains 218 grid points, and Region C contains 123 grid points. The boundary between Region A and Region B is clear, while Region C has a discrete distribution.

[0181] The server calculates the average molar proportion of elements at atomic nodes within each component segregation region. Region A contains 0.24 Fe, 0.22 Co, 0.28 Ni, 0.12 Cr, and 0.14 Mn; Region B contains 0.18 Fe, 0.16 Co, 0.14 Ni, 0.32 Cr, and 0.20 Mn. The difference in the molar proportion of Cr between Region A and Region B reaches 0.20, the largest difference among all element pairs. The server marks Region A and Region B as candidate regions for amplitude modulation decomposition products.

[0182] Based on the spatial boundary and internal elemental molar ratio of candidate region A (amplitude modulated decomposition product), the server determined that its Ni-rich and Cr-poor characteristics were compatible with the FCC phase structure, predicting the formation of a Ni-rich FCC amplitude modulated decomposition product phase. Based on the Cr-rich and Ni-poor characteristics of candidate region B, the server predicted the formation of a Cr-rich BCC amplitude modulated decomposition product phase. According to the ratio of spatial grid points in the two regions, the server calculated the volume fraction of the Ni-rich FCC phase to be 0.706, and the volume fraction of the Cr-rich BCC phase to be 0.294.

[0183] The server identifies the predicted phase structure types of the amplitude modulation decomposition products as Ni-rich FCC and Cr-rich BCC, with their volume fractions of 0.706 and 0.294, respectively, as supplementary phase composition information. This information is then combined with the equilibrium phase composition sequence predicted by the main process (FCC phase molar fraction 0.792, BCC phase molar fraction 0.208) to form a complete phase composition prediction report. The report is returned to the user terminal via the output interface, providing information on the stable phase structure of the alloy in equilibrium and the metastable amplitude modulation decomposition products that may appear during aging treatment.

[0184] In this embodiment of the invention, the method further includes:

[0185] Collect atomic orbital energy level parameters and orbital radius expansion coefficients corresponding to the element types in multi-component alloy systems, and construct a basic parameter library of atomic orbital characteristics.

[0186] When performing multi-level topological aggregation on the initial unit cell graph, an orbital hybridization state marker is introduced for each topological level. The orbital hybridization state marker determines the hybridization orbital type of the central atom node based on the element type name of the central atom node and the geometric arrangement of its coordinating atom nodes.

[0187] The hybrid orbital orientation vector and hybrid orbital occupancy parameter corresponding to the hybrid orbital type are embedded into the generation process of the local chemical environment embedding vector, so that the local chemical environment embedding vector carries directional valence bond distribution information.

[0188] In the stage of generating the electron orbital interactive embedding vector, the orbital overlap direction factor is calculated based on the hybrid orbital type of the atomic nodes at both ends and the spatial orientation vector of the atomic connection edge. The orbital overlap direction factor is then multiplied by the overlap integral feature scalar to obtain the direction-sensitive overlap integral feature value.

[0189] The direction-sensitive overlap integral eigenvalues ​​are used to replace the original overlap integral eigens scalars for subsequent calculation of the electron orbital interaction embedding vector, so that the electron orbital interaction embedding vector can reflect the modulation effect of crystallographic orientation on orbital coupling strength.

[0190] The initial unit cell diagram is expanded into an expanded diagram structure containing virtual atomic nodes. The virtual atomic nodes are inserted into the interstitial positions of the lattice and their element type names are marked as vacuum element identifiers. Virtual atomic connection edges are established between the virtual atomic nodes and the adjacent real atomic nodes, and the edge type attribute of the virtual atomic connection edges is marked as interstitial edge type.

[0191] The multi-level topological aggregation and heterogeneous graph neural network phase identification model inference are performed on the extended graph structure to generate an extended phase stability characterization field that includes the influence of gap positions.

[0192] Based on the distribution of the phase stability characterization vector magnitude at the virtual atom node positions in the extended phase stability characterization field, the occupancy tendency of interstitial atoms and the ordering trend of interstitial atoms in the target multi-component alloy are evaluated.

[0193] The interstitial atom occupancy tendency and interstitial atom ordering trend are correlated and mapped with the mechanical property database of the target multi-component alloy, and interstitial atom control suggestions are output to guide the selection of microalloying element types and addition amounts for multi-component alloys.

[0194] During the training phase of the heterogeneous graph neural network phase recognition model, an independent parameter regularization constraint is applied to the edge message generator function of the virtual atomic connection edge to constrain the perturbation amplitude of the virtual atomic connection edge to the feature update of the real atomic node within a preset reasonable range.

[0195] This invention provides a computer device 100, which includes a processor and a non-volatile memory storing computer instructions. When the computer instructions are executed by the processor, the computer device 100 executes the aforementioned method for predicting the phase composition of multi-component alloys based on graph neural networks. Figure 2 As shown, Figure 2This is a structural block diagram of a computer device 100 provided in an embodiment of the present invention. The computer device 100 includes a memory 111, a processor 112, and a communication unit 113. To enable data transmission or interaction, the memory 111, processor 112, and communication unit 113 are electrically connected to each other directly or indirectly. For example, these components can be electrically connected to each other through one or more communication buses or signal lines.

[0196] For illustrative purposes, the foregoing description has been made with reference to specific embodiments. However, the foregoing illustrative discussions are not intended to be exhaustive or to limit the present disclosure to the precise forms disclosed. Numerous modifications and variations are possible in accordance with the foregoing teachings. These embodiments were chosen and described in order to best illustrate the principles of the present disclosure and its practical application, thereby enabling those skilled in the art to best utilize the disclosure and to employ various embodiments with different modifications to suit a particular intended application.

Claims

1. A method for predicting the phase composition of multi-component alloys based on graph neural networks, characterized in that, The method includes: Obtain the set of composition information and crystal structure prototype category identifier of the target multi-component alloy. The set of composition information includes the names of all elements involved in the alloy composition and the molar ratio of each element. Based on the set of component information and the crystal structure prototype category identifier, an initial unit cell diagram of a multi-component alloy system is constructed. The initial unit cell diagram includes a set of atomic nodes labeled by element type names and a set of atomic connection edges determined by the spatial adjacency relationship between atoms. Multi-level topological aggregation is performed on the initial unit cell graph to generate local chemical environment embedding vectors at the atomic node level and electron orbital interaction embedding vectors at the atomic connection edge level. The local chemical environment embedding vectors describe the elemental distribution characteristics of coordinating atoms around the target atomic node, and the electron orbital interaction embedding vectors describe the coupling characteristics of electron cloud overlap and valence electron concentration between adjacent atomic nodes. The local chemical environment embedding vector and the electron orbital interaction embedding vector are input into the pre-constructed heterogeneous graph neural network phase identification model. The atomic node features and atomic connection edge features are cross-updated through the first message passing mechanism under the heterogeneous graph structure to generate a phase stability characterization field that integrates crystal field splitting information. The equilibrium phase composition sequence of the target multi-component alloy is analyzed based on the spatial distribution state of the phase stability characterization field. The equilibrium phase composition sequence includes the predicted phase structure type identifier and the mole fraction ratio of the phase structure type identifier in the alloy system.

2. The method according to claim 1, characterized in that, The initial unit cell diagram of the multi-component alloy system constructed based on the set of component information and the crystal structure prototype category identifier includes: Based on the crystal structure prototype category identifier, a preset crystallography database is searched to obtain the corresponding lattice points; Based on the set of component information, element type names are assigned to each lattice site to form an atomic node set; The set of atomic nodes is expanded to a supercell of a preset size to generate a supercell set of atomic nodes; Based on the preset nearest neighbor cutoff radius parameter, atomic connection edges are established between atomic nodes in the supercell atomic node set to form an atomic connection edge set, and each atomic connection edge is assigned an edge type attribute label based on the types of atomic elements at both ends and the connection direction. The set of atomic nodes and the set of atomic connection edges are integrated to construct the initial primitive cell graph, and a periodic boundary condition encoding operation is performed on the initial primitive cell graph.

3. The method according to claim 1, characterized in that, The step of performing multi-level topological aggregation on the initial unit cell graph to generate local chemical environment embedding vectors at the atomic node level and electron orbital interaction embedding vectors at the atomic connection edge level includes: Using the atomic nodes in the initial primitive cell graph as the center, extract the coordination atomic subgraph structure covering the preset nearest neighbor shell, and divide the topological hierarchy according to the number of connection edge steps; The frequency of occurrence of each element type within each topological level is counted to generate an element type frequency distribution vector. The vectors of each level are then weighted and aggregated using a level attenuation factor to generate an initial description vector of the local chemical environment. The local chemical environment initial description vector is concatenated and transformed with the element intrinsic attribute embedding vector of the target atom node to generate the local chemical environment embedding vector. For the atomic connection edges in the initial primitive cell graph, the electron orbital interaction embedding vector is calculated and transformed based on the element intrinsic attribute parameters of the atomic nodes at both ends and the edge type attribute marker.

4. The method according to claim 1, characterized in that, The step involves inputting the local chemical environment embedding vector and the electron orbital interaction embedding vector into a pre-constructed heterogeneous graph neural network phase identification model. Through a first message passing mechanism under the heterogeneous graph structure, a cross-update operation is performed on the atomic node features and atomic connection edge features to generate a phase stability characterization field that integrates crystal field splitting information. This includes: The local chemical environment embedding vectors corresponding to all atomic nodes in the initial unit cell graph are assembled into an initial feature matrix of atomic nodes, and the electron orbit interaction embedding vectors corresponding to all atomic connection edges are assembled into an initial feature matrix of edges. In the first message passing layer of the heterogeneous graph neural network phase recognition model, for each atomic connection edge, the initial feature vector of the atomic connection edge is concatenated with the feature vectors of the atomic nodes at both ends in the current iteration to obtain the edge message generation input vector. The edge message generation input vector is input into the edge message generator function, which is a fully connected neural network structure containing at least two hidden units, and outputs the edge message passing vector corresponding to the atomic connection edge. For each atomic node, collect the edge message passing vectors generated by all atomic connection edges with that atomic node as the receiving end, and allocate the edge message passing vectors to different edge type channels according to the edge type attribute label of each atomic connection edge. Within each edge type channel, an element-wise average pooling operation is performed on the collected edge message passing vectors to generate the channel aggregate message vector corresponding to that edge type channel. Then, the channel aggregate message vectors of each edge type channel are weighted and summed, and the weights are calculated by the edge type attention mechanism. The weighted summed aggregated message vector is joined with the atomic node feature vector in the current iteration by a residual concatenation operation, and then input into the atomic node feature update gated loop unit to perform the atomic node feature vector update operation, generating the atomic node feature vector for the next iteration. After completing the cross-update operation of atomic node features and atomic connection edge features for a preset number of iterations, a set of steady-state atomic node features output by the heterogeneous graph neural network phase recognition model is obtained. Each atomic node feature vector in the set of steady-state atomic node features integrates comprehensive information of its surrounding local chemical environment and long-range electron orbit coupling. Based on the crystal field symmetry parameters corresponding to the crystal structure prototype category identifier, a crystal field splitting perturbation transformation is applied to each atomic node feature vector in the steady-state atomic node feature set. The crystal field splitting perturbation transformation projects the atomic node feature vector to the irreducible representation subspace based on the point symmetry of the lattice point where the atomic node is located. The atomic node feature vectors after crystal field splitting perturbation transformation are arranged according to the spatial coordinates of the atomic nodes in the supercell space to form a phase stability characterization field with spatial continuous distribution characteristics. The phase stability characterization field is in the form of a vector field and each spatial grid point corresponds to a phase stability characterization vector. Spatial smoothing is performed on the phase stability characterization field. A Laplacian smoothing operator based on graph topology is used to propagate gradient constraints on the phase stability characterization vectors between adjacent atomic nodes, so that the vector changes of the phase stability characterization field in the topological adjacency region exhibit continuous transition characteristics.

5. The method according to claim 1, characterized in that, The equilibrium phase composition sequence of the target multi-component alloy is analyzed based on the spatial distribution state of the phase stability characterization field. This equilibrium phase composition sequence includes a predicted phase structure type identifier and the mole fraction of that phase structure type identifier in the alloy system, comprising: The phase stability representation vector corresponding to each spatial grid point in the phase stability representation field is input to the pre-trained first fully connected classifier network layer, and the first fully connected classifier network layer outputs the probability distribution vector of the spatial grid point belonging to each candidate phase structure type identifier in the preset phase structure type list. For each spatial grid point, the candidate phase structure type identifier with the highest probability value in the probability distribution vector is selected as the local phase attribution label of the spatial grid point, and spatially adjacent spatial grid points with the same local phase attribution label are aggregated into continuous phase region patches. The initial estimate of the volume ratio of the phase structure type identifier corresponding to the continuous phase region patch in the alloy system is calculated based on the proportion of the number of spatial grid points contained in the continuous phase region patch to the total number of spatial grid points. The preset phase boundary energy correction module is invoked to perform interface effect correction on the initial volume ratio estimate. The phase boundary energy correction module calculates the interface energy contribution based on the interface area between adjacent phase region patches and the heterogeneous phase interface energy parameters, and readjusts the volume ratio of each phase structure type identifier. The volume ratio after interface effect correction is mapped to mole fraction ratio. During the mapping process, the ratio conversion is performed under the mass conservation constraint based on the theoretical crystallographic density parameters and unit cell volume parameters corresponding to each phase structure type. Collect all the converted phase structure type identifiers and their corresponding mole fraction ratios to form a preliminary phase composition sequence, and filter out phase structure type identifiers with mole fraction ratios lower than a preset threshold. A Gibbs phase law compliance constraint verification operation is performed on the filtered preliminary phase composition sequence. When the numerical relationship between the number of phase structure type identifiers and the number of component element types in the preliminary phase composition sequence does not conform to the Gibbs phase law, the phase structure type identifier with the smallest mole fraction ratio is deleted and the mole fraction ratio of the remaining phase structure type identifiers is renormalized until the Gibbs phase law is satisfied. According to the phase diagram topology rules, a conjugate phase verification operation is performed on the preliminary phase composition sequence to remove the identifiers of isolated phase structure types that cannot coexist with adjacent phase structures in thermodynamic equilibrium from the preliminary phase composition sequence; The phase composition sequence after the conjugate phase verification operation is output as the equilibrium phase composition sequence of the target multi-component alloy. Each phase structure type identifier in the equilibrium phase composition sequence corresponds to a normalized mole fraction ratio value.

6. The method according to claim 1, characterized in that, The method further includes: A chemical disorder occupancy perturbation operation is applied to the initial unit cell diagram to generate multiple perturbed unit cell diagram copies; The multi-level topological aggregation and the heterogeneous graph neural network phase identification model inference are performed on each of the perturbation primitive cell graph replicas to generate a corresponding perturbation phase stability characterization field replica. Perform a statistical ensemble averaging operation on all copies of the perturbation phase stability characterization field to generate an average phase stability characterization field, which is then used to analyze the equilibrium phase composition sequence. Adjust the supercell size of the initial primitive cell diagram based on the spatial correlation of the average phase stability characterization field. Sensitivity analysis is performed on the molar ratio values ​​of elements in the component information set, and the incremental learning process of the heterogeneous graph neural network phase recognition model is triggered based on the deviation between the analysis results and the experimental data. A second message passing mechanism for propagating spin polarization information is configured in the heterogeneous graph neural network phase identification model.

7. The method according to claim 1, characterized in that, The method further includes: The initial primitive graph is transformed into a dual graph to generate an edge circulation embedding vector, and the edge circulation embedding vector is fused with the electron orbital interaction embedding vector to generate an enhanced edge feature vector for message passing in the heterogeneous graph neural network phase identification model. Temporal difference analysis is performed on the atomic node feature vectors during the iterative process of the heterogeneous graph neural network phase identification model to dynamically determine the convergence iteration round; Variants of the heterogeneous graph neural network phase identification model with corresponding symmetry parameters are configured for different crystal structure prototype category identifiers; Before inputting the local chemical environment embedding vector and the electron orbital interaction embedding vector into the heterogeneous graph neural network phase identification model, a vector quantization distillation operation is performed on both to eliminate noise. The phase stability characterization field is subjected to temperature-effect annealing correction based on the heat treatment process parameters, and the phase composition sequence evolution spectrum at different temperatures is analyzed based on the correction results to extract the critical temperature parameters of phase transition and the composition range of the phase region boundary. Based on the phase transition critical temperature parameter and the composition range of the phase region boundary, a recommended range of component element molar ratios that meet the target phase composition requirements is output.

8. The method according to claim 1, characterized in that, The method further includes: Based on the set of atomic connection edges in the initial unit cell diagram, the proportion of heterogeneous atomic connection edges is calculated as a chemical order parameter. The chemical order parameter is injected into the first message passing mechanism of the heterogeneous graph neural network phase recognition model to adjust the initial bias weights of the edge type attention mechanism. When updating atomic node features, a higher scaling factor is assigned to the message vector from heterogeneous atomic connection edges based on the chemical order parameter; Based on the vector similarity of adjacent atomic node pairs in the phase stability characterization field, the phase separation tendency of the alloy system is determined. When a phase separation tendency is determined, spatial clustering is performed on the phase stability characterization field to identify component clustering regions; By comparing the differences in elemental molar ratios in different component segregation regions, candidate regions for amplitude modulation decomposition products can be identified. Based on the candidate region of amplitude modulation decomposition products, the phase structure and proportion of amplitude modulation decomposition products are predicted, and the phase structure and proportion of amplitude modulation decomposition products are output together with the equilibrium phase composition sequence as a supplement.

9. The method according to claim 1, characterized in that, The method further includes: Construct a basic parameter library of atomic orbital features containing atomic orbital energy levels and radius parameters; when performing multi-level topological aggregation on the initial unit cell diagram, introduce hybrid orbital type labels based on their element type and coordination geometry for the atomic nodes; Based on the hybrid orbital type label, the generated local chemical environment embeds a vector carrying valence bond direction information; When generating the electron orbital interaction embedding vector, the direction-sensitive overlap integral eigenvalue is calculated by combining the hybrid orbital type label with the spatial orientation of the atomic connection edge. The initial unit cell graph is expanded into an expanded graph structure containing virtual atomic nodes marked as vacuum and the gap edges they connect; Perform the multi-level topological aggregation and model inference on the extended graph structure to generate an extended phase stability characterization field that includes the influence of gap positions; The expansion phase stability characterization field is used to evaluate the occupancy and ordering trends of interstitial atoms; The mechanical properties are correlated with the occupancy of interstitial atoms and the ordering trend, and suggestions for microalloying control are output.

10. A multi-component alloy phase composition prediction system based on graph neural networks, characterized in that, Includes at least one service node; The service node includes a storage unit and a computing unit; the storage unit is used to store program code; the computing unit is used to run the program code to execute the multi-component alloy phase composition prediction method based on graph neural networks as described in any one of claims 1 to 9.

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