CN-122024951-A - Perovskite formation energy prediction method based on graph neural network and functional subgraph

Abstract

The invention provides a perovskite formation energy prediction method based on a graph neural network and a functional subgraph. Firstly, dividing a crystal diagram into an octahedral subgraph with a B-site atom as a center and a coordination polyhedral subgraph with an A-site atom as a center according to a functional unit aiming at a perovskite crystal structure, and representing a key local coordination environment, secondly, introducing a local dynamic coordinate system into the functional subgraph, projecting the relative position between the central atom and a neighborhood atom as a geometric description quantity insensitive to global translation and rotation, and taking the geometric description quantity and the key length, the key angle and the coordination distortion related characteristics as inputs of a graph neural network together, and finally, fusing the distance and the element electronegativity side weight priori in the message transmission process, and polymerizing information in the subgraph through an attention mechanism to finally realize the prediction of the formation energy of a perovskite material. The method is suitable for high-throughput screening and synthesizable evaluation of large-scale perovskite material libraries.

Inventors

• WAN XILI
• LI ZHIQIAN
• GUAN XINJIE

Assignees

• 南京工业大学

Dates

Publication Date

20260512

Application Date

20260114

Claims (6)

1. 1. The perovskite formation energy prediction method based on the graph neural network and the functional subgraph is characterized by comprising the following steps of: step 1) obtaining crystal structure data of perovskite materials from a material database, constructing a crystal diagram taking atoms as nodes and neighbor atom pairs as edges under a periodic boundary condition, and respectively endowing the nodes and the edges with element attributes and geometric attributes as initial characteristics; Step 2) dividing the crystal diagram into at least two types of partial functional subgraphs according to functional units based on coordination structure differences of different sites in the perovskite crystal, wherein the functional subgraphs comprise octahedral subgraphs formed by 6 anions nearest to the functional subgraphs and coordination polyhedral subgraphs formed by 12 anions nearest to the functional subgraphs and taking an atom at the position A as the center; Step 3) in the forward propagation process of each layer of the graph neural network, aiming at each central atom in the functional subgraph, constructing a local dynamic coordinate system on line according to the edge weight corresponding to the neighborhood atom of the central atom, and projecting the relative position vector between the central atom and the neighborhood atom of the central atom into the local dynamic coordinate system to obtain geometric description quantity insensitive to global translation and rotation; Step 4) the geometric description quantity, the key length, the key angle and the polyhedral distortion degree obtained based on coordination environment statistics are used as node characteristics or edge characteristics to be input together, edge weight prior integrating distance and element electronegativity is introduced, and feature aggregation is carried out in the functional subgraph through an attention message transmission mechanism, so that high-level representation of each functional subgraph is obtained; And 5) reading and fusing the characteristic representations of the different types of functional subgraphs, and outputting a formation energy prediction result of the corresponding perovskite material through a regression prediction module.
2. 2. The method according to claim 1, wherein the functional subgraphs include two types of BO 6 ,AO 12 , namely an octahedral subgraph composed of 6 anions whose centers are at the B-site atoms and whose nearest centers are at the periodic boundary conditions, and a ligand polyhedral subgraph composed of 12 anions whose centers are at the periodic boundary conditions and whose centers are at the a-site atoms.
3. 3. The perovskite formation energy prediction method based on the graph neural network and the functional subgraph according to claim 1, characterized in that the side weight prior considers the interatomic distance and the element electronegativity at the same time, and the weight calculation mode satisfies the following form: Where w cj is the edge weight, d cj represents the shortest mirror distance between atom c and atom j, σ is the distance decay scale parameter, α is the electronegativity adjusting coefficient, and x c ,x j represents the electronegativity of the corresponding atom, respectively.
4. 4. The perovskite formation prediction method based on the graph neural network and the functional subgraph according to claim 1, wherein the step 3) includes the following sub-steps: Step 3.1) to eliminate the influence of the overall translation and rotation of the crystal structure on the geometric feature characterization, and to enhance the characterization capability of the model on the local coordination environment, a local dynamic coordinate system is constructed for the central atom in each functional subgraph, and the specific steps are as follows. Firstly, calculating the shortest mirror image relative position vector between the central atom c and the neighborhood atom j by taking the space coordinate rc of the central atom c as a reference origin: Δr cj ＝r j -r c Where r c ,r j represents the Cartesian coordinates of the central atom c and its neighbor atom j, respectively. Secondly, selecting a neighborhood atom j with the largest weight from neighborhood atoms of central atoms according to the prior size of the edge weights in the graph structure, carrying out normalization processing on a corresponding relative position vector of the neighborhood atom j to obtain a first base vector u 1 of a local dynamic coordinate system, selecting a neighborhood atom k with the non-collinear direction of the first base vector and the next largest weight from other neighborhood atoms, carrying out orthogonalization processing on the relative position vector of the neighborhood atom k to obtain a second base vector u 2 , and constructing a third base vector u 3 by carrying out cross multiplication operation on the first base vector and the second base vector on the basis, and arranging the three groups of base vectors according to columns to form a local dynamic coordinate system matrix corresponding to the central atom. The calculation formula is as follows: u 3 ＝u 1 ×u 2 ,U＝[u 1 ,u 2 ,u 3 ] Wherein Δr cj represents the shortest mirrored relative position vector of the central atom c and its weighted greatest neighbor atom j under periodic boundary conditions, k is a non-collinear and weighted next greatest neighbor with U 1 , its corresponding relative position vector is Δr ck* ,u 1 ,u 2 ,u 3 is three mutually orthogonal basis vectors, and U is a set of orthogonal basis vectors. Step 3.2) projecting the relative position vector between the central atom c and the neighborhood atom j thereof into a local dynamic coordinate system U to obtain the geometric description quantity insensitive to global translation and rotation, wherein the calculation formula is as follows: Wherein the method comprises the steps of Represents the coordinate vector of the neighborhood atom j in a local dynamic coordinate system constructed by taking the central atom c as a reference, and phi cj is the included angle between the relative position vector of the central atom c pointing to the neighbor atom j and the first base vector u 1 . Step 3.3) calculating the variance with respect to the average value thereof based on the key length and key angle characteristics obtained in step 3.2, to obtain a polyhedral distortion degree: θ cjk ＝∠(Δr cj ,Δr ck ) Wherein θ cjk represents the angle between the relative position vectors pointing from the central atom to two different neighborhood atoms j and k in a local coordination environment with the central atom c as the vertex. δ poly is the degree of polytropic distortion, λ len ,λ ang is the weight coefficient for balancing bond length and bond angle contributions and λ len +λ ang =1, n represents the coordination number of the central atom c, m is the total number of adjacent atom pairs (j, k), Respectively represent the average value of the corresponding key length and the included angle. Combining the polyhedral distortion degree with element attribute characteristics and local geometric characteristics of a central atom to form input characteristics of a central node in the layer 1 graph information transmission process, and using the input characteristics for subsequent information transmission and characteristic aggregation: Wherein, the Features are input for the first layer edge, For the first level node input features, CN c is the central coordination number.
5. 5. The perovskite formation prediction method based on the graph neural network and the functional subgraph according to claim 1, wherein the step 4) includes the following sub-steps: Step 4.1) in a BO 6 、AO 12 subgraph of the perovskite material, carrying out polymerization treatment on node characteristics based on an attention mechanism, wherein a polymerization formula is as follows: Wherein, the Is in a hidden state for the central node of the first layer, For the hidden state of layer i neighbor j, w q ,w k ,w o , a is a learnable parameter, For the side node fusion function, func is a linear non-activated function, beta is a priori injection weight, For the purpose of normalizing the side weights a priori, Is the attention coefficient. Step 4.2) after the multi-layer feature aggregation is completed, respectively reading out the node features of the two types of subgraphs, and fusing the features of the two types of subgraphs, wherein the process meets the following form: F loc ＝[F BO6 ||F AO12 ] Where L is the number of layers of the neural network, pool represents a pooled read operation, preferably an average pooled, And representing the hidden state of the node i in the L layer, and F loc represents the fused local structural feature representation. Step 4.3) inputting the fusion feature F loc obtained in the step 4.2) into a regression prediction module to establish a mapping relationship between the structural feature and the perovskite material formation energy, and outputting a predicted formation energy value Its predictive process can be expressed as: Wherein MLP () represents the formation of a regressive function.
6. 6. The perovskite formation prediction method based on the graph neural network and the functional subgraph according to claim 1, wherein the step 5) includes the following sub-steps: step 5.1) Using the actual formation energy E f of the perovskite material and the corresponding predicted formation energy On the basis, a loss function is constructed and a model is trained, wherein the loss function adopts an average absolute error and has the following form: Where Loss is the Mean Absolute Error (MAE) and N is the number of samples in the training set. Step 5.2) after model training is completed, evaluating the model performance according to the error between the predicted forming energy and the actual forming energy, preferably using Mean Absolute Error (MAE) and Mean Square Error (MSE) as model performance evaluation indexes, wherein the calculation modes are as follows: wherein E f is a true value of the formation energy, Corresponding to the predicted formation energy.

Description

Perovskite formation energy prediction method based on graph neural network and functional subgraph Technical field: the invention provides a perovskite material formation energy prediction method based on a graph neural network and a perovskite functional subgraph, and belongs to the technical field of material informatics and computational materialics. The background technology is as follows: Perovskite materials are receiving continuous attention because of their wide application prospects in the fields of photovoltaics, catalysis, energy storage, electronic devices, and the like. The formation energy of the material is a core index for measuring the thermodynamic stability and the synthesizability of the material, and is a key link of high-throughput screening and material reverse design. The acquisition of the formation energy of the conventional perovskite material mainly depends on a calculation method based on a first principle, such as density functional theory calculation. Although the method has higher reliability in the aspect of precision, the calculation process is complex, the calculation cost is high, and the requirement of high-flux screening is difficult to meet when facing large-scale material space. With the development of machine learning technology, a material property prediction method based on data driving is gradually applied to the field of molecular/crystal property performance prediction. Existing methods typically use artificially structured crystal descriptors or representing the entire crystal structure as a graph structure, and use a graph neural network for feature learning and property prediction. However, such methods still have certain drawbacks in practical applications. Firstly, the prior method mostly adopts a fixed truncated radius to define an atomic neighborhood, but is difficult to effectively capture periodic boundary information and potential long-range interaction in a crystal structure, and limits the perception capability of a model on transcytosis coupling effect. Secondly, in order to ensure that the prediction structure input has translational invariance and rotational invariance, the main stream model often only adopts unchanged characteristics such as interatomic distance and the like as input, but directional geometric information such as key angles, coordination inclinations and the like can be lost, so that the recognition capability of the model on key structure changes such as polyhedral distortion and the like is weakened. In addition, functional local units (such as BO 6 octahedron and AO 12 coordination polyhedron) taking B site or A site as a center are commonly existed in the perovskite structure, but the current mainstream method generally models the whole unit cell as a unified graph, so that independent contribution of the functional sub-graphs is easy to dilute in the polymerization process, and the structural detail is underexpressed. Therefore, how to simultaneously maintain periodic perceptibility, construct geometric features with stable directionality, and highlight the role of functional structural units is still a problem to be solved in perovskite diagram learning modeling. Therefore, it is necessary to provide a method capable of effectively fusing information of different functional structures while maintaining local coordination geometric characteristics of crystals and realizing accurate and efficient prediction of perovskite material formation so as to meet the actual requirements of large-scale material screening and synthesizability evaluation. The invention comprises the following steps: The invention provides a perovskite formation energy prediction method based on a graph neural network and a functional subgraph, which aims to solve the problems that the conventional perovskite formation energy prediction method is insufficient in periodic feature modeling, insufficient in geometric sensitivity to local coordination, difficult to consider both prediction accuracy and calculation efficiency and the like. The method comprises the steps of carrying out graph representation construction on a perovskite crystal structure under periodic boundary constraint, obtaining a BO 6 octahedron subgraph and an AO 12 coordination polyhedron subgraph according to structural characteristics of the perovskite crystal by cutting according to functional units so as to highlight structural information of a key local coordination environment, constructing a local dynamic coordinate system in the subgraph in the characteristic learning process of a graph neural network, coding relative position information between a central atom and a neighborhood atom of the central atom into geometric characteristics with directional invariance, combining physical priori information such as interatomic distance, electronegativity and the like, and realizing aggregation and updating of multi-scale characteristics in the subgraph through an attention mechanism. Bas