Inorganic crystal synthesizability prediction method based on crystal diagram and phonon kinetics

Abstract

The invention discloses an inorganic crystal synthesizability prediction method based on a crystal diagram and phonon kinetics, and relates to the technical field of inorganic crystal synthesizability prediction.The inorganic crystal synthesizability prediction method comprises the steps that an invariant crystal diagram for rotation, reflection, translation and lattice translation is constructed; transmitting messages among the nodes through a Transform layer, and aggregating all neighbor messages to update node features to obtain graph embedding of a crystal structure; restoring force acting on all atoms is predicted through a machine learning potential model, and phonon spectrum characteristics capable of depicting the dynamic stability of the crystal are obtained in combination with a finite displacement method; graph embedding and phonon spectrum characteristics of the crystal structure are used as input, information exchange between the crystal structure and dynamic stability is carried out through a bidirectional gating circulation unit, and then the synthesizability of the inorganic crystal is predicted. Therefore, by adopting the method, the physical characteristics of the crystal can be more comprehensively described, and the accuracy and the reliability of crystal synthesizability prediction are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of inorganic crystal synthesizability prediction, and in particular to a method for predicting inorganic crystal synthesizability based on crystal graph and phonon dynamics. Background Art

[0002] In the field of materials science, the design and synthesis of new inorganic functional materials has always been a core goal. In recent years, the development of high-performance computing, electronic structure calculations and data-driven methods has greatly accelerated the design of innovative materials, especially in the fields of energy storage, electrocatalysis and photovoltaics. However, a key challenge is to determine whether the candidate materials can be synthesized in experiments. Currently, the prediction of material synthesizability mainly relies on experimental observations and empirical methods, and there is a lack of universally applicable and efficient models, which seriously limits the speed of experimental material discovery and development.

[0003] Traditional methods for predicting crystal synthesizability have significant limitations. One common approach is based on the principle of minimum free energy, focusing on structures whose total energy corresponds to a global minimum, thereby indirectly reflecting synthesizability. However, this method is generally applicable only to ground-state structures and ignores the dynamic properties of the crystal. Furthermore, while the Gibbs free energy is a key measure of crystal stability, its experimental determination requires complex thermodynamic measurements, such as phase transition temperature and heat capacity, which limits its application in studying material stability and synthesizability. In theoretical calculations, density functional theory (DFT)-based calculations of formation energies or energies above the convex hull are widely used to provide preliminary estimates of synthesizability. However, high-throughput screening of large numbers of crystal structures has revealed that many theoretically low-energy geometries remain unsynthesized in experiment, demonstrating that relying solely on ground-state energy as an indicator of synthesizability is unreliable. Furthermore, the concept of the "amorphous limit" proposed by researchers provides an upper limit on the synthesizability of a material, but each new composition requires a new energy reference point, making this method composition-dependent.

[0004] The introduction of machine learning methods has brought new hope to materials science. These methods predict the synthesizability of materials by identifying underlying patterns from large-scale datasets. Some methods utilize deep networks to learn the relationship between elemental composition and synthesizability, enabling rapid exploration of chemical space but unable to distinguish polymorphs. Other methods encode crystal structures as voxel images and use convolutional neural networks to extract spatial features to predict synthesizability, but this voxelization process can lose some precise structural details. Still others incorporate periodicity by combining real-space and reciprocal-space descriptors via discrete Fourier transforms. Meanwhile, graph neural networks (GNNs), a powerful approach that has pioneered in materials informatics by using crystal graph representations, have laid the foundation for subsequent models such as the crystal graph convolutional neural network (CGCNN) and the crystal similarity score (CLscore). However, these methods primarily rely on mapping static structural descriptors of crystals to synthesizability, ignoring the intrinsic dynamic properties associated with atomic vibrations. This incomplete feature representation introduces systematic uncertainty, which can lead to false or inaccurate correlations, ultimately compromising model reliability and predictive accuracy. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for predicting the synthesizability of inorganic crystals based on crystal graphs and phonon dynamics, which can integrate the dynamic stability characteristics and static structural characteristics of crystals and enhance the model's ability to predict the synthesizability of inorganic crystals.

[0006] To achieve the above object, the present invention provides a method for predicting the synthesizability of inorganic crystals based on crystal graphs and phonon dynamics, comprising the following steps:

[0007] S1. Take the atoms in the unit cell as nodes, and select the r nearest atoms with each atom as the center. The distance between the central atom and these r atoms is used as the edge between the corresponding node pairs. For each atom, dynamically select the distance between the three nearest periodic repeating atoms that are linearly independent of itself, and embed them into the graph in the form of self-loop edges to construct a crystal graph.

[0008] S2. Use CGCNN to map atomic numbers to a continuous vector space to form initial node features. Use Gaussian radial basis functions to encode the Euclidean distances of atomic pairs to construct initial edge features. Then, use the Transformer layer to transfer information from neighbor nodes to the central node based on the initial node features and initial edge features. Aggregate all neighbor messages to update node features and obtain a graph embedding of the crystal structure.

[0009] S3. Construct a unit cell to capture the interatomic interactions outside the basic unit cell. By introducing small atomic displacements along the three axes of the spatial coordinates for each symmetry-inequivalent atom, the machine learning potential model is used to predict the restoring force acting on all atoms in each displacement configuration, and the finite displacement method is used to obtain the phonon spectrum characteristics.

[0010] S4. Taking the graph embedding of the crystal structure and the phonon spectrum characteristics as input, information exchange between the crystal geometry and dynamic stability is performed through a bidirectional gated recurrent unit, thereby accurately predicting the synthesizability of inorganic crystals.

[0011] Preferably, in step S2, the message passing scheme of the Transformer layer is as follows:

[0012] The message from node j to node i is sent by the corresponding query q ji , key k ji Sum value v ji composition;

[0013] in,

[0014]

[0015]

[0016] In the formula, LN Q 、LN K 、LN V 、LN e are linear transformations of query, key, value, and edge features, respectively. | respectively Hadamard product and cascade symbol, for dimension, LNnorm is the layer normalization operation, LN update is the linear transformation used to compute the update message, is the message of the hth edge between nodes j and i, is the attention coefficient of the hth edge between nodes j and i;

[0017] Then, the information of r edges in the node neighborhood is aggregated to calculate the message of the central node, and the message is used to update the features of the central node as follows:

[0018]

[0019] Where σ is the activation function used, BN is batch normalization, LNorm and LNmsg are the linear transformations used to update the message and old atomic features on the edge, respectively. are the features of the central nodes of the l+1th and lth layers, respectively, m i Message to the central node.

[0020] Preferably, in step S3, the phonon spectrum characteristics include phonon frequency and vibration mode, which are obtained by constructing the phonon spectrum through PHONOPY and diagonalizing the dynamics matrix.

[0021] Preferably, in step S4, a fusion feature is obtained by a bidirectional gated recurrent unit, which integrates forward and backward context information to capture the complex interaction between crystal structure and dynamic properties, as follows:

[0022]

[0023] In the formula, B is the fusion feature, BiGRU is the bidirectional gated recurrent unit, and f' i is the feature of the central node after the Transformer layer, f d,i is the phonon spectrum characteristic, and n is the number of nodes.

[0024] Therefore, the present invention adopts the above-mentioned method for predicting the synthesizability of inorganic crystals based on crystal graphs and phonon dynamics, which has the following technical effects:

[0025] (1) The present invention adopts a period-invariant crystal graph construction method and utilizes the repetitive spacing of the explicitly coded lattice to ensure that the crystal graph remains invariant under translation, rotation, and reflection transformations, providing rich structural information for the model. At the same time, the phonon spectrum characteristics are extracted by pre-training the machine learning interatomic potential energy model, and the force constant matrix of small atomic displacement is calculated and diagonalized to ensure the accuracy of the dynamic stability feature prediction in the presence of noise.

[0026] (2) The present invention fully utilizes the crystal graph characteristics and dynamic stability characteristics through a bidirectional gated recurrent unit, effectively captures the complex interaction between structure and dynamic properties, and significantly improves the prediction accuracy of the synthesizability of inorganic crystal materials.

[0027] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is a flow chart of a method for predicting the synthesizability of inorganic crystals based on crystal maps and phonon dynamics;

[0029] Figure 2 A schematic diagram of the structure of the edge from the yellow atom j to the central node i when r=2 in two-dimensional space in an embodiment of a method for predicting the synthesizability of inorganic crystals based on crystal graphs and phonon dynamics. DETAILED DESCRIPTION

[0030] The present invention can be explained in more detail by the following examples. The purpose of disclosing the present invention is to protect all changes and improvements within the scope of the present invention. The present invention is not limited to the following examples.

[0031] Example 1

[0032] like Figure 1 As shown, the present invention provides a method for predicting the synthesizability of inorganic crystals based on crystal graphs and phonon dynamics, and uses the Materials Project (MP) dataset for model training and verification, which specifically includes the following steps:

[0033] S1. Since the crystal structure presents a periodic arrangement in three-dimensional space, it consists of a unit cell and an atomic basis, which is a group of atoms associated with the unit cell. In order to accurately represent the periodic characteristics of the crystal, the construction of the crystal graph captures the periodicity by considering the relative positions of atoms and their periodic copies in the lattice. Not only the most recent r periodic copies of each pair of atoms are considered, but also the three most recent periodic repeating atoms that are linearly independent of each atom are dynamically selected for each atom and embedded into the graph in the form of self-loop edges, ensuring the invariance of the crystal representation to rotation, reflection, arbitrary translation and lattice translation, such as Figure 2 Specifically, when constructing a crystal graph, the graph nodes represent atoms and all their copies in infinite three-dimensional space; the edges are represented by the geometric distances between nodes to reflect the strength of the physical interactions and spatial relationships between nodes.

[0034] For the central node, through the set Determine the edges connecting the node as follows:

[0035]

[0036] Where x' j represents the position vector of atom j and its periodic copies, x i represents the position vector of the central node i, j' represents atom j and its replicas, d j'i Represents the distance between nodes j' and i Sort(D ji )[:r] represents the operation of selecting the r nearest elements based on the k-nearest neighbor distance metric, L represents the lattice vector, k represents an integer vector, ε ji represents the set of edges between atom j and atom i, e ji Represents the characteristics of the edge between atoms j and i.

[0037] Lattice vector l i∈L is a key factor in describing the periodic pattern of the crystal and determines many physical properties of the crystal. In order to accurately distinguish the symmetric geometric features of different crystalline materials, it is crucial to explicitly embed these periodic patterns into the crystal graph. The most direct approach is to use lattice vectors derived from the input lattice matrix to define additional edges of the crystal graph. However, since the same crystal can be described by different lattice basis vectors, there are multiple representations of its corresponding graph structure, which may cause inconsistencies in the prediction results, thereby destroying the periodic invariance of the lattice representation. To address this problem, a central node and its three spatial periodic copies are introduced in this embodiment, and by constructing edges connecting the central node and these three copy nodes, the periodicity of the crystal is embedded in the graph structure in the form of "self-loop edges". The selection process of these three periodic copy nodes is carried out dynamically, as shown below:

[0038] i'=argmin j∈P\{i} ||x' i -x i ||2;

[0039]

[0040] in,

[0041] Based on the vector e i'i 、e i”i 、e i”'i and e i'i +e i”i 、e i”i +e i”'i 、e i”'i +e i'i The length of the lattice is effectively embedded into the crystal graph through the “self-loop edge”, thus ensuring the period invariance of the crystal graph.

[0042] S2. First, use CGCNN to extract the initial node features f of the crystal graph i 、f j ; Secondly, use f i 、f j and edge features e ij , the information is transferred from the neighbor nodes to the central node i through the Transformer layer according to the node features and the corresponding edge features; then, all neighbor messages are aggregated to update the node features and obtain the graph embedding of the crystal structure.

[0043] Among them, the message passing process of the Transformer layer is:

[0044] The message from node j to central node i is represented by the corresponding query q ji , key k ji Sum value vji composition.

[0045] in,

[0046]

[0047] In the formula, LN Q 、LN K 、LN V 、LN e are linear transformations of query, key, value, and edge features, respectively. | respectively Hadamard product and cascade symbol, for dimension, LNnorm is the layer normalization operation, LN update is the linear transformation used to compute the update message, is the message of the hth edge between nodes j and i, is the attention coefficient of the h-th edge between nodes j and i.

[0048] Then, the information of r edges in the node neighborhood is aggregated to calculate the message of the central node, and the message is used to update the features of the central node as follows:

[0049]

[0050] Where σ is the activation function used, BN is batch normalization, LNorm and LNmsg are the linear transformations used to update the message and old atomic features on the edge, respectively. are the features of the central nodes of the l+1th and lth layers, respectively, m i Message to the central node.

[0051] S3. The static geometric structure only provides the equilibrium position between atoms, while the atomic vibration reflects the "curvature" of the potential energy surface around the atoms. Existing prediction methods based on three-dimensional crystal structure often only consider the static geometric characteristics of the crystal, ignoring the characteristic of crystal atomic vibration. At the same time, high-precision force predictions can have physical significance, and the existing discrete Fourier transform (DFT) will incur huge computational costs for these calculations, which limits its application in large crystal systems or across polycrystalline materials. To this end, this embodiment uses a machine learning potential model, combined with the finite displacement method to obtain phonon spectrum characteristics, and incorporates dynamic stability into the model, specifically:

[0052] First, a supercell is constructed to capture the atomic interactions outside the basic unit cell, and within this framework, small atomic displacements are introduced along the three axes (x, y, and z) of the spatial coordinates for each atom with unequal symmetry.

[0053] The restoring forces acting on all atoms in each displaced configuration are then predicted using a pre-trained machine learning potential model (MACE-MP-0). The MACE-MP-0 model is obtained by training the MACE model on the MPtrj dataset.

[0054] Finally, the force constants are derived based on the predicted restoring forces, and the dynamical matrix is ​​constructed and diagonalized using PHONOPY to obtain the phonon frequencies and vibration modes, i.e., the phonon spectral characteristics f d,i .

[0055] S4. Embed the crystal structure graph into f' i Harmonic phonon spectrum characteristics f d,i As input, information exchange between crystal structure and dynamic stability is carried out through a bidirectional gated recurrent unit (BiGRU), which strengthens the representation ability of the model and further predicts the synthesizability of inorganic crystals.

[0056] Among them, the expression of BiGRU processing features is as follows:

[0057]

[0058] In the formula, B is the fusion feature, BiGRU is the bidirectional gated recurrent unit, and f' i is the feature of the central node after the Transformer layer, f d,i The phonon spectrum is a feature, and n is the number of nodes. By introducing the phonon spectrum, the dynamic stability of the crystal is successfully captured, addressing the shortcomings of traditional methods that rely solely on static structural descriptors. By integrating the dynamic stability features with the crystal graph features, the model can more comprehensively describe the physical properties of the crystal, significantly improving the accuracy and reliability of the predictions.

[0059] On a dataset of ternary compounds, the proposed method achieved a precision of 0.916 and a recall of 0.863. This high-precision prediction capability was particularly strong in identifying low-energy, unsynthetic crystals, effectively reducing the false positive rate and significantly improving the model's reliability and accuracy. Furthermore, by comparing the model with experimental data, it successfully predicted multiple low-energy, unsynthetic crystals, validating its reliability in practical applications.

[0060] Example 2

[0061] The present invention provides a method for predicting the synthesizability of inorganic crystals based on crystal graphs and phonon dynamics, which is also applied to the generalization ability test of different material systems.

[0062] This embodiment selected 41 different material systems. Compared with the calculation method of existing energy indicators, the accuracy of predicting the synthesizability of low-energy crystals by the method of the present invention was significantly improved, showing good generalization ability. In addition, the model performed well in multiple material systems (such as MP and JARVIS data sets), and successfully predicted a variety of low-energy non-synthesizable crystals. This shows that the method of the present invention can maintain good predictive performance in crystalline materials with different physical and chemical properties, verifying its applicability in different material systems. This generalization ability not only means that the model is applicable to specific material systems, but also can maintain high-precision predictions in a wide range of material categories, providing a wider range of applicability for materials science research.

[0063] Therefore, the present invention adopts the above-mentioned method for predicting the synthesizability of inorganic crystals based on crystal graphs and phonon dynamics, which can capture the dynamic stability of crystals, make up for the shortcomings of traditional methods that only rely on static structural descriptors, and enable the model to more comprehensively describe the physical properties of crystals, thereby significantly improving the accuracy and reliability of the prediction.

[0064] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for predicting the synthesizability of inorganic crystals based on crystal graphs and phonon dynamics, characterized in that: The following steps are involved: S1. Take the atoms in the unit cell as nodes, and select the r nearest atoms with each atom as the center. The distance between the central atom and these r atoms is used as the edge between the corresponding node pairs. For each atom, dynamically select the distance between the three nearest periodic repeating atoms that are linearly independent of itself, and embed them into the graph in the form of self-loop edges to construct a crystal graph. S2. Use CGCNN to map atomic numbers to a continuous vector space to form initial node features. Use Gaussian radial basis functions to encode the Euclidean distances of atomic pairs to construct initial edge features. Then, use the Transformer layer to transfer information from neighbor nodes to the central node based on the initial node features and initial edge features. Aggregate all neighbor messages to update node features and obtain a graph embedding of the crystal structure. S3. Construct a unit cell to capture the interatomic interactions outside the basic unit cell. By introducing small atomic displacements along the three axes of the spatial coordinates for each symmetry-inequivalent atom, the machine learning potential model is used to predict the restoring force acting on all atoms in each displacement configuration, and the finite displacement method is used to obtain the phonon spectrum characteristics. S4. Taking the graph embedding of the crystal structure and the phonon spectrum characteristics as input, information exchange between the crystal geometry and dynamic stability is performed through a bidirectional gated recurrent unit, thereby accurately predicting the synthesizability of inorganic crystals.

2. The method for predicting the synthesizability of inorganic crystals based on crystal graphs and phonon dynamics according to claim 1, characterized in that: In step S2, the message passing scheme of the Transformer layer is as follows: The message from node j to node i is sent by the corresponding query q ji , key k ji Sum value v ji composition; in, In the formula, LN Q 、LN K 、LN V 、LN e are linear transformations of query, key, value, and edge features, respectively. | respectively Hadamard product and cascade symbol, for dimension, LNnorm is the layer normalization operation, LN update is the linear transformation used to compute the update message, is the message of the hth edge between nodes j and i, is the attention coefficient of the hth edge between nodes j and i; Then, the information of r edges in the node neighborhood is aggregated to calculate the message of the central node, and the message is used to update the features of the central node as follows: Where σ is the activation function used, BN is batch normalization, LNorm and LNmsg are the linear transformations used to update the message and old atomic features on the edge, respectively. are the features of the central nodes of the l+1th and lth layers, respectively, m i Message to the central node.

3. The method for predicting the synthesizability of inorganic crystals based on crystal graphs and phonon dynamics according to claim 1, characterized in that: In step S3, the phonon spectrum characteristics include phonon frequency and vibration mode, which are obtained by constructing the phonon spectrum and diagonalizing the dynamics matrix using PHONOPY.

4. The method for predicting the synthesizability of inorganic crystals based on crystal graphs and phonon dynamics according to claim 1, characterized in that: In step S4, a fusion feature is obtained by a bidirectional gated recurrent unit, which integrates forward and backward context information to capture the complex interaction between crystal structure and dynamic properties, as follows: In the formula, B is the fusion feature, BiGRU is the bidirectional gated recurrent unit, and f' i is the feature of the central node after the Transformer layer, f d,i is the phonon spectrum characteristic, and n is the number of nodes.

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