A crystal property prediction method based on physical information enhanced graph neural network representation learning

Abstract

This invention discloses a crystal property prediction method based on physically-informed graph neural network representation learning, comprising: acquiring crystal structure data; constructing a crystal polygon graph based on the crystal structure data; initializing node features by constructing atomic descriptors using atomic physicochemical properties based on the nodes of the crystal polygon graph, wherein the atomic descriptors include one-hot encoding of discrete properties and one-hot encoding of continuous properties after clustering and binning; constructing physical edge features based on the electronegativity difference between atoms based on the edges of the crystal polygon graph, and forming fused edge features by combining geometric structure edge features; calculating edge weights based on the fused edge features using a distance decay weight function, performing edge-level feature updates and node-level message passing based on the edge weights, and constructing a crystal property prediction model; predicting the properties of the input crystal structure based on the crystal property prediction model, and outputting the crystal property prediction results. This invention can improve the interpretability and physical reliability of the prediction results.

Description

Technical Field

[0001] This invention belongs to the field of crystal material property prediction technology, and particularly relates to a crystal property prediction method based on physical information-enhanced graph neural network representation learning. Background Technology

[0002] Research on the prediction of crystalline material properties is crucial for discovering novel materials with ideal characteristics. While traditional physical simulation methods based on density functional theory (DFT) offer high simulation performance, their high computational load severely hinders research progress in applications such as large-scale screening of potentially valuable materials. Therefore, high-throughput computational methods based on machine learning have attracted widespread attention. In recent years, graph neural networks and their Transformer-based variants have played a central role in materials structure research due to their excellent performance in predicting material properties, and have become efficient alternatives to traditional simulation methods such as DFT calculations.

[0003] Atoms in crystals carry a wealth of physical and chemical properties. Inspired by potential energy research, some studies have innovatively used interatomic potential energy as a side feature to capture long-range interactions, demonstrating the significant contribution of potential energy features to the prediction of material properties and providing new ideas for research by researchers such as He et al., dedicated to modeling complete interatomic interactions. Recent studies have shown that atomic properties such as electronegativity contain important information for predicting electronic properties. However, it remains to be addressed how to systematically introduce physical properties related to crystal properties, ensuring universality while avoiding information redundancy, and efficiently embedding them into crystal diagrams and graph neural networks for collaborative modeling. To this end, it is necessary to achieve synergistic optimization of physical priors and data-driven learning in feature design, crystal diagram construction, and model architecture, and to verify the actual contribution of features constructed based on physical properties to crystal properties through interpretability analysis, thereby forming an effective way to accelerate the discovery of new materials.

[0004] In recent years, research based on graph neural networks has largely focused on the impact of crystal geometry and atomic integrity interactions on property prediction. However, the role of node feature initialization has often been overlooked. Existing work typically uses only atomic numbers or relies on previously proposed atomic embedding data to initialize node information. Although graph neural networks have the ability to automatically extract latent features, their ability to represent crystal structures is severely weakened when the input raw node information is too simple, redundant, or erroneous. It is worth noting that the formation of crystal properties originates from the synergistic effect of all atomic properties within the crystal. Different physical properties contribute differently to each target property, but relying solely on a single physical property makes it difficult to learn accurate representations for different properties. Therefore, constructing information-rich and physically meaningful combinations of atomic properties for node initialization is a key approach to enhancing the representational power and generalization performance of graph network models, contributing to the deepening and expansion of crystal property prediction research at the physical level.

[0005] Revealing the explicit relationship between crystal properties and physical attributes is of great significance for crystal representation learning. Although some studies have identified some atomic attributes that significantly influence crystal properties from the perspective of feature importance, these rely on traditional machine learning methods, which focus on directly quantifying the correlation between attributes and targets, making it difficult to reveal the complex dependencies learned within the crystal graph neural network. Therefore, traditional feature importance analysis methods alone cannot fully characterize the true contribution of each physical attribute in the model's decision-making process. Systematic measurement and analysis methods should be developed from the model's internal computational processes to quantify the relative importance of atomic attributes in the graph network, reveal the nonlinear mapping relationship between atomic attributes and macroscopic crystal properties, and improve the interpretability and physical reliability of prediction results. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention proposes a crystal property prediction method based on physical information-enhanced graph neural network representation learning. This method can reveal the nonlinear mapping relationship between atomic properties and macroscopic crystal properties, thereby improving the interpretability and physical reliability of the prediction results.

[0007] To achieve the above objectives, this invention provides a method for predicting crystal properties based on physically-informed graph neural network representation learning, comprising: Acquire crystal structure data, construct a crystal polygon graph based on the crystal structure data, perform periodic boundary condition processing on all atoms in the unit cell, and introduce a deterministic periodic pattern to ensure the consistency of the graph construction; Based on the nodes of the crystal polygon graph, atomic descriptors are constructed using atomic physicochemical properties to initialize node features. The atomic descriptors include one-hot encoding of discrete attributes and one-hot encoding of continuous attributes after clustering and binning. Based on the edges of the crystal polygon, physical edge features are constructed based on the difference in electronegativity between atoms, and combined with geometric structure edge features to form fused edge features; Based on the fused edge features, edge weights are calculated using a distance decay weighting function. Edge-level feature updates and node-level message passing are then performed based on the edge weights to construct a crystal property prediction model. Based on the crystal property prediction model, the properties of the input crystal structure are predicted, and the crystal property prediction results are output.

[0008] Optionally, constructing a crystal polygon based on the crystal structure data includes: The local neighborhood of each central atom is determined based on the preset cutoff radius and the maximum number of neighbors. The order of replication and unfolding of the unit cell along the three basis vectors of the lattice vector is fixed, and the priority of equidistant neighbors is handled by a stable sorting strategy, so as to ensure the determinism and periodicity invariance of the crystal diagram construction.

[0009] Optionally, the atomic physicochemical properties include: group number, periodicity, block, number of valence electrons, Sanderson electronegativity, atomic radius, ionization energy, electron affinity, atomic volume, lattice constant, and C6 dispersion coefficient; The discrete attributes include group number, periodicity, zone, and number of valence electrons; The continuous attributes include Sanderson electronegativity, atomic radius, ionization energy, electron affinity, atomic volume, lattice constant, and C6 dispersion coefficient. K-means clustering is used to bin the continuous attributes, and all-zero vector encoding is used for missing values.

[0010] Optionally, based on the edges of the crystal polygon, physical edge features are constructed based on the interatomic electronegativity difference, and combined with geometric structure edge features to form fused edge features, including: Based on the edges of the crystal polygon, and according to the Sanderson electronegativity difference between the central atom and its neighboring atoms, feature derivation is performed using cosine functions and radial basis functions to obtain electronegative edge features. Construct physical edge features based on electronegativity edge features; Based on the physical edge features, a fused edge feature is formed by combining the geometric structure edge features, wherein the geometric structure edge features include: Euclidean distance features mapped by radial basis functions and relative position vector features.

[0011] Optionally, the distance decay weighting function Using piecewise polynomial form: ; ; in, Indicates the distance between atoms. Yes The result after normalizing the maximum and minimum values. It is a fixed radius value. Corresponding cutoff radius, The value of is 0.6, which controls the exponent to ensure that the function is first-order differentiable at the piecewise points.

[0012] Optionally, edge-level feature updates and node-level message passing based on the edge weights include: The edge features are weighted according to the edge weights, and the edge features are updated through a multilayer perceptron and activation function; The updated edge features are concatenated with the node features to generate a message vector; The message vectors are aggregated based on the central node, the node features are updated through activation functions and normalization layers, and after iteratively executing multi-layer message passing, the global crystal characterization is obtained through the readout layer, and the property prediction value is output through the fully connected layer.

[0013] Optionally, the method further includes: performing interpretability analysis on the atomic descriptor, calculating the contribution of each atomic attribute to the property prediction using the cumulative gradient method, evaluating the stability of the contribution ranking by changing the integration step number, and reconstructing the atomic descriptor based on the contribution of key atomic attributes.

[0014] Optionally, based on the crystal property prediction model, the properties of the input crystal structure are predicted, and the output crystal property prediction results include: Receive candidate crystal structures output by the generative model; The candidate structures are screened using the crystal property prediction model with high throughput. Candidate structures whose prediction results meet the target property threshold are output to first-principles calculations for verification, thereby realizing the reverse design of crystal structures.

[0015] Compared with the prior art, the present invention has the following advantages and technical effects: This invention initializes nodes by constructing atomic descriptors using carefully selected physicochemical properties and enhances edge features using electronegativity differences, thereby generating highly expressive node and edge representations in periodic crystal diagrams. Next, the cumulative gradient method is used to analyze physical properties that significantly contribute to the prediction model, forming a complete workflow from atomic descriptor construction to importance analysis of different properties, and then reconstructing the property composition based on the analysis results. This helps to further advance crystal property prediction research at the physical level. The model's performance is evaluated by predicting on two benchmark sets and comparing the results with mainstream prediction models currently in research. Finally, the prediction model and the generative model are deeply integrated to construct a reverse design process for crystal structures, accelerating the discovery of crystal structures with potential applications. Attached Figure Description

[0016] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of a crystal property prediction method based on physical information-enhanced graph neural network representation learning according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the two-dimensional plane of the crystal structure and the domain structure based on the polygon graph in an embodiment of the present invention; Figure 3 This is a diagram of the graph neural network representation learning architecture based on physical information enhancement according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the cumulative gradient method according to an embodiment of the present invention; Figure 5 This is a detailed flowchart of the crystal property prediction method according to an embodiment of the present invention. Detailed Implementation

[0017] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0018] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0019] This embodiment proposes a crystal property prediction method based on physically-informed graph neural network representation learning, such as... Figure 1 As shown, the specific steps include: Acquire crystal structure data, construct a crystal polygon graph based on the crystal structure data, perform periodic boundary condition processing on all atoms in the unit cell, and introduce a deterministic periodic pattern to ensure the consistency of the graph construction; Based on the nodes of the crystal polygon graph, atomic descriptors are constructed using atomic physicochemical properties to initialize node features. The atomic descriptors include one-hot encoding of discrete attributes and one-hot encoding of continuous attributes after clustering and binning. Based on the edges of the crystal polygon, physical edge features are constructed based on the difference in electronegativity between atoms, and combined with geometric structure edge features to form fused edge features; Based on the fused edge features, edge weights are calculated using a distance decay weighting function. Edge-level feature updates and node-level message passing are then performed based on the edge weights to construct a crystal property prediction model. Based on the crystal property prediction model, the properties of the input crystal structure are predicted, and the crystal property prediction results are output.

[0020] Specifically, this embodiment initializes nodes by constructing atomic descriptors using carefully selected physicochemical properties and enhances edge features using electronegativity differences, thereby generating highly expressive node and edge representations in periodic crystal diagrams, providing a powerful tool for accelerating the discovery of new materials. This invention mainly involves four modules. The first module proposes atomic descriptors for initializing graph neural network nodes by utilizing basic physical and chemical properties. This module aims to explicitly encode inherent atomic properties, enhancing the ability of graph network models to capture the fundamental physical properties of materials. The effectiveness and robustness of this descriptor are verified, improving the fidelity and generalization ability of the material modeling paradigm. The second module evaluates the contribution of different properties in the atomic descriptors to the prediction of crystal properties in the graph neural network using a gradient-based cumulative gradient method, and verifies the effectiveness and robustness of this method on the model, achieving interpretable analysis of the importance of atomic properties. The third module feeds physical edge features constructed based on atomic electronegativity along with structural edge features of the crystal into a message passing mechanism, helping the model to more accurately capture key information in the crystal structure. The fourth module proposes a property prediction architecture based on graph neural networks to handle atomic descriptors and electronegativity edge features with rich physical information, and then accurately predicts material properties based on the constructed crystal graph. By introducing deterministic periodic patterns during the crystal graph construction process, the stability of the neighborhood construction of each central atom is ensured, solving the problem of non-uniqueness of polygon graph construction caused by a fixed cutoff radius. Simultaneously, an efficient edge weight function based on inter-atomic distance is proposed to distinguish the importance of different atom pairs, which not only improves model training efficiency but also effectively weakens the noise influence of neighboring atoms near the cutoff radius, enhancing the model's expressive power. Through collaboration with a generative model, this framework can perform real-time property evaluation of different crystal structures, significantly shortening the cycle from structure design to experimental verification.

[0021] Furthermore, constructing a crystal polygon based on the crystal structure data includes: The local neighborhood of each central atom is determined based on the preset cutoff radius and the maximum number of neighbors. The order of replication and unfolding of the unit cell along the three basis vectors of the lattice vector is fixed, and the priority of equidistant neighbors is handled by a stable sorting strategy, so as to ensure the determinism and periodicity invariance of the crystal diagram construction.

[0022] Furthermore, the atomic physicochemical properties include: group number, periodicity, block, number of valence electrons, Sanderson electronegativity, atomic radius, ionization energy, electron affinity, atomic volume, lattice constant, and C6 dispersion coefficient; The discrete attributes include group number, periodicity, zone, and number of valence electrons; The continuous attributes include Sanderson electronegativity, atomic radius, ionization energy, electron affinity, atomic volume, lattice constant, and C6 dispersion coefficient. K-means clustering is used to bin the continuous attributes, and all-zero vector encoding is used for missing values.

[0023] Specifically, to address the lack of feature patterns, a method for generating atomic descriptors based on one-hot encoding is proposed. Compared to embedding methods that directly use atomic numbers, this method preserves explicit physical and chemical information, helping the model to learn more deeply the potential relationship between crystal structure and target properties. Eleven atomic attributes are selected to construct atomic descriptors and are divided into discrete and continuous attributes based on data characteristics. For continuous attributes, since the numerical ranges of different attributes vary significantly, directly using the original values ​​as input can negatively impact model training and convergence due to dimensional differences. To alleviate this problem, each continuous attribute is first binned using a clustering method, and then the bin labels are one-hot encoded to obtain a fixed-dimensional discrete representation. A "zero vector" strategy is used to handle missing values, explicitly classifying missing values ​​as separate categories and avoiding bias introduced by using different interpolation strategies. For discrete attributes, since the values ​​of each attribute are a fixed and finite set, each possible value is directly treated as an independent category and one-hot encoded. Finally, the one-hot encoded vectors of all continuous and discrete attributes are concatenated according to the feature dimension to obtain a 116-dimensional atomic descriptor vector.

[0024] Furthermore, based on the edges of the crystal polygon, physical edge features are constructed based on the interatomic electronegativity difference, and combined with geometric structure edge features to form fused edge features, including: Based on the edges of the crystal polygon, and according to the Sanderson electronegativity difference between the central atom and its neighboring atoms, feature derivation is performed using cosine functions and radial basis functions to obtain electronegative edge features. Construct physical edge features based on electronegativity edge features; Based on the physical edge features, a fused edge feature is formed by combining the geometric structure edge features, wherein the geometric structure edge features include: Euclidean distance features mapped by radial basis functions and relative position vector features.

[0025] Specifically, in materials chemistry and electronic structure research, the electronegativity difference between atoms has been widely used as an empirical indicator for estimating changes in chemical bond polarity and electronic structure. Recent materials science and machine learning research has incorporated electronegativity as an important feature for predicting band gaps. In this module, because graph structures can naturally represent the electronegativity relationship between two adjacent atoms through edges, constructing the electronegativity difference feature between atoms as a supplement to crystal structure information helps the model learn more deeply the potential relationship between crystal structure and target properties.

[0026] To maintain scale consistency between node and edge features, Sanderson electronegativity is used in AtomNet to construct new edge features. Electronegative edge features are derived through cosine functions and radial basis functions, which can transform scalar distances into a high-dimensional space, enabling a more detailed representation of geometric relationships. The cosine function allows the model to focus on features with large electronegativity differences, ignoring atom pairs with small differences or the same atom type.

[0027] Furthermore, the distance decay weighting function Using piecewise polynomial form: ; ; in, Indicates the distance between atoms. Yes The result after normalizing the maximum and minimum values. It is a fixed radius value. Corresponding cutoff radius, The value of is 0.6, which controls the exponent to ensure that the function is first-order differentiable at the piecewise points.

[0028] Specifically, a polygon graph method based on truncation radius is first used to construct the crystal graph, applying periodic boundary conditions to all atoms within the unit cell to maintain the invariance of the crystal structure. In the polygon graph, when selecting the k nearest neighbors of the central atom, multiple candidate neighbors are often equidistant from the central atom. This makes neighbor selection in each graph construction non-deterministic, leading to instability in the crystal graph construction and violating the periodic invariance of the crystal. Therefore, a deterministic periodic pattern is introduced during crystal graph construction: the order of copying and unfolding the three basis vectors along the lattice vector of the unit cell is fixed, thus defining a definite priority and order for neighbor selection for each node. This eliminates the randomness and inconsistency introduced by equidistant conflicts, thereby ensuring the consistency and periodic invariance of the graph construction.

[0029] Secondly, the model's message passing process consists of two parts: node-level message passing and edge-level feature update. The edge-level feature update determines the importance of edges based on the distance decay weight function, and then passes the weighted edge feature matrix to the node-level message passing mechanism to achieve neighborhood clustering.

[0030] Finally, a distance decay weight function is proposed, following the physical law that inter-atomic interactions gradually weaken with increasing distance. This function applies continuous piecewise polynomial decay over distance. When the distance between atomic pairs is small, a higher weight value is maintained. For edges with larger distances, a smooth polynomial decay function is applied to calculate the corresponding weights. The distance decay weight function is continuous and first-order differentiable at the segmentation points and cutoff radii, ensuring smooth gradient propagation and numerical stability during model training. Simultaneously, by smoothly decaying the contribution of each edge during message aggregation, the excessive influence of distant neighbors is effectively suppressed.

[0031] Furthermore, edge-level feature updates and node-level message passing based on the edge weights include: The edge features are weighted according to the edge weights, and the edge features are updated through a multilayer perceptron and activation function; The updated edge features are concatenated with the node features to generate a message vector; The message vectors are aggregated based on the central node, the node features are updated through activation functions and normalization layers, and after iteratively executing multi-layer message passing, the global crystal characterization is obtained through the readout layer, and the property prediction value is output through the fully connected layer.

[0032] Specifically, the cumulative gradient (IG) method can quantify the contribution of different properties in crystalline materials to the prediction of crystal structure properties. The IG value of each feature dimension in each atom is defined as the aggregation of gradients along the straight line connecting the baseline input and the actual input. Because the atom descriptor is represented as a one-hot encoded value, and IG calculation is performed by interpolating the gradient from the baseline input to the actual input along the straight line, the interpolation points are equally spaced values. However, these values ​​differ from the input data during model training, and it is necessary to prove the reliability of the feature importance results calculated by the IG method in the model. Therefore, this paper proposes to verify the effectiveness and robustness of the IG method by quantitatively evaluating the changes in IG values ​​at different integration steps.

[0033] In the attribution analysis, atomic attributes are used as the grouping unit. Individual IG values ​​belonging to the same group within an atomic descriptor are merged into the overall contribution of that group, thus directly quantifying and explaining the contribution of each type of atomic attribute to the model's predictions. To test the robustness of this contribution value to the number of integration steps, sensitivity analysis is performed at different integration steps: Spearman's rank correlation coefficient and Kendall's rank correlation coefficient are used to assess the consistency of attribute importance ranking, and the mean relative change (MRC) is used to quantify the average change in the IG value of each attribute at different integration steps. These three indicators evaluate the stability of different experimental results from three complementary dimensions: global ranking trend, ranking consistency, and numerical stability, ensuring the comprehensiveness and reliability of the evaluation.

[0034] On multiple prediction tasks, we compared the proposed model with several state-of-the-art neural network-based methods using two benchmark datasets: Materials Project and Jarvis DFT 3D 2021. We followed the data partitioning method proposed by Matformer and used mean absolute error (MAE) as the evaluation metric. For all tasks, we calculated the average value of ten random initialization seeds to ensure the model's robustness. Regarding model efficiency, we compared it with current mainstream models based on the Jarvis DFT3D 2021 dataset, considering factors such as architecture type, single-round training time, number of training rounds, total training time, and number of model parameters. Furthermore, stable experimental results validated the effectiveness of the proposed framework for crystal characterization and property prediction using atomic descriptors, electronegativity edge features, atomic descriptor interpretability analysis, and polygonal graph neural networks in terms of crystal characterization capabilities and interpretability.

[0035] Furthermore, the method also includes: performing interpretability analysis on the atomic descriptor, calculating the contribution of each atomic attribute to the property prediction using the cumulative gradient method, evaluating the stability of the contribution ranking by changing the integration step number, and reconstructing the atomic descriptor based on the contribution of key atomic attributes.

[0036] Furthermore, based on the crystal property prediction model, the properties of the input crystal structure are predicted, and the output crystal property prediction results include: Receive candidate crystal structures output by the generative model; The candidate structures are screened using the crystal property prediction model with high throughput. Candidate structures whose prediction results meet the target property threshold are output to first-principles calculations for verification, thereby realizing the reverse design of crystal structures.

[0037] Specifically, in contemporary computational materials science, crystal property prediction models are no longer isolated evaluation tools, but rather core components working in collaboration with generative artificial intelligence. This dual-engine architecture of "generation + prediction" is fundamentally changing the paradigm for discovering novel functional materials. Generative models (such as generative adversarial networks, variational autoencoders, and diffusion models) excel at exploring near-infinite chemical spaces, deconstructing and reconstructing the Cartesian coordinates, lattice vectors, and atomic site information of atoms by learning the data distribution of known crystals. However, in the pursuit of energy minimization, generative models often generate a large number of geometrically plausible but physically unstable "illusory" structures.

[0038] Traditional verification methods rely on first-principles calculations based on density functional theory (DFT). Although DFT has extremely high accuracy, its computational cost increases cubically with the number of atoms, becoming unacceptable when faced with tens of thousands of candidate structures generated by generative models.

[0039] Crystal property prediction models play the role of "initial screening experts" in this context: High-fidelity simulation: using deep learning (such as crystal graph neural networks) to capture the nonlinear mapping between structure and properties.

[0040] Millisecond-level inference: Reduces the DFT evaluation that originally took hours or even days to the millisecond level.

[0041] Multi-dimensional filtering: By setting thresholds for target attributes (such as band gap, formation energy, and convex hull energy difference), unqualified candidates are quickly eliminated, and only the most promising structures are sent to the backend for high-precision verification.

[0042] The deep fusion of predictive and generative models constructs a closed loop of reverse design: Goal-oriented: First define the required physical properties.

[0043] Generative evolution: Generative models produce potential structures.

[0044] Predictive feedback: The predictive model evaluates its performance and provides gradient feedback to guide the generative model to optimize for higher performance regions.

[0045] This collaborative model not only greatly reduces the time cost of discovering new materials, but more importantly, it can break through the limitations of human intuition and discover those strange crystal structures that exist deep in the chemical space and have never been explored before.

[0046] The following is a detailed description of this embodiment: like Figure 5 As shown, this embodiment specifically includes: Step 1: Data Acquisition and Preprocessing First, raw data is read from the specified materials database (Materials Project and Jarvis DFT 3D 2021), cleaned, filtered, and segmented, and finally a data loader suitable for training deep learning models is constructed. This process mainly includes the following steps: Dataset configuration and system initialization: First, the name of the target dataset (e.g., dft_3d_2021 or megnet) and the target crystal properties to be predicted (such as shear modulus, bulk modulus, band gap, and formation energy) are determined according to the configuration file. To ensure the reproducibility of experimental results, a fixed random seed is set in the system. The online database is downloaded using the jarvis.db.figshare module.

[0047] Data reading and cleaning: The system adopts different reading strategies depending on the selected dataset.

[0048] For the volumetric modulus and shear modulus tasks on the Materials Project dataset: The system loads the pre-stored serialized files of the training, validation, and test sets, respectively. After loading, the system iterates through each data sample, checking whether the target attribute value is valid. Specifically, the system discards samples with empty (None) target attribute values, or those marked as missing or non-numerical (NaN), retaining only valid data.

[0049] For the dft_3d_2021 and megnet datasets: the system directly calls the database interface (jarvis.db.figshare.data) to load all the raw data. Then, the system iterates through and filters the data; the processing logic is as follows: If the target attribute value is in list format, convert it to a tensor and retain it; If the target attribute value is a scalar, check its validity (non-empty, non-missing, and non-NaN), and only retain valid samples; After cleaning, the system calls the dataset partitioning function, randomly shuffles the data index using a random seed, and divides the data into training, validation, and test sets according to a preset ratio (8:1:1 ratio for training, validation, and test sets).

[0050] Graph Structure Dataset Construction: After acquiring and partitioning the basic data, the system instantiates a dataset object based on configuration parameters. During this process, the system receives key crystal graph construction parameters, including: Cutoff radius: A distance threshold used to determine the range of an atom's neighborhood; Maximum number of neighbors: Limits the maximum number of connected edges per atom; Atomic initialization feature: Specifies how the atomic feature is initialized.

[0051] Batch Data Loader Generation: Finally, the system uses the data loading interface of the deep learning framework to encapsulate the above dataset object into an iterable loader. The loader configuration is as follows: Training set loader: Enables data shuffling to enhance the model's generalization ability; Validation and test set loaders: disable data shuffling to maintain evaluation consistency; General configuration: Set batch size, number of worker threads, and memory lock to optimize data reading efficiency and training speed.

[0052] Inference Data Loading: This module also provides data loading functionality for inference mode. The system reads a JSON file containing crystal structure information (lattice matrix, coordinates, element types, etc.) and constructs a dataset and loader for inference without relying on target attribute tags, for predicting the properties of new materials.

[0053] Step 2: Crystal diagram construction: Two-dimensional plane crystal structures and polygonal graph-based neighborhood structures, such as Figure 2 As shown, this invention uses a polygonal diagram method based on the cutoff radius to construct a crystal diagram, applying periodic boundary conditions to all atoms within the unit cell to satisfy the invariance of the crystal structure. Specifically, a cutoff radius is set around each central atom (…). This treats all atoms within that radius as local neighbors. Based on the cutoff radius, a maximum number of neighbors for each central atom is set (…). This is to avoid constructing an excessively large neighborhood graph due to the small size of the crystal cell, which would affect the model's learning ability and cause a large amount of computational resource overhead.

[0054] For each crystal sample, the system performs the following operations to construct the geometric structure: Structure parsing: Parses the input dictionary data into a structure object containing a lattice matrix, Cartesian coordinates, and a list of elements.

[0055] Periodic boundary treatment: Considering the periodic structural characteristics of crystal materials, the system sets periodic boundary conditions to ensure that atomic interactions across the unit cell boundary are considered in all three spatial dimensions (x, y, z).

[0056] Neighborhood graph construction: Using preset cutoff radius and maximum neighbor count parameters, the spatial distance between atoms is calculated. The system calls a radius graph algorithm based on periodic boundary conditions to establish edge connections for atom pairs whose distance is within the cutoff radius. If no edges exist in the generated graph, the sample is considered invalid data and discarded.

[0057] After completing the above processing, the system organizes all the constructed graph data objects and serializes and saves them as a single binary file to facilitate fast reading and memory mapping loading during subsequent training.

[0058] In a polygon graph, select the central atom. of When constructing the nearest neighbor array, multiple candidate neighbors are often equidistant from the central atom. This makes the neighbor selection during each graph construction nondeterministic, leading to instability in crystal graph construction and violating the periodicity invariance of the crystal. Therefore, a deterministic periodic mode is introduced during crystal graph construction: fixing the unit cell along the lattice vector. The order in which the three basis vectors are copied and expanded defines a definite priority and order for neighbor selection for each node. This eliminates the randomness and inconsistency introduced by equidistance conflicts, thus ensuring the consistency and periodicity invariance of the graph construction.

[0059] Suppose there are m atoms in the unit cell, and the three-dimensional coordinates of the atoms are... lattice vector is The cutoff radius is Å, tolerance is For each central atom, select the top n neighbors in ascending order of distance, and ensure that this selection is reproducible even when there are multiple equidistant neighbors.

[0060] This embodiment initializes all possible combinations of atom pairs based on the number of atoms. , The results were calculated using the cutoff radius and lattice vector respectively. Maximum number of repeating cells in a direction And based on the maximum repetition value in the three directions, the possible set of unit cell offset indices is calculated respectively. .in, Let's do it again. Calculate the Cartesian product to obtain the offset triplet. .

[0061] ; Indexing of arbitrary central atoms (Traversing in ascending order by index) and any candidate neighbor atom index n within the unit cell (traversing in ascending order by index), for each offset triplet Calculate the neighbor coordinates in a repeating unit cell And calculate the Euclidean distance. .like If so, mark the candidate as invalid (equivalent to setting the distance to 0). ), so that it can be automatically discarded later.

[0062] For each central atom All valid candidates are sorted in ascending order of distance, and the top n neighbors are selected. Past methods often relied on unstable sorting algorithms, which could lead to non-unique crystal diagram structures constructed from the same crystal material. To ensure consistency in selection when distances are equal, we use a stable sorting algorithm and ensure the initial enumeration order is determined. With the initial order fixed, the stable sorting preserves the original relative order of equal-value elements, making the final neighbor selection reproducible. (Assume neighbor atoms p, q, s are equidistant from the central atom, and the relative positions of these neighbor atoms before sorting are...) A stable sorting algorithm can guarantee that the neighbor atomic sequence after sorting by distance is In other words, neighbors The location is still in the neighbor's Previously, the neighbor The location is still in the neighbor's Before).

[0063] Finally, for each center Output its selected set of neighbors (including the indices of the neighbors in the original unit cell and the vector difference between the neighbors and the central atom in Cartesian coordinates).

[0064] The deterministic periodic pattern ensures the consistency and reproducibility of crystal graph construction when equidistant neighbors exist by using 1) a fixed offset and index traversal order, and 2) a stable sorting strategy. This effectively overcomes the instability problem of traditional graph-based crystal graph construction processes.

[0065] Step 3: Representation of nodes and edges: Atomic descriptors: To construct the atomic descriptor, 11 atomic attributes were selected: group number, periodicity, block, number of valence electrons, Sanderson electronegativity, atomic radius, ionization energy, electron affinity, atomic volume, lattice constant, and C6 dispersion coefficient. The first four attributes were treated as discrete attributes, while the rest were treated as continuous attributes.

[0066] For continuous attributes, the significant differences in numerical ranges between different attributes mean that directly using the original values ​​as input can negatively impact model training and convergence due to dimensional discrepancies. To mitigate this issue, each continuous attribute is first binned using K-means (K=10), and then the bin labels are one-hot encoded to obtain a fixed-dimensional discrete representation. Missing values ​​are handled using an "all-zero vector" strategy, explicitly classifying missing values ​​as a separate category and avoiding bias introduced by using different interpolation strategies.

[0067] ; ; ; ; ; in, It is an atomic number of The atom corresponds to the first The true value of a continuous attribute. The corresponding maximum atomic number. This represents the result calculated using K-means. The set of cluster centroid values, Indicates having the first The set of atomic numbers of valid attribute values. Cluster labels representing atoms. It is an atom A list of K-dimensional one-hot encoded features. correspond The one-hot encoded value of the k-th column.

[0068] For discrete attributes, since each attribute has a fixed and finite set of values, each possible value is directly treated as an independent category and one-hot encoded. The specific calculation process is as follows: ; ; ; in, It is an atom The corresponding number The true value of a discrete attribute. The first corresponding discrete attribute Categories This indicates the total number of attribute categories. It is an atom of Unique thermal characteristics, correspond The Middle The one-hot encoded values ​​of the columns. Finally, the one-hot encoded vectors of all continuous and discrete attributes are concatenated according to the feature dimension to obtain a 116-dimensional atomic descriptor vector. .

[0069] Electronegative edge characteristics: Because graph structures can naturally represent the electronegativity relationship between two adjacent atoms through edges, constructing electronegativity difference features between atoms as a supplement to crystal structure information helps the model learn more deeply the potential relationship between crystal structure and target properties. To maintain the scale consistency between node and edge features, Sanderson electronegativity is chosen to construct edge features. .

[0070] For each atom pair Define electronegativity difference characteristics based on the Sanderson scale. As input for edge features. Electronegativity edge features Mapping the cosine function to the radial basis functions: The cosine function causes the model to focus on features with large electronegativity differences, ignoring atom pairs with small differences or the same atom type.

[0071] ; ; in, , Represents a constant. It is a fixed value of 2.14, representing any two atoms The maximum absolute value of the Sanderson electronegativity difference . It is a radial basis function with K elements, capable of transforming scalar distances into high-dimensional spaces, enabling a more detailed representation of geometric relationships. Meanwhile, The representation of each element k is as follows: ; in These are fixed values ​​that determine the center and width of the k-th radial basis function. Value at The two are evenly spaced apart from 1, while The value is equal to all k. .

[0072] Geometric structure edge features: For each atom pair The edge features are determined by Euclidean distance. Relative position vectors based on Cartesian coordinate system and edge features based on Sanderson electronegativity It consists of three parts. (Euclidean distance) Mapped to K-dimensional edge features via radial basis functions (RBF). , where K is the number of RBF bases. Relative position vectors According to atomic pairs Location Calculated edge features. Mapped by the cosine function and RBF as The three edge structure data are concatenated according to the feature dimension, and then a new edge embedding is obtained by passing it through a multilayer perceptron (MLP).

[0073] By combining distance and direction vectors, edge embedding can capture the geometric relationships required for geometric structure modeling, and then electronegative edge features provide additional crystal structure information based on physical properties. The construction process of edge embedding is represented as follows: ; Step 4: Model Building like Figure 3 As shown, the message passing process of the model consists of two parts: node-level message passing and edge-level feature update. The role of edge-level feature update is to determine the importance of edges based on the distance decay weight function, and then pass the weighted edge feature matrix to the node-level message passing to achieve neighborhood aggregation.

[0074] During the edge-level feature update process, atomic pairs Central atomic features Neighboring atomic characteristics Sum of edge features The features are fed into an MLP for feature dimension adjustment mapping. The first linear layer of the MLP reduces the feature dimension to 1 / 3, followed by a SiLU activation function and a linear layer with the feature dimension unchanged. Then, a normalization layer and a Sigmoid activation function are used to normalize the features, accelerating model learning and convergence and avoiding gradient explosion / vanishing problems. Based on AtomNet's performance on different crystal properties tasks, batch normalization or layer normalization is used as the normalization layer. Next, weighted edge features are calculated based on the distance decay weight function, and residual connections are used to update the edge features. This helps improve the model's expressive power because static edge features can only provide fixed relational information, while dynamically updated edges allow the model to learn how relations change with node states or the global environment. The edge feature update process is shown below: ; in, Indicates the first Atom pairs of layers Edge features. It is the Sigmoid activation function, and NormLayer represents the normalization layer. and They represent the first The central atom of the layer Neighboring atoms The node characteristics. It represents the Hadamardi (or Hadama) stack. This represents the distance decay weighting function.

[0075] Considering that frequent updates to edge features may introduce training fluctuations, we limit the frequency of edge feature updates to ensure stable model training. Therefore, the edge feature update process is rewritten as: ; in, It is a hyperparameter, and its value range is... .when When the value is 0, it means that the edge features are not updated; when When the value is equal to 3, it means that the edge features are updated throughout the entire process.

[0076] The message passing mechanism first processes the central atomic features of the splicing through an MLP. Neighboring atomic characteristics Sum of edge features Construct a new node representation. Then, perform a Hadamard product directly with the weighted edge feature matrix output from the edge-level feature update to achieve weighted calculation and obtain the message. . Node Messages are aggregated around a central node, and then data normalization and nonlinear mapping are performed using a batch normalization layer and the SiLU activation function. Finally, similar to edge features, node representations are updated through residual connections. The message passing and node feature update process is represented as follows: ; ; in, Indicates atomic pairs The Layer message vector. , These correspond to the SiLU activation function and the batch normalization layer, respectively. Representative node The set of neighboring nodes.

[0077] To comply with the physical law that interatomic interactions gradually weaken with increasing distance, a distance decay weighting function is proposed. This function applies a continuous piecewise polynomial decay over distances. When the distance between atomic pairs is small, a higher weight is maintained. For the remaining edges with larger distances, a smooth polynomial decay function is applied to calculate the corresponding weights.

[0078] ; ; in, Indicates the distance between atoms . Yes The result after normalization of the maximum and minimum values, where It is a fixed value (1 Å). Corresponding cutoff radius (5 Å) The value of is 0.6, which controls the exponent to ensure that the function is first-order differentiable at the piecewise points.

[0079] The distance decay weight function is continuous and first-order differentiable at the segmentation point and the cutoff radius, ensuring smooth gradient propagation and numerical stability during model training. Simultaneously, by smoothly decaying the contribution of each edge during message aggregation, the excessive influence of distant neighbors is effectively suppressed.

[0080] Step 5: Model Performance Validation To ensure reliable evaluation of the diverse structures generated by the generative model, the Matformer data partitioning criteria were followed, and the mean absolute error (MAE) was used as the core evaluation metric. For each prediction task, ten random initialization seeds were used for independent experiments, and the mean was taken after removing outliers (maximum and minimum values). This rigorous statistical approach ensures that the model can still provide robust and consistent performance predictions when faced with complex structures generated by the generative model whose physical properties are not yet clear. Regarding model efficiency, it was compared with current mainstream models based on the Jarvis DFT 3D 2021 dataset in terms of architecture type, single-round training time, number of training rounds, total training time, and number of model parameters. Furthermore, stable experimental results validated the effectiveness of the proposed framework for crystal characterization and property prediction using atomic descriptors, electronegativity edge features, atomic descriptor interpretability analysis, and multi-sided graph neural networks in terms of crystal characterization capability and interpretability.

[0081] To verify the effectiveness of each component of this invention in practical characterization, ablation experiments were conducted to quantify the contribution of each innovative component to prediction accuracy: 1) Atom descriptor: The atom descriptor was compared with the traditional single atom number embedding. The results show that the descriptor proposed in this invention can characterize the physicochemical environment of atoms at a deeper level, which is crucial for determining whether the generated structure conforms to physical laws. 2) Electronegativity edge feature: By removing the edge feature based on Sanderson electronegativity, the key role of this feature in enhancing crystal characterization ability was verified, making it more interpretable when predicting electrical properties. 3) Distance decay weight function: Compared with the cosine weight function proposed in other studies, the distance decay weight function adopted by AtomNet significantly improves computational efficiency while maintaining high prediction accuracy, making it more suitable for real-time inference of large-scale generation tasks.

[0082] Step Six: Interpretability Analysis: Cumulative gradient (IG) method Figure 4 It can quantitatively analyze the impact of different properties in crystalline materials on crystal structure. The contribution of the properties predicted. Among them, The lattice vectors of the unit cell are represented. It is the three-dimensional spatial coordinate matrix of the atom. The feature representation matrix corresponding to each atom. Calculating the IG value for each feature requires defining a baseline input. Specifically, the feature matrix of the baseline input... Set to zero. and Keep the original data unchanged. This allows us to quantify the individual contributions of different atomic properties to the prediction of crystal properties.

[0083] The IG value for each feature dimension in each atom is defined as the aggregation of gradients along the line connecting the baseline input and the actual input: ; in and The figures are respectively the first one in the figure. The actual input and baseline input for each node feature. This represents the trained AtomNet. It represents the number of integration steps; the more steps, the closer the value is to the definition of integration.

[0084] Because atomic descriptors are represented as one-hot encoded values, and IG computation calculates gradient integration along a straight line from the baseline input to the true input, the interpolation points are equally spaced values. However, these values ​​differ from the input data during model training, necessitating proof that the feature importance results calculated by the IG method in the model are reliable. Therefore, this paper proposes to verify the effectiveness and robustness of the IG method on AtomNet by quantitatively evaluating the changes in IG values ​​at different integration steps.

[0085] In attribution analysis, atomic attributes are used as grouping units. Individual IG values ​​belonging to the same group within an atomic descriptor are combined to form the overall contribution of that group, thus directly quantifying and explaining the contribution of each type of atomic attribute to the model's predictions. To test the effect of this contribution value on the number of integration steps... Robustness, at different integration steps Sensitivity analysis was conducted: Spearman's rank correlation coefficient and Kendall's rank correlation coefficient were used to assess the consistency of the attribute importance ranking, and the average relative change was used to quantify the IG value of each attribute under different conditions. The average variation range. These three indicators assess the stability of different experimental results from three complementary dimensions: global ranking trend, ranking consistency, and numerical stability, ensuring the comprehensiveness and reliability of the assessment.

[0086] ; ; ; in, , They represent the first Atom properties at different integration steps The overall contribution Indicates the first Ranking of the contribution of each atomic property among all atomic properties It represents the number of atomic properties. It is a uniform logarithm, used for statistics. The quantity. It is an inconsistent logarithm, used in statistics. The quantity. It is a very small positive number, so we avoid having a denominator of zero.

[0087] Step 7: Model Application The primary application of crystal property prediction models is in combination with generative models to accelerate the discovery of potentially valuable crystal structures. The input data for the target property prediction process depends on all Cartesian coordinates of atoms in the crystal structure, the three lattice vectors of the lattice vector, and the type of each atom. A corresponding pre-trained model is selected based on the specific prediction task to ensure the accuracy of the prediction results. For structural data provided by generative models, manual processing is required before inputting it into the prediction model, as different generative models output essentially different crystal structure files. The model requires each crystal structure object in the data list to be a dictionary type, and it must contain three key-value pairs: atomic Cartesian coordinates, lattice vector, and atom type. The model automatically constructs the crystal diagram and performs inference learning, ultimately outputting a list of target attribute values ​​and saving it as a corresponding JSON file.

[0088] Although the input data is obtained entirely by a generative model searching the chemical space with the goal of minimizing the energy of the crystal structure, additional methods are still needed to verify the stability of the structure. Traditional first-principles calculations are very expensive and not conducive to rapid verification. High-precision deep learning models can achieve high-throughput prediction of the properties of generated structures, quickly eliminating candidate structures that deviate significantly from the target property thresholds. The collaborative work of crystal property prediction models and generative models has become the mainstream method for discovering novel crystalline materials.

[0089] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for crystal property prediction based on physical information enhanced graph neural network representation learning, characterized in that, include: Acquire crystal structure data, construct a crystal polygon graph based on the crystal structure data, perform periodic boundary condition processing on all atoms in the unit cell, and introduce a deterministic periodic pattern to ensure the consistency of the graph construction; Based on the nodes of the crystal polygon graph, atomic descriptors are constructed using atomic physicochemical properties to initialize node features. The atomic descriptors include one-hot encoding of discrete attributes and one-hot encoding of continuous attributes after clustering and binning. Based on the edges of the crystal polygon, physical edge features are constructed based on the difference in electronegativity between atoms, and combined with geometric structure edge features to form fused edge features; Based on the fused edge features, edge weights are calculated using a distance decay weighting function. Edge-level feature updates and node-level message passing are then performed based on the edge weights to construct a crystal property prediction model. Based on the crystal property prediction model, the properties of the input crystal structure are predicted, and the crystal property prediction results are output.

2. The method of claim 1, wherein, Constructing a crystal polygon based on the crystal structure data includes: The local neighborhood of each central atom is determined based on the preset cutoff radius and the maximum number of neighbors. By fixing the order of replication and expansion of the three basis vectors along the lattice vector of the unit cell, and using a stable sorting strategy to handle the priority of equidistant neighbors, the deterministic and periodic invariance of the crystal diagram construction is guaranteed.

3. The method of claim 1, wherein, The atomic physicochemical properties include: group number, periodicity, block, number of valence electrons, Sanderson electronegativity, atomic radius, ionization energy, electron affinity, atomic volume, lattice constant, and C6 dispersion coefficient; The discrete attributes include group number, periodicity, zone, and number of valence electrons; The continuous attributes include Sanderson electronegativity, atomic radius, ionization energy, electron affinity, atomic volume, lattice constant, and C6 dispersion coefficient. K-means clustering is used to bin the continuous attributes, and all-zero vector encoding is used for missing values.

4. The method of claim 1, wherein, Based on the edges of the crystal polygon, physical edge features are constructed based on the interatomic electronegativity difference, and combined with geometric structure edge features to form fused edge features, including: Based on the edges of the crystal polygon, and according to the Sanderson electronegativity difference between the central atom and its neighboring atoms, feature derivation is performed using cosine functions and radial basis functions to obtain electronegative edge features. Construct physical edge features based on electronegativity edge features; Based on the physical edge features, a fused edge feature is formed by combining the geometric structure edge features, wherein the geometric structure edge features include: Euclidean distance features mapped by radial basis functions and relative position vector features.

5. The method of claim 1, wherein, The distance decay weight function In a piecewise polynomial form: ； ； where, denotes the interatomic distance, is the value of is the result of maximum and minimum value normalization, is a fixed radius value, corresponds to the cut-off radius, is 0.6, and the function is first-order derivable at the segmentation point by controlling the index.

6. The method of claim 1, wherein, Edge-level feature updating and node-level message passing based on the edge weights include: The edge features are weighted according to the edge weights, and the edge features are updated through a multilayer perceptron and activation function; The updated edge features are concatenated with the node features to generate a message vector; The message vectors are aggregated based on the central node, the node features are updated through activation functions and normalization layers, and after iteratively executing multi-layer message passing, the global crystal characterization is obtained through the readout layer, and the property prediction value is output through the fully connected layer.

7. The method of claim 1, wherein, The method further includes: performing interpretability analysis on the atomic descriptors, calculating the contribution of each atomic attribute to the property prediction using the cumulative gradient method, evaluating the stability of the contribution ranking by changing the integration step number, and reconstructing the atomic descriptors by selecting key atomic attributes based on the contribution.

8. The method of claim 1, wherein, Based on the crystal property prediction model, the properties of the input crystal structure are predicted, and the output crystal property prediction results include: Receive candidate crystal structures output by the generative model; The candidate structures are screened using the crystal property prediction model with high throughput. Candidate structures whose prediction results meet the target property threshold are output to first-principles calculations for verification, thereby realizing the reverse design of crystal structures.

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