A method and system for optimizing the ground-state structure of doped clusters based on machine learning

Abstract

The present invention relates to the field of machine learning technology, and discloses a method and system for optimizing the ground state structure of a doped cluster based on machine learning. The method comprises: collecting original doped cluster data and optimizing it as a standard doped cluster data set, and dividing the standard doped cluster data set into a training set, a validation set, and a test set; constructing a doped cluster potential energy surface fitting machine learning network by adding an interatomic interaction attention mechanism to the original SchNet, and training it using the training set and the validation set; inputting the test set into the trained doped cluster potential energy surface fitting machine learning network to obtain and output the final doped cluster potential energy surface; and using an artificial bee colony algorithm to perform structure search and optimization on the final doped cluster potential energy surface, continuously updating the structure until the lowest energy ground state structure is found. The present invention improves the accuracy of potential energy surface fitting, enhances computational efficiency, and has good portability.

Description

Technical Field

[0001] The present invention relates to the field of machine learning technology, and in particular to a method and system for optimizing the ground state structure of doping clusters based on machine learning. Background Art

[0002] Clusters are multinuclear aggregates intermediate between atoms, molecules, and macroscopic matter. They possess a defined atomic composition and chemical structure, representing the nascent state of condensed matter. The electronic structure and optical properties of clusters vary significantly with size. This variation can link macroscopic properties to the microscopic structure of matter, offering significant insights into the mechanisms of material transformation. Clusters serve as fundamental building blocks for the construction of novel functional materials and are a crucial avenue for preparing nanomaterials with unique properties. By assembling clusters with specific functions into ordered structures, high-performance optical, electrical, or magnetic materials can be obtained. By varying reaction conditions and ligand types during cluster synthesis, key properties such as porosity, adsorption properties, and catalytic activity can be finely tuned to meet diverse application requirements. The microstructure of clusters is difficult to determine using experimental methods alone; theoretical calculations are essential. Determining the ground-state structure of clusters requires a global search on a high-dimensional potential energy surface, a fundamental and crucial topic in cluster research. For a cluster containing N atoms, the number of local minima on the potential energy surface increases exponentially with the dimensionality 3N. As clusters grow in size, their potential energy surfaces become extremely complex, making it very difficult to find their ground-state structures. Developing an efficient global optimization model is an urgent problem in the field of clusters.

[0003] The commonly used methods for accurately describing the potential energy surface of larger systems are ab initio methods and density functional theory methods in quantum mechanics calculations. However, these methods increase exponentially with the scale of the system. Even with some approximations, dealing with larger systems still requires a large amount of computing resources. With the development of artificial intelligence technology, machine learning is undoubtedly a very promising tool. Summary of the Invention

[0004] The purpose of the present invention is to solve the problems in the prior art.

[0005] The technical solution adopted by the present invention to solve the technical problem is: to provide a method for optimizing the ground state structure of doping clusters based on machine learning, comprising the following steps:

[0006] Collecting original doping cluster data and optimizing them as a doping cluster standard data set, wherein the original doping cluster data includes structural information and energy information of the doping clusters; and dividing the doping cluster standard data set into a training set, a validation set, and a test set;

[0007] By adding the interatomic interaction attention mechanism to the original SchNet, a doping cluster potential energy surface fitting machine learning network is constructed and trained using the training set and validation set. The test set is input into the trained doping cluster potential energy surface fitting machine learning network to obtain and output the final doping cluster potential energy surface.

[0008] The artificial bee colony algorithm is used to perform structural search and optimization on the potential energy surface of the final doped cluster, and the structure is continuously updated until the lowest energy ground state structure is found.

[0009] Preferably, the original doping cluster data are collected using Gaussian 09, PBE0 hybrid density functional theory method and 3-21G basis set.

[0010] Preferably, the structural information of the doping cluster is the molecular formula and the three-dimensional Cartesian coordinates of the molecule.

[0011] Preferably, the doped clusters in the doped cluster standard data set are all boron atom clusters doped with one selenium atom; the doped clusters are divided into nine types according to the number of boron atoms, and the number of boron atoms ranges from 16 to 24.

[0012] Preferably, the collecting of original doping cluster data and optimization thereof includes:

[0013] Calculate the partial derivative of the system energy with respect to each atomic position as the energy gradient of the system;

[0014] Based on the energy gradient of the system, the atomic positions are gradually moved to update the atomic coordinates, so that the energy of the system is gradually reduced, the optimized cluster structure and energy are obtained, and the doped cluster data set is obtained.

[0015] Preferably, the process of inputting the test set into the trained doping cluster potential energy surface fitting machine learning network to obtain and output the final doping cluster potential energy surface includes the following steps:

[0016] Input the molecular formula of the cluster, the molecular three-dimensional Cartesian coordinates and the energy value as a label;

[0017] The molecular formula is encoded according to the periodic table to obtain the atomic number, and the atomic number is embedded into the feature matrix;

[0018] The atomic distance is obtained by subtracting the absolute value of the atomic coordinates, and the atomic distance is expanded by the radial basis function to expand the dimension;

[0019] The feature matrix and the interatomic distances after dimension expansion enter the interatomic interaction attention mechanism for feature extraction and parameter update, and the feature information containing the structure-energy correspondence network is obtained as the final doping cluster potential energy surface output.

[0020] Preferably, the feature matrix and the interatomic distances after the dimension expansion enter the interatomic interaction attention mechanism for feature extraction and parameter update, including the following steps:

[0021] Feature extraction: The feature matrix is multiplied element-by-element by the atomic distance after the expanded dimension through a filter generation function module to output the node features.

[0022] Feature update: construct a learnable shared matrix to reconstruct the linear transformation of node features, and use a feedforward neural network to build a shared attention function to smoothly normalize the node features and update the node features;

[0023] Feature aggregation, finally, the updated node features and the extracted node features are aggregated through the residual network to obtain the feature information of the structure-energy correspondence network.

[0024] Preferably, the training is performed using a training set and a validation set, and the optimization function adopted is a stochastic gradient descent function, and the mean absolute error, root mean square error, optimal convergence training cycle and optimal convergence loss value are used as evaluation indicators for the improved SchNet doped cluster potential energy surface fitting machine learning network.

[0025] Preferably, the use of an artificial bee colony algorithm to perform structure search and optimization on the potential energy surface of the final doped cluster comprises the following steps:

[0026] Initialization step: using artificial bee colony algorithm to search on the potential energy surface of the final doping cluster, initialize the bee colony and its position and calculate the fitness;

[0027] In the iterative step, the swarm position is updated through local search and global random search is performed during the exploration phase;

[0028] Calculation step, repeat the iterative step until the maximum number of iterations and fitness threshold are reached, record the best position in each iteration, use the final doped cluster potential energy surface to calculate the energy of each structure, and finally output the lowest energy ground state doped cluster structure and energy.

[0029] The present invention also provides a doping cluster ground state structure optimization system based on machine learning, comprising the following steps:

[0030] A data processing module collects original doping cluster data and optimizes it as a doping cluster standard data set, wherein the original doping cluster data includes structural information and energy information of the doping clusters; and divides the doping cluster standard data set into a training set, a validation set, and a test set;

[0031] A model training module constructs a doping cluster potential energy surface fitting machine learning network by improving SchNet and trains it using a training set and a validation set; the test set is input into the trained doping cluster potential energy surface fitting machine learning network to obtain and output the final doping cluster potential energy surface; the improved SchNet refers to adding an interatomic interaction attention mechanism to the feature extraction and convolutional filtering network modules of the original SchNet;

[0032] The structure search module uses the artificial bee colony algorithm to perform structure search and optimization on the potential energy surface of the final doping cluster, continuously updating the structure until the ground state structure with the lowest energy is found.

[0033] The present invention has the following beneficial effects:

[0034] (1) Improve the accuracy of potential energy surface fitting. The machine learning model can adjust the framework according to the specific task, which is conducive to improving the accuracy of potential energy surface fitting, thereby ensuring that the searched ground state structure is more experimentally meaningful.

[0035] (2) Improve computational efficiency. Applying machine learning to the search for the ground-state structure of doped clusters can reduce the computing resources occupied and reduce computational costs. The model only needs to be fully trained in the early stages to be able to search for the ground-state structure of doped clusters for a long time.

[0036] (3) Good scalability. Machine learning models can be fine-tuned or retrained by inputting new data sets, which can be expanded to higher accuracy and larger systems.

[0037] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, but the present invention is not limited to the embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A diagram showing the steps of a method according to an embodiment of the present invention;

[0039] Figure 2 A schematic diagram of a flow chart of an embodiment of the present invention;

[0040] Figure 3 This is a diagram showing the machine learning network structure of the doping cluster potential energy surface fitting according to an embodiment of the present invention;

[0041] Figure 4 A schematic diagram of a process for performing ground state structure search using an artificial bee colony algorithm according to an embodiment of the present invention;

[0042] Figure 5 2 is a system structure diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0043] See also Figure 1 and Figure 2FIG. 1 is a diagram showing steps and a flow chart of a method according to an embodiment of the present invention, which includes the following steps:

[0044] S101, collecting original doping cluster data and optimizing it as a doping cluster standard data set, wherein the original doping cluster data includes structural information and energy information of the doping cluster; and dividing the doping cluster standard data set into a training set, a validation set, and a test set;

[0045] S102, by adding the interatomic interaction attention mechanism to the original SchNet, a doping cluster potential energy surface fitting machine learning network is constructed, and the training set and the validation set are used for training; the test set is input into the trained doping cluster potential energy surface fitting machine learning network to obtain and output the final doping cluster potential energy surface;

[0046] S103, using the artificial bee colony algorithm to perform structure search and optimization on the potential energy surface of the final doped cluster, continuously updating the structure until the ground state structure with the lowest energy is found.

[0047] Specifically, the present invention uses Gaussian 09 at the PBE0 / 3-21G computational level to perform an unbiased search for cluster structures, constructing a standard dataset of doped clusters. The SchNet machine learning model is then improved, and the clusters are then fed into the improved SchNet machine learning model. Feature extraction is performed using the interatomic interaction attention mechanism to obtain the potential energy surface of the corresponding clusters. This potential energy surface is then applied to the search for the cluster ground-state structure, ultimately obtaining the ground-state structure of the doped clusters. The following is a detailed description divided into four main sections.

[0048] (1) Cluster data set collection: Nine doped clusters with boron clusters as the main body were selected, random structure search was performed and initial energy calculation was performed using Gaussian 09 to establish the original doped cluster data set. The original clusters were then optimized at the PBE0 / 3-21G calculation level, and the original doped cluster data set was expanded. For the construction of the standard doped cluster data set, the original doped cluster structure was generated by random search and density functional theory calculation was performed at the PBE0 / 3-21G level. All energy calculations and geometry optimizations of the doped clusters were performed using the Gaussian 09 program. The original doped cluster data was optimized by calculating the energy gradient of the system, that is, the partial derivative of the system energy with respect to each atomic position. This reflects the direction of the force and indicates how the atoms should move to reduce the total energy of the system. If all gradients are zero, it means that the system is at the minimum energy point; the atomic positions are gradually moved to update the atomic coordinates, so that the energy of the system gradually decreases, and the optimized cluster structure and energy are obtained, thus obtaining the standard doped cluster data set. By constraining the filters in the continuous filter convolutional layer to be rotationally invariant, we create a feature prior, replacing the data augmentation process to reduce computational effort. During model training, the dataset is randomly split in an 8:1:1 ratio: 80% as the training set, 10% as the validation set, and the remaining 10% as a separate test set.

[0049] In this example, nine representative dopant clusters were randomly generated, and energy and optimization calculations were performed using Gaussian 09. This yielded a standard dataset of dopant clusters, employing density functional theory (DFT) methods and the PBE0 / 3-21G basis set, which balances accuracy and computational speed. This dataset encompasses not only low-energy structures but also, compared to most open-source datasets, high-energy structures. This allows the machine learning model to obtain a relatively complete structure-energy relationship, enabling a more accurate fit of the potential energy surface of the dopant clusters.

[0050] (2) Feature extraction algorithm: The traditional machine learning potential energy function aims to use machine learning methods to approximate the mapping between material structure and energy to simulate the atomic interaction potential energy model, effectively avoiding the errors caused by the use of empirical parameters in traditional empirical force fields and the problem of low portability. Although machine learning methods for constructing potential energy surfaces have made progress, there are still many problems, mainly including the following three aspects: processing high-dimensional data and feature selection strategies, the construction of molecular descriptors, and scarce high-quality cluster databases. To address the above problems, the present invention proposes an inter-atomic interaction attention mechanism, which is introduced into the feature extraction and convolutional filter network modules of the original SchNet to improve the feature capture of the atomic environment. By constructing an end-to-end machine learning model, the regression task of atomic feature vectors to energy is realized to save computational costs and improve the portability of the model, and reduce human intervention and debugging of descriptor hyperparameters.

[0051] The attention mechanism is a computational model that makes models more efficient and flexible when processing sequence data. The core idea of the attention mechanism is to focus the model on the most relevant parts of the input data, thereby improving its efficiency and performance. By adaptively focusing on important information in the input sequence, the attention mechanism significantly improves the performance of the model when processing sequence data. The interatomic interaction attention mechanism is constructed as follows: First, node information is integrated with the high-dimensional extended dynamic filtering network of Schnet to construct feature relationships between atoms and bonds, while avoiding the computational overhead of dense matrix multiplication. Graph attention methods are then used to model the importance of different interatomic interactions. Finally, using the concept of residual networks, node-edge and node-node information are simultaneously aggregated to update the feature information for output. This embodiment of the present invention addresses the problem that dopant atoms have a more significant weight in machine learning models, and the existing filter convolution module does not pay enough attention to dopant atom features. By integrating the interatomic interaction attention mechanism into Schnet feature extraction, it simultaneously aggregates node-edge and node-node information in the molecular graph, allowing the machine learning model to better learn atomic features and atomic environments. The interatomic interaction attention mechanism can help the network better focus on the feature representation of doping atoms, thereby improving the accuracy of potential energy surface fitting.

[0052] (3) Parameter update. The embodiment of the present invention uses the SMU algorithm to smooth the activation function to reduce the overfitting caused by high-energy abnormal structures. When training machine learning models, problems such as gradient vanishing and overfitting are often encountered. Especially when dealing with high-energy abnormal structures, high-energy abnormal structures usually cause the model to overfit the training data, thereby affecting the generalization ability of the model. The activation function is responsible for introducing nonlinearity and helping the model learn complex mapping relationships. It plays an important role in the parameter update process. The SMU algorithm smoothes the activation function through maximum unit approximation, thereby obtaining continuity and differentiability, thereby optimizing the gradient update process and maintaining the continuity and smoothness of the potential energy surface.

[0053] The SMU algorithm is an activation function used in machine learning. It can approximate the maximum operation from the smooth approximation of the absolute value function, thereby providing a smoother gradient update. The activation function smoothed by the SMU algorithm is smooth and differentiable in the entire domain, which makes it easier to calculate the gradient during backpropagation and optimization, thereby providing a more stable parameter update process and accelerating convergence. Compared with traditional activation functions, the activation function smoothed by the SMU algorithm can still maintain a non-zero gradient when the input value is large or small, which helps to alleviate the gradient disappearance problem. Due to its smoothness, the SMU has a certain ability to suppress noise in the input data. Compared with traditional activation functions, the robustness of the model is significantly improved. The embodiment of the present invention uses the idea of the SMU algorithm to smooth the activation process of the interaction between nodes, specifically constructing a learnable shared matrix to reconstruct the linear transformation of the input node features, and using a feedforward neural network to construct a shareable attention function, and perform smooth normalization to update the node features. Finally, the two features obtained through the idea of the residual network are aggregated to output feature information.

[0054] For details, see Figure 3 As shown, the embodiment of the present invention fits the doping cluster potential energy surface obtained by improving SchNet to a machine learning network, and its internal execution process is as follows:

[0055] Input molecular formula (i.e., the atoms contained in the cluster), molecular coordinates (three-dimensional Cartesian coordinates), and energy values as labels; the atomic number encodes the molecular formula in the order of the periodic table, for example, CO2: [6, 8, 8]; the interatomic distance is obtained by subtracting the absolute value of the atomic coordinates; the atomic number is embedded through features to obtain a feature matrix; the interatomic distance is expanded by radial basis function to expand the dimension. If the interatomic distance is 4 and the sampling interval is 0.5, it is expanded to [0, 0.5, 1, …, 3.5, 4] and Gaussian transformation is performed so that the closer the neighboring atoms are to the central atom, the greater the weight they occupy, and finally [e 0 , e- 0.5 , e -1 , …,e -3.5, e -4 ]; The feature matrix obtained by feature embedding of the atomic number enters the inter-atomic interaction attention mechanism. In subsequent convolution filtering and other calculations, it undergoes element-by-element multiplication with the atomic distance after the expansion dimension to obtain edge features, etc.

[0056] To address the overfitting problem caused by high-energy anomaly data in doped clusters in machine learning models, this embodiment of the present invention proposes using a performance-smoothing maximum unit to smooth the gradient update process during backpropagation. By smoothing the absolute value function and fitting a smoothing formula for the corresponding activation function, the gradient is smoothly transferred during backpropagation, reducing unnecessary local minima and discontinuities. This effectively avoids overfitting caused by high-energy anomaly data, improving the stability of the numerical calculation and the reliability of the model.

[0057] (4) Ground state structure search: Ground state structure search is the ultimate goal of cluster potential energy surface fitting. This requires not only the selection of appropriate methods such as classical molecular dynamics and density functional theory to calculate the energy, but also the selection of appropriate optimization algorithms, taking into account both global optimization search and local optimization. For the initial structure to be optimized, initial guesses are usually generated through literature, known structures or simple configurations, or a large number of initial structures are randomly generated for low-computational-level pre-optimization search and higher-precision secondary optimization search. This usually consumes a lot of time and computing resources. The ground state structure search process adopts a scheme that combines the two initial structure acquisition methods of initial guessing and random generation to ensure a more accurate ground state structure and set reasonable energy and force convergence standards. The embodiment of the present invention uses the artificial bee colony algorithm to perform optimization search on the doping cluster potential energy surface of the improved SchNet, replacing the traditional low-computational level pre-optimization search and higher-precision secondary optimization search, which greatly saves computing resources and saves computing time; then the results of the optimization search are statistically analyzed, and the configuration with the lowest energy is selected as the final result. Finally, the ground state doping cluster structure and energy with the lowest energy are output, and the stability of the obtained ground state structure is verified by vibration analysis and other methods to complete the ground state structure search of the doping cluster. For the specific process, see Figure 4 As shown, the process includes: initializing the swarm and its position, and calculating the fitness; then updating the swarm position through local search, and performing a global random search in the exploration phase; recording the best position in each iteration until the maximum number of iterations and the fitness threshold are reached, and using the improved SchNet doping cluster potential energy surface to calculate the energy of each structure, reducing the computational burden, and finally outputting the lowest energy ground-state doping cluster structure and energy.

[0058] In accordance with the task characteristics of doped clusters having more complex potential energy surfaces, the embodiment of the present invention uses an artificial bee colony algorithm to replace traditional annealing simulations and genetic algorithms. The artificial bee colony algorithm evaluates the fitness of each bee based on the potential energy value and is used to select employed bees and scout bees. Employed bees randomly select other bees for information exchange based on their current position and fitness. If the fitness of the new position is higher, the bee position is updated. To prevent the algorithm from falling into a local optimum, employed bees are converted into scout bees when they iterate to a threshold. The artificial bee colony algorithm has the advantage of being able to perform both global and local searches when searching for the lowest energy structure of a cluster, providing a more effective means of searching for ground state structures.

[0059] For details, see Figure 5 FIG. 1 is a system structure diagram of an embodiment of the present invention, including:

[0060] The data processing module 501 collects and optimizes the original doping cluster data as a doping cluster standard data set, wherein the original doping cluster data includes structural information and energy information of the doping clusters; and divides the doping cluster standard data set into a training set, a validation set, and a test set;

[0061] Model training module 502, by adding an interatomic interaction attention mechanism to the original SchNet to construct a doping cluster potential energy surface fitting machine learning network, and train it using a training set and a validation set; input the test set into the trained doping cluster potential energy surface fitting machine learning network to obtain and output the final doping cluster potential energy surface;

[0062] The structure search module 503 uses an artificial bee colony algorithm to perform structure search and optimization on the potential energy surface of the final doping cluster, and continuously updates the structure until the ground state structure with the lowest energy is found.

[0063] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for optimizing the ground state structure of doping clusters based on machine learning, characterized in that: The following steps are involved: Collecting original doping cluster data and optimizing them as a doping cluster standard data set, wherein the original doping cluster data includes structural information and energy information of the doping clusters; and dividing the doping cluster standard data set into a training set, a validation set, and a test set; By adding the interatomic interaction attention mechanism to the original SchNet, a doping cluster potential energy surface fitting machine learning network is constructed and trained using the training set and validation set. The test set is input into the trained doping cluster potential energy surface fitting machine learning network to obtain and output the final doping cluster potential energy surface. Use the artificial bee colony algorithm to search and optimize the structure on the potential energy surface of the final doped cluster, and continuously update the structure until the lowest energy ground state structure is found; The process of inputting the test set into the trained doping cluster potential energy surface fitting machine learning network to obtain and output the final doping cluster potential energy surface includes the following steps: Input the molecular formula of the cluster, the molecular three-dimensional Cartesian coordinates and the energy value as a label; The molecular formula is encoded according to the periodic table to obtain the atomic number, and the atomic number is embedded into the feature matrix; The atomic distance is obtained by subtracting the absolute value of the atomic coordinates, and the atomic distance is expanded by the radial basis function to expand the dimension; The feature matrix and the interatomic distances after the expansion dimension are fed into the interatomic interaction attention mechanism for feature extraction and parameter update, and feature information including the structure-energy correspondence network is obtained as the final doping cluster potential energy surface output; The feature matrix and the interatomic distances after the expansion dimension enter the interatomic interaction attention mechanism for feature extraction and parameter update, including the following steps: Feature extraction: The feature matrix is multiplied element-by-element by the atomic distance after the expanded dimension through a filter generation function module to output the node features; Feature update: construct a learnable shared matrix to reconstruct the linear transformation of node features, and use a feedforward neural network to build a shared attention function to smoothly normalize the node features and update the node features; Feature aggregation, finally, the updated node features and the extracted node features are aggregated through the residual network to obtain the feature information of the structure-energy correspondence network; The inter-atomic interaction attention mechanism adopts a graph attention method to model the importance of different inter-atomic interactions; The method of using the artificial bee colony algorithm to perform structure search and optimization on the final doping cluster potential energy surface includes the following steps: Initialization step: using artificial bee colony algorithm to search on the potential energy surface of the final doping cluster, initialize the bee colony and its position and calculate the fitness; In the iterative step, the swarm position is updated through local search and global random search is performed during the exploration phase; Calculation step, repeat the iterative step until the maximum number of iterations and fitness threshold are reached, record the best position in each iteration, use the final doped cluster potential energy surface to calculate the energy of each structure, and finally output the lowest energy ground state doped cluster structure and energy.

2. The method for optimizing the ground state structure of doping clusters based on machine learning according to claim 1, characterized in that: The original doping cluster data were collected using Gaussian 09, PBE0 hybrid density functional theory method and 3-21G basis set.

3. The method for optimizing the ground state structure of doping clusters based on machine learning according to claim 1, characterized in that: The structural information of the doping cluster is the molecular formula and the three-dimensional Cartesian coordinates of the molecule.

4. The method for optimizing the ground state structure of doping clusters based on machine learning according to claim 1, wherein: The doped clusters in the doped cluster standard data set are all boron atom clusters doped with one selenium atom; the doped clusters are divided into nine types according to the number of boron atoms, and the number of boron atoms ranges from 16 to 24.

5. The method for optimizing the ground state structure of doping clusters based on machine learning according to claim 3, characterized in that: The original doping cluster data is collected and optimized, and the optimization process includes: Calculate the partial derivative of the system energy with respect to each atomic position as the energy gradient of the system; Based on the energy gradient of the system, the atomic positions are gradually moved to update the atomic coordinates, so that the energy of the system is gradually reduced, the optimized cluster structure and energy are obtained, and the doped cluster data set is obtained.

6. The method for optimizing the ground state structure of doping clusters based on machine learning according to claim 1, characterized in that: The training is performed using a training set and a validation set, the optimization function adopted is a stochastic gradient descent function, and the mean absolute error, root mean square error, optimal convergence training cycle and optimal convergence loss value are used as evaluation indicators for the improved SchNet doped cluster potential energy surface fitting machine learning network.

7. A doping cluster ground state structure optimization system based on machine learning, comprising the following steps: A data processing module collects original doping cluster data and optimizes it as a doping cluster standard data set, wherein the original doping cluster data includes structural information and energy information of the doping clusters; and divides the doping cluster standard data set into a training set, a validation set, and a test set; A model training module constructs a doping cluster potential energy surface fitting machine learning network by improving SchNet and trains it using a training set and a validation set; the test set is input into the trained doping cluster potential energy surface fitting machine learning network to obtain and output the final doping cluster potential energy surface; the improved SchNet refers to adding an interatomic interaction attention mechanism to the feature extraction and convolutional filtering network modules of the original SchNet; The structure search module uses the artificial bee colony algorithm to search and optimize the structure on the potential energy surface of the final doping cluster, continuously updating the structure until the lowest energy ground state structure is found; The process of inputting the test set into the trained doping cluster potential energy surface fitting machine learning network to obtain and output the final doping cluster potential energy surface includes the following steps: Input the molecular formula of the cluster, the molecular three-dimensional Cartesian coordinates and the energy value as a label; The molecular formula is encoded according to the periodic table to obtain the atomic number, and the atomic number is embedded into the feature matrix; The atomic distance is obtained by subtracting the absolute value of the atomic coordinates, and the atomic distance is expanded by the radial basis function to expand the dimension; The feature matrix and the interatomic distances after the expansion dimension are fed into the interatomic interaction attention mechanism for feature extraction and parameter update, and feature information including the structure-energy correspondence network is obtained as the final doping cluster potential energy surface output; The feature matrix and the interatomic distances after the expansion dimension enter the interatomic interaction attention mechanism for feature extraction and parameter update, including the following steps: Feature extraction: The feature matrix is multiplied element-by-element by the atomic distance after the expanded dimension through a filter generation function module to output the node features; Feature update: construct a learnable shared matrix to reconstruct the linear transformation of node features, and use a feedforward neural network to build a shared attention function to smoothly normalize the node features and update the node features; Feature aggregation, finally, the updated node features and the extracted node features are aggregated through the residual network to obtain the feature information of the structure-energy correspondence network; The inter-atomic interaction attention mechanism adopts a graph attention method to model the importance of different inter-atomic interactions; The method of using the artificial bee colony algorithm to perform structure search and optimization on the final doping cluster potential energy surface includes the following steps: Initialization step: using artificial bee colony algorithm to search on the potential energy surface of the final doping cluster, initialize the bee colony and its position and calculate the fitness; In the iterative step, the swarm position is updated through local search and global random search is performed during the exploration phase; Calculation step, repeat the iterative step until the maximum number of iterations and fitness threshold are reached, record the best position in each iteration, use the final doped cluster potential energy surface to calculate the energy of each structure, and finally output the lowest energy ground state doped cluster structure and energy.

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