CN-116050473-B - Parameterized Hamiltonian volume construction method based on atomic neighborhood graph representation

CN116050473BCN 116050473 BCN116050473 BCN 116050473BCN-116050473-B

Abstract

The invention relates to a parameterized Hamiltonian quantity construction method based on atomic neighborhood graph representation, which comprises the steps of constructing a crystal graph according to crystal structure information of materials, wherein each node of the crystal graph represents corresponding atoms in a unit cell and all periodic mirror images of the atoms, updating feature vectors of the nodes based on a graph neural network formed by a plurality of graph roll lamination layers so that output feature vectors of the nodes contain atomic local chemical environment representation, and learning and acquiring parameterized Hamiltonian matrix elements of the corresponding materials from the output feature vectors based on a multi-layer perceptron model. The method can solve the problems that the Hamiltonian amount obtained by fitting by a machine learning method cannot ensure the real space symmetry of a system and the general usability of a network model, and the like, and has the advantages of high efficiency and high precision.

Inventors

CHANG SHENG
WANG ZIFENG
WANG TENGFEI

Assignees

武汉大学

Dates

Publication Date: 20260508
Application Date: 20221116

Claims (6)

1. A parameterized hamiltonian construction method based on atomic neighborhood graph representation, the method comprising the steps of: Constructing a crystal diagram according to the crystal structure information of the material, wherein each node of the crystal diagram represents a corresponding atom in a unit cell and all periodic mirror images thereof; updating the feature vector of the node based on a graph neural network composed of a plurality of graph roll layers, so that the output feature vector of the node contains an atomic local chemical environment representation; learning and obtaining parameterized Hamiltonian matrix elements of corresponding materials from the output feature vectors based on a multi-layer perceptron model; the method for updating the feature vector of the node based on the graph neural network formed by a plurality of graph volume laminates comprises the following steps: Defining a graph convolution layer, wherein the graph convolution layer is used for aggregating neighborhood characteristics of nodes; Forming a graph convolutional neural network by a plurality of graph convolution layers, and applying the graph convolution neural network to the crystal graph to update node feature vectors; The updated output characteristic vector of the node is embedded into the local chemical environment of the corresponding atom of the node; the gallery is defined according to a first formula, the first formula comprising: , Wherein, the Is that The feature vectors of the layer nodes are used, Is in combination with Adjacent nodes The feature vector of the layer node, In order to activate the function, In order for the offset to be a function of, The set of neighbors of node i, The function of the normalization is performed such that, Scalar weights for edges and expressions are , Training a weight matrix for the nodes; the multi-layer perceptron model-based learning and obtaining parameterized Hamiltonian matrix elements of corresponding materials from the output feature vectors comprises the following steps: Learning the in-situ energy of the corresponding input material from the output feature vector based on a first multi-layer perceptron model; learning jump energy of the corresponding input material from the output feature vector based on a second multi-layer perceptron model; Constructing a parameterized Hamiltonian matrix element of the corresponding material based on the potential energy and the jump energy; The bit energy comprises: Wherein In order to be able to place the energy in place, Is an MLP model with scalar output, Is a node Is provided; the jump energy includes: Wherein In order for the jump to be able to take place, Is the atomic orbital center-to-center spacing.
2. The parameterized hamiltonian construction method based on atomic neighborhood graph representation according to claim 1, wherein the constructing the crystal graph based on the crystal structure information of the material comprises the steps of: According to the crystal structure information of the material, taking atoms and chemical bonds in a unit cell as nodes and edges of the crystal diagram respectively, and determining the number of the nodes and edges in the crystal diagram; Initializing the feature vectors of the nodes and the edges, wherein the initial feature vector of the nodes is an embedded vector representing element types, and the feature vector of the edges is an atomic center distance function.
3. The parameterized hamiltonian construction method based on an atomic neighborhood graph representation according to claim 2, wherein the steps of using atoms and chemical bonds in one unit cell as nodes and edges of the crystal graph, respectively, comprise: In determining the edges of the crystal map, a cutoff distance for atomic orbital interactions is set, and when the distance between two atoms is less than the cutoff distance, then an edge is considered between the two atoms.
4. The method of claim 1, wherein when defining the graph volume layer, atomic nodes with consistent local environments have the same output eigenvector.
5. The method for constructing parameterized Hamiltonian amount based on atomic neighborhood graph representation according to claim 1, wherein, The first multi-layer perceptron model is also used for enabling nodes with the same output characteristic vector to finally obtain the same in-place energy; The second multi-layer perceptron model is also used for enabling the output characteristic vectors to be consistent and the node pairs with the same side length to finally obtain the same jump energy.
6. The method for constructing a parameterized Hamiltonian volume based on an atomic neighborhood graph representation according to claim 5, wherein the second multi-layer perceptron model is determined based on a second, third, or fourth formula, and The second formula includes: , , the third formula includes: , , The fourth formula shown includes: , , Wherein, the For the second model of the multi-layer perceptron, Is the output feature vector of node i, As the output characteristic vector of the node j, the jump energy between the node i and the track of the node j As atomic orbit center-to-center spacing, a function For treating And And ensures the symmetry of the hamiltonian jump energy, The function is a multi-layer perceptron.

Description

Parameterized Hamiltonian volume construction method based on atomic neighborhood graph representation Technical Field The invention relates to the technical field of parameterized Hamiltonian volume construction, in particular to a parameterized Hamiltonian volume construction method based on atomic neighborhood graph representation. Background At present, in the construction method of the parameterized Hamiltonian matrix, the parameterized Hamiltonian method based on a machine learning fitting material system has more and more attention because the advantages of high efficiency and high precision are simultaneously considered, and the research on the energy band structure and the electron transport property of novel materials can be satisfied. In practical application, the related technology needs to take the energy band data calculated by the first sexual principle as input, and the neurons of the neural network are in one-to-one correspondence with matrix elements of the Hamiltonian amount. And calculating the Hamiltonian quantity expressed by the neural network by using a physical formula to obtain an energy band, comparing the energy band with the real energy band of the material, reversely spreading errors to each neuron, optimizing the neuron value by using a gradient descent algorithm, and finally fitting to obtain a Hamiltonian matrix value with predefined precision. In the Hamiltonian matrix obtained by fitting the neural network, although the effect of reducing the energy band is good, the Hamiltonian matrix fitted does not have clear physical significance due to the randomness of the fitting and the uncertainty of the size of the Hamiltonian matrix. Some techniques adopt a fine tuning hamiltonian matrix model based on a template, the method needs to have certain knowledge on fitting materials, takes a first principle energy band of a substance (or an energy band obtained by experimental measurement) and a guessed hamiltonian volume template as input, takes an optimized hamiltonian volume matrix as output, and the obtained hamiltonian volume fitting first principle energy band has higher precision and clearer physical significance, but still cannot guarantee the real space symmetry of the hamiltonian matrix. Still other techniques are based on Slater-Koster to provide a double-center approximation model, wherein matrix elements (potential energy and jump energy between tracks) in the Hamiltonian amount are represented by a fixed fitting formula, and energy bands are fitted by the matrix elements to obtain the Hamiltonian amount of a material system, but the Hamiltonian matrix obtained by the scheme has obvious physical significance but generally low precision although only interaction between nearest neighbor atoms is considered by the Slater-Koster double-center approximation model. Therefore, how to fit the Hamiltonian matrix value with clear physical meaning based on the neural network model and simultaneously achieve high efficiency and high precision are the problems to be solved urgently. Disclosure of Invention The embodiment of the invention provides a parameterized Hamiltonian amount construction method based on atomic neighborhood graph representation, which is used for solving the problems that Hamiltonian amount obtained by fitting by a machine learning method cannot ensure real space symmetry of a system, the universality of a network model is poor and the like, and has the advantages of high efficiency and high precision. In one aspect, an embodiment of the present invention provides a parameterized hamiltonian configuration method based on an atomic neighborhood graph representation, where the method includes the steps of: Constructing a crystal diagram according to the crystal structure information of the material, wherein each node of the crystal diagram represents a corresponding atom in a unit cell and all periodic mirror images thereof; updating the feature vector of the node based on a graph neural network composed of a plurality of graph roll layers, so that the output feature vector of the node contains an atomic local chemical environment representation; and learning and obtaining parameterized Hamiltonian matrix elements of the corresponding materials from the output feature vectors based on a multi-layer perceptron model. In some embodiments, the constructing a crystal map according to the crystal structure information of the material includes the steps of: According to the crystal structure information of the material, taking atoms and chemical bonds in a unit cell as nodes and edges of the crystal diagram respectively, and determining the number of the nodes and edges in the crystal diagram; Initializing the feature vectors of the nodes and the edges, wherein the initial feature vector of the nodes is an embedded vector representing element types, and the feature vector of the edges is an atomic center distance function. In some embodiments, the steps of using atoms a