A parameterized hamiltonian construction method based on atomic neighborhood graph representation

Abstract

The application relates to a parameterized Hamiltonian construction method based on an atomic neighborhood graph representation, comprising the following steps: constructing a crystal graph according to crystal structure information of a material, wherein each node of the crystal graph represents a corresponding atom in a unit cell and all periodic mirror images thereof; updating a feature vector of the node based on a graph neural network composed of multiple graph convolution layers, so that the output feature vector of the node contains an atomic local chemical environment representation; and learning and obtaining a parameterized Hamiltonian matrix element of the corresponding material from the output feature vector based on a multilayer perceptron model. The method can solve the problems that a Hamiltonian fitted by a machine learning method cannot guarantee real-space symmetry of a system and a network model has poor universality, and has the advantages of high efficiency and high precision.

Description

Technical Field

[0001] This invention relates to the field of parametric Hamiltonian construction technology, and in particular to a method for constructing parametric Hamiltonians based on atomic neighborhood graph representation. Background Technology

[0002] Currently, among the methods for constructing parameterized Hamiltonian matrices, the parameterized Hamiltonian method based on machine learning to fit material systems has attracted increasing attention due to its advantages of both high efficiency and high accuracy, which can meet the needs of studying the band structure and electronic transport properties of novel materials.

[0003] In practical applications, related technologies require first-principles calculations of band structure data as input, mapping each neuron of the neural network to a specific element of the Hamiltonian matrix. The band structure is then calculated from the Hamiltonian represented by the neural network using physical formulas and compared to the material's actual band structure. Errors are backpropagated to each neuron, and gradient descent is used to optimize the neuron values, ultimately fitting a Hamiltonian matrix value with a predefined precision. While this type of neural network-fitted Hamiltonian matrix effectively reconstructs the band structure, the randomness of the fitting process and the uncertainty in the size of the Hamiltonian matrix result in a lack of clear physical meaning.

[0004] Some techniques employ template-based fine-tuned Hamiltonian matrix models. Such methods require a certain understanding of the material being fitted. They take the first-principles band structure of the material (or the band structure obtained by experimental measurement) and the conjectured Hamiltonian template as inputs, and the optimized Hamiltonian matrix as outputs. The obtained Hamiltonian fits the first-principles band structure with higher accuracy and clearer physical meaning, but still cannot guarantee the real-space symmetry of the Hamiltonian matrix.

[0005] Some techniques are based on the Slater-Koster bicentric approximation model, using a fixed fitting formula to represent the matrix elements (in-situ energy and hopping energy between orbitals) in the Hamiltonian and then fitting the energy bands to obtain the Hamiltonian of the material system. However, since the Slater-Koster bicentric approximation model only considers the interaction between nearest-neighbor atoms, although the Hamiltonian matrix obtained by this method has a clear physical meaning, its accuracy is generally not high. Therefore, how to fit a physically meaningful Hamiltonian matrix value based on a neural network model, while simultaneously achieving high efficiency and high accuracy, is an urgent problem to be solved. Summary of the Invention

[0006] This invention provides a parameterized Hamiltonian construction method based on atomic neighborhood graph representation, which solves the problems that Hamiltonians obtained by machine learning methods cannot guarantee the real space symmetry of the system and the poor generality of the network model, while taking into account the advantages of high efficiency and high accuracy.

[0007] On one hand, embodiments of the present invention provide a method for constructing parameterized Hamiltonians based on atomic neighborhood graph representation, characterized in that the method includes the following steps:

[0008] A crystal diagram is constructed based on the crystal structure information of the material, wherein each node of the crystal diagram represents the corresponding atom in the unit cell and all its periodic mirror images;

[0009] The feature vectors of the nodes are updated based on a graph neural network composed of multiple graph convolutional layers, so that the output feature vectors of the nodes contain representations of the local chemical environment of atoms.

[0010] Based on the multilayer perceptron model, the parameterized Hamiltonian matrix elements of the corresponding material are learned from the output feature vector.

[0011] In some embodiments, constructing a crystal map based on the crystal structure information of the material includes the following steps:

[0012] Based on the crystal structure information of the material, the atoms and chemical bonds in a unit cell are respectively used as nodes and edges of the crystal diagram, and the number of nodes and edges in the crystal diagram is determined.

[0013] The feature vectors of the nodes and edges are initialized. The initial feature vector of the node is an embedding vector representing the element type, and the feature vector of the edge is an atomic center spacing function.

[0014] In some embodiments, the step of using atoms and chemical bonds within a unit cell as nodes and edges of the crystal diagram, respectively, includes the following steps:

[0015] When determining the edges of a crystal diagram, a cutoff distance for atomic orbital interactions is set. If the distance between two atoms is less than the cutoff distance, then the two atoms are considered to have an edge.

[0016] In some embodiments, updating the feature vector of the node based on a graph neural network composed of multiple graph convolutional layers includes the following steps:

[0017] Define a graph convolutional layer, which is used to aggregate the neighborhood features of nodes;

[0018] A graph convolutional neural network is composed of multiple graph convolutional layers, and the graph convolutional neural network is applied to the crystal graph to update the node feature vectors;

[0019] The updated node's output feature vector is embedded with the local chemical environment of the corresponding atom.

[0020] In some embodiments, when defining the graph convolutional layer, atomic nodes with consistent local environments have the same output feature vector.

[0021] In some embodiments, the graph convolutional layer is defined according to a first formula, which includes:

[0022]

[0023] in, The feature vector of the (l+1) layer node, To and The feature vectors of adjacent nodes in layer l, where σ(...) is the activation function, and b (l) For bias, n(i) is the neighborhood set of node i, c ji Normalization function, e ji Let be the scalar weight of the edge and its expression be W (l) The weight matrix can be trained for nodes.

[0024] In some embodiments, the step of learning and obtaining the parameterized Hamiltonian matrix elements of the corresponding material from the output feature vector based on the multilayer perceptron model includes the following steps:

[0025] Based on the first multilayer perceptron model, the in-situ energy of the corresponding input material is learned from the output feature vector;

[0026] Based on the second multilayer perceptron model, the jump energy of the corresponding input material is learned from the output feature vector;

[0027] Based on the in-situ energy and jump energy, construct the parameterized Hamiltonian matrix elements of the corresponding material.

[0028] In some embodiments, the first multilayer perceptron model is also used to ensure that nodes with the same output feature vector eventually obtain the same in-situ energy.

[0029] The second multilayer perceptron model is also used to ensure that node pairs with consistent output feature vectors and the same side length ultimately obtain the same jump energy.

[0030] In some embodiments, the second multilayer perceptron model is determined based on a second formula, a third formula, or a fourth formula, and

[0031] The second formula includes:

[0032] h(i,j)=MLP2[f(a i a j d ij )],

[0033] f(a i a j d ij )=f(a j a i d ji )=[g(a i )+g(a j )] / d ij 2 ,

[0034] The third formula includes:

[0035] h(i,j)=MLP2[f(a i a j d ij )],

[0036] f(a i a j d ij )=f(a j a i d ji )=g(a i *a j ) / d ij 2 ,

[0037] The fourth formula shown includes:

[0038] h(i,j)=MLP2[f(a i a j d ij )],

[0039] f(a i a j d ij )=f(a j a i d ji )=g(a i +a j ) / d ij 2 ,

[0040] Wherein, MLP2 is the second multilayer perceptron model, a i Let a be the output feature vector of node i. j Let h(i,j),d be the output feature vector of node j, and h(i,j),d be the jump energy between the orbits of node i and node j. ij The distance between the centers of atomic orbitals is given by the function f, which is used to process a. i and a j And it ensures the symmetry of the Hamiltonian jump energy, and the g function is a multilayer perceptron.

[0041] This invention innovatively uses a graph neural network model to construct an atomic neighborhood-dependent Hamiltonian, which solves the problems that the Hamiltonian obtained by machine learning methods cannot guarantee the real space symmetry of the system and the poor generality of the network model, while also taking into account the advantages of high efficiency and high accuracy. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 A schematic diagram of a parameterized Hamiltonian construction method based on atomic neighborhood graph representation provided in an embodiment of the present invention;

[0044] Figure 2 This is a schematic diagram of the 13AGNR crystal structure provided in an embodiment of the present invention;

[0045] Figure 3 This is a schematic diagram of the parameterized Hamiltonian construction process provided in an embodiment of the present invention.

[0046] Figure 4 This is a schematic diagram of the method for constructing the parameterized Hamiltonian of 13AGNR crystal material according to an embodiment of the present invention. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] like Figure 1 As shown, this embodiment of the invention provides a method for constructing a parameterized Hamiltonian based on an atomic neighborhood graph representation, including the following steps:

[0049] S100: Construct a crystal diagram based on the crystal structure information of the material, wherein each node of the crystal diagram represents the corresponding atom in the unit cell and all its periodic mirror images;

[0050] S200: Update the feature vector of the node based on a graph neural network composed of multiple graph convolutional layers, so that the output feature vector of the node contains a representation of the local chemical environment of the atom;

[0051] S300: Based on the multilayer perceptron model, learn from the output feature vector and obtain the parameterized Hamiltonian matrix elements of the corresponding material.

[0052] It should be noted that the aforementioned local chemical environment of an atom can be understood as other atoms and chemical bonds within the range of that atom, or it can be determined by setting a cutoff distance for interatomic interactions, representing other atoms and chemical bonds within the range of that atom cutoff distance.

[0053] It is understandable that by including the representation of the local chemical environment of atoms in the output feature vector of nodes, the invention essentially utilizes a graph neural network to construct a linear superposition of atomic orbitals (LCAO) Hamiltonian that aggregates atomic neighborhood interactions, which is more accurate than the Hamiltonian obtained by the LCAO method in related technologies. This invention innovatively uses a graph neural network model to construct an atomic neighborhood information-dependent Hamiltonian, solving the problems of Hamiltonians obtained by machine learning methods not guaranteeing the real space symmetry of the system and the poor generalizability of network models, while simultaneously achieving the advantages of high efficiency and high accuracy.

[0054] In some embodiments, S100 includes:

[0055] S110: Based on the crystal structure information of the material, the atoms and chemical bonds in a unit cell are respectively used as nodes and edges of the crystal diagram, and the number of nodes and edges in the crystal diagram is determined.

[0056] S120: Initialize the feature vectors of the nodes and edges. The initial feature vector of the node is an embedding vector representing the element type, and the feature vector of the edge is an atomic center spacing function.

[0057] Preferably, when determining the edges of the crystal diagram, a cutoff distance for atomic orbital interactions is set. When the distance between two atoms is less than the cutoff distance, it is considered that there is an edge between the two atoms.

[0058] In some embodiments, S200 includes the step of:

[0059] S210: Define a graph convolutional layer, which is used to aggregate the neighborhood features of nodes;

[0060] S220: A graph convolutional neural network is composed of multiple graph convolutional layers, and the graph convolutional neural network is applied to the crystal graph to update the node feature vectors;

[0061] The updated node's output feature vector is embedded with the local chemical environment of the corresponding atom.

[0062] Preferably, when defining the graph convolutional layer, atomic nodes with consistent local environments are made to have the same output feature vector.

[0063] Preferably, the method is defined according to a first formula, and the first formula includes:

[0064]

[0065] in, The feature vector of the (l+1) layer node, To and The feature vectors of adjacent nodes in layer l, where σ(...) is the activation function, and b (l) For bias, n(i) is the neighborhood set of node i, c ji Normalization function, e ji Let be the scalar weight of the edge and its expression be W (l) The weight matrix can be trained for nodes.

[0066] Understandably, in order to update the feature vectors of nodes and edges, a basic graph convolution function can be built using the GraphConv package built into the Graph Neural Network Library (DGL) as an example.

[0067] In some embodiments, S300 includes the step:

[0068] S310: Learn the in-situ energy of the corresponding input material from the output feature vector based on the first multilayer perceptron model;

[0069] S320: Learn the jump energy of the corresponding input material from the output feature vector based on the second multilayer perceptron model;

[0070] S330: Construct the parameterized Hamiltonian matrix elements of the corresponding material based on the in-situ energy and jump energy.

[0071] Preferably, the first multilayer perceptron model is also used to ensure that nodes with the same output feature vector eventually obtain the same in-situ energy;

[0072] Preferably, the second multilayer perceptron model is also used to ensure that node pairs with consistent output feature vectors and the same side length ultimately obtain the same jump energy.

[0073] Preferably, the second multilayer perceptron model is determined based on the second, third, or fourth formula, and

[0074] The second formula includes:

[0075] h(i,j)=MLP2[f(a i a j d ij )],

[0076] f(a i a j d ij )=f(a j a i d ji )=[g(a i )+g(a j )] / d ij 2 ,

[0077] The third formula includes:

[0078] h(i,j)=MLP2[f(a i a j d ij )],

[0079] f(a i a j d ij )=f(a j a i d ji )=g(a i *a j ) / d ij 2 ,

[0080] The fourth formula shown includes:

[0081] h(i,j)=MLP2[f(a i a j d ij )],

[0082] f(a i a j d ij )=f(a j a i d ji )=g(a i +a j ) / d ij 2 ,

[0083] Wherein, MLP2 is the second multilayer perceptron model, a i Let a be the output feature vector of node i. j Let h(i,j),d be the output feature vector of node j, and h(i,j) be the jump energy between the orbits of node i and node j. ijThe distance between the centers of atomic orbitals is given by the function f, which is used to process a. i and a j And it ensures the symmetry of the Hamiltonian jump energy, and the g function is a multilayer perceptron.

[0084] The parameterized Hamiltonian construction method based on atomic neighborhood graph representation provided by this invention has certain generalization potential. For a given material system, the trained network can be applied to cases where the input material has different sizes, which is equivalent to obtaining a learnable mapping function that can map the crystal diagram to the Hamiltonian matrix elements. The Hamiltonian constructed based on the atomic neighborhood graph representation network model obtained by the embodiments of this invention has a clearer physical meaning, and while maintaining the efficiency advantages of the parameterized LCAO method, it can also achieve the same level of accuracy as first-principles calculations.

[0085] like Figure 2 As shown, in a specific embodiment, when constructing a parameterized Hamiltonian based on the atomic neighborhood diagram representation of 13-atom graphene nanoribbons (13AGNR), a crystal diagram of the interactions between aggregated atomic neighborhoods is first constructed. Figure 2 In the 13AGNR unit cell, there are 30 atoms (carbon and hydrogen atoms), so the number of nodes in the crystal diagram is determined to be 30. Each node represents the corresponding atom in the unit cell and the mirror image of the corresponding atom in all other periodic unit cells.

[0086] It should be noted that the edges between nodes i and j should consider not only atoms i and j within the same unit cell, but also atoms located in different unit cells. Therefore, the resulting crystal diagram may have multiple edges between a pair of nodes. Different edges can be distinguished by their lengths, which can well reflect the periodicity of the crystal.

[0087] In this embodiment, crystal structure encoding is performed using nodes a and b, and the graph is initialized by assigning feature vectors to nodes and edges. The node feature vectors are element embedding vectors, and the edge feature vectors are Bessel function extensions, thus constructing a 13AGNR crystal graph.

[0088] like Figure 3 As shown, in a specific embodiment, according to Figure 3The 13AGNR crystal diagram shown is constructed by aggregating the neighborhood features of nodes in a graph convolutional layer and encoding them into the node feature vectors. A graph convolutional neural network (GCN) model, consisting of a series of graph convolutional layers, is applied to the 13AGNR crystal diagram. The GCN model is used to mix the feature vectors of the input graph nodes, encoding their local chemical environment into the final output feature vector. For the in-situ energy and hopping energy of the interaction between atomic orbitals, two MLP models are introduced to learn the LCAO Hamiltonian elements of the input crystal from the output node feature vectors, ultimately obtaining the parameterized Hamiltonian matrix elements of the material. Figure 2 and Figure 3 In the equation, H0 is the Hamiltonian matrix of the unit cell, and H1 is the Hamiltonian matrix constructed by the unit cell and its neighboring unit cells.

[0089] like Figure 4 As shown, in a specific embodiment, the method for constructing the parameterized Hamiltonian of the 13AGNR crystal material includes the following steps:

[0090] Step S1: Construct a crystal diagram based on the 13AGNR crystal structure information. This specifically includes reading the 13AGNR crystal structure information and determining the number of nodes and edges in the crystal diagram. The crystal structure information may include lattice information, types of atoms, coordinates, and the number of atoms in a unit cell.

[0091] Step S2: Initialize the feature vectors of nodes and edges using element embedding vectors and Bessel functions.

[0092] Step S3: Define graph convolutional layers, construct a GCN model using multiple graph convolutional layers, and aggregate and update the feature vectors of nodes using the GCN model. It can be understood that the output feature vectors of nodes processed by the GCN model can be considered as embedding the local chemical environment of atoms.

[0093] Specifically, taking the GraphConv package of graph convolutional layer functions built into the Graph Neural Network Library (DGL) as an example, we can construct a basic graph convolutional function, which is used to update the node feature vector, and it can be represented as:

[0094]

[0095] in, The feature vector of the (l+1) layer node, To and The feature vectors of adjacent nodes in layer l, where σ(...) is the activation function, and b (l) For bias, n(i) is the neighborhood set of node i, c ji Normalization function, e ji Let be the scalar weight of the edge, and its specific expression is: W (l)The weight matrix can be trained for nodes.

[0096] Understandably, after N graph convolutional layers, each node will update the information within its neighborhood N times and embed this information into its feature vector. Therefore, after multiple layers of graph convolution, the output feature vector of a node can be viewed as a representation of the corresponding atomic orbitals containing the local atomic environment.

[0097] Step S4: Introduce two multilayer perceptron models (MLP1 and MLP2), and train them respectively on-situ energies and hopping energies for the corresponding atomic orbital interactions. Specifically:

[0098] For the in-situ energy of the 13GNGR Hamiltonian, according to the characteristics of LCAO Hamiltonian parameterization for graphene materials, only carbon atom p is considered. z If the orbital is used as a basis function of the Hamiltonian, then the potential energy o(i) is expressed as: o(i) = MLP1(a i ), where MLP1 is an MLP model with scalar output, a i For the output feature vector of node i, MLP1 guarantees that p lies on the equivalent atom (i.e., an atom facing the same local environment). z The orbital potential energy is the same.

[0099] For the jump energy of the 13GNGR Hamiltonian, p is determined using the Slater-Koster relation. z The jump term between orbits, considering the planar structure of 13GNGR, the jump energy h(i,j) between orbits is expressed as h(i,j)=MLP2[f(a i a j d ij )], where d ij Let f be the inter-orbital spacing. Here, the function f must satisfy the condition that the jump energy of an electron from orbital i to orbital j is equal to the jump energy of an electron from orbital j to orbital i, that is: h(i,j)=h(j,i)=MLP2[f(a i a j d ij )]=MLP2[f(a j a i d ji )).

[0100] In the function f above, since a i and a j It is commutative, satisfying the prior knowledge of the transition energy between physical orbital pairs. For the function f, it can be constructed by the following three methods:

[0101] The first method: f(a) i a j dij )=f(a j a i d ji )=[g(a i )+g(a j )] / d ij 2 or

[0102] The second method: f(a) i a j d ij )=f(a j a i d ji )=g(a i *a j ) / d ij 2 or

[0103] The third method: f(a) i a j d ij )=f(a j a i d ji )=g(a i +a j ) / d ij 2 ,

[0104] In this context, the function g in function f is a multilayer perceptron (MLP) used to process the output node feature vector a. i and a j All three methods can guarantee that p is located on the equivalent atom z The jump energy between orbital pairs is the same. Different function forms yield Hamiltonian accuracies; the following steps select the f-function given by the first method to continue this embodiment.

[0105] Step S5: Construct the Hamiltonian matrix elements of 13AGNR. Specifically, the real-space Hamiltonian matrix H constructed by the LCAO method consists of the in-situ energy of the base orbits and the jump energies between different orbits, with the specific form: H = ∑ i o(i)+∑ i≠j h(i,j), where o(i) and h(i,j) represent the in-situ energy and jump energy of the Hamiltonian matrix value constructed by the neural network model, respectively.

[0106] This invention constructs a parameterized Hamiltonian for 13AGNR crystal material using a graph neural network to construct a crystal diagram representing the interactions between aggregated atomic neighborhoods and two MLP1 and MLP2 models. The in-situ energy and hopping energy of the interactions between atomic orbitals, obtained from model training, are used to construct the 13AGNR parameterized Hamiltonian matrix elements. This invention fully considers the problems of previous machine learning methods lacking clear physical meaning and having poor generality when fitting Hamiltonians. It innovatively constructs the parameterized Hamiltonian matrix based on the classic LCAO method, using a crystal diagram representation method representing aggregated atomic neighborhood features. The Hamiltonian matrix obtained based on the network model training has a clear physical meaning and, while maintaining the efficiency advantages of the parametric LCAO method, achieves the same level of accuracy as first-principles calculation methods.

[0107] It should be understood that any parts not described in detail in this specification belong to the prior art.

[0108] It should be understood that the above description of the simpler embodiments is more detailed and should not be construed as a limitation on the scope of protection of this invention. Those skilled in the art, under the guidance of this invention, can make substitutions or modifications without departing from the scope of protection of the claims of this invention, all of which fall within the scope of protection of this invention. The scope of protection of this invention should be determined by the appended claims.

[0109] Those skilled in the art will understand that all or some of the steps, systems, and apparatuses disclosed above, and their functional modules / units, can be implemented as software, firmware, hardware, or suitable combinations thereof. In hardware implementations, the division between functional modules / units mentioned above does not necessarily correspond to the division of physical components; for example, a physical component may have multiple functions, or a function or step may be performed collaboratively by several physical components. Some or all physical components may be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit (ASIC). Such software can be distributed on a computer-readable storage medium, which may include computer-readable storage media (or non-transitory media) and communication media (or transient media).

[0110] It should be noted that in this invention, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0111] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A method for constructing parameterized Hamiltonians based on atomic neighborhood graph representation, characterized in that, The method includes the following steps: A crystal diagram is constructed based on the crystal structure information of the material, wherein each node of the crystal diagram represents the corresponding atom in the unit cell and all its periodic mirror images; The feature vectors of the nodes are updated based on a graph neural network composed of multiple graph convolutional layers, so that the output feature vectors of the nodes contain representations of the local chemical environment of atoms. Based on the multilayer perceptron model, the parameterized Hamiltonian matrix elements of the corresponding material are learned from the output feature vector; The method of updating the feature vector of the node based on a graph neural network composed of multiple graph convolutional layers includes the following steps: Define a graph convolutional layer, which is used to aggregate the neighborhood features of nodes; A graph convolutional neural network is composed of multiple graph convolutional layers, and the graph convolutional neural network is applied to the crystal graph to update the node feature vectors; The updated node's output feature vector embeds the local chemical environment of the corresponding atom. The graph convolutional layer is defined according to a first formula, which includes: ， in, for The feature vector of the layer node, To and Adjacent nodes Layer node feature vectors For activation function, For bias, The neighborhood set of node i Normalization function, Let be the scalar weight of the edge and its expression be , The weight matrix can be trained for each node; The method of learning and obtaining the parameterized Hamiltonian matrix elements of the corresponding material from the output feature vector based on the multilayer perceptron model includes the following steps: Based on the first multilayer perceptron model, the in-situ energy of the corresponding input material is learned from the output feature vector; Based on the second multilayer perceptron model, the jump energy of the corresponding input material is learned from the output feature vector; Based on the in-situ energy and jump energy, construct the parameterized Hamiltonian matrix elements of the corresponding material; The in-situ energy includes: ,in For incumbent energy, It is an MLP model with scalar output. For nodes The output feature vector; The jump energy includes: ,in For jumping energy, This represents the center-to-center distance between atomic orbitals.

2. The method for constructing a parameterized Hamiltonian based on atomic neighborhood graph representation as described in claim 1, characterized in that, The process of constructing a crystal map based on the crystal structure information of the material includes the following steps: Based on the crystal structure information of the material, the atoms and chemical bonds in a unit cell are respectively used as nodes and edges of the crystal diagram, and the number of nodes and edges in the crystal diagram is determined. The feature vectors of the nodes and edges are initialized. The initial feature vector of the node is an embedding vector representing the element type, and the feature vector of the edge is an atomic center spacing function.

3. The method for constructing a parameterized Hamiltonian based on atomic neighborhood graph representation as described in claim 2, characterized in that, The step of using atoms and chemical bonds within a unit cell as nodes and edges of the crystal diagram includes the following steps: When determining the edges of a crystal diagram, a cutoff distance for atomic orbital interactions is set. If the distance between two atoms is less than the cutoff distance, then the two atoms are considered to have an edge.

4. The method for constructing a parameterized Hamiltonian based on atomic neighborhood graph representation as described in claim 1, characterized in that, When defining the graph convolutional layer, atomic nodes with consistent local environments are made to have the same output feature vector.

5. The method for constructing a parameterized Hamiltonian based on atomic neighborhood graph representation as described in claim 1, characterized in that, The first multilayer perceptron model is also used to ensure that nodes with the same output feature vector eventually obtain the same in-situ energy. The second multilayer perceptron model is also used to ensure that node pairs with consistent output feature vectors and the same side length ultimately obtain the same jump energy.

6. The method for constructing a parameterized Hamiltonian based on atomic neighborhood graph representation as described in claim 5, characterized in that, The second multilayer perceptron model is determined based on the second, third, or fourth formula, and The second formula include: ， ， The third formula includes: ， ， The fourth formula shown includes: ， ， in, This is the second multilayer perceptron model. Let i be the output feature vector of node i. Let i be the output feature vector of node j, and let j be the jump energy between the orbits of node i and node j. The distance between the centers of atomic orbitals, the function For processing and And ensure the symmetry of the Hamiltonian jump energy, The function is a multilayer perceptron.

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