Machine learning based optimization method for quantum dot material synthesis

Abstract

The application relates to the technical field of deep learning, and discloses a quantum dot material synthesis optimization method based on machine learning, which comprises the following steps: constructing a graph structure input layer comprising reactant molecular nodes and precursor chemical bond edges; adopting a double-branch graph attention network, wherein a first branch extracts ligand binding energy graph features of a nucleation stage, and a second branch extracts monomer concentration time sequence change graph features of a growth stage; introducing a nucleation and growth quality conservation constraint term in a loss function layer; and inputting feature vectors output by the double-branch into a full connection layer after concatenation, so as to output an optimal synthesis parameter combination. The application internalizes a physical kinetic mechanism in a network architecture, realizes feature decoupling of the nucleation and growth stages, overcomes the defect that an existing model cannot represent kinetic differences, so that the accuracy of parameter optimization is low, and reduces the occurrence rate of side reactions caused by non-optimal synthesis parameters.

Description

Technical Field

[0001] This invention relates to the field of deep learning technology and discloses an optimization method for the synthesis of quantum dot materials based on machine learning. Background Technology

[0002] In the field of quantum dot material synthesis optimization, end-to-end mapping models based on deep learning are commonly used to find the optimal synthesis parameters. In the specific implementation of conventional technical solutions, operators directly concatenate initial parameters such as precursor concentration, reaction temperature, and reaction time into a high-dimensional vector, which is then input into a multi-layer fully connected neural network. The hidden layers of the network extract parameter features through weight matrix multiplication and nonlinear activation functions, while the output layer directly regresses to predict the target spectral parameters or yield. In this calculation process, the entire quantum dot synthesis reaction is treated as a static black box; the model input is the initial reaction conditions, and the output is the final reaction result, completely ignoring the intermediate stages of reactant state changes and physicochemical evolution.

[0003] This conventional approach, which treats the synthesis process as a static black box, suffers from a core technical problem: existing network models cannot characterize the kinetic differences between the nucleation and growth stages in quantum dot synthesis, causing the models to get stuck in local optima when faced with high-dimensional parameter coupling. Quantum dot synthesis actually consists of two stages with distinct physical mechanisms: nucleation and growth. The nucleation stage is dominated by ligand binding energy, while the growth stage is dominated by temporal changes in monomer concentration. Existing fully connected networks extract these characteristics by mixing them within the same network layer, thus severing the phased kinetic evolution and making it impossible for the model's output synthesis parameters to accurately reflect the actual chemical reaction process. Summary of the Invention

[0004] The purpose of this invention is to provide a machine learning-based optimization method for the synthesis of quantum dot materials, which can effectively solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: The optimization method for quantum dot material synthesis based on machine learning includes: obtaining precursor and ligand information of the quantum dot synthesis system, and constructing a graph structure input layer containing reactant molecular nodes and precursor chemical bond edges; The quantum dot synthesis process is divided into a nucleation stage and a growth stage, and a dual-branch graph attention network is used to process the graph structure input layer. The first branch of the dual-branch graph attention network extracts ligand binding energy map features during the nucleation stage, and the second branch of the dual-branch graph attention network extracts monomer concentration temporal variation map features during the growth stage. A nucleation-growth quality conservation constraint term is introduced into the loss function layer to calculate the loss value between the predicted features and the true features output by the dual-branch graph attention network. The ligand binding energy map feature vector output from the first branch is cascaded with the monomer concentration time-series change map feature vector output from the second branch. The cascaded feature vector is then input into the fully connected layer, and the output includes the optimal combination of synthesis parameters, including precursor injection temperature, heating rate, and reaction time.

[0006] Preferably, the construction of the graph structure input layer containing reactant molecule nodes and precursor chemical bond edges includes: extracting the atom types and chemical valence states from the precursor and ligand information as initial node features, mapping the atom types to a first feature vector, mapping the chemical valence states to a second feature vector, and concatenating the first feature vector and the second feature vector to generate the node feature matrix of the reactant molecule nodes; The covalent bond type and bond length in the precursor and ligand information are extracted as initial edge features. The covalent bond type is mapped to a third feature vector, and the bond length is mapped to a fourth feature vector. The third feature vector and the fourth feature vector are concatenated to generate the edge feature matrix of the precursor chemical bond edges.

[0007] Preferably, the extraction of ligand binding energy graph features in the nucleation stage by the first branch of the dual-branch graph attention network includes: inputting the node feature matrix in the graph structure input layer into the first graph attention layer of the first branch, and calculating the first attention coefficient between adjacent reactant molecule nodes in the nucleation stage; The first intermediate node feature matrix is ​​obtained by weighted summation of the feature vectors of adjacent reactant molecule nodes based on the first attention coefficient. Perform a dot product operation between the first intermediate node feature matrix and the edge feature matrix in the graph structure input layer, input the dot product result into the first activation function of the first branch, and output the ligand binding energy graph features of the nucleation stage.

[0008] Preferably, the second branch of the dual-branch graph attention network extracts the temporal variation graph features of monomer concentration during the growth stage by: expanding the node feature matrix in the graph structure input layer into a node temporal feature sequence according to a preset time step; The node temporal feature sequence is input into the second graph attention layer of the second branch to calculate the second attention coefficient between nodes across time steps in the growth stage; Based on the second attention coefficient, the node features within the same time step in the node temporal feature sequence are weighted and aggregated. The aggregated feature sequence is then input into the second activation function of the second branch, and the monomer concentration temporal change map feature of the growth stage is output.

[0009] Preferably, the introduction of the nucleation-growth mass conservation constraint term in the loss function layer includes: obtaining the first node feature vector of the reactant molecule node in the first branch at the end of the nucleation stage, and obtaining the second node feature vector of the reactant molecule node in the second branch at the end of the growth stage; Calculate the L2 norm difference between the feature vectors of the first node and the feature vectors of the second node; Multiply the L2 norm difference by a preset penalty coefficient to generate the nucleation-growth quality conservation constraint term. The nucleation-growth quality conservation constraint term is superimposed onto the basis expression of the mean squared error loss function to generate the total loss function of the loss function layer.

[0010] Preferably, the step of inputting the cascaded feature vector into the fully connected layer and outputting the optimal combination of synthesis parameters including precursor injection temperature, heating rate and reaction time includes: inputting the cascaded feature vector into the first linear mapping layer of the fully connected layer, mapping the dimension of the cascaded feature vector to a preset hidden dimension, and generating a hidden layer feature vector; The hidden layer feature vector is sequentially input into the second and third linear mapping layers of the fully connected layer, and the dimensions of the hidden layer feature vector are mapped to the dimensions of the corresponding precursor injection temperature, the corresponding heating rate, and the corresponding reaction time, respectively, to generate output vectors of the corresponding dimensions.

[0011] Preferably, after generating the node feature matrix of the reactant molecule nodes, the method further includes: constructing a learnable parameter matrix with the same number of reactant molecule nodes; The node feature matrix is ​​multiplied bitwise with the learnable parameter matrix to generate an updated node feature matrix; The updated node feature matrix is ​​normalized for each row of feature vectors, and the normalized node feature matrix is ​​used as the final node feature matrix of the graph structure input layer. The normalization process involves calculating the L2 norm of each row of feature vectors and dividing each row of feature vectors by the corresponding L2 norm.

[0012] Preferably, the calculation of the first attention coefficient between adjacent reactant molecule nodes in the nucleation stage includes: inputting the node feature matrix into a preset number of attention heads of the first graph attention layer, and each attention head independently calculating the sub-attention coefficient between adjacent reactant molecule nodes; The sub-attention coefficients output by the preset number of attention heads are concatenated according to the channel dimension to generate a concatenated attention coefficient matrix; Perform a Softmax operation on each row vector in the concatenated attention coefficient matrix, and use the matrix after the Softmax operation as the first attention coefficient.

[0013] Preferably, inputting the node temporal feature sequence into the second graph attention layer of the second branch includes: for each time step in the node temporal feature sequence, extracting the node feature matrix of the current time step and the node feature matrix of the previous adjacent time step; Calculate the difference matrix between the node feature matrix of the current time step and the node feature matrix of the previous adjacent time step; The difference matrix is ​​concatenated with the node feature matrix of the current time step and then input into the second graph attention layer as the input feature of the second graph attention layer at the current time step.

[0014] Preferably, before generating the total loss function of the loss function layer, the method further includes: calculating the Laplacian matrix of the node feature matrix composed of the first node feature vectors; Calculate the product between the Laplacian matrix and the transpose of the node feature matrix formed by the first node eigenvectors; Perform a trace operation on the product and use the result of the trace operation as a graph topology regularization constraint term; The graph topology regularization constraint term is superimposed on the total loss function, wherein the Laplacian matrix is ​​generated based on the adjacency relationship in the edge feature matrix of the precursor chemical bond edges.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention constructs a graph-structured input layer containing reactant molecule nodes and precursor chemical bond edges. It employs a dual-branch graph attention network to extract ligand binding energy graph features during the nucleation stage and monomer concentration temporal variation graph features during the growth stage, respectively. This departs from existing techniques that treat the synthesis process as a static black box. This design, which internalizes the physical dynamics mechanism into the network architecture, utilizes attention coefficients to weightedly sum and fuse edge features of adjacent molecule nodes, and uses attention coefficients across time steps to weightedly aggregate the temporal feature sequences of nodes. This achieves decoupling of the physical mechanisms of the nucleation and growth stages at the feature extraction level. The concatenated feature vectors from the two branches are then input into a fully connected layer to output synthesis parameters. This ensures that the parameter combination output by the model conforms to the temporal physical evolution of quantum dot synthesis, overcoming the shortcomings of existing techniques that cannot characterize kinetic differences, leading to low accuracy in parameter optimization.

[0016] 2. This invention introduces nucleation and growth mass conservation constraints into the loss function. By calculating the L2 difference between the feature vectors of nodes in two stages and superimposing it into the mean squared error loss function, the deviation of network features from the physical mass conservation law is limited from a mathematical constraint level. A learnable parameter matrix is ​​introduced to perform positional multiplication and normalization on the initial node feature matrix, increasing the flexibility of node feature representation. Multiple attention heads are concatenated and normalized exponentially to generate attention coefficients. Combined with the calculation of the difference matrix between adjacent time steps as input features, this enhances the feature extraction capability of the graph neural network in both temporal and spatial dimensions. Furthermore, trace operations using the Laplacian matrix generate graph topology regularization constraints that are superimposed on the total loss function, maintaining the smoothness of the molecular topology and suppressing side reactions caused by suboptimal synthesis parameters. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the overall process of optimizing the synthesis of quantum dot materials based on machine learning, as described in this invention. Figure 2 This is a flowchart illustrating the construction process of the graph structure input layer of the present invention. Figure 3 This is a flowchart of the ligand binding energy map feature extraction process for the first branch (nucleation stage) of this invention; Figure 4 This is a flowchart of the feature extraction process for the time-series variation of monomer concentration in the second branch (growth stage) of this invention. Figure 5 A flowchart is introduced for the calculation of the loss function and constraint terms in this invention; Figure 6 This is a flowchart illustrating the optimal combination of synthesis parameters for the fully connected layer output in this invention. Detailed Implementation

[0018] 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, not all, of the embodiments of the present invention. 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.

[0019] Please refer to Figure 1This embodiment provides a machine learning-based optimization method for quantum dot material synthesis. It acquires precursor and ligand information for the quantum dot synthesis system and constructs a graph structure input layer containing reactant molecule nodes and precursor chemical bond edges. The precursor and ligand information for the quantum dot synthesis system includes the chemical structural formulas of the precursor and ligand molecules, the molar concentration of the precursor, the molar ratio of the ligands, the type of reaction solvent, and the elemental composition of the target quantum dot. For the acquired precursor and ligand information, each independent atom is extracted as a reactant molecule node, and the covalent chemical bonds between atoms are extracted as precursor chemical bond edges. An undirected graph structure is constructed, where the set of nodes corresponds to all atoms in the reactant molecules, and the set of edges corresponds to all covalent chemical bonds between atoms. The graph structure input layer is generated based on this undirected graph structure.

[0020] In this embodiment, the quantum dot synthesis process is divided into a nucleation stage and a growth stage, and a dual-branch graph attention network is used to process the graph structure input layer. The nucleation stage of the quantum dot synthesis process is the entire process after the precursor is injected into the reaction system, the precursor decomposes to form monomers, and the monomers collide and aggregate to form stable crystal nuclei. The time interval of the nucleation stage is from the moment of precursor injection to the moment when the crystal nucleus concentration reaches its peak. The growth stage of quantum dot synthesis involves the continuous diffusion and bonding of monomers to the surface of the crystal nucleus after nucleus formation, resulting in the continuous growth of the nucleus size to the target size. The growth stage spans from the moment the nucleus concentration reaches its peak until the reaction terminates. The dual-branch graph attention network comprises two parallel feature extraction branches. These branches share the input data from the graph structure input layer and independently extract features for the physicochemical mechanisms of the nucleation and growth stages, respectively. The network structures of the two branches are independent, and their weight parameters are not shared during training.

[0021] In this embodiment, the first branch of the dual-branch graph attention network extracts the ligand binding energy graph features of the nucleation stage. The first branch is the nucleation stage feature extraction branch; its input is the node feature matrix and edge feature matrix of the graph structure input layer, and its output is the ligand binding energy graph features of the nucleation stage. The ligand binding energy is the binding free energy between the ligand molecule and the atoms on the surface of the quantum dot crystal nucleus. The magnitude of the ligand binding energy directly determines the adsorption strength and adsorption configuration of the ligand on the crystal nucleus surface, thereby regulating the crystal nucleus size distribution, crystallinity, and dispersion during the nucleation stage. The first branch calculates the attention coefficient between adjacent reactant molecule nodes through the graph attention layer, and weights and aggregates the features of adjacent nodes based on the attention coefficient. After fusing the edge features of chemical bonds, it generates the ligand binding energy graph features characterizing the binding ability of the ligand and the crystal nucleus.

[0022] Specifically, the first attention layer of the first branch uses the following calculation method when calculating the first attention coefficient between adjacent reactant molecule nodes during the nucleation stage:

[0023] in, For the first The node obtained by the attention head calculation With nodes Sub-attention coefficients between The number of the attention head. , The preset total number of attention points; For the first Each attention head corresponds to a learnable weight matrix, and the dimension of the weight matrix is... , The dimension of the input node feature vector. The feature mapping dimension for each attention head; For nodes The input feature vector, For nodes The input feature vector, nodes For nodes The adjacent nodes, i.e., nodes With nodes There are covalent chemical bonds connecting them; This is a scaling factor used to avoid the vanishing gradient problem of the Softmax function caused by an excessively large inner product result. The Softmax function is used to normalize the sub-attention coefficients of all adjacent nodes corresponding to the same node, so that the sum of all sub-attention coefficients corresponding to the same node is 1.

[0024] Based on the calculated first attention coefficient, the feature vectors of adjacent reactant molecule nodes are weighted and summed to obtain the first intermediate node feature matrix. The calculation method is as follows:

[0025] in, This is the first intermediate node characteristic matrix, where the number of rows represents the total number of reactant molecule nodes, and the number of columns is... ; To The feature vectors output by each attention head are concatenated along the channel dimension. For nodes The set consisting of all adjacent nodes; For nodes The weighted eigenvectors of all neighboring nodes are summed.

[0026] The obtained first intermediate node feature matrix is ​​multiplied by the edge feature matrix in the graph structure input layer. The result of the dot product is input into the first activation function of the first branch, and the ligand binding energy graph features of the nucleation stage are output. The calculation method is as follows:

[0027] in, This represents the ligand binding energy characteristics during the nucleation stage; The first activation function is LeakyReLU. The Hadamard product operation is the multiplication of corresponding elements of two matrices. The edge feature matrix is ​​the input layer of the graph structure, and the dimension of the edge feature matrix matches the dimension of the first intermediate node feature matrix.

[0028] In this embodiment, the second branch of the dual-branch graph attention network extracts the temporal variation features of monomer concentration during the growth stage. The second branch is the growth stage feature extraction branch; its input is the node feature matrix of the graph structure input layer, and its output is the temporal variation features of monomer concentration during the growth stage. The monomer concentration during the growth stage is the molar concentration of free monomers in the reaction system that can be used for quantum dot growth. The temporal variation of monomer concentration directly determines the growth rate, size uniformity, and optical properties of the quantum dots. Drastic fluctuations in monomer concentration can lead to secondary nucleation or Ostwald ripening, disrupting the monodispersity of the quantum dots. The second branch expands the static node feature matrix into a temporal feature sequence according to a preset time step. It calculates the attention coefficients between nodes across time steps using the graph attention layer, and weights and aggregates the node features within the same time step based on these attention coefficients to generate a temporal variation graph feature characterizing the change in monomer concentration over time.

[0029] Specifically, when processing the node feature matrix of the graph structure input layer, the second branch first expands the node feature matrix into a node temporal feature sequence according to a preset time step, and the calculation method is as follows:

[0030] in, For the first The node time series feature matrix corresponding to each time step; This is the initial node feature matrix in the input layer of the graph structure; For the first The time step encoding vector corresponding to each time step is generated using a sinusoidal positional encoding method, and its dimension matches the number of columns in the initial node feature matrix; The total number of time steps is a preset value, and the ratio of the total number of time steps to the total duration of the growth phase and the preset number of time steps is equal.

[0031] The node temporal feature sequence is input into the second graph attention layer of the second branch, and the second attention coefficient between nodes across time steps in the growth stage is calculated as follows:

[0032] in, For time step nodes With time step nodes The second attention coefficient between; This is a learnable attention weight vector; For time step The corresponding feature mapping weight matrix, For time step The corresponding feature mapping weight matrix; For time step node eigenvectors, For time step node eigenvectors; This is a concatenation operation of feature vectors; It is the set of all reactant molecular nodes; It is the set of all time steps; is the natural exponential function; LeakyReLU is the nonlinear activation function used in the second graph attention layer.

[0033] Based on the calculated second attention coefficient, the node features within the same time step in the node temporal feature sequence are weighted and aggregated. The aggregated feature sequence is then input into the second activation function of the second branch, outputting the monomer concentration temporal change map features during the growth stage. The calculation method is as follows:

[0034] in, The graph shows the temporal variation of monomer concentration during the growth phase. The second activation function is the Tanh activation function. For the same time step internal nodes With nodes The second attention coefficient between; This involves summing the weighted aggregate features over all time steps. This is a weighted summation operation performed on the feature vectors of all nodes within the same time step.

[0035] In this embodiment, a nucleation-growth mass conservation constraint term is introduced into the loss function layer to calculate the loss value between the predicted features and the true features output by the bi-branch graph attention network. The input to the loss function layer consists of the predicted features output by the two branches of the bi-branch graph attention network and the true features obtained from the quantum dot synthesis experiment. The true features include the measured ligand binding energy data during the nucleation stage and the measured time-series change data of monomer concentration during the growth stage. The nucleation-growth mass conservation constraint term is constructed based on the law of conservation of mass in chemical reactions. The total mass of precursors and ligands in the reaction system remains constant throughout the nucleation and growth stages. The sum of the reactant mass consumed during the nucleation stage and the reactant mass consumed during the growth stage is equal to the initial total mass of precursors and ligands in the reaction system minus the remaining total mass of reactants at the end of the reaction. Through the nucleation-growth mass conservation constraint term, the node features output by the two branches of the bi-branch graph attention network are constrained, preventing abnormal fluctuations in features that violate the law of conservation of mass.

[0036] When introducing the nucleation-growth mass conservation constraint term in the loss function layer, the first node feature vector of the reactant molecule node in the first branch at the end of the nucleation stage is first obtained, and the second node feature vector of the reactant molecule node in the second branch at the end of the growth stage is obtained. The L2 norm difference between the first node feature vector and the second node feature vector is calculated. The L2 norm difference is multiplied by a preset penalty coefficient to generate the nucleation-growth mass conservation constraint term. The calculation method is as follows:

[0037] in, This is a constraint term related to the conservation of nucleation-growth mass. The preset penalty coefficient ranges from 0.01 to 10. This is a matrix composed of the eigenvectors of the first node at the end of the nucleation stage; The matrix formed by the eigenvectors of the second node at the end of the growth phase; This is the Frobenius norm operation for a matrix, which is the square root of the sum of the squares of all elements in the matrix.

[0038] The generated nucleation-growth quality conservation constraint term is superimposed onto the basis expression of the mean squared error loss function to generate the total loss function of the loss function layer, calculated as follows:

[0039] in, This is the total loss function; The basis expression for the mean squared error loss function is calculated as the mean of the squares of the differences between the predicted features and the true features. The predicted features include the predicted ligand binding energy output from the first branch and the predicted monomer concentration time-series change output from the second branch. The true features include the experimentally measured ligand binding energy and the monomer concentration time-series change.

[0040] In this embodiment, the ligand binding energy map feature vector output from the first branch and the monomer concentration time-series change map feature vector output from the second branch are cascaded. The cascaded feature vector is input into the fully connected layer, and the output includes the optimal combination of synthesis parameters including precursor injection temperature, heating rate, and reaction time. The feature cascading operation is performed along the channel dimension of the feature vector, concatenating the one-dimensional feature vectors output from the two branches into a single high-dimensional feature vector in channel order. The cascaded feature vector simultaneously contains ligand binding energy characteristics during the nucleation stage and monomer concentration temporal variation characteristics during the growth stage. The fully connected layer contains multiple sequentially connected linear mapping layers. These linear mapping layers use learnable weight matrices and bias terms to map the high-dimensional cascaded feature vectors to the target parameter dimension step by step. In the final optimal combination of synthesis parameters, the precursor injection temperature is the reaction system temperature when the precursor solution is injected into the reaction system, the heating rate is the rate of temperature change from the nucleation temperature to the growth temperature after the nucleation stage, and the reaction time is the total duration from the start to the end of the reaction.

[0041] The concatenated feature vectors are input into the first linear mapping layer of the fully connected layer, which maps the dimensions of the concatenated feature vectors to a preset hidden dimension, generating hidden layer feature vectors. The calculation method is as follows:

[0042] in, These are the hidden layer feature vectors; This is the learnable weight matrix of the first linear mapping layer; For the learnable bias term of the first linear mapping layer; The cascaded feature vector is generated by concatenating the ligand binding energy map feature vector output from the first branch and the monomer concentration time-series change map feature vector output from the second branch in the channel dimension.

[0043] The generated hidden layer feature vectors are sequentially input into the second and third linear mapping layers of the fully connected layer. The dimensions of the hidden layer feature vectors are mapped to the dimensions corresponding to the precursor injection temperature, the heating rate, and the reaction time, respectively, generating output vectors of the corresponding dimensions. The calculation method is as follows:

[0044]

[0045]

[0046] in, The output vector corresponding to the injection temperature of the precursor; This is the output vector corresponding to the heating rate; This is the output vector corresponding to the reaction time; , , These are the learnable weight matrices for the second, third, and fourth linear mapping layers, respectively. , , These are the learnable bias terms for the second, third, and fourth linear mapping layers, respectively.

[0047] Table 1. Basic Information on Precursors and Ligands for Quantum Dot Synthesis Systems ; This table serves as the basic data source for constructing the graph structure input layer. Each entry in the table corresponds to a set of precursor and ligand combinations in the quantum dot synthesis system. The chemical structural formulas of the precursors and ligands are the source of extraction for the chemical bond edges of the reactant molecular nodes and precursors. The molar ratio information provides a reference for the weight allocation of node features, and the target quantum dot type is the target guide for optimizing the synthesis parameters.

[0048] In this embodiment, a complete end-to-end processing flow for optimizing quantum dot material synthesis based on machine learning is implemented. By constructing a graph structure input layer containing reactant molecule nodes and precursor chemical bond edges, accurate characterization of the reactant molecule structure in the quantum dot synthesis system is achieved. Through parallel processing of a bi-branch graph attention network, ligand binding energy graph features in the nucleation stage and monomer concentration temporal variation graph features in the growth stage are extracted respectively, achieving decoupling of the physical mechanisms of the nucleation and growth stages at the feature extraction level. By introducing a nucleation-growth mass conservation constraint term in the loss function layer, the risk of network features deviating from the mass conservation law of chemical reactions is mathematically limited. Through linear mapping of feature cascades and fully connected layers, accurate regression from multi-dimensional reaction features to target synthesis parameters is achieved, and the output synthesis parameter combination can match the temporal physical evolution process of quantum dot synthesis.

[0049] In a preferred embodiment, reference Figure 2When constructing the graph structure input layer containing reactant molecule nodes and precursor chemical bond edges, the atom types and chemical valence states in the precursor and ligand information are extracted as initial node features. Atom types are mapped to a first feature vector, and chemical valence states are mapped to a second feature vector. The first and second feature vectors are concatenated to generate the node feature matrix of reactant molecule nodes. Atom type extraction is based on the chemical structure formulas of precursors and ligands, identifying the element type of each atom. Based on inherent properties such as atomic number, electronic structure, electronegativity, and atomic radius in the periodic table, a pre-trained atom embedding model maps the atom type to a fixed-dimensional first feature vector. This pre-trained atom embedding model, trained on a massive molecular structure dataset, can map atoms of different elements to a distinguishable feature space. Chemical valence state extraction is based on the bonding situation of atoms in the molecule, identifying the oxidation state, number of bonding electrons, and number of lone pairs of electrons. The chemical valence state is converted into a one-hot encoded vector, which is then mapped to a fixed-dimensional second feature vector through a linear mapping layer. The dimension of the second feature vector matches the dimension of the first feature vector.

[0050] Specifically, the node feature matrix of reactant molecule nodes is generated as follows:

[0051] in, The initial node feature matrix has rows equal to the total number of reactant molecule nodes and columns equal to the sum of the dimensions of the first and second eigenvectors. The matrix is ​​formed by the first eigenvectors generated by mapping the atom types, with the number of rows being the total number of reactant molecule nodes and the number of columns being the dimension of the first eigenvector; The matrix formed by the second eigenvectors generated by the chemical valence mapping has rows representing the total number of reactant molecule nodes and columns representing the dimension of the second eigenvectors. This is an operation that concatenates two matrices along the feature dimension.

[0052] The covalent bond type and bond length are extracted from the precursor and ligand information as initial edge features. The covalent bond type is mapped to a third feature vector, and the bond length is mapped to a fourth feature vector. The third and fourth feature vectors are concatenated to generate the edge feature matrix of precursor chemical bonds. Covalent bond type extraction is based on the chemical bond information in the precursor and ligand chemical structures, identifying different covalent bond types such as single, double, triple, and coordinate bonds. The covalent bond type is converted into a one-hot encoded vector, which is then mapped to a fixed-dimensional third feature vector through a linear mapping layer. Bond length extraction is based on the spatial configuration of the molecular structure, obtaining the spatial distance between two bonded atoms. After standardization, the bond length values ​​are mapped to a fixed-dimensional fourth feature vector through a linear mapping layer. The dimension of the fourth feature vector matches the dimension of the third feature vector. The edge feature matrix is ​​generated as follows:

[0053] in, The initial edge feature matrix has rows equal to the total number of precursor chemical bond edges and columns equal to the sum of the dimensions of the third and fourth eigenvectors. The matrix formed by the third eigenvectors generated for the covalent bond type mapping has the number of rows equal to the total number of precursor chemical bond edges and the number of columns equal to the dimension of the third eigenvectors. The matrix formed by the fourth eigenvector generated by the bond length mapping has the number of rows equal to the total number of precursor chemical bond edges and the number of columns equal to the dimension of the fourth eigenvector.

[0054] After generating the node feature matrix of reactant molecule nodes, a learnable parameter matrix with the same number of reactant molecule nodes is constructed. The node feature matrix and the learnable parameter matrix are then multiplied element-wise to generate an updated node feature matrix. Each row of the feature vectors in the updated node feature matrix is ​​normalized. This normalized node feature matrix is ​​used as the final node feature matrix for the graph structure input layer. The learnable parameter matrix has the same dimension as the initial node feature matrix, initially set to a matrix of all 1s. During model training, the elements of the learnable parameter matrix are iteratively updated using the backpropagation algorithm to adaptively adjust the weights of different node features. Normalization involves calculating the L2 norm of each row of feature vectors and dividing each row by its corresponding L2 norm, ensuring that the L2 norm of each row of feature vectors is 1, thus guaranteeing the stability of the node feature distribution. The specific calculation method is as follows:

[0055] in, This is the final node feature matrix of the graph structure input layer; The learnable parameter matrix, dimensions, and initial node feature matrix. Completely identical; This refers to the Hadamard product operation; To calculate the L2 norm for each row of eigenvectors of the matrix, divide each row of eigenvectors by its own L2 norm.

[0056] Table 2. Mapping Dimension Correspondence Table of Node Features and Edge Features ; This table clarifies the mapping dimension configuration and data flow path of various features in the graph structure input layer. After configuration, the total dimension of node features and the total dimension of edge features can be completely matched with the input layer dimension of the bi-branch graph attention network, ensuring that the feature operation of the graph attention layer can be executed normally. The dimension of the learnable parameter matrix is ​​consistent with the dimension of the initial node feature matrix, realizing the element-wise weight adjustment of each node feature.

[0057] The pre-trained atom embedding model was trained using contrastive learning on the QM9 molecular dataset. During training, atoms with similar chemical properties were mapped to nearby positions in the feature space, while atoms with different chemical properties were mapped to more distant positions, ensuring the distinguishability of atom type features. One-hot encoding of chemical valence states, targeting common valence states from -4 to +7, generated 12-dimensional one-hot encoded vectors. These vectors were then mapped to a 32-dimensional second feature vector through a linear mapping layer, enhancing feature expressiveness. One-hot encoding of covalent bond types, targeting five common chemical bond types (single, double, triple, coordinate, and hydrogen bonds), generated 5-dimensional one-hot encoded vectors. These vectors were then mapped to a 32-dimensional third feature vector through a linear mapping layer. Bond length standardization employed Z-score standardization, converting bond length values ​​into standardized values ​​with a mean of 0 and a variance of 1. These standardized values ​​were then mapped to a 16-dimensional fourth feature vector through a linear mapping layer.

[0058] In this embodiment, the construction logic and internal processing flow of the graph structure input layer are refined. By splicing multi-dimensional features of atom type and chemical valence state, a comprehensive characterization of reactant molecular nodes is achieved. By splicing multi-dimensional features of covalent bond type and bond length, a precise characterization of precursor chemical bond edges is achieved. By introducing a learnable parameter matrix that matches the dimensions of the node feature matrix, the weights of different node features are adaptively adjusted, improving the flexibility of node feature expression. By performing row-by-row normalization on the updated node feature matrix, the stability of the node feature distribution is ensured, avoiding the model training instability problem caused by feature value fluctuations, and providing a high-quality input foundation for feature extraction in the subsequent bi-branch graph attention network.

[0059] In a preferred embodiment, reference Figure 3When the first branch of the dual-branch graph attention network extracts the ligand binding energy map features of the nucleation stage, it inputs the node feature matrix from the graph structure input layer into the first graph attention layer of the first branch. It calculates the first attention coefficients between adjacent reactant molecule nodes in the nucleation stage, and then performs a weighted summation of the feature vectors of adjacent reactant molecule nodes based on these first attention coefficients to obtain the first intermediate node feature matrix. This first intermediate node feature matrix is ​​then multiplied by the edge feature matrix from the graph structure input layer. The result of this dot product is input into the first activation function of the first branch, outputting the ligand binding energy map features of the nucleation stage. The first branch contains a first graph attention layer, a feature fusion layer, and a first activation function layer connected sequentially. The input to the first graph attention layer is the final node feature matrix from the graph structure input layer, and the output is a weighted aggregated node feature matrix. The feature fusion layer fuses the weighted aggregated node feature matrix with the edge feature matrix, and the first activation function layer performs a nonlinear transformation on the fused features to output the final ligand binding energy map features.

[0060] When calculating the first attention coefficient between adjacent reactant molecular nodes during the nucleation stage, the node feature matrix is ​​input into a predetermined number of attention heads in the first graph attention layer. Each attention head independently calculates the sub-attention coefficients between adjacent reactant molecular nodes. The sub-attention coefficients output by the predetermined number of attention heads are concatenated according to the channel dimension to generate a concatenated attention coefficient matrix. A Softmax operation is performed on each row vector in the concatenated attention coefficient matrix, and the matrix after the Softmax operation is used as the first attention coefficient. The predetermined total number of attention heads is 8, the feature mapping dimension of each attention head is 16, and the total output dimension after concatenating the 8 attention heads is 128. The weight matrices of each attention head are independent of each other and do not interfere with each other during training. This allows for the capture of different dimensions of intermolecular interaction features, including the influence of different types of intermolecular forces such as van der Waals forces, hydrogen bonds, and electrostatic interactions on ligand binding energy. After performing a Softmax operation on each row vector in the concatenated attention coefficient matrix, the sum of the attention coefficients of all adjacent nodes corresponding to the same node is 1, realizing the normalization of the weighted aggregation weights of adjacent node features.

[0061] The first attention layer employs a masking mechanism, calculating attention coefficients only for adjacent nodes connected by covalent chemical bonds. For nodes without chemical bonds, the attention coefficient is set to negative infinity, becoming 0 after a softmax operation. This ensures that only features from adjacent nodes participate in weighted aggregation, consistent with the topological connectivity of molecular structures. The first activation function uses the LeakyReLU activation function, with a slope of 0.2 on the negative half-axis, avoiding the neuron death problem caused by ReLU activation and improving the stability of model training. A global average pooling layer is set at the end of the first branch, performing global average pooling on the node-dimensional features, converting the two-dimensional node feature matrix into a one-dimensional feature vector for subsequent feature concatenation operations.

[0062] refer to Figure 4 When the second branch of the dual-branch graph attention network extracts the temporal variation features of monomer concentration during the growth stage, it expands the node feature matrix in the graph structure input layer into a node temporal feature sequence according to a preset time step. This node temporal feature sequence is then input into the second graph attention layer of the second branch. The second attention coefficients between nodes across time steps during the growth stage are calculated. Based on these second attention coefficients, the node features within the same time step in the node temporal feature sequence are weighted and aggregated. The aggregated feature sequence is then input into the second activation function of the second branch, outputting the temporal variation features of monomer concentration during the growth stage. The second branch contains a temporal expansion layer, a differential feature concatenation layer, a second graph attention layer, a second activation function layer, and a temporal global pooling layer, connected in sequence. The temporal expansion layer converts the static node feature matrix into a temporal feature sequence. The differential feature concatenation layer generates and concatenates the differential features between adjacent time steps. The second graph attention layer calculates the attention coefficients across time steps and performs weighted feature aggregation. The second activation function layer performs a nonlinear transformation on the aggregated features. The temporal global pooling layer performs global pooling on the temporal features, generating a one-dimensional feature vector.

[0063] When inputting the node temporal feature sequence into the second graph attention layer of the second branch, for each time step in the node temporal feature sequence, the node feature matrix of the current time step and the node feature matrix of the previous adjacent time step are extracted. The difference matrix between the node feature matrix of the current time step and the node feature matrix of the previous adjacent time step is calculated. The difference matrix is ​​concatenated with the node feature matrix of the current time step and then input into the second graph attention layer as the input feature of the second graph attention layer at the current time step. The preset time step length is 10 seconds, and the total number of time steps is adjusted according to the total duration of the growth stage. When the total duration of the growth stage is 30 minutes, the total number of time steps is 180. For the first time step, the node feature matrix of the previous adjacent time step is the node feature matrix at the end of the nucleation stage to ensure the continuity of the temporal features. The difference matrix is ​​calculated by subtracting the node feature matrix of the previous adjacent time step from the node feature matrix of the current time step. The difference matrix can characterize the change range of node features between adjacent time steps, corresponding to the rate of change of monomer concentration in the reaction system. After concatenating the difference matrix with the node feature matrix of the current time step, the attention layer of the second graph can simultaneously capture the monomer concentration state and concentration change trend of the current time step, thereby improving the ability to extract the temporal evolution features of the growth stage.

[0064] The second attention layer employs a masked attention mechanism, calculating attention coefficients only for nodes at the current time step and the previous adjacent time step. This avoids interference from features at future time steps, aligning with the temporal causal relationship of the reaction process. The second activation function uses the Tanh activation function, mapping feature values ​​to the range of -1 to 1, ensuring the stability of the temporal feature distribution. The temporal global pooling layer at the end of the second branch performs global average pooling on the temporal features, converting the three-dimensional feature tensor containing the temporal dimension into a one-dimensional feature vector. This vector maintains the same dimension as the feature vector output from the first branch, and is used for subsequent feature concatenation operations.

[0065] Table 3. Layer structure and parameter configuration of the bi-branch graph attention network. ; ; This table clarifies the input and output dimensions, activation function types, and core functions of each layer in the dual-branch graph attention network. The one-dimensional feature vectors output by the first and second branches both have a dimension of 128, ensuring that the feature vectors of the two branches can be cascaded without bias in the channel dimension. The input and output dimensions of each layer are matched to ensure that there will be no dimension mismatch problem during the flow of feature data within the network.

[0066] In this embodiment, the internal layer structure and computational logic of the dual-branch graph attention network are refined. Through a multi-attention head mechanism, parallel capture of intermolecular interaction features at different dimensions during the nucleation stage is achieved, improving the richness and accuracy of ligand binding energy-related features. By calculating the difference matrix of adjacent time steps and splicing features, the second graph attention layer can simultaneously capture the monomer concentration state and rate of change during the growth stage, enhancing the ability to characterize temporal evolution features. Through cross-time step attention coefficient calculation and weighted aggregation, the precise extraction of the temporal change law of monomer concentration during the growth stage is achieved, further strengthening the decoupling of the physical mechanisms of the nucleation and growth stages, and ensuring that the features extracted by the two branches can correspond to the core physicochemical processes of the two stages respectively.

[0067] In a preferred embodiment, reference Figure 5 When introducing the nucleation-growth quality conservation constraint term into the loss function layer, the first node feature vector of the reactant molecule node in the first branch at the end of the nucleation stage is obtained, and the second node feature vector of the reactant molecule node in the second branch at the end of the growth stage is obtained. The L2 difference between the first and second node feature vectors is calculated, and the L2 difference is multiplied by a preset penalty coefficient to generate the nucleation-growth quality conservation constraint term. This constraint term is then superimposed into the basis expression of the mean squared error loss function to generate the total loss function of the loss function layer. The first node feature vector at the end of the nucleation stage is the node feature vector output by the first graph attention layer of the first branch corresponding to the last time step of the nucleation stage, and the second node feature vector at the end of the growth stage is the node feature vector output by the second graph attention layer of the second branch corresponding to the last time step of the growth stage. The dimensions of the two node feature vectors are exactly the same, ensuring that the calculation of the L2 difference can be performed normally. The value of the preset penalty coefficient is dynamically adjusted according to the convergence state of the model during training. In the early stage of training, the penalty coefficient is set to a smaller value to ensure that the model can quickly fit the training data. In the later stage of training, the penalty coefficient is set to a larger value to strengthen the role of mass conservation constraint and avoid model overfitting.

[0068] Before generating the total loss function of the loss function layer, the Laplacian matrix of the node feature matrix formed by the first node's feature vectors is calculated. The product of the Laplacian matrix and the transpose of the node feature matrix formed by the first node's feature vectors is then calculated. The trace operation is performed on the product, and the result is used as a graph topology regularization constraint term. This graph topology regularization constraint term is then added to the total loss function. The Laplacian matrix is ​​generated based on the adjacency relationships in the edge feature matrix of the precursor chemical bond edges. The elements of the adjacency matrix are assigned values ​​based on whether there is a covalent chemical bond between two nodes; a value of 1 is assigned if a covalent chemical bond exists, and a value of 0 is assigned if no covalent chemical bond exists. The degree matrix is ​​a diagonal matrix, with diagonal elements representing the degree of the corresponding node, i.e., the total number of chemical bonds connected to that node. The Laplacian matrix is ​​the degree matrix minus the adjacency matrix. The graph topology regularization constraint term is calculated as follows:

[0069] in, For graph topology regularization constraints; The trace operation is performed on a matrix, which calculates the sum of all elements on the diagonal of the matrix. This is the transpose of the feature matrix of the first node at the end of the nucleation stage; The Laplacian matrix is ​​a graph structure whose dimensions match the number of rows in the feature matrix of the first node.

[0070] The graph topology regularization constraint term is multiplied by a preset regularization coefficient and then added to the total loss function. The final total loss function is calculated as follows:

[0071] in, This is the preset regularization coefficient, with a value ranging from 0.001 to 1; the meanings of the other parameters remain consistent with the previous formula definitions.

[0072] refer to Figure 6The cascaded feature vector is input into the fully connected layer. When the output contains the optimal combination of synthesis parameters including precursor injection temperature, heating rate, and reaction time, the cascaded feature vector is input into the first linear mapping layer of the fully connected layer. The dimension of the cascaded feature vector is mapped to a preset hidden dimension to generate a hidden layer feature vector. The hidden layer feature vector is then sequentially input into the second and third linear mapping layers of the fully connected layer. The dimensions of the hidden layer feature vector are mapped to the corresponding dimensions of precursor injection temperature, heating rate, and reaction time, respectively, to generate output vectors of the corresponding dimensions. The fully connected layer contains four sequentially connected linear mapping layers. The first linear mapping layer is the hidden layer with a preset hidden dimension of 512, mapping the 256-dimensional cascaded feature vector to a 512-dimensional hidden layer feature vector. The second, third, and fourth linear mapping layers are the output layers, mapping the 512-dimensional hidden layer feature vector to a 1-dimensional output value of precursor injection temperature, a 1-dimensional output value of heating rate, and a 1-dimensional output value of reaction time, respectively. No additional activation functions are set between linear mapping layers. A Dropout layer is set only after the first linear mapping layer, with a Dropout rate of 0.2, to avoid overfitting and improve the model's generalization ability.

[0073] Table 4. Comparison of convergence performance of loss function under different combinations of constraints. ; This table compares the convergence performance and generalization ability of models under different combinations of constraints, using the same training and test datasets. Both the training set fitting error and the test set generalization error are mean squared errors. The number of convergence iterations is the number of iterations required for the model's loss value to decrease to a stable range. The data in the table shows that after introducing the nucleation-growth mass conservation constraint and the graph topology regularization constraint, the number of convergence iterations decreases, the training set fitting error slightly increases, but the test set generalization error decreases. This demonstrates that the two constraints can improve the model's generalization ability, prevent overfitting, and accelerate the model's convergence speed.

[0074] The model training process employs the Adam optimizer to optimize the learnable parameters, with a learning rate of 0.001, weight decay of 0.0001, batch size of 32, and 2000 training epochs. The generalization error on the test set is validated every 10 epochs. Training is terminated early when the generalization error on the test set fails to decrease for 50 consecutive epochs, and the optimal model parameters are saved. After model training, the precursor and ligand information of the quantum dot synthesis system to be optimized are input into the model. The model automatically constructs a graph structure input layer, extracts features through a two-branch graph attention network, and finally outputs the optimal combination of synthesis parameters. Operators then conduct quantum dot synthesis experiments based on the output combination of synthesis parameters, obtaining quantum dot materials that meet the target performance requirements.

[0075] In this embodiment, the constraint mechanism of the loss function and the linear mapping logic of the fully connected layer are refined. By introducing the nucleation-growth mass conservation constraint term, the mathematical aspect ensures that the features learned by the model conform to the basic law of mass conservation in chemical reactions, avoiding abnormal fluctuations in features that violate physicochemical laws. By introducing the graph topology regularization constraint term, the smoothness of the molecular topology is maintained, preventing the model from learning abnormal features that do not conform to chemical bond connections, and suppressing side reactions caused by suboptimal synthesis parameters. Through the multi-layer linear mapping of the fully connected layer, accurate regression from the high-dimensional fused feature vector to the target synthesis parameters is achieved, ensuring the rationality and usability of the optimal combination of synthesis parameters of precursor injection temperature, heating rate, and reaction time, which can be directly used to guide the synthesis experiments of quantum dot materials.

Claims

1. A machine learning-based optimization method for quantum dot material synthesis, characterized in that, include: Obtain precursor and ligand information for quantum dot synthesis systems, and construct a graph structure input layer containing reactant molecule nodes and precursor chemical bond edges; The quantum dot synthesis process is divided into a nucleation stage and a growth stage, and a dual-branch graph attention network is used to process the graph structure input layer. The first branch of the dual-branch graph attention network extracts ligand binding energy map features during the nucleation stage, and the second branch of the dual-branch graph attention network extracts monomer concentration temporal variation map features during the growth stage. A nucleation-growth quality conservation constraint term is introduced into the loss function layer to calculate the loss value between the predicted features and the true features output by the dual-branch graph attention network. The ligand binding energy map feature vector output from the first branch is cascaded with the monomer concentration time-series change map feature vector output from the second branch. The cascaded feature vector is then input into the fully connected layer, and the output includes the optimal combination of synthesis parameters, including precursor injection temperature, heating rate, and reaction time.

2. The machine learning-based quantum dot material synthesis optimization method according to claim 1, characterized in that, The construction of the graph structure input layer containing reactant molecule nodes and precursor chemical bond edges includes: extracting the atom types and chemical valence states from the precursor and ligand information as initial node features, mapping the atom types to a first feature vector, mapping the chemical valence states to a second feature vector, and concatenating the first feature vector and the second feature vector to generate the node feature matrix of the reactant molecule nodes; The covalent bond type and bond length in the precursor and ligand information are extracted as initial edge features. The covalent bond type is mapped to a third feature vector, and the bond length is mapped to a fourth feature vector. The third feature vector and the fourth feature vector are concatenated to generate the edge feature matrix of the precursor chemical bond edges.

3. The machine learning-based quantum dot material synthesis optimization method according to claim 1, characterized in that, The first branch of the bi-branch graph attention network extracts ligand binding energy graph features of the nucleation stage by: inputting the node feature matrix in the graph structure input layer into the first graph attention layer of the first branch, and calculating the first attention coefficient between adjacent reactant molecule nodes in the nucleation stage. The first intermediate node feature matrix is ​​obtained by weighted summation of the feature vectors of adjacent reactant molecule nodes based on the first attention coefficient. Perform a dot product operation between the first intermediate node feature matrix and the edge feature matrix in the graph structure input layer, input the dot product result into the first activation function of the first branch, and output the ligand binding energy graph features of the nucleation stage.

4. The machine learning-based quantum dot material synthesis optimization method according to claim 1, characterized in that, The second branch of the bi-branch graph attention network extracts the temporal variation graph features of monomer concentration during the growth stage by: expanding the node feature matrix in the graph structure input layer into a node temporal feature sequence according to a preset time step; The node temporal feature sequence is input into the second graph attention layer of the second branch to calculate the second attention coefficient between nodes across time steps in the growth stage; Based on the second attention coefficient, the node features within the same time step in the node temporal feature sequence are weighted and aggregated. The aggregated feature sequence is then input into the second activation function of the second branch, and the monomer concentration temporal change map feature of the growth stage is output.

5. The machine learning-based quantum dot material synthesis optimization method according to claim 1, characterized in that, The introduction of the nucleation-growth mass conservation constraint term in the loss function layer includes: obtaining the first node feature vector of the reactant molecule node in the first branch at the end of the nucleation stage, and obtaining the second node feature vector of the reactant molecule node in the second branch at the end of the growth stage; Calculate the L2 norm difference between the feature vectors of the first node and the feature vectors of the second node; Multiply the L2 norm difference by a preset penalty coefficient to generate the nucleation-growth quality conservation constraint term. The nucleation-growth quality conservation constraint term is superimposed onto the basis expression of the mean squared error loss function to generate the total loss function of the loss function layer.

6. The machine learning-based quantum dot material synthesis optimization method according to claim 1, characterized in that, The step of inputting the cascaded feature vector into the fully connected layer and outputting the optimal combination of synthesis parameters including precursor injection temperature, heating rate and reaction time includes: inputting the cascaded feature vector into the first linear mapping layer of the fully connected layer, mapping the dimension of the cascaded feature vector to a preset hidden dimension, and generating a hidden layer feature vector. The hidden layer feature vector is sequentially input into the second and third linear mapping layers of the fully connected layer, and the dimensions of the hidden layer feature vector are mapped to the dimensions of the corresponding precursor injection temperature, the corresponding heating rate, and the corresponding reaction time, respectively, to generate output vectors of the corresponding dimensions.

7. The machine learning-based quantum dot material synthesis optimization method according to claim 2, characterized in that, After generating the node feature matrix of the reactant molecule nodes, the method further includes: constructing a learnable parameter matrix with the same number of reactant molecule nodes; The node feature matrix is ​​multiplied bitwise with the learnable parameter matrix to generate an updated node feature matrix; The updated node feature matrix is ​​normalized for each row of feature vectors, and the normalized node feature matrix is ​​used as the final node feature matrix of the graph structure input layer. The normalization process involves calculating the L2 norm of each row of feature vectors and dividing each row of feature vectors by the corresponding L2 norm.

8. The machine learning-based quantum dot material synthesis optimization method according to claim 3, characterized in that, The calculation of the first attention coefficient between adjacent reactant molecule nodes in the nucleation stage includes: inputting the node feature matrix into a preset number of attention heads of the first graph attention layer, and each attention head independently calculating the sub-attention coefficient between adjacent reactant molecule nodes; The sub-attention coefficients output by the preset number of attention heads are concatenated according to the channel dimension to generate a concatenated attention coefficient matrix; Perform a Softmax operation on each row vector in the concatenated attention coefficient matrix, and use the matrix after the Softmax operation as the first attention coefficient.

9. The machine learning-based quantum dot material synthesis optimization method according to claim 4, characterized in that, The step of inputting the node temporal feature sequence into the second graph attention layer of the second branch includes: for each time step in the node temporal feature sequence, extracting the node feature matrix of the current time step and the node feature matrix of the previous adjacent time step; Calculate the difference matrix between the node feature matrix of the current time step and the node feature matrix of the previous adjacent time step; The difference matrix is ​​concatenated with the node feature matrix of the current time step and then input into the second graph attention layer as the input feature of the second graph attention layer at the current time step.

10. The machine learning-based quantum dot material synthesis optimization method according to claim 5, characterized in that, Before generating the total loss function of the loss function layer, the method further includes: calculating the Laplacian matrix of the node feature matrix composed of the first node feature vectors; Calculate the product between the Laplacian matrix and the transpose of the node feature matrix formed by the first node eigenvectors; Perform a trace operation on the product and use the result of the trace operation as a graph topology regularization constraint term; The graph topology regularization constraint term is superimposed on the total loss function, wherein the Laplacian matrix is ​​generated based on the adjacency relationship in the edge feature matrix of the precursor chemical bond edges.

Images