Molecular property prediction method based on quantum entropy graph structure coding

Abstract

The invention discloses a molecular property prediction method based on quantum entropy graph structure coding, and belongs to the field of graph representation learning. Firstly, quantum entropy is applied to a node sub-graph and a total graph, and the problem of capturing node neighborhood structure and global structure information is solved. Secondly, quantum entropy is used for a complementary set of a node subgraph, and the problem of capturing the global position of a positioning node is solved; and then synthesizing the entropy of the three parts and generating a quantum entropy structure code of the node by using a Hall WO quantity for measuring a weighted quantum entropy difference. For the quantum entropy structure coding of the edge, the difference between the quantum entropy of the image after the edge is deleted and the molecular image is measured by using the Hall WO quantity so as to capture the information of three aspects of the neighborhood structure, the global structure and the global position of the edge. In consideration of calculation overhead, an approximation algorithm insensitive to the size of the graph is designed based on a degree sequence, calculation of all eigenvalues of a large-scale graph Laplacian matrix is avoided, and application of the large-scale graph is expanded.

Description

Technical Field

[0001] The present invention relates to the field of graph representation learning, and particularly to a method for predicting molecular properties based on quantum entropy graph structure encoding. Background Art

[0002] Graph neural networks (GNNs) have achieved powerful modeling capabilities for molecular graph structure data through message passing mechanisms. They can effectively capture chemical bonding relationships and local functional group characteristics, and are widely used in molecular property prediction tasks. However, their expressive power (graph structure discrimination ability) has been proven to be limited by the 1-WL graph isomorphism test algorithm. Therefore, the limited expressive power causes them to identify different chemical molecular structures as the same chemical molecule when predicting, resulting in poor performance of graph neural networks in molecular property prediction applications. To break through this limitation, Morris et al. [Morris C, Ritzert M, Fey M, et al. Weisfeiler and leman go neural: Higher-order graph neural

[0003] networks[C] / / Proceedings of the AAAI conference on artificial intelligence. 2019, 33(01): 4602-4609] proposed a graph neural network model based on higher-order dependencies, which enhances the expressive power by directly constructing a graph neural network equivalent to the 3-WL algorithm. However, although this method improves the expressive power, its computational complexity is relatively high, which limits its wide use in practical applications.

[0004] Structure encoding is a method to enhance the expressive power of graph neural networks by explicitly injecting graph structure attribute information. Its core idea is to use the inherent topological features of the graph (such as node centrality, subgraph statistics, spectral features, etc.) as additional inputs to make up for the structural information that cannot be captured during the message passing process of graph neural networks. However, although existing methods can improve the expressive power of graph neural networks, they cannot effectively capture three types of information: node subgraphs, global positions of nodes, and global structures of graphs, resulting in a bottleneck in their expressive power that does not exceed the 3-WL algorithm. To overcome the above problems and meet the high requirements for predicting chemical molecular properties in applications such as drug discovery, the present invention proposes a method for predicting molecular properties based on quantum entropy graph structure encoding, which is deployed into the message passing framework of graph neural networks through a plug-and-play method for graph-level classification tasks on chemical molecular graphs.

[0005] The present invention introduces quantum information theory, performs quantum representation on graphs, and uses quantum entropy to capture information on three aspects: the node neighborhood structure, the global position of nodes, and the global structure of the graph, so as to enhance the graph structure discrimination ability. The present invention uses the Holevo quantity in quantum communication theory to integrate the three parts of entropy to obtain the quantum entropy structure encoding of nodes. To avoid high computational overhead on large-scale graphs, the present invention proposes an approximate algorithm for this method. The present invention designs a pluggable method to add the quantum entropy structure encoding into a graph neural network, effectively enhancing the graph neural network's ability to distinguish chemical molecular structure differences, and at the same time effectively improving its performance in graph representation learning, providing a highly reliable tool for the molecular property prediction scenario in drug discovery applications. Summary of the Invention

[0006] Aiming at the bottleneck problem of the graph structure discrimination ability of graph neural networks, the present invention mainly solves the problem that existing methods have limitations in capturing three types of information: node subgraphs, the global positions of nodes, and the global structure of graphs. A molecular property prediction method based on quantum entropy graph structure encoding is proposed. Quantum representation is performed on graphs, and quantum entropy is used to capture the above three types of information to enhance the graph structure discrimination ability. At the same time, the Holevo quantity in quantum communication theory is used to integrate the three parts of entropy to obtain the quantum entropy structure encoding of nodes, and it is added to the graph neural network in a pluggable manner to enhance the graph structure discrimination ability. An approximate algorithm is proposed to expand the algorithm feasibility for large molecular graphs, and accurate and effective structure encoding is generated efficiently.

[0007] The technical solution of the present invention:

[0008] A molecular property prediction method based on quantum entropy graph structure encoding includes the following steps:

[0009] Step 100, calculate the quantum entropy structure encoding of nodes based on quantum information theory;

[0010] Step 101, for each node v, divide the molecular graph G=(V, E) into its corresponding molecular subgraph G v =(V v , E v ), the complement of the molecular subgraph where and the molecule G, V represents the set of all nodes in graph G, E represents the set of all edges in graph G, V v represents the set of all nodes in the molecular subgraph G v , E v represents the set of all edges in G v , represents the set of all nodes in the complement of the molecular subgraph , represents The set of all edges, |·| represents the number of elements in the set. In the molecular graph scenario, it refers to the number of atoms or chemical bonds; in a chemical molecular graph, nodes represent atoms, and a molecular subgraph represents a local structure composed of an atom as the center, the atoms directly connected to it, and the chemical bonds between them.

[0011] Step 102, calculate G v , and the von Neumann graph entropy S(G v ) of the molecular graph G, S(G), the calculation method is as follows:

[0012]

[0013] where, is the neighbor set of node v, corresponding to the atoms directly connected to the central atom in a chemical molecule; |N(v)| represents the number of neighbor nodes of node v, and in a chemical molecule, this value reflects the valence of the atom; n represents the number of nodes (i.e., atoms) in the molecular graph, reflecting the size of the molecule. is the spectrum of the graph, related to the vibration mode or energy state of the molecular structure; vol(G) is the volume of the graph, that is, the sum of the degrees of all atoms in the graph, reflecting the total number of chemical bonds in the molecule; vol(G v ) represents the volume of G v . represents 's volume.

[0014] Step 103, apply the Holevo quantity to the molecular graph and calculate the quantum entropy structure encoding Q v of node v, the calculation method is as follows:

[0015]

[0016] Step 200, calculate the quantum entropy structure encoding of the edges based on quantum information theory;

[0017] Step 201, for edge e = (u, v), by splitting the graph into a single edge and the graph after deleting the edge where, the von Neumann graph entropy of a single edge is defined as 0, u and v are elements in the node set, which are the two end nodes of edge e, V represents the set of all nodes in the graph, represents the set of all edges in the graph after deleting edge e; in a molecular graph, an edge represents a chemical bond, such as a single bond, double bond or triple bond, and the graph after deleting the edge simulates the impact of chemical bond breakage on the molecular structure, thereby quantifying the importance of this chemical bond through the change in quantum entropy;

[0018] Step 202, calculate the graph after deleting the edge The corresponding von Neumann graph entropy The calculation method is as follows:

[0019]

[0020] Wherein, represents the volume of;

[0021] Step 203, calculate the quantum entropy structure encoding of edge e to quantify the importance of chemical bonds to molecular functions. The calculation method is as follows:

[0022]

[0023] Step 300, to improve the calculation efficiency, when the number of nodes in the molecular graph reaches the threshold that affects the calculation efficiency (this threshold can be flexibly set according to factors such as actual computing resources and calculation time requirements), skip the specific execution of Steps 100 - 103 and Steps 200 - 203, execute this step to calculate the approximate von Neumann graph entropy, and then calculate the approximate quantum entropy structure encoding of nodes and the approximate quantum entropy structure encoding of edges; when the scale of the molecular graph is less than or equal to the set threshold, skip Steps 301 - 302.

[0024] Step 301, estimate the von Neumann graph entropy using the degree sequence to obtain the approximate von Neumann graph entropy. The calculation method is as follows:

[0025]

[0026] Wherein, d i represents the degree of the i-th node, which is the number of chemical bonds connected to the corresponding atom in the molecular graph;

[0027] Step 302, through the calculation methods provided in Step 102, Step 103, Step 202, and Step 203, combined with Step 301, calculate the approximate quantum entropy structure encoding of nodes and edges. Among them, the calculation method of the approximate quantum entropy structure encoding of nodes is as follows:

[0028]

[0029] Wherein, S(G v )′, respectively represent the approximate von Neumann graph entropy of G v , . The calculation formula is as follows:

[0030]

[0031] The calculation method of the approximate quantum entropy structure encoding of edges is as follows:

[0032]

[0033] Among them, represents the graph after deleting edges The corresponding approximate von Neumann graph entropy, the calculation formula is as follows:

[0034]

[0035] Step 400, combine the calculated node quantum entropy structure encoding, edge quantum entropy structure encoding with the graph neural network to obtain the final node embedding representation. Select the calculation method of quantum entropy structure encoding according to the molecular graph node scale, that is: when the number of molecular graph nodes is less than or equal to the set threshold, use the node quantum entropy structure encoding and edge quantum entropy structure encoding to calculate the graph and add it to the graph neural network; when the number of molecular graph nodes is greater than the set threshold, use the node approximate quantum entropy structure encoding and edge approximate quantum entropy structure encoding to calculate the graph and add it to the graph neural network. After multi-layer message passing, aggregate the final features of all nodes, generate the graph-level representation of the molecular graph and input it into the prediction network to predict its chemical properties;

[0036] Step 401, based on the comparison of the Holevo quantity, determine the quantization of the importance of the edge quantum entropy structure encoding or edge approximate quantum entropy structure encoding for the message channel. If the number of molecular graph nodes is less than or equal to the set threshold, based on the edge quantum entropy structure encoding obtained in step 203, multiply the message aggregated from neighbor nodes, and the calculation method of the node embedding representation at the k-th layer is as follows:

[0037]

[0038] Among them, AGG(·) represents the aggregation function; is the neighbor set of node i; represents the node embedding representation of neighbor node u at the k-th layer;

[0039] If the number of molecular graph nodes is greater than the set threshold, based on the edge approximate quantum entropy structure encoding obtained in step 302, multiply the message aggregated from neighbor nodes, and the calculation method of the node embedding representation at the k-th layer is as follows:

[0040]

[0041] Step 402, at the k + 1-th layer, the final embedding representation of the node is generated by the following method: Select the node quantum entropy structure encoding or node approximate quantum entropy structure encoding according to the molecular graph node scale, multiply it by the node embedding representation of the previous k-th layer, and aggregate and combine it with the node embedding representation of the k-th layer obtained in step 401. The specific implementation is as follows:

[0042] When the number of nodes in the molecular graph is less than or equal to the set threshold, the node quantum entropy structure encoding obtained based on step 103 is used, and the calculation method is as follows:

[0043]

[0044] where COMBINE(·) represents the combination function; represents the node embedding representation of node v at the k-th layer;

[0045] When the number of nodes in the molecular graph is greater than the set threshold, the node approximate quantum entropy structure encoding obtained based on step 302 is used, and the calculation method is as follows:

[0046]

[0047] Step 403, after completing the iterative update of all graph neural network layers, the total number of layers of the graph neural network is K, and the graph-level representation h of the molecular graph is generated through the READOUT readout function G and input into the prediction network to output the molecular property y;

[0048]

[0049] y = PredictNet(h G );

[0050] where READOUT(·) represents the summation readout function, that is, the sum of all node feature representations; V represents the set of all nodes in graph G; represents the final embedding representation of node v at the K-th layer; PredictNet(·) represents the prediction network, such as a fully connected neural network, etc.

[0051] It should be noted that using multiplication operations to incorporate the node quantum entropy structure encoding and edge quantum entropy structure encoding into the message passing and message aggregation processes does not introduce additional model parameters, nor does it increase the length of the transmitted messages or the width of the message passing layers.

[0052] Advantages of the present invention: The present invention provides a method for predicting molecular properties based on quantum entropy graph structure encoding, which uses quantum entropy to capture information on the node neighborhood structure, global structure, and global position of nodes. First, quantum entropy is applied to the node subgraph and the entire graph respectively to solve the problem of capturing node neighborhood structure and global structure information. Second, quantum entropy is used for the complement of the node subgraph to solve the problem of capturing the global position of the node. Then, the Holevo quantity that measures the weighted quantum entropy difference is used to synthesize the entropy of the three parts and generate the quantum entropy structure encoding of the node. For the quantum entropy structure encoding of edges, the present invention uses the Holevo quantity to measure the difference between the quantum entropy of the graph after deleting the edge and the molecular graph to capture information on the edge neighborhood structure, global structure, and global position. Considering the computational overhead, the present invention designs an approximation algorithm that is insensitive to the graph size based on the degree sequence to avoid calculating all the eigenvalues of the Laplacian matrix of large-scale graphs, so as to extend the application to large-scale graphs. Since the Holevo quantity represents the information-carrying capacity of the quantum channel, finally, the quantum entropy structure encodings of edges and nodes are respectively added to the processes of message passing and message aggregation, effectively improving the expressive power of the graph neural network and enhancing the performance of the molecular graph classification task. Description of the Drawings

[0053] Figure 1 is the implementation flowchart of a method for predicting molecular properties based on quantum entropy graph structure encoding provided by the present invention;

[0054] Figure 2 is the implementation flowchart of step 100;

[0055] Figure 3 is the implementation flowchart of step 200;

[0056] Figure 4 is the implementation flowchart of step 300;

[0057] Figure 5 is the implementation flowchart of step 400. Detailed Embodiment

[0058] To make the technical problems solved by the present invention, the technical solutions adopted, and the achieved technical effects clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, it should be noted that, for the sake of description, only parts related to the present invention are shown in the drawings rather than all the content.

[0059] In a preferred embodiment of the present invention, the selection threshold of the molecular graph scale for selecting the quantum entropy structure encoding calculation method is set to 2000 nodes. For molecular graphs with the number of nodes less than or equal to the set threshold, exact calculation can be adopted (Steps 100-103 and Steps 200-203); for large-scale molecular graphs with the number of nodes greater than the set threshold, the approximate algorithm in Step 300 can be adopted to improve the calculation efficiency.

[0060] Figure 1 is a flowchart of the implementation of a molecular property prediction method based on quantum entropy graph structure encoding provided by the present invention. As Figure 1 shown, a molecular property prediction method based on quantum entropy graph structure encoding provided by an embodiment of the present invention includes:

[0061] Step 100, calculating the quantum entropy structure encoding of nodes based on quantum information theory;

[0062] In this step, taking the MUTAG dataset [Debnath A K, Lopez de Compadre R L, Debnath G, et al. Structure-activity relationship of mutagenic aromatic and heteroaromatic nitro compounds. correlation with molecular orbital energies and hydrophobicity [J]. Journal of medicinal chemistry, 1991, 34(2): 786-797.] as an example, a molecular graph and a set of node partitions (in the present invention, the one-hop subgraph of the node and its complement) are required as the input for calculating the quantum entropy structure encoding of nodes by the proposed quantum entropy-based graph structure encoding method.

[0063] As Figure 2 shown, Step 100 includes the following Steps 101, 102, and 103:

[0064] Step 101, for each molecular graph G in the MUTAG dataset, divide the molecular graph G=(V, E) into its corresponding molecular subgraph G v =(V v , E v ) centered on the atomic node v, the complement of the molecular subgraph where and the molecule G, V represents the set of all nodes in graph G, E represents the set of all chemical bond edges in graph G, and V v represents the set of all nodes in the molecular subgraph G v in, Ev Denote \(G\) v as the set of all chemical bond edges in Denote the complement of the molecular subgraph as the set of all atomic nodes in Denote the set of all chemical bond edges. \(|\cdot|\) represents the number of elements in the set, that is, the number of atoms or chemical bonds in the molecular graph. In a chemical molecular graph, nodes represent atoms, and a node subgraph represents a local structure composed of an atom as the center, the atoms directly connected to it, and the chemical bonds between them. For example, taking the nitro nitrogen atom of o-nitroaniline as an example, the node subgraph contains this nitrogen atom, the 2 oxygen atoms and 1 carbon atom directly connected to it, and the chemical bonds between them.

[0065] In this step, taking the nitro nitrogen atom of o-nitroaniline as an example, the node subgraph represents a local structure centered on the nitro nitrogen atom, including the 2 oxygen atoms and 1 carbon atom directly connected to it and their chemical bonds; the complement of the node subgraph contains all the atoms and the chemical bonds between atoms removed from the original graph \(G\) v This division can capture the local chemical environment of the nitro functional group (-NO2), while the complement characterizes the structure of the rest of the molecule. The nitro functional group plays a key role in mutagenicity prediction. Therefore, through subgraph division, the model's ability to represent specific functional groups can be enhanced.

[0066] Step 102, calculate the von Neumann graph entropy \(S(G)\) v , and \(S(\overline{G})\) v ), corresponding to the molecular graph \(G\) respectively. The calculation method of the von Neumann graph entropy of graph \(G\) is as follows:

[0067]

[0068] where is the neighbor set of node \(v\), corresponding to the atoms directly connected to the central atom in a chemical molecule; \(|N(v)|\) represents the number of neighbor nodes of node \(v\), which reflects the valence of the atom in a chemical molecule; \(n\) represents the number of nodes (i.e., atoms) in the molecular graph, reflecting the size of the molecule; \(\lambda\) i is the spectrum of the graph, related to the vibration mode or energy state of the molecular structure; \(vol(G)\) is the volume of the graph, that is, the sum of the degrees of all atoms in the graph, reflecting the total number of chemical bonds in the molecule; \(vol(G\) v ) represents the volume of \(G\) v ; represents the volume of

[0069] In this step, taking the nitro nitrogen atom of the o-nitroaniline molecular graph (containing 12 nodes and 13 edges) as an example, S(G v ), The values of S(G) are 1.103, 0.892, and 2.214 respectively.

[0070] Step 103: Apply the Hallworth quantity to the molecular graph and calculate the quantum entropy structure encoding value Q v of the node v, and the calculation method is as follows:

[0071]

[0072] In this step, based on the calculation results of Step 102, the Q v value corresponding to the nitro nitrogen atom node of o-nitroaniline is finally calculated to be 0.227.

[0073] Step 200: Calculate the quantum entropy structure encoding of the edge based on the quantum information theory. As Figure 3 shown, Step 200 includes the following steps 201 to 203:

[0074] Step 201: For the edge e=(u, v), by splitting the graph into a single edge (the von Neumann graph entropy of a single edge is defined as 0) and the graph after deleting the edge where u and v are elements in the node set, which are the two end nodes of the edge e, V represents the set of all nodes in the graph, represents the set of all edges in the graph after deleting the edge e. In the molecular graph, the edge represents a chemical bond, such as a single bond, double bond, or triple bond. The graph after deleting the edge simulates the impact of chemical bond cleavage on the molecular structure, thereby quantifying the importance of the chemical bond through the change in quantum entropy;

[0075] In this step, taking the N-O bond (u is the nitrogen atom and v is the oxygen atom) in the o-nitroaniline molecular graph (containing 12 nodes and 13 edges) as an example, the graph after deleting the chemical bond edge of this chemical bond includes 12 nodes and 12 edges remaining in the molecular graph after removing the edge, simulating the impact of chemical bond cleavage in the nitro group on the molecular structure.

[0076] Step 202: Calculate the von Neumann graph entropy corresponding to the graph after deleting the edge The calculation method is as follows:

[0077]

[0078] In this step, based on Step 201, the obtained value is 2.024.

[0079] Step 203: Calculate the quantum entropy structure encoding of edge e to quantify the importance of chemical bonds for molecular functions. The calculation method is as follows:

[0080]

[0081] In this step, based on Steps 201 and 202, the calculated value of P corresponding to the N-O bond of the o-nitroaniline molecule is 0.082. The entropy after deleting the edge u,v and the difference from the entropy of the original graph S(G) = 2.214 (P = 0.082) quantify the contribution of this chemical bond to the overall stability of the molecule. In mutagenicity prediction, the N-O bond of the nitro group is a key active site, and its high value of P u,v indicates that the model can effectively identify the importance of such key chemical bonds. u,v

[0082] Step 300: Based on the approximate von Neumann graph entropy, calculate the approximate quantum entropy structure encoding of nodes and edges. In this step, the scale of the o-nitroaniline molecule graph is smaller than the predetermined threshold, and Steps 300 - 302 can actually be skipped and directly enter Step 400. This example is only for demonstrating the calculation process of Steps 301 - 302. As Figure 4 shown, Step 300 includes the following Steps 301 and 302:

[0083] Step 301: Estimate the von Neumann graph entropy using the degree sequence to obtain the approximate von Neumann graph entropy. The calculation method is as follows:

[0084]

[0085] where d i represents the degree of the i-th node, which corresponds to the number of chemical bonds of the atom in the molecular graph. In the o-nitroaniline molecule: the degree of the benzene ring carbon atom node is d i = 3 (connected to two adjacent carbon atoms and one hydrogen substituent), reflecting its sp 2 hybridization characteristics;

[0086] In this step, by normalizing the degree of each node in the graph, dividing it by the volume vol(G) of the graph, the relative proportion of the degree of each node in the overall graph is obtained Then take the logarithm of this relative proportion, multiply it by the relative proportion itself, sum it up and take the negative sign. The result obtained is the approximate value of the von Neumann graph entropy of graph G. For large-scale molecules (such as proteins or polymers), the complexity of accurate spectral decomposition is extremely high. By approximating the entropy through the degree sequence, the model can quickly estimate the overall structural complexity of the molecule.

[0087] Step 302: Calculate the approximate quantum entropy structure encoding of nodes and edges by combining Step 301 with the calculation methods provided in Step 102, Step 103, Step 202, and Step 203.

[0088] In this step, substitute the approximate value of the von Neumann graph entropy calculated in Step 301 into Step 103 and Step 203 to obtain the approximate quantum entropy structure encoding of nodes and edges. The calculation method of the approximate quantum entropy structure encoding of nodes is as follows:

[0089]

[0090] where S(G v )′, represents the approximate von Neumann graph entropy of G v , , and its calculation formula is as follows:

[0091]

[0092] The calculation method of the approximate quantum entropy structure encoding of edges is as follows:

[0093]

[0094] where represents the approximate von Neumann graph entropy corresponding to the graph after deleting the edge, and its calculation formula is as follows:

[0095]

[0096] Step 400: Combine the calculated node quantum entropy structure encoding and edge quantum entropy structure encoding with the graph neural network to obtain the final node embedding representation. Adaptively select the input encoding according to the scale of the molecular graph nodes: when the number of nodes in the molecular graph is less than or equal to the set threshold, use the node quantum entropy structure encoding and edge quantum entropy structure encoding to calculate the graph and add it to the graph neural network; when the number of nodes in the molecular graph is greater than the set threshold, use the node approximate quantum entropy structure encoding and edge approximate quantum entropy structure encoding to calculate the graph and add it to the graph neural network. After multi-layer message passing, aggregate the final features of all nodes, generate the graph-level representation of the molecular graph, and input it into the prediction network to predict its chemical properties;. As Figure 5 shown, Step 400 includes the following steps 401 to 403:

[0097] Step 401: Based on the comparison of the Holevo quantity, determine the quantization of the importance of the edge quantum entropy structure encoding or edge approximate quantum entropy structure encoding for the message channel. Since the scale of the o-nitroaniline molecular graph is less than the set threshold, use the edge quantum entropy structure encoding obtained in Step 203, and multiply it by the message aggregated from the neighbor nodes. The calculation method of the node embedding representation at the k-th layer is as follows:

[0098]

[0099] Among them, AGG(·) represents an aggregation function; is the neighbor set of node i; represents the node embedding representation of neighbor node u at the k-th layer;

[0100] Step 402, at the (k + 1)-th layer, the final embedding representation of the node is generated as follows: Since the number of nodes in the o-nitroaniline molecular graph is less than the set threshold, the node quantum entropy structure encoding obtained based on Step 103 is used, multiplied by the node embedding representation of the previous round (the k-th layer), and aggregated and combined with the node embedding representation of the k-th layer obtained in Step 401. The calculation method is as follows:

[0101]

[0102] Among them, COMBINE(·) represents a combination function; represents the node embedding representation of node v at the k-th layer;

[0103] Step 403, after completing the iterative update of all K layers of the graph neural network, generate the graph-level representation h of the molecular graph G , and input it into the prediction network to output the molecular property y;

[0104]

[0105] y = PredictNet(h G );

[0106] Among them, READOUT(·) represents a summation readout function, that is, summing up all node feature representations; V represents the set of all nodes in graph G; represents the final embedding representation of node v at the K-th layer; PredictNet(·) represents a prediction network, such as a fully connected neural network, etc.

[0107] In this step, READOUT(·) is set as a summation readout function, that is, summing up all node feature representations; the total number of layers K of the graph neural network is set to 5; PredictNet(·) is set as a support vector machine algorithm. In the experiment, a binary classification prediction task is performed on all molecular graphs in the MUTAG dataset. In message passing, the node quantum entropy structure encoding of atoms and the edge quantum entropy structure encoding of chemical bonds are integrated into the embedding representation of o-nitroaniline. For example, the node quantum entropy structure encoding Q v of the nitro nitrogen atom is 0.227, enhancing the model's attention to its local functional groups, while the edge quantum entropy structure encoding P u,vIf it is 0.082, the weight of this key in message aggregation is strengthened. After 5-layer iteration, the READOUT function sums up all node embeddings to generate the molecular representation h G , and the input support vector machine is used to predict mutagenicity. The experimental results show that the prediction result of the model for o-nitroaniline is 'yes', which is consistent with the true label, verifying the effectiveness of quantum entropy encoding in capturing key structure-property relationships.

[0108] Taking o-nitroaniline as an example, this embodiment demonstrates how quantum entropy encoding improves the prediction accuracy of the model for molecular properties through the quantification of local subgraphs, global structures, and chemical bond importance. This method can be extended to other drug molecules (such as antibiotics or anticancer compounds). By adaptively selecting precise or approximate encoding strategies, it balances computational efficiency and prediction performance, providing a reliable tool for drug discovery.

[0109] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: modifications made to the technical solutions recorded in the foregoing embodiments, or equivalent replacements of some or all of the technical features therein, do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for predicting molecular properties based on quantum entropy graph structure encoding, characterized in that It includes the following steps: Step 100, calculating the quantum entropy structure encoding of nodes based on quantum information theory; Step 200, calculating the quantum entropy structure encoding of edges based on quantum information theory; Step 300, when the number of nodes in the molecular graph reaches a threshold that affects the calculation efficiency, skip Step 100 and Step 200, execute this step to calculate the approximate von Neumann graph entropy, and then calculate the approximate quantum entropy structure encoding of nodes and the approximate quantum entropy structure encoding of edges; when the scale of the molecular graph is less than or equal to the set threshold, skip Step 300; Step 400, combining the calculated quantum entropy structure encoding of nodes and the quantum entropy structure encoding of edges with a graph neural network to obtain the final node embedding representation; select the calculation method of the quantum entropy structure encoding according to the scale of the molecular graph nodes, that is: when the number of nodes in the molecular graph is less than or equal to the set threshold, use the quantum entropy structure encoding of nodes and the quantum entropy structure encoding of edges to calculate the graph and add it to the graph neural network; when the number of nodes in the molecular graph is greater than the set threshold, use the approximate quantum entropy structure encoding of nodes and the approximate quantum entropy structure encoding of edges to calculate the graph and add it to the graph neural network; after multi-layer message passing, aggregate the final features of all nodes, generate the graph-level representation of the molecular graph and input it into the prediction network to predict its chemical properties.

2. The molecular property prediction method based on quantum entropy graph structure encoding according to claim 1, wherein The specific content of the above-mentioned Step 100 is as follows: Step 101, for each node v, divide the molecular graph G = (V, E) into its corresponding molecular subgraph G v =(V v , E v ), the complement of the molecular subgraph where and molecule G, V represents the set of all nodes in graph G, E represents the set of all edges in graph G, V v represents the set of all nodes in the molecular subgraph G v , E v represents the set of all edges in G v , represents the set of all nodes in the complement of the molecular subgraph , represents the set of all edges, |·| represents the number of elements in the set, in the context of a molecular graph, it refers to the number of atoms or chemical bonds; in a chemical molecular graph, nodes represent atoms, and a molecular subgraph represents a local structure composed of an atom as the center, the atoms directly connected to it, and the chemical bonds between them; Step 102, calculate G v , and the von Neumann graph entropy S(G v ) S(G) of the molecular graph G respectively, and the calculation method is as follows: Among them, is the neighbor set of node v, corresponding to the atoms directly connected to the central atom in a chemical molecule; |N(v)| represents the number of neighbor nodes of node v, and in a chemical molecule, this value reflects the valence of the atom; n represents the number of nodes, i.e., atoms, in the molecular graph, reflecting the size of the molecule; λ i is the spectrum of the graph, related to the vibration mode or energy state of the molecular structure; vol(G) is the volume of the graph, i.e., the sum of the degrees of all atoms in the graph, reflecting the total number of chemical bonds in the molecule; vol(G v ) represents the volume of G v ; represents ; Step 103: Apply the Hallward amount to the molecular graph and calculate the quantum entropy structure encoding Q of node v v , and the calculation method is as follows:

3. A method for predicting molecular properties based on quantum entropy graph structure encoding according to claim 1, characterized in that, The specific content of the above-mentioned Step 200 is as follows: Step 201, for edge e = (u, v), by splitting the graph into a single edge and the graph after deleting the edge wherein, the von Neumann graph entropy of the single edge is defined as 0, u and v are elements in the node set, which are the two end nodes of edge e, and V represents the set of all nodes in the graph, represents the set of all edges in the graph after deleting edge e; in the molecular graph, the edge represents a chemical bond, and the graph after deleting the edge simulates the influence of chemical bond breakage on the molecular structure, thereby quantifying the importance of the chemical bond through the change in quantum entropy; Step 202, calculate the graph after deleting the edges The corresponding von Neumann graph entropy The calculation method is as follows: Among them, represents volume; Step 203, calculating the quantum entropy structure encoding of edge e to quantify the importance of chemical bonds to molecular functions. The calculation method is as follows:

4. A method for predicting molecular properties based on quantum entropy graph structure encoding according to claim 1, characterized in that, The specific content of the above-mentioned Step 300 is as follows: Step 301, estimating the von Neumann graph entropy using the degree sequence to obtain the approximate von Neumann graph entropy. The calculation method is as follows: where d i represents the degree of the i-th node, which corresponds to the number of chemical bonds of the atom in the molecular graph; Step 302, through the calculation methods provided in Step 102, Step 103, Step 202, and Step 203, combined with Step 301, calculate the approximate quantum entropy structure encoding of nodes and edges; among them, the calculation method of the approximate quantum entropy structure encoding of nodes is as follows: Among them, S(G v )′, respectively represent the approximate von Neumann graph entropy of G v , , and the calculation formula is as follows: The calculation method of the approximate quantum entropy structure encoding of edges is as follows: Among them, represents the graph after deleting edges The corresponding approximate von Neumann graph entropy is calculated as follows:

5. A method for predicting molecular properties based on quantum entropy graph structure encoding according to claim 1, characterized in that The specific content of the above-mentioned Step 400 is as follows: Step 401, based on the comparison of the Holevo quantity, determine the quantification of the importance of the edge quantum entropy structure encoding or the approximate edge quantum entropy structure encoding to the message channel; if the number of nodes in the molecular graph is less than or equal to the set threshold, based on the edge quantum entropy structure encoding obtained in Step 203, multiply the message aggregated from neighbor nodes. The calculation method of the node embedding representation in the k-th layer is as follows: Among them, AGG(·) represents an aggregation function; is the neighbor set of node i; represents the node embedding representation of neighbor node u at the k-th layer; If the number of nodes in the molecular graph is greater than the set threshold, based on the approximate edge quantum entropy structure encoding obtained in Step 302, multiply the message aggregated from neighbor nodes. The calculation method of the node embedding representation in the k-th layer is as follows: Step 402, at the (k + 1)-th layer, the final embedding representation of the node is generated as follows: Select node quantum entropy structure encoding or node approximate quantum entropy structure encoding according to the molecular graph node scale, multiply it by the node embedding representation of the previous k-th layer, and aggregate and combine it with the node embedding representation of the k-th layer obtained in Step 401. The specific implementation is as follows: If the number of nodes in the molecular graph is less than or equal to the set threshold, use the quantum entropy structure encoding of nodes obtained in Step 103. The calculation method is as follows: Among them, SOMBINE(·) represents the combination function; represents the node embedding representation of node v at the k-th layer; If the number of nodes in the molecular graph is greater than the set threshold, use the approximate quantum entropy structure encoding of nodes obtained in Step 302. The calculation method is as follows: Step 403, after completing the iterative update of all graph neural network layers, the total number of layers of the graph neural network is K, and the graph-level representation h of the molecular graph is generated through the READOUT function G , and input it into the prediction network to output the molecular property y; y = PredictNet(h G ); where READOUT(·) represents the summation readout function, that is, summing up all node feature representations; V represents the set of all nodes in graph G; represents the final embedding representation of node v at the K-th layer; PredictNet(·) represents the prediction network.

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