A method for predicting polymer properties based on virtual geometric graphs

Abstract

The application relates to the technical field of polymer material structure characterization and property prediction, and discloses a polymer property prediction method based on a virtual geometric graph, which reads a polymer repeating unit structure formula, identifies a connection point mark and replaces the same with a preset atom, and determines a periodic connection atom; three-dimensional coordinates of each atom are generated based on a repeating unit copy, distance and position parameters between atoms are extracted, and periodic mapping parameters are obtained; the periodic mapping parameters are mapped to a Mobius ring coordinate space, atomic periodic mapping coordinates are generated, and a polymer periodic virtual geometric graph including an atomic node, a common edge, a periodic constraint edge and a virtual geometric node is constructed; graph structure features are extracted and are subjected to radial basis coding, geometric message passing is performed, polymer graph characterization is obtained, and a polymer property prediction result is output. The application can improve the integrity of polymer structure characterization, and is favorable for improving the accuracy and stability of property prediction.

Description

Technical Field

[0001] This application relates to the field of polymer material structure characterization and property prediction technology, and more specifically, to a polymer property prediction method based on virtual geometry. Background Technology

[0002] The crystallization temperature, glass transition temperature, mechanical strength, permeability, and dimensional stability of polymers directly affect their processing, performance, and application. Therefore, predicting polymer properties based on their structure has always been an important technical direction in materials design and screening. In existing technologies, polymer properties are usually obtained through experimental testing, theoretical calculations, or data-driven prediction methods based on molecular structure. Although experimental testing can directly obtain the target properties, it is usually time-consuming, costly, and difficult to adapt to the rapid screening of large-scale candidate polymers. Although theoretical calculations can provide some structural analysis capabilities, they are often computationally burdensome when dealing with polymer systems with complex chain structures and many conformational changes, making it difficult to balance efficiency and applicability.

[0003] Therefore, polymer property prediction methods based on structure characterization have gradually become an important technical approach. Existing methods typically represent polymer repeating units as molecular descriptors, ordinary molecular diagrams, or general structure vectors, and then establish property prediction models based on the structural representation results. However, polymers are different from ordinary small molecules. Polymer repeating units usually contain polymerization connection sites, and the actual structure has periodic connection relationships extending along the polymerization direction. If polymer repeating units are only represented as independent and limited ordinary molecular fragments, it is usually only possible to describe the atomic connection relationships within the repeating unit, and it is difficult to accurately express the periodic connection relationships corresponding to the connection sites.

[0004] Furthermore, existing structural representations mostly focus on atom types, chemical bond connections, or general spatial distance information, lacking a unified expression of periodic connections, positional distribution along the polymerization direction, and local spatial geometry. As a result, subsequent property prediction processing often struggles to simultaneously utilize the chemical structure information within repeating units, cross-period connection information, and geometric structure information related to periodic extension, easily leading to incomplete polymer structure characterization and consequently affecting the accuracy, stability, and applicability to different polymer structures of the property prediction results.

[0005] Therefore, there is an urgent need for a polymer property prediction method based on virtual geometry that can characterize the internal chemical connections, periodic connections, and related spatial geometric relationships of polymer repeating units, forming a unified structural expression result suitable for subsequent property prediction processing. Summary of the Invention

[0006] In order to overcome the above-mentioned defects of the prior art, the purpose of this invention is to provide a polymer property prediction method based on virtual geometry, so as to solve the problem that the existing polymer structure representation methods are difficult to simultaneously express the chemical connection relationship, periodic connection relationship and spatial geometric relationship within repeating units, resulting in incomplete structural characterization in subsequent property prediction processing.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: This application discloses a method for predicting polymer properties based on virtual geometry, including: Step S1: Read the polymer repeating unit structure, identify the connection point markers, replace each connection point marker with a preset atom to obtain a copy of the repeating unit, and determine the atom corresponding to the replacement position as the periodic connection atom; Step S2: Generate the three-dimensional coordinates of each atom based on the repeating unit copy, extract the distance between atoms based on the three-dimensional coordinates of each atom, extract the position parameters of each atom based on the direction of the line connecting the atoms of the two periods in the repeating unit copy, normalize the position parameters, and obtain the period mapping parameters. Step S3: Map the periodic mapping parameters to the Möbius ring coordinate space to obtain the atomic periodic mapping coordinates; generate atomic nodes and ordinary edges based on the atoms and chemical bonds in the repeating unit copy; generate periodic constraint edges based on the connection relationship between periodically connected atoms; generate virtual geometric nodes based on the atomic periodic mapping coordinates to obtain the polymer periodic virtual geometry graph. Step S4: Extract atomic node attributes, ordinary edge connection features, periodic constraint edge connection features, and spatial relationship features of atomic nodes relative to virtual geometric nodes based on the polymer periodic virtual geometry graph. Perform radial basis encoding on the distance between atoms and the distance from atomic nodes to virtual geometric nodes to obtain geometric encoding features. Step S5: Based on the polymer periodic virtual geometry graph and geometric coding features, perform geometric message passing between atomic nodes and between atomic nodes and virtual geometry nodes to obtain the polymer graph representation, and output the polymer property prediction results based on the polymer graph representation.

[0008] Furthermore, methods for identifying connection point markers include: The atomic symbols, chemical bond symbols, and connection point markers in the polymer repeating unit structure are structurally decomposed; each atomic symbol, chemical bond symbol, and connection point marker is numbered to obtain an atomic marker table, a chemical bond marker table, and a connection point marker table; based on the adjacency relationship in the structure, the atomic number and chemical bond number adjacent to each connection point marker are recorded to obtain a connection point adjacency relationship table.

[0009] Furthermore, the method for obtaining a copy of the repeating unit and determining the atom corresponding to the replacement position as a periodic connection atom includes: Read the link point replacement rules, which specify the preset atom type for each link point marker and the chemical bond connection method to be retained during replacement; copy the structure analysis results of the repeating unit to obtain a copy record of the repeating unit; replace each link point marker with the corresponding preset atom according to the numbering order in the link point marker table, and retain the adjacent atoms and chemical bond connection relationships corresponding to each link point marker; write the replacement position number, the replaced atom number, the original link point marker number, and the adjacent atom number for each replacement position to obtain the replacement position correspondence table; extract the atom corresponding to the replacement position based on the replacement position correspondence table, and determine the atom corresponding to the replacement position as the periodic linking atom.

[0010] Furthermore, methods for generating the three-dimensional coordinates of each atom based on repeating unit copies include: Read the duplicate unit copy and the periodic connection atomic table, and establish a conformation generation record based on the atom type, chemical bond type, and atomic connection relationship in the duplicate unit copy; write the corresponding bond length constraints and bond angle constraints according to the atom type and chemical bond type in the conformation generation record to generate an initial conformation record; perform three-dimensional conformation solving processing on the initial conformation record to obtain the initial spatial coordinates of each atom in the duplicate unit copy; perform number correction processing on the initial spatial coordinates so that each atom number corresponds to a three-dimensional coordinate value to obtain an atomic coordinate table; associate the atomic coordinate table with the periodic connection atomic table to obtain the three-dimensional coordinates of each atom.

[0011] Furthermore, the periodic mapping parameters are obtained, including: Read the three-dimensional coordinates of each atom, and calculate the spatial distance between any two atoms by pairwise combination according to the atom number to obtain the inter-atom distance matrix; extract the three-dimensional coordinates of two periodically connected atoms from the atom coordinate table, and generate a periodic direction vector by taking the three-dimensional coordinates of one periodically connected atom as the starting point and the three-dimensional coordinates of the other periodically connected atom as the ending point; perform projection processing on the three-dimensional coordinates of each atom using the periodic direction vector as the projection direction to obtain the original position parameters of each atom along the periodic direction vector; perform linear normalization processing on each original position parameter to obtain the periodic mapping parameters.

[0012] Furthermore, methods for obtaining atomic periodic mapping coordinates include: The process involves reading the periodic mapping parameters, atomic coordinate table, and periodic direction vector, and decomposing the three-dimensional coordinates of each atom into axial and lateral components based on the periodic direction vector. The periodic mapping parameters of each atom are sorted according to their numerical values; when identical periodic mapping parameters exist, their order is determined by the atom number, and position numbers are assigned sequentially to obtain a circumferential position sequence. Based on the position number of each atom in the circumferential position sequence, the lateral components of each atom are written into the corresponding cross-sectional positions to obtain a cross-sectional position sequence. The traversal direction and flip boundary position are determined based on the position number in the circumferential position sequence, and a single flip process is performed on the cross-sectional position sequence. Finally, the circumferential position numbers are paired with the corresponding cross-sectional positions to obtain the atomic periodic mapping coordinates.

[0013] Furthermore, methods for obtaining the polymer periodic virtual geometry include: Each atom in the repeating unit copy is written into the node table to obtain atomic nodes; each chemical bond in the chemical bond list is written into the edge table to obtain ordinary edges; the atomic nodes corresponding to the atoms connecting two periods are written into the edge table as connection endpoints to obtain periodic constraint edges; the circumferential positions in the atomic periodic mapping coordinates are sorted, and the circumferential position intervals between adjacent atoms are calculated to obtain a circumferential interval sequence; the absolute value of the difference between each circumferential interval and its previous circumferential interval is calculated in sequence. When the absolute value of the difference is greater than the interval change judgment value, the corresponding circumferential position is determined as the interval change position, and multiple continuous coordinate segments are obtained by using each interval change position as the segment boundary; the average value of the circumferential positions and the average value of the cross-sectional positions in each continuous coordinate segment are calculated to obtain the center coordinates, and virtual geometric nodes are generated based on the center coordinates; the corresponding atomic nodes are associated with the corresponding virtual geometric nodes based on the continuous coordinate segments to which each atomic periodic mapping coordinate belongs; the atomic nodes, ordinary edges, periodic constraint edges, virtual geometric nodes, and association relationships are merged to obtain the polymer periodic virtual geometry graph.

[0014] Furthermore, methods for obtaining geometrically encoded features include: Extract the atom type, number of chemical bonds, number of ordinary edge adjacencies, and number of periodically constrained edge adjacencies of the atomic nodes; extract the circumferential position difference, cross-sectional position difference, and corresponding connection type of the atoms at both ends of ordinary and periodically constrained edges; extract the circumferential position difference, cross-sectional position difference, and distance value between the atomic nodes and virtual geometric nodes; read the radial basis encoding parameters and perform radial basis encoding processing on each distance value in the inter-atom distance matrix and each distance value from the atomic node to the virtual geometric node; combine the above atomic node attributes, ordinary edge connection features, periodically constrained edge connection features, spatial relationship features, inter-atom distance encoding results, and distance encoding results from the atomic node to the virtual geometric node to obtain the geometric encoding features.

[0015] Furthermore, methods for obtaining polymer characterization include: The initial states of atomic nodes and virtual geometric nodes are obtained based on the atomic node state initialization parameter table and the virtual geometric node state initialization parameter table, respectively. The initial states of ordinary edges, periodic constraint edges, and associated edges are obtained based on the ordinary edge state initialization parameter table, the periodic constraint edge state initialization parameter table, and the associated edge state initialization parameter table, respectively. Atom-to-atomic aggregated messages are obtained based on the inter-atomic message mapping parameter table, and geometric associated aggregated messages are obtained based on the atom-to-virtual geometric node message mapping parameter table and the virtual geometric node-to-atomic message mapping parameter table. The states of atomic nodes and virtual geometric nodes are updated based on the atomic node state update parameter table and the virtual geometric node state update parameter table, and the state update process is repeated according to the message passing rounds. The final atomic node states are aggregated to obtain atomic node aggregated vectors, and the final virtual geometric node states are aggregated to obtain virtual geometric node aggregated vectors. The atomic node aggregated vectors and the virtual geometric node aggregated vectors are combined to obtain the polymer graph representation.

[0016] Furthermore, methods for outputting polymer property prediction results include: Read the atomic node state update parameter table and the virtual geometry node state update parameter table to obtain the updated atomic node state table and the updated virtual geometry node state table, respectively. Repeat the state update process according to the message passing rounds recorded in the message passing configuration table, and output the final atomic node state table and the final virtual geometry node state table when the message passing round is reached. Perform item-by-item summation on all atomic node states in atomic number order to obtain the atomic node aggregation vector. Perform item-by-item summation on all virtual geometry node states in virtual geometry node number order to obtain the virtual geometry node aggregation vector. Concatenate the atomic node aggregation vector and the virtual geometry node aggregation vector in sequence to obtain the polymer graph representation. Read the property prediction configuration table, obtain the initial prediction value corresponding to each target property according to the property prediction mapping parameter table, and obtain the target property prediction value according to the result recovery rule table. Write the predicted value to the property prediction result table to obtain the polymer property prediction result.

[0017] Compared with related technologies, this application has the following advantages: Compared with existing technologies, the polymer property prediction method based on virtual geometry provided in this application constructs a unified chain of structural expression and property prediction processing around the periodic connection relationship and spatial geometric relationship of polymer repeating units. This can improve the integrity of polymer structure characterization and help improve the accuracy and stability of subsequent polymer property prediction results.

[0018] This application identifies the connection point markers in the polymer repeating unit structure and replaces each connection point marker with a preset atom. At the same time, the atom corresponding to the replacement position is determined as the periodic connection atom. This transforms the connection point markers, which were originally only used to represent the polymer connection position, into processing objects that can participate in the subsequent three-dimensional coordinate generation and periodic relationship extraction. This is beneficial for providing a clear processing basis for subsequent periodic direction extraction and unified structural expression.

[0019] This application generates the three-dimensional coordinates of each atom based on the copy of the repeating unit, and extracts the position parameters of each atom according to the direction of the connection between the atoms of the two periodic connections, and further obtains the periodic mapping parameters. This not only preserves the spatial distance relationship between atoms within the repeating unit, but also preserves the positional distribution relationship of each atom along the aggregation direction, which is beneficial to improving the problem in the prior art that can only characterize the local connection relationship and is difficult to reflect the periodic extension relationship.

[0020] This application maps periodic mapping parameters to the Möbius strip coordinate space to obtain atomic periodic mapping coordinates. Furthermore, it generates periodic constraint edges based on the connection relationships between periodically connected atoms and generates virtual geometric nodes based on the atomic periodic mapping coordinates, thereby obtaining a polymer periodic virtual geometric graph. This allows the chemical bond connections within repeating units, the periodic connections between the beginning and end of repeating units, and the spatial geometric relationships corresponding to the atomic distribution to be uniformly written into the same graph structure, which is beneficial to improving the integrity and consistency of polymer structure representation.

[0021] This application extracts atomic node attributes, ordinary edge connection features, periodic constraint edge connection features, and spatial relationship features of atomic nodes relative to virtual geometric nodes based on polymer periodic virtual geometric graphs. It also performs radial basis encoding on the distance between atoms and the distance from atomic nodes to virtual geometric nodes to obtain geometric encoding features. This allows continuous spatial distance information and graph structure relationship information to participate in subsequent processing in a unified encoding form, which is beneficial to improving the utilization of spatial geometric information in the property prediction process.

[0022] This application, based on the periodic virtual geometry graph and geometric coding features of polymers, performs geometric message passing between atomic nodes and between atomic nodes and virtual geometric nodes to obtain polymer graph representations, and outputs polymer property prediction results based on polymer graph representations. This allows chemical connection information, periodic connection information, and spatial geometric information to participate in state updates and characterization generation in the same processing chain, which is beneficial to improving the accuracy, stability, and applicability of polymer property prediction results to different polymer structures. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of a polymer property prediction method based on virtual geometry provided in this application. Detailed Implementation

[0024] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0025] Please see Figure 1 As shown, this embodiment provides a polymer property prediction method based on virtual geometry, including the following steps: Step S1: Read the polymer repeating unit structure, identify the connection point markers, replace each connection point marker with a preset atom to obtain a copy of the repeating unit, and determine the atom corresponding to the replacement position as the periodic connection atom to obtain the periodic connection atom table.

[0026] In some embodiments, the purpose of reading the polymer repeating unit structure and identifying the connection point markers is to extract the correspondence between atoms, chemical bonds, and connection point markers from the polymer repeating unit structure, and to obtain the repeating unit structure analysis results required for subsequent connection point replacement processing; the implementation steps include: Step 1011: Read the structural formula of the polymer repeating unit and perform structural decomposition according to the atomic symbols, chemical bond symbols and connection point markings in the structural formula; the connection point markings are used to indicate the polymerization connection positions in the polymer repeating unit.

[0027] Step 1012: Number each atomic symbol in the structural decomposition result to obtain an atomic label table; number each chemical bond symbol to obtain a chemical bond label table; number each connection point label to obtain a connection point label table.

[0028] Step 1013: Based on the adjacency relationship in the structural formula, record the atom number and chemical bond number adjacent to each connection point to obtain the connection point adjacency relationship table.

[0029] Step 1014: Correspond the atomic labeling table, chemical bond labeling table, connection point labeling table, and connection point adjacency relationship table to obtain the analysis results of the repeating unit structure.

[0030] Step 1015: Use the result of the analysis of the repeating unit structure as input for the connection point marker replacement process in the second heading.

[0031] In some embodiments, each connection point marker is replaced with a preset atom to obtain a copy of the repeating unit, and the atom corresponding to the replacement position is determined as a periodic connection atom. The purpose of obtaining the periodic connection atom table is to convert the connection point markers into atom objects that can participate in the generation of three-dimensional coordinates, and to determine the periodic direction for extracting the required periodic connection atoms. The implementation steps include: Step 1021: Read the analysis results of the repeating unit structure and read the connection point replacement rules; the connection point replacement rules are used to give the preset atom type corresponding to the connection point marker of each polymer property prediction method based on virtual geometry and the chemical bond connection mode to be retained during replacement.

[0032] Step 1022: Copy the result of the repeated unit structure analysis to obtain a copy record of the repeated unit.

[0033] Step 1023: According to the numbering order in the connection point mark table, replace each connection point mark in the duplicate unit copy record with the preset atom corresponding to the connection point replacement rule, and retain the adjacent atoms and chemical bond connection relationships corresponding to the connection point mark in the connection point adjacency relationship table.

[0034] Step 1024: Write the replacement position number, the replaced atom number, the original connection point mark number, and the adjacent atom number for each replacement position to obtain the replacement position correspondence table.

[0035] Step 1025: Extract the atoms corresponding to the replacement positions according to the replacement position correspondence table, and determine the atoms corresponding to the replacement positions as periodic connection atoms to obtain the periodic connection atom table.

[0036] Step 1026: The duplicate cell copy record and the periodic connection atomic table are associated and stored to obtain the duplicate cell copy, and the duplicate cell copy and the periodic connection atomic table are used as inputs for the three-dimensional coordinate generation process in subsequent steps.

[0037] For example, to illustrate the process of replacing connection point markers and determining periodically connected atoms, we can assume that there are two connection point markers in the analysis result of the repeating unit structure. The first connection point marker is adjacent to atom number 1, and the second connection point marker is adjacent to atom number 4. According to the connection point replacement rules, the first connection point marker is replaced with a preset atom number 7, and the second connection point marker is replaced with a preset atom number 8, while retaining the adjacent atoms and chemical bond connections corresponding to the original connection positions. Then, the replacement position number 01, the replaced atom number 7, the original connection point marker number A, and the adjacent atom number 1 are written into the replacement position correspondence table for the first replacement position, and the replacement position number 02, the replaced atom number 8, the original connection point marker number B, and the adjacent atom number 4 are written into the table for the second replacement position. Atom numbers 7 and 8 are then extracted from the replacement position correspondence table and identified as periodically connected atoms, resulting in a table of periodically connected atoms. In this way, the connection point markers in the repeating unit copy, which originally only represented aggregation connection positions, are replaced with atomic objects that can participate in subsequent three-dimensional coordinate generation processing.

[0038] Step S2: Generate the three-dimensional coordinates of each atom based on the repeating unit copy and the periodically connected atom table, extract the distance between atoms based on the three-dimensional coordinates of each atom, and extract the position parameters of each atom based on the direction of the line connecting two periodically connected atoms in the repeating unit copy. Normalize the position parameters to obtain the periodic mapping parameters.

[0039] In some embodiments, the purpose of generating the three-dimensional coordinates of each atom based on the repeating unit copy is to obtain spatial coordinate results that correspond one-to-one with the atom numbers in the repeating unit copy, providing input for subsequent inter-atom distance extraction and periodic mapping parameter extraction. The implementation steps include: Step 2011: Read the repeating unit copy and the periodic connection atom table, and establish a conformation generation record based on the atom type, chemical bond type and atom connection relationship in the repeating unit copy.

[0040] Step 2012: Based on the atom type and chemical bond type in the conformation generation record, write the corresponding bond length constraints and bond angle constraints to generate the initial conformation record.

[0041] Step 2013: Read the atom types, chemical bond connections, bond length constraints, and bond angle constraints from the initial conformation record. First, establish the initial spatial arrangement based on the atom connection order. Then, perform iterative adjustments to the spatial position of each atom based on the bond length constraints and bond angle constraints until the connection distance and connection angle between each atom are consistent with the corresponding constraints in the initial conformation record, thus obtaining the initial spatial coordinates of each atom in the repeating unit copy.

[0042] Step 2014: Read the initial spatial coordinates and the atomic numbering order in the duplicate unit copy. Extract the initial spatial coordinates of each atom in the order of atomic numbering, and pair each atomic number with its corresponding three-dimensional coordinate and write it into the coordinate record. When the atomic numbering order in the coordinate record is inconsistent with the atomic numbering order in the duplicate unit copy, rearrange the coordinate record according to the atomic numbering order in the duplicate unit copy to obtain the atomic coordinate table. The atomic coordinate table records the atomic number and its corresponding three-dimensional coordinate.

[0043] Step 2015: Read the atomic coordinate table and the periodic connected atom table. Based on the atom number in the periodic connected atom table, extract the three-dimensional coordinates of the corresponding periodic connected atom from the atomic coordinate table. Then, read all the atom numbers and three-dimensional coordinates in the atomic coordinate table in atomic number order, and write the three-dimensional coordinates of the periodic connected atom and the three-dimensional coordinates of the other atoms into the coordinate record to obtain the three-dimensional coordinates of each atom. Use the three-dimensional coordinates of each atom as input for the extraction of inter-atomic distance and position parameters in Title 4.

[0044] In some embodiments, the distance between atoms is extracted based on the three-dimensional coordinates of each atom, and the position parameters of each atom are extracted based on the direction of the line connecting two periodically connected atoms in the repeating unit copy. The position parameters are normalized to obtain the periodic mapping parameters. The purpose is to convert the three-dimensional coordinates into parameter results that characterize the spatial relationship between atoms and the positional relationship along the extension direction of the repeating unit copy. The implementation steps include: Step 2021: Read the three-dimensional coordinates of each atom, and calculate the spatial distance between any two atoms by combining them in pairs according to the atom numbers, so as to obtain the inter-atom distance matrix.

[0045] Step 2022: Read the periodic connected atom table, extract the three-dimensional coordinates of two periodic connected atoms from the atom coordinate table, and generate a periodic direction vector with the three-dimensional coordinates of one periodic connected atom as the starting point and the three-dimensional coordinates of the other periodic connected atom as the ending point.

[0046] Step 2023: Read the three-dimensional coordinates and periodic direction vector of each atom, and use the starting coordinates of the periodic direction vector as the reference starting point; for each atom, first calculate the coordinate difference vector between the three-dimensional coordinates of the atom and the reference starting point, then calculate the component value of the coordinate difference vector in the direction of the periodic direction vector, and determine the component value as the original position parameter of the atom along the periodic direction vector; write the original position parameters of each atom into the position parameter table according to the atom number order to form the position parameter table.

[0047] Step 2024: Extract the projection results of the two periodically connected atoms, take the projection result of the starting periodically connected atom as the normalization start position, take the projection result of the ending periodically connected atom as the normalization end position, perform linear normalization on each original position parameter in the position parameter table to obtain the periodic mapping parameters, and write the periodic mapping parameters corresponding to each atom into the periodic mapping parameter table.

[0048] Furthermore, to illustrate the position parameter normalization process, we can assume that the projection results of two periodically connected atoms are 2.0 and 6.0, respectively. The periodically connected atom with a projection result of 2.0 is taken as the starting position for normalization, and the periodically connected atom with a projection result of 6.0 is taken as the ending position. If the original position parameter of atom number 2 is 3.0, then after performing linear normalization on this original position parameter, the periodic mapping parameter corresponding to atom number 2 is 0.25. If the original position parameter of atom number 3 is 4.0, then the periodic mapping parameter corresponding to atom number 3 is 0.50. If the original position parameter of atom number 4 is 5.0, then the periodic mapping parameter corresponding to atom number 4 is 0.75. This example shows that the projection results of each atom originally distributed in three-dimensional space are uniformly converted into periodic mapping parameters that reflect their relative positional relationship along the extension direction of the repeating unit copy.

[0049] Step 2025: The inter-atomic distance matrix and the periodic mapping parameter table are associated and stored to obtain the periodic mapping parameters. The inter-atomic distance matrix and the periodic mapping parameters are then used as inputs for the Möbius strip coordinate space mapping processing in subsequent steps.

[0050] Step S3: Map the periodic mapping parameters to the Möbius strip coordinate space to obtain the atomic periodic mapping coordinates; generate atomic nodes and ordinary edges based on the atoms and chemical bonds in the repeating unit copy; generate periodic constraint edges based on the connection relationship between periodically connected atoms; generate virtual geometric nodes based on the atomic periodic mapping coordinates to obtain the polymer periodic virtual geometry diagram.

[0051] In some embodiments, mapping the periodic mapping parameters to the Möbius strip coordinate space to obtain atomic periodic mapping coordinates aims to convert the positional relationship of each atom along the extension direction of the repeating unit copy into a coordinate expression with a periodic flip relationship, thereby obtaining the atomic periodic mapping coordinates required for subsequent virtual geometric node generation; the implementation steps include: Step 3011: Read the periodic mapping parameter table, atomic coordinate table and periodic direction vector, and decompose the three-dimensional coordinates of each atom into axial components along the periodic direction vector and lateral components perpendicular to the periodic direction vector according to the periodic direction vector.

[0052] Step 3012: Read the periodic mapping parameter table, sort the periodic mapping parameters of each atom according to their numerical values, and assign position numbers in the sorting results to obtain the circumferential position sequence; each position number in the circumferential position sequence corresponds to an atom and is used to characterize the circumferential arrangement position of the corresponding atom in the Möbius strip coordinate space; then read the lateral components of each atom, and write the lateral components of each atom into the corresponding cross-sectional positions according to the position numbers of each atom in the circumferential position sequence to obtain the cross-sectional position sequence that corresponds one-to-one with the circumferential position sequence.

[0053] Step 3013: Read the circumferential position sequence and the cross-sectional position sequence. Determine the traversal direction according to the position number in the circumferential position sequence from small to large, and count the total number of position numbers. When the total number of position numbers is even, the middle two position numbers are used as the flip boundary position. When the total number of position numbers is odd, the middle position number is used as the flip boundary position. For each cross-sectional position before the flip boundary position, maintain the original writing direction. For each cross-sectional position at and after the flip boundary position, rewrite in the opposite direction to the original writing direction to obtain the cross-sectional position sequence after a single flip.

[0054] Step 3014: Read the circumferential position sequence, the cross-sectional position sequence after a single flip, and the atom number. Pair the circumferential position number of each atom with the corresponding cross-sectional position to generate the mapping coordinate item of the atom. Then write the mapping coordinate items of each atom into the coordinate table in the order of atom number to obtain the atomic periodic mapping coordinates. Write the atomic periodic mapping coordinates of each atom into the atomic periodic mapping coordinate table in the order of atom number.

[0055] For example, to illustrate the coordinate space mapping process of a Möbius strip, we can assume that six atoms participate in the mapping. Their periodic mapping parameters, sorted from smallest to largest, correspond to atom numbers 1, 2, 3, 4, 5, and 6, respectively, and are assigned position numbers 1, 2, 3, 4, 5, and 6, resulting in a circumferential position sequence. If the lateral components of each atom are 0.20, 0.35, 0.40, 0.38, 0.25, and 0.10, respectively, then the initial cross-sectional position sequence is obtained. Since the total number of position numbers is six, the position between the two middle position numbers can be defined as the flip boundary position. By maintaining the original writing direction for the cross-sectional positions before the flip boundary position, and rewriting the cross-sectional positions at and after the flip boundary position in the opposite direction to the original writing direction, a sequence of cross-sectional positions after a single flip is obtained. Subsequently, the circumferential position number 1 of atom number 1 is paired with the corresponding cross-sectional position, and the circumferential position number 2 of atom number 2 is paired with the corresponding cross-sectional position, until the circumferential position numbers of all atoms are paired with their corresponding cross-sectional positions, resulting in an atomic periodic mapping coordinate table. Through this process, the linear positional relationship along the extension direction of the repeating unit replica can be converted into a periodic coordinate expression with a single flip relationship.

[0056] Step 3015: Use the atomic periodic mapping coordinate table as input for the generation and processing of atomic nodes, ordinary edges, periodic constraint edges, and virtual geometric nodes in subsequent steps.

[0057] In some embodiments, the purpose of generating atomic nodes and ordinary edges based on atoms and chemical bonds in the repeating unit replicas, generating periodic constraint edges based on the connection relationships between periodically connected atoms, and generating virtual geometric nodes based on atomic periodic mapping coordinates to obtain a polymer periodic virtual geometry graph is to uniformly write the chemical bond connection relationships, periodic connection relationships, and periodic mapping coordinate relationships in the repeating unit replicas into the same graph structure, thereby obtaining the polymer periodic virtual geometry graph required for subsequent feature extraction and geometric message passing. The implementation steps include: Step 3021: Read the duplicate unit copy, the periodic connection atom table, and the atomic periodic mapping coordinate table; write each atom in the duplicate unit copy into the node table to obtain the atom node; the node table records the atom number, atom type, and atomic periodic mapping coordinate.

[0058] Step 3022: Read the chemical bond list in the repeating unit replica, and write each chemical bond in the chemical bond list into the edge table to obtain ordinary edges; ordinary edges are used to represent the chemical bond connection relationship inside the repeating unit replica.

[0059] Step 3023: Read the periodic connection atom table, and write the atom nodes corresponding to the two periodic connection atoms into the edge table as connection endpoints to obtain the periodic constraint edges; the periodic constraint edges are used to represent the head-to-tail connection relationship of the repeating unit replicas in the aggregation direction.

[0060] Step 3024: Read the atomic periodic mapping coordinate table, sort the atoms according to the circumferential positions in the atomic periodic mapping coordinates, and calculate the circumferential position intervals between adjacent atoms to obtain the circumferential interval sequence.

[0061] Step 3025: Read the circumferential interval sequence, calculate the absolute value of the difference between each circumferential interval and its previous circumferential interval in circumferential position sequence; when the absolute value of the difference is greater than the interval change judgment value, determine the corresponding circumferential position as the interval change position; use each interval change position as the segment boundary of the continuous coordinate segment, segment the sorted atomic periodic mapping coordinates to obtain multiple continuous coordinate segments.

[0062] In some implementations, the method for setting the interval change judgment value includes: reading the circumferential interval sequence, calculating the absolute value of the difference between adjacent circumferential intervals to obtain the interval change amount sequence; performing statistical analysis on the interval change amount sequence to extract the benchmark statistic reflecting the level of regular change and the fluctuation statistic reflecting the degree of dispersion; determining the interval change judgment value based on the combination result of the benchmark statistic and the fluctuation statistic; and determining the position where the absolute value of the difference is greater than the interval change judgment value as the interval change position.

[0063] Step 3026: For each continuous coordinate segment, extract all atomic periodic mapping coordinates within the continuous coordinate segment, take the average value for the circumferential position and the average value for the cross-sectional position respectively, and combine the two average values ​​as the center coordinates of the continuous coordinate segment; then generate virtual geometric nodes according to the one-to-one correspondence between the continuous coordinate segment and the center coordinates to obtain the virtual geometric node table.

[0064] The example illustrates the generation process of continuous coordinate segments and virtual geometric nodes. We can assume that the atomic periodic mapping coordinates, sorted by circumferential position, have adjacent circumferential position intervals of 0.10, 0.11, 0.09, 0.34, and 0.08, respectively. After calculating the absolute value of the difference between adjacent circumferential intervals, we can obtain the corresponding interval change sequence. The change between the fourth circumferential interval and its preceding circumferential interval is significantly greater than the others and is determined to be a position greater than the interval change judgment value. Therefore, the circumferential position corresponding to this position is determined as the interval change position. Using this interval change position as the segment boundary, the entire atomic periodic mapping coordinates can be divided into a preceding continuous coordinate segment and a following continuous coordinate segment. If the circumferential positions of each atom in the preceding continuous coordinate segment are 0.10, 0.21, 0.30, and 0.39, and the cross-sectional positions are 0.20, 0.35, 0.40, and 0.38, then the average of the circumferential positions within this continuous coordinate segment is 0.25, and the average of the cross-sectional positions is 0.33. These two are combined as the center coordinates of the first virtual geometric node. If the circumferential positions of each atom in the following continuous coordinate segment are 0.73 and 0.81, and the cross-sectional positions are 0.25 and 0.10, then the center coordinates of the second virtual geometric node can be obtained. In this way, multiple virtual geometric nodes can be generated from multiple continuous coordinate segments.

[0065] Step 3027: Based on the continuous coordinate segments to which each atomic periodic mapping coordinate belongs, write the corresponding atomic nodes and corresponding virtual geometric nodes into the associated edge table to obtain the geometric association table between atomic nodes and virtual geometric nodes.

[0066] Step 3028: Read the node table, edge table, virtual geometry node table, and geometric association table; write the atomic nodes and virtual geometry nodes in the node table into the node record in node number order, and write the ordinary edges and periodic constraint edges in the edge table and the associated edges in the geometric association table into the edge record in edge number order; for each edge record, write the corresponding start node number, end node number, and edge type, and make the start node number and end node number in the edge record point to the corresponding node in the node record respectively; store the node record and edge record together to obtain the polymer periodic virtual geometry graph; use the polymer periodic virtual geometry graph as input for subsequent atomic node attribute extraction, ordinary edge connection feature extraction, periodic constraint edge connection feature extraction, spatial relationship feature extraction, and geometric message passing processing.

[0067] Step S4 involves extracting atomic node attributes, ordinary edge connection features, periodic constraint edge connection features, and spatial relationship features between atomic nodes and virtual geometric nodes based on the polymer periodic virtual geometry graph. Radial basis encoding is then performed on the distances between atoms and the distances from atomic nodes to virtual geometric nodes to obtain geometric encoding features. The purpose of this process is to convert the node information, edge information, and spatial location information in the polymer periodic virtual geometry graph into encoded results that can be directly invoked in subsequent geometric message passing processing. The implementation steps include: Step 401: Read the polymer periodic virtual geometry, interatomic distance matrix, atomic periodic mapping coordinate table and virtual geometry node table, and extract the node table, ordinary edge table, periodic constraint edge table and geometric relationship table from the polymer periodic virtual geometry to obtain the feature extraction input record.

[0068] Step 402: Read the node table, extract the atomic node attributes for each atomic node to obtain the atomic node attribute table; the atomic node attribute table records at least the atom number, atom type, number of chemical bond connections, number of ordinary edge adjacencies, and number of periodic constraint edge adjacencies; among which, the number of chemical bond connections is obtained by counting the chemical bond connections in the repeating unit replica, the number of ordinary edge adjacencies is obtained by counting the number of times the atomic node appears in the ordinary edge table, and the number of periodic constraint edge adjacencies is obtained by counting the number of times the atomic node appears in the periodic constraint edge table.

[0069] Step 403: Read the ordinary edge table, extract the ordinary edge connection features for each ordinary edge, and obtain the ordinary edge connection feature table; the ordinary edge connection feature table shall at least record the ordinary edge number, the starting atom number, the ending atom number, the chemical bond type, the chemical bond order, and the circumferential position difference and cross-sectional position difference between the starting atom and the ending atom in the atomic periodic mapping coordinate table; wherein, the circumferential position difference and the cross-sectional position difference are obtained by subtracting the atomic periodic mapping coordinates of the corresponding two atoms.

[0070] Step 404: Read the periodic constraint edge table, extract the periodic constraint edge connection features for each periodic constraint edge, and obtain the periodic constraint edge connection feature table; the periodic constraint edge connection feature table shall at least record the periodic constraint edge number, the connection start atom number, the connection end atom number, the periodic connection direction mark, and the circumferential position difference and cross-sectional position difference between the connection start atom and the connection end atom in the atomic periodic mapping coordinate table; wherein, the periodic connection direction mark is determined according to the writing order in the periodic connection atom table.

[0071] Step 405: Read the geometric relationship table, the atomic periodic mapping coordinate table, and the virtual geometric node table. For each group of atomic nodes and virtual geometric nodes with established relationships, extract the spatial relationship features of the atomic nodes relative to the virtual geometric nodes to obtain a spatial relationship feature table. The spatial relationship feature table records at least the atom number, the virtual geometric node number, the difference between the circumferential position of the atom and the circumferential position of the virtual geometric node, the difference between the cross-sectional position of the atom and the cross-sectional position of the virtual geometric node, and the distance value from the atomic node to the virtual geometric node. The distance value from the atomic node to the virtual geometric node is calculated based on the coordinate difference between the atomic periodic mapping coordinates and the center coordinates of the virtual geometric node.

[0072] Step 406: Read the radial basis coding configuration to obtain the coding center value sequence and coding width parameter; the coding center value sequence is obtained by dividing the value range of the distance set to be coded, and the coding width parameter is determined by the interval between adjacent coding center values; write the coding center value sequence and coding width parameter into the radial basis coding parameter table.

[0073] Step 407: Read the inter-atomic distance matrix and the radial basis function (RBF) coding parameter table. The RBF coding parameter table records the sequence of coding center values ​​and the coding width parameter corresponding to each coding center value. For each distance value in the inter-atomic distance matrix, perform the following processing sequentially: calculate the difference between the distance value and the current coding center value, generate an exponential term based on the square of the difference and the corresponding coding width parameter, and then perform exponential mapping processing on the exponential term to obtain the basis function response value corresponding to the current coding center value; write all basis function response values ​​corresponding to the same distance value into the coding vector according to the order of the coding center value sequence to obtain the inter-atomic distance coding vector of the corresponding atom pair; repeat the above processing for all distance values ​​in the inter-atomic distance matrix to obtain the inter-atomic distance coding table.

[0074] Step 408: Read the distance values ​​from atomic nodes to virtual geometric nodes in the spatial relationship feature table, and perform the same radial basis encoding process as in step 407 on each distance value to obtain the distance encoding table from atomic nodes to virtual geometric nodes.

[0075] To illustrate the radial basis function (RBF) encoding process for inter-atomic distances, we can assume the sequence of encoding center values ​​recorded in the RBF encoding parameter table is 0.5, 1.0, and 1.5, with the corresponding encoding width parameters determined in the same way. If the distance between atom number 2 and atom number 5 is 1.1, we calculate the differences between the distance value 1.1 and the encoding center values ​​0.5, 1.0, and 1.5, respectively. Based on each difference and the corresponding encoding width parameter, we generate exponential terms. After performing exponential mapping on each exponential term, we obtain three basis function response values. Since the distance value 1.1 is closer to the encoding center value 1.0, the basis function response value corresponding to encoding center value 1.0 is larger, while the basis function response values ​​corresponding to encoding center values ​​0.5 and 1.5 are smaller. Subsequently, these three basis function response values ​​are written into the same encoding vector in the order of the encoding center value sequence to obtain the inter-atomic distance encoding vector corresponding to the atom pair of atom numbers 2 and 5. Repeating this process for other distance values ​​in the inter-atomic distance matrix yields the inter-atomic distance encoding table.

[0076] Step 409: Write the atomic node attribute table, ordinary edge connection feature table, periodic constraint edge connection feature table, spatial relationship feature table, inter-atomic distance encoding table, and distance encoding table from atomic nodes to virtual geometric nodes according to the atomic number, ordinary edge number, periodic constraint edge number, and geometric association relationship number to obtain the geometric encoding feature table.

[0077] Step 410: Use the geometric coding feature table as input for geometric message passing processing in subsequent steps.

[0078] Step S5: Based on the polymer periodic virtual geometry graph and geometric coding features, perform geometric message passing between atomic nodes and between atomic nodes and virtual geometry nodes to obtain the polymer graph representation, and output the polymer property prediction results based on the polymer graph representation.

[0079] In some implementations, geometric message passing between atomic nodes and between atomic nodes and virtual geometric nodes is performed based on the polymer periodic virtual geometry graph and geometric coding features to obtain a polymer graph representation. The purpose of this is to enable the chemical bond connections represented by ordinary edges, the cross-period connections represented by periodic constraint edges, and the spatial associations between atomic nodes and virtual geometric nodes to participate in the state update process, thereby obtaining a polymer graph representation that can be used for property prediction. The implementation steps include: Step 5011: Read the polymer cycle virtual geometry graph and the geometry encoding feature table, and read the message passing configuration table; the message passing configuration table shall at least record the atomic node state dimension, virtual geometry node state dimension, edge state dimension, associated edge state dimension, message passing round, message aggregation method, and state update method.

[0080] Step 5012: Read the atomic node attribute table and the atomic node state initialization parameter table; the atomic node state initialization parameter table is used to give the dimensional correspondence and parameter coefficients between the atomic node attribute vector and the atomic node state vector; perform state initialization processing on each atomic node attribute vector according to the atomic node state initialization parameter table to obtain the atomic node initial state table.

[0081] Step 5013: Read the virtual geometric node table, spatial relationship feature table, and virtual geometric node state initialization parameter table; first, collect all spatial relationship features associated with each virtual geometric node according to the virtual geometric node number, then perform summation processing on the collected spatial relationship features to obtain the spatial relationship aggregation vector of the corresponding virtual geometric node; then combine the center coordinates of the virtual geometric node with the spatial relationship aggregation vector, and perform state initialization processing according to the virtual geometric node state initialization parameter table to obtain the initial state table of the virtual geometric node.

[0082] Step 5014: Read the ordinary edge connection feature table, the periodic constraint edge connection feature table, the spatial relationship feature table, the inter-atomic distance encoding table, and the distance encoding table from atomic nodes to virtual geometric nodes, and read the ordinary edge state initialization parameter table, the periodic constraint edge state initialization parameter table, and the associated edge state initialization parameter table respectively; generate the ordinary edge initial state table based on the ordinary edge connection features and the corresponding inter-atomic distance encoding results, generate the periodic constraint edge initial state table based on the periodic constraint edge connection features and the corresponding inter-atomic distance encoding results, and generate the associated edge initial state table based on the spatial relationship features and the corresponding distance encoding results from atomic nodes to virtual geometric nodes.

[0083] Step 5015: Read the message passing round and perform state update processing according to the number of loops corresponding to the message passing round; In each round of state update processing, first perform geometric message passing between atomic nodes: For each target atomic node, traverse all ordinary edges and periodic constraint edges connected to the target atomic node, read the current state of the adjacent source atomic node, the current state of the corresponding edge and the current state of the target atomic node, and concatenate the current states of the adjacent source atomic node, the current state of the corresponding edge and the current state of the target atomic node in order to obtain the inter-atomic message input vector.

[0084] Step 5016: Read the inter-atomic message mapping parameter table. The inter-atomic message mapping parameter table records the dimensional correspondence and parameter coefficients between the input items of each dimension of the inter-atomic message input vector and the output items of each dimension of the candidate message. Based on the inter-atomic message mapping parameter table, perform a dimensional weighted accumulation process on each inter-atomic message input vector according to the dimensional correspondence, and write the bias term to obtain the candidate messages sent from the adjacent source atomic nodes to the target atomic nodes. Then, collect all candidate messages according to the target atomic node number, establish an accumulation vector with the same dimension as the candidate messages for each target atomic node, and add all candidate messages belonging to the same target atomic node item by item according to the dimension to obtain the inter-atomic aggregated message corresponding to each target atomic node.

[0085] Step 5017: In each round of state update processing, perform geometric message passing between atomic nodes and virtual geometric nodes: For each associated edge, read the current state of the atomic node at one end of the associated edge, the current state of the virtual geometric node at the other end, and the current state of the associated edge, and concatenate the current states of the atomic node, the virtual geometric node, and the associated edge in order to obtain the associated message input vector.

[0086] Step 5018: Read the atomic-to-virtual geometric node message mapping parameter table and the virtual geometric node-to-atomic message mapping parameter table. The atomic-to-virtual geometric node message mapping parameter table is used to provide the dimensional correspondence and parameter coefficients between the associated message input vector and the candidate message sent from the atomic node to the virtual geometric node. The virtual geometric node-to-atomic message mapping parameter table is used to provide the dimensional correspondence and parameter coefficients between the associated message input vector and the candidate message sent from the virtual geometric node to the atomic node. Based on the corresponding parameter tables, perform a dimensional weighted accumulation process on each associated message input vector and write the bias term to obtain the candidate message sent from the atomic node to the virtual geometric node and the candidate message sent from the virtual geometric node to the atomic node. Then, collect the candidate messages according to the receiver number, establish an accumulation vector with the same dimension as the candidate message for each receiver, and add all candidate messages belonging to the same receiver item by dimension to obtain the geometric association aggregate message corresponding to the atomic node and the geometric association aggregate message corresponding to the virtual geometric node.

[0087] Step 5019: Read the atomic node state update parameter table, and concatenate the current state of each atomic node, the corresponding inter-atomic aggregation message, and the corresponding geometric association aggregation message in sequence to obtain the atomic node state update input vector; perform mapping processing on the atomic node state update input vector according to the atomic node state update parameter table to obtain the updated atomic node state table.

[0088] Step 5020: Read the virtual geometric node state update parameter table; the virtual geometric node state update parameter table records the dimensional correspondence and parameter coefficients between the input items of each dimension of the virtual geometric node state update input vector and the output items of each dimension of the updated virtual geometric node state; concatenate the current state of each virtual geometric node and the corresponding geometric association aggregation message in sequence to obtain the virtual geometric node state update input vector; then, according to the virtual geometric node state update parameter table, perform a dimension-wise weighted accumulation process on the virtual geometric node state update input vector and write it into the bias term to obtain the updated virtual geometric node state table.

[0089] Step 5021: Determine whether the current state update round has reached the message passing round recorded in the message passing configuration table; if the message passing round has not been reached, use the updated atomic node state table, the updated virtual geometric node state table, the initial state table of ordinary edges, the initial state table of periodic constraint edges, and the initial state table of associated edges as input for the next round of state update processing, and repeat steps 5015 to 5020; when the message passing round is reached, output the final atomic node state table and the final virtual geometric node state table.

[0090] Step 5022: Read the final atomic node state table and perform summation processing on all atomic node states in atomic number order. The summation processing includes: establishing an atomic node accumulation vector with the same dimension as the atomic node state, and reading each atomic node state sequentially in atomic number order, adding each atomic node state to the atomic node accumulation vector item by item according to the dimension to obtain the atomic node aggregation vector; Read the final virtual geometric node state table and perform summation processing on all virtual geometric node states in virtual geometric node number order. The summation processing includes: establishing a virtual geometric node accumulation vector with the same dimension as the virtual geometric node state, and reading each virtual geometric node state sequentially in virtual geometric node number order, adding each virtual geometric node state to the virtual geometric node accumulation vector item by item according to the dimension to obtain the virtual geometric node aggregation vector.

[0091] Step 5023: Concatenate the atomic node aggregation vector and the virtual geometric node aggregation vector in sequence to obtain the polymer graph representation, and use the polymer graph representation as the input for polymer property prediction processing in subsequent steps.

[0092] Furthermore, to illustrate the formation process of the polymer graph representation, it can be assumed that after a predetermined number of message passing rounds, the final atomic node state table contains three atomic nodes with state vectors of [0.20, 0.35], [0.10, 0.40], and [0.30, 0.25], respectively. After performing a step-by-step summation on all atomic node states in atomic number order, the atomic node aggregation vector [0.60, 1.00] can be obtained. Simultaneously, if the final virtual geometric node state table contains two virtual geometric nodes with state vectors of [0.15, 0.20] and [0.05, 0.30], then after performing a step-by-step summation on all virtual geometric node states in virtual geometric node number order, the virtual geometric node aggregation vector [0.20, 0.50] can be obtained. Finally, concatenating the atomic node aggregation vector and the virtual geometric node aggregation vector in sequence yields the polymer graph representation [0.60, 1.00, 0.20, 0.50]. This example demonstrates that the geometric message passing results between atomic nodes and between atomic nodes and virtual geometric nodes are ultimately summarized into a polymer graph representation that can be directly used for property prediction processing.

[0093] In some implementations, the purpose of outputting polymer property prediction results based on polymer graph characterization is to map the polymer graph characterization to numerical results corresponding to the target properties and generate polymer property prediction results according to a unified field format; the implementation steps include: Step 5031: Read the polymer graph characterization and the property prediction configuration table; the property prediction configuration table records at least the target property definition table, the property prediction mapping parameter table, and the result recovery rule table; the target property definition table records the target property name, output order, and result unit; the property prediction mapping parameter table records the input dimension number, output dimension number, dimension correspondence, parameter coefficient, and bias term corresponding to each target property; the result recovery rule table records the recovery method, recovery coefficient, recovery bias term, and result unit correspondence corresponding to each target property; wherein, the recovery method includes at least one of proportional recovery processing and proportional plus bias recovery processing, and the recovery coefficient and recovery bias term are used to convert the internal predicted value into the target property result value.

[0094] Step 5032: Based on the output order in the target property definition table, write the features of each dimension in the polymer graph representation in the order of dimension number to obtain the property prediction input vector; each input item in the property prediction input vector corresponds one-to-one with the corresponding feature in the polymer graph representation.

[0095] Step 5033: Read the property prediction mapping parameter table and perform mapping processing item by item according to the target property number; for each target property, first read the input dimension number, parameter coefficient and bias term corresponding to the target property, then extract the input value of the corresponding dimension from the property prediction input vector, multiply each input value with the corresponding parameter coefficient item by item and sum them, and finally write the bias term to obtain the initial prediction value corresponding to the target property; repeat the above process for all target properties to obtain the initial prediction value corresponding to each target property.

[0096] Step 5034: Read the result recovery rule table and perform result recovery processing on the initial predicted value corresponding to each target property according to the target property number; when the recovery method recorded in the result recovery rule table is proportional recovery processing, multiply the initial predicted value by the recovery coefficient to obtain the target property prediction value; when the recovery method recorded in the result recovery rule table is proportional plus bias recovery processing, first multiply the initial predicted value by the recovery coefficient, and then add the recovery bias term to obtain the target property prediction value; repeat the above processing for all target properties to obtain the target property prediction value corresponding to each target property.

[0097] Step 5035: According to the output order in the target property definition table, write the property name, predicted value and unit of each target property into the property prediction result table to obtain the polymer property prediction result; the property prediction result table shall include at least the property name field, the predicted value field and the unit field.

[0098] Step 5036: The polymer property prediction results are used as the final output of the method of this application.

[0099] To illustrate the process of generating the predicted values ​​of the target properties, the polymer graph obtained in step 5022 can be characterized as [0.60, 1.00, 0.20, 0.50]. If the property prediction configuration table records that the first target property calls the input values ​​of the first and second dimensions, with parameter coefficients of 0.8 and 0.4 respectively and a bias term of 0.1, then the initial predicted value corresponding to the first target property can be obtained by multiplying 0.60 by 0.8 and 1.00 by 0.4, and then adding 0.1. If the result recovery rule table records that the target property uses proportional recovery processing with a recovery coefficient of 10, then the initial predicted value can be multiplied by the recovery coefficient to obtain the target property prediction value corresponding to the target property. If the second target property calls the input values ​​of the third and fourth dimensions, with parameter coefficients of 0.5 and 0.6 respectively and a bias term of 0.2, and the result recovery rule table records that it uses proportional plus bias recovery processing, then after obtaining the initial predicted value corresponding to the second target property, the initial predicted value can be multiplied by the recovery coefficient and the recovery bias term added to obtain the second target property prediction value. Subsequently, according to the output order in the target property definition table, the property name, target property prediction value, and result unit of each target property are written into the property prediction result table to form the final output result.

[0100] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope defined in the claims.

Claims

1. A method for predicting polymer properties based on virtual geometry, characterized in that, include: Step S1: Read the polymer repeating unit structure, identify the connection point markers, replace each connection point marker with a preset atom to obtain a copy of the repeating unit, and determine the atom corresponding to the replacement position as the periodic connection atom; Step S2: Generate the three-dimensional coordinates of each atom based on the repeating unit copy, extract the distance between atoms based on the three-dimensional coordinates of each atom, extract the position parameters of each atom based on the direction of the line connecting the atoms of the two periods in the repeating unit copy, normalize the position parameters, and obtain the period mapping parameters. Step S3: Map the periodic mapping parameters to the Möbius ring coordinate space to obtain the atomic periodic mapping coordinates; generate atomic nodes and ordinary edges based on the atoms and chemical bonds in the repeating unit copy; generate periodic constraint edges based on the connection relationship between periodically connected atoms; generate virtual geometric nodes based on the atomic periodic mapping coordinates to obtain the polymer periodic virtual geometry graph. Step S4: Extract atomic node attributes, ordinary edge connection features, periodic constraint edge connection features, and spatial relationship features of atomic nodes relative to virtual geometric nodes based on the polymer periodic virtual geometry graph. Perform radial basis encoding on the distance between atoms and the distance from atomic nodes to virtual geometric nodes to obtain geometric encoding features. Step S5: Based on the polymer periodic virtual geometry graph and geometric coding features, perform geometric message passing between atomic nodes and between atomic nodes and virtual geometry nodes to obtain the polymer graph representation, and output the polymer property prediction results based on the polymer graph representation.

2. The polymer property prediction method based on virtual geometry according to claim 1, characterized in that, Methods for identifying connection point markers include: The atomic symbols, chemical bond symbols, and connection point markers in the polymer repeating unit structure are structurally decomposed; each atomic symbol, chemical bond symbol, and connection point marker is numbered to obtain an atomic marker table, a chemical bond marker table, and a connection point marker table; based on the adjacency relationship in the structure, the atomic number and chemical bond number adjacent to each connection point marker are recorded to obtain a connection point adjacency relationship table.

3. The polymer property prediction method based on virtual geometry according to claim 2, characterized in that, Methods for obtaining duplicate unit copies and identifying the atoms corresponding to the replacement positions as periodic connection atoms include: Read the link point replacement rules, which specify the preset atom type for each link point marker and the chemical bond connection method to be retained during replacement; copy the structure analysis results of the repeating unit to obtain a copy record of the repeating unit; replace each link point marker with the corresponding preset atom according to the numbering order in the link point marker table, and retain the adjacent atoms and chemical bond connection relationships corresponding to each link point marker; write the replacement position number, the replaced atom number, the original link point marker number, and the adjacent atom number for each replacement position to obtain the replacement position correspondence table; extract the atom corresponding to the replacement position based on the replacement position correspondence table, and determine the atom corresponding to the replacement position as the periodic linking atom.

4. The polymer property prediction method based on virtual geometry according to claim 1, characterized in that, Methods for generating the three-dimensional coordinates of each atom based on repeated unit copies include: Read the duplicate unit copy and the periodic connection atomic table, and establish a conformation generation record based on the atom type, chemical bond type, and atomic connection relationship in the duplicate unit copy; write the corresponding bond length constraints and bond angle constraints according to the atom type and chemical bond type in the conformation generation record to generate an initial conformation record; perform three-dimensional conformation solving processing on the initial conformation record to obtain the initial spatial coordinates of each atom in the duplicate unit copy; perform number correction processing on the initial spatial coordinates so that each atom number corresponds to a three-dimensional coordinate value to obtain an atomic coordinate table; associate the atomic coordinate table with the periodic connection atomic table to obtain the three-dimensional coordinates of each atom.

5. The polymer property prediction method based on virtual geometry according to claim 4, characterized in that, The periodic mapping parameters are obtained, including: Read the three-dimensional coordinates of each atom, and calculate the spatial distance between any two atoms by pairwise combination according to the atom number to obtain the inter-atom distance matrix; extract the three-dimensional coordinates of two periodically connected atoms from the atom coordinate table, and generate a periodic direction vector by taking the three-dimensional coordinates of one periodically connected atom as the starting point and the three-dimensional coordinates of the other periodically connected atom as the ending point; perform projection processing on the three-dimensional coordinates of each atom using the periodic direction vector as the projection direction to obtain the original position parameters of each atom along the periodic direction vector; perform linear normalization processing on each original position parameter to obtain the periodic mapping parameters.

6. The polymer property prediction method based on virtual geometry according to claim 5, characterized in that, Methods for obtaining atomic periodic mapping coordinates include: The process involves reading the periodic mapping parameters, atomic coordinate table, and periodic direction vector, and decomposing the three-dimensional coordinates of each atom into axial and lateral components based on the periodic direction vector. The periodic mapping parameters of each atom are sorted according to their numerical values; when identical periodic mapping parameters exist, their order is determined by the atom number, and position numbers are assigned sequentially to obtain a circumferential position sequence. Based on the position number of each atom in the circumferential position sequence, the lateral components of each atom are written into the corresponding cross-sectional positions to obtain a cross-sectional position sequence. The traversal direction and flip boundary position are determined based on the position number in the circumferential position sequence, and a single flip process is performed on the cross-sectional position sequence. Finally, the circumferential position numbers are paired with the corresponding cross-sectional positions to obtain the atomic periodic mapping coordinates.

7. The polymer property prediction method based on virtual geometry according to claim 6, characterized in that, Methods for obtaining polymer periodic virtual geometry include: Each atom in the repeating unit copy is written into the node table to obtain atomic nodes; each chemical bond in the chemical bond list is written into the edge table to obtain ordinary edges; the atomic nodes corresponding to the atoms connecting two periods are written into the edge table as connection endpoints to obtain periodic constraint edges; the circumferential positions in the atomic periodic mapping coordinates are sorted, and the circumferential position intervals between adjacent atoms are calculated to obtain a circumferential interval sequence; the absolute value of the difference between each circumferential interval and its previous circumferential interval is calculated in sequence. When the absolute value of the difference is greater than the interval change judgment value, the corresponding circumferential position is determined as the interval change position, and multiple continuous coordinate segments are obtained by using each interval change position as the segment boundary; the average value of the circumferential positions and the average value of the cross-sectional positions in each continuous coordinate segment are calculated to obtain the center coordinates, and virtual geometric nodes are generated based on the center coordinates; the corresponding atomic nodes are associated with the corresponding virtual geometric nodes based on the continuous coordinate segments to which each atomic periodic mapping coordinate belongs; the atomic nodes, ordinary edges, periodic constraint edges, virtual geometric nodes, and association relationships are merged to obtain the polymer periodic virtual geometry graph.

8. The polymer property prediction method based on virtual geometry according to claim 7, characterized in that, Methods for obtaining geometrically encoded features include: Extract the atom type, number of chemical bonds, number of ordinary edge adjacencies, and number of periodically constrained edge adjacencies of the atomic nodes; extract the circumferential position difference, cross-sectional position difference, and corresponding connection type of the atoms at both ends of ordinary and periodically constrained edges; extract the circumferential position difference, cross-sectional position difference, and distance value between the atomic nodes and virtual geometric nodes; read the radial basis encoding parameters and perform radial basis encoding processing on each distance value in the inter-atom distance matrix and each distance value from the atomic node to the virtual geometric node; combine the above atomic node attributes, ordinary edge connection features, periodically constrained edge connection features, spatial relationship features, inter-atom distance encoding results, and distance encoding results from the atomic node to the virtual geometric node to obtain the geometric encoding features.

9. The polymer property prediction method based on virtual geometry according to claim 8, characterized in that, Methods for obtaining polymer characterization include: The initial states of atomic nodes and virtual geometric nodes are obtained based on the atomic node state initialization parameter table and the virtual geometric node state initialization parameter table, respectively. The initial states of ordinary edges, periodic constraint edges, and associated edges are obtained based on the ordinary edge state initialization parameter table, the periodic constraint edge state initialization parameter table, and the associated edge state initialization parameter table, respectively. Atom-to-atomic aggregated messages are obtained based on the inter-atomic message mapping parameter table, and geometric associated aggregated messages are obtained based on the atom-to-virtual geometric node message mapping parameter table and the virtual geometric node-to-atomic message mapping parameter table. The states of atomic nodes and virtual geometric nodes are updated based on the atomic node state update parameter table and the virtual geometric node state update parameter table, and the state update process is repeated according to the message passing rounds. The final atomic node states are aggregated to obtain atomic node aggregated vectors, and the final virtual geometric node states are aggregated to obtain virtual geometric node aggregated vectors. The atomic node aggregated vectors and the virtual geometric node aggregated vectors are combined to obtain the polymer graph representation.

10. The polymer property prediction method based on virtual geometry according to claim 9, characterized in that, Methods for outputting polymer property prediction results include: Read the atomic node state update parameter table and the virtual geometry node state update parameter table to obtain the updated atomic node state table and the updated virtual geometry node state table, respectively. Repeat the state update process according to the message passing rounds recorded in the message passing configuration table, and output the final atomic node state table and the final virtual geometry node state table when the message passing round is reached. Perform item-by-item summation on all atomic node states in atomic number order to obtain the atomic node aggregation vector. Perform item-by-item summation on all virtual geometry node states in virtual geometry node number order to obtain the virtual geometry node aggregation vector. Concatenate the atomic node aggregation vector and the virtual geometry node aggregation vector in sequence to obtain the polymer graph representation. Read the property prediction configuration table, obtain the initial prediction value corresponding to each target property according to the property prediction mapping parameter table, and obtain the target property prediction value according to the result recovery rule table. Write the predicted value to the property prediction result table to obtain the polymer property prediction result.

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