Material formula generation method based on performance sensitivity adaptive hierarchical sampling

Abstract

The present application relates to the technical field of computer-aided material design, in particular to a material chemical formula generation method based on performance sensitivity adaptive hierarchical sampling, which comprises the following steps: inputting an element list; querying a performance sensitivity knowledge base to obtain sensitivity levels and adjustment factors; analyzing a composite element and extracting multi-dimensional element features, and quantitatively calculating element combination complexity; based on the number of elements, sensitivity and complexity, adaptively selecting a corresponding sampling strategy and dynamically allocating a sampling amount; generating a chemical formula and removing duplicates; and outputting a chemical formula list and full-process metadata. Through the performance sensitivity driven resource allocation, composite element atomic level analysis, feature space clustering and other innovations, the present application improves the computing efficiency by tens to hundreds of times, reduces the response time to seconds or minutes, and has the characteristics of traceability, scalability and strong universality, effectively accelerating the material screening and discovery process.

Description

Technical Field

[0001] This invention relates to the field of computer-aided materials design technology, specifically a method for generating material chemical formulas based on performance-sensitive adaptive hierarchical sampling. Background Technology

[0002] As new materials research and development moves towards high throughput and precision, computer-aided materials design has become a key means to shorten research and development cycles and reduce experimental costs. In the development of multi-element material systems (such as alloys, oxides, and semiconductor composites), it is necessary to generate a large number of potential chemical formula combinations, combine them with computational models to predict their properties, and then screen out candidate materials with application value. The core requirement of this process is to minimize unnecessary calculations and improve research and development efficiency while ensuring that sampling points cover key regions of chemical space and reflect the laws governing performance changes.

[0003] Traditional chemical formula combination generation methods mainly rely on exhaustive methods, uniform random sampling methods, or simple grid sampling methods. These methods have played a certain role in the past research and development of basic materials. However, as material systems become more multi-component composites (such as ternary or higher alloys, functional materials containing composite elements) and performance requirements become more precise, their limitations are becoming increasingly apparent. Specifically, these limitations are manifested in the following ways:

[0004] Low computational efficiency: In a multi-element system, the full combinatorial search space grows exponentially, resulting in lengthy computation time, which cannot meet the needs of real-time interaction and high-throughput computing.

[0005] The sampling is highly indiscriminate: it fails to consider the different sensitivities of different performance indicators to changes in composition, and adopts a uniform sampling strategy, resulting in wasted computing resources in low-value areas and insufficient allocation in high-value areas;

[0006] The results are not representative enough: uniform sampling can easily overlook the detailed features of performance-sensitive areas, which leads to a decrease in the accuracy of subsequent material screening and performance analysis;

[0007] Complex elements are difficult to handle: Existing methods cannot effectively resolve the atomic structure and characteristics of complex elements such as AlO3, which affects the accuracy of chemical formula analysis and feature extraction.

[0008] Severe system response latency: In real-world application scenarios such as WebAPI services, long-duration computational tasks significantly reduce user experience and system availability.

[0009] Therefore, there is an urgent need for an efficient generation method that can combine material chemical characteristics and performance sensitivity, intelligent decision sampling strategies, and adaptive adjustment of sampling resources to significantly improve computational efficiency while ensuring the representativeness of the samples. Summary of the Invention

[0010] The purpose of this invention is to provide a method for generating material chemical formulas based on performance-sensitive adaptive hierarchical sampling, so as to solve the problems mentioned in the background art.

[0011] To achieve the above objectives, the present invention provides the following technical solution: a method for generating material chemical formulas based on performance-sensitivity adaptive hierarchical sampling, comprising the following steps:

[0012] S1. Input element list: Input a list of elements that make up the material, which includes basic elements and composite elements;

[0013] S2. Performance Sensitivity Analysis: Query the preset performance sensitivity mapping knowledge base to obtain the sensitivity level corresponding to the target performance index, and determine the corresponding sampling quantity adjustment factor based on the sensitivity level;

[0014] S3. Calculation of element combination complexity: Analyze the composite elements in the element list, extract the multi-dimensional features of each element, and calculate the element combination complexity score based on feature diversity, number of atom types and number of composite elements.

[0015] S4. Adaptive Sampling Strategy Selection and Sampling Quantity Allocation: Based on the number of elements, the sensitivity level, and the complexity score, select one of the following sampling methods as the optimal sampling strategy: precise adaptive sampling, Dirichlet optimized sampling, or hierarchical clustering sampling. Simultaneously, based on the preset basic sampling quantity according to the number of elements, the complexity score, and the sampling quantity adjustment factor, calculate and allocate the sampling quantity using a preset calculation formula that includes complexity-related terms and sensitivity factors. The sampling quantity shall not exceed the preset maximum sampling quantity limit for the corresponding number of elements.

[0016] S5. Chemical formula generation: Based on the optimal sampling strategy and the determined sampling quantity, generate a list of chemical formula combinations for the materials, and remove duplicates from the list of chemical formula combinations.

[0017] S6. Result Output and Storage: Output the list of chemical formula combinations and save the sampling strategy, calculation parameters and metadata for subsequent traceability and analysis.

[0018] Preferably, the performance sensitivity mapping knowledge base in step S2 comes from a preset material performance sensitivity structured knowledge base;

[0019] The sensitivity levels include high sensitivity, medium sensitivity, and low sensitivity, where the high sensitivity level corresponds to a sampling quantity adjustment factor of 1.5, the medium sensitivity level corresponds to a factor of 1.0, and the low sensitivity level corresponds to a factor of 0.8.

[0020] The target performance indicators include thermoelectric figure of merit (ZT), power factor (PF), Seebeck coefficient, oxygen evolution onset potential (onset), Tafel slope, melting point (Tm), permittivity, contact resistance (Rc), superconducting critical temperature (SC_copper / SC_traditional), and thermal conductivity.

[0021] Preferably, the multidimensional features in step S3 are 5-dimensional elemental features, specifically including atomic number, electronegativity, atomic radius, group, and period.

[0022] The analytical process of the composite element is as follows: the composite element is decomposed into basic atomic components, the weights are determined according to the proportion of each atom in the composite element, and the five-dimensional feature vectors of each atomic component are weighted and averaged based on the weights to obtain the five-dimensional feature vector of the composite element.

[0023] Preferably, the calculation process of the element combination complexity score in S3 is as follows:

[0024] S31. Constructing the feature matrix: Combining the basic elements and composite elements into a 5-dimensional feature matrix. , where n is the number of elements and m=5 is the feature dimension;

[0025] S32. Feature Diversity Calculation: Calculate the standard deviation of each dimension of the feature matrix along the column direction. Standard deviation Reflecting each element in the first The degree of dispersion on the dimensional feature is calculated using the following formula:

[0026] ;

[0027] in, For the first The element in the first... eigenvalues ​​of dimension For the first The mean of the dimensional features;

[0028] The standard deviation Divide by the feature mean of the corresponding dimension to obtain the normalized standard deviation normalized_std;

[0029] S33. Atom Type Count Adjustment: Calculate the atom type count unique_atoms to obtain the atom type count adjustment factor A= To prevent high-atomic-number systems from excessively increasing complexity;

[0030] S34. Composite Element Adjustment: Calculate the composite element adjustment factor B based on the number of composite elements (compound_count), using the following formula:

[0031] B = 1.0 + 0.2 × compound_count;

[0032] S35. Complexity Synthesis: Multiply the mean normalized standard deviation of each dimension, the atomic type adjustment factor, and the composite element adjustment factor to obtain a complexity score between 0 and 1. The calculation formula is as follows:

[0033] ;

[0034] in The mean of the normalized standard deviation.

[0035] Preferably, the selection logic for the optimal sampling strategy in step S4 is as follows:

[0036] If the number of composite elements is less than 3, then select exact adaptive sampling directly.

[0037] If the number of composite elements is ≥3 and the target performance index is either high sensitivity level or complexity score >0.3, then stratified clustering is selected.

[0038] Except for the two cases mentioned above, Dirichlet-optimized sampling is selected.

[0039] Preferably, the number of samples in step S4 is calculated using the following formula:

[0040] ;

[0041] in: The base sampling size is preset based on the number of elements, specifically as follows:

[0042] When the number of elements is 2, the corresponding basic sampling quantity is 1000;

[0043] When the number of elements is 3, the corresponding basic sampling quantity is 5000;

[0044] When the number of elements is 4, the corresponding basic sampling quantity is 15000;

[0045] When the number of elements is 5, the corresponding basic sampling quantity is 30000;

[0046] For every 1 increase in the number of elements, the base sampling size increases by a fixed gradient of 15000.

[0047] The complexity score calculated in step S3;

[0048] This is the sampling quantity adjustment factor obtained in step S2;

[0049] The sampling amount does not exceed the maximum sampling amount limit preset for the corresponding number of elements, that is:

[0050] The maximum sampling size is 5000 when the number of elements is 2;

[0051] The maximum sampling size is 20000 when the number of elements is 3;

[0052] The maximum sampling size is 50,000 when the number of elements is 4;

[0053] The maximum sampling size is 100,000 when the number of elements is 5;

[0054] For every 1 increase in the number of elements, the maximum sampling size increases by a fixed gradient of 50,000.

[0055] Preferably, when the optimal sampling strategy in step S4 is Dirichlet-optimized sampling, its implementation process is as follows:

[0056] For each element, its Pauling scale electronegativity is determined by the formula... Calculate the Dirichlet distribution parameter;

[0057] in Let the Pauling scale electronegativity of the i-th element be ;

[0058] Based on the adjusted The parameter vector generates a random proportion of the final sample size group.

[0059] For any combination where the proportion of any element is ≤0.001, round to 3 decimal places and finely adjust the sum of the proportions of each element in each combination to 1.0; Note: formula: proportions = np.round(Dirichlet distribution sample size group random proportion, 3);

[0060] proportions[:, -1] = 1.0 - np.sum(proportions[:, :-1], axis=1) # Recalculate the last column to ensure that the sum of the proportions in each row is exactly equal to 1.0;

[0061] In the formula, 3.0 is the electronegativity normalization benchmark value, determined based on statistical analysis and parameter tuning experiments of 80 common elements in the Pauling electronegativity scale, ensuring... The parameter distribution is reasonable and conforms to the rules of element chemical affinity.

[0062] Preferably, when the optimal sampling strategy in step S4 is precise adaptive sampling, its implementation process is as follows:

[0063] Step size calculation: The adaptive step size is calculated using the formula step size = 1.0 / (recommended sampling amount - 1), and the step size is normalized to an integer multiple of 0.001. The recommended sampling amount is the number of samples determined in step S4.

[0064] Mesh enumeration: According to the normalized step size, traverse all combinations that satisfy the sum of the proportions of the elements being 1.0 to generate a complete mesh sampling combination;

[0065] Chemical formula construction: Generate the corresponding chemical formula string based on the element ratio of each grid combination.

[0066] Preferably, when the optimal sampling strategy in step S4 is hierarchical clustering sampling, its implementation process is as follows:

[0067] Candidate sample generation: Generate candidate samples five times the target sampling amount, with an upper limit of 200,000. The candidate samples are generated using the Dirichlet optimization sampling method.

[0068] Feature extraction: Extract a multi-dimensional feature vector for each candidate sample, including the proportion of each element in each chemical formula, statistical features (proportion mean, standard deviation, maximum value, minimum value), and weighted average of element features (weighted average of atomic number, electronegativity, and atomic radius).

[0069] Dimensionality Reduction and Clustering: Multidimensional feature vectors are reduced to 3 dimensions using PCA, and K-means clustering is performed, resulting in a cluster size of [number missing]. ;

[0070] Stratified sampling: Samples are drawn uniformly from each cluster, and the number of samples drawn is the quotient of the target sample size and the number of clusters. If the total number of samples drawn is less than the target sample size, the remaining candidate samples are randomly supplemented.

[0071] Preferably, the deduplication process in step S5 specifically involves: performing a consistency check on the generated candidate chemical formula list, removing identical chemical formula entries, and ensuring that each entry in the final output target chemical formula list is unique; the specified decimal place is 3 digits, that is, determining whether there is a duplicate when the element ratio in the chemical formula is accurate to the thousandths place.

[0072] Compared with the prior art, the beneficial effects of the present invention are:

[0073] This invention achieves atomic-level analysis of composite elements and quantification of complexity through five interconnected modules: performance sensitivity quantification and classification, element combination complexity calculation, adaptive sampling strategy selection and sampling quantity allocation, dynamic sampling quantity allocation, and feature space-driven hierarchical clustering sampling. It intelligently selects three sampling strategies—precise adaptive, Dirichlet optimization, or hierarchical clustering—based on the number of elements, performance sensitivity level, and complexity score, dynamically adjusting the sampling quantity and key parameters. Ultimately, while ensuring the representativeness of sampling points and chemical space coverage, the number of samples is reduced by one to two orders of magnitude, computational efficiency is improved by tens to hundreds of times, and response time is reduced from hours to seconds or minutes. Furthermore, the system is modular, scalable, and traceable, effectively accelerating the screening and development of new materials and is applicable to various material systems. Attached Figure Description

[0074] Figure 1 This is a schematic diagram of the overall framework of the material chemical formula generation method based on performance sensitivity adaptive hierarchical sampling of the present invention;

[0075] Figure 2 This is a schematic diagram of the adaptive sampling strategy decision-making process of the material chemical formula generation method based on performance sensitivity adaptive hierarchical sampling of the present invention;

[0076] Figure 3 This is a schematic diagram of the hierarchical clustering sampling execution process of the material chemical formula generation method based on performance sensitivity adaptive hierarchical sampling of the present invention. Detailed Implementation

[0077] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0078] Please see Figure 1-3 This invention provides a technical solution: a method for generating material chemical formulas based on performance-sensitivity adaptive hierarchical sampling, comprising the following steps:

[0079] S1. Input element list: Input a list of elements that make up the material. The element list includes basic elements and composite elements.

[0080] S2. Performance Sensitivity Analysis: Query the preset performance sensitivity mapping knowledge base to obtain the sensitivity level corresponding to the target performance indicator, and determine the corresponding sampling quantity adjustment factor based on the sensitivity level;

[0081] The performance sensitivity mapping knowledge base is derived from a pre-defined structured knowledge base for material performance sensitivity. This knowledge base (generated from the application "Quantification and Grading Method of Material Performance Sensitivity Based on Multidimensional Statistical Analysis" filed on 2026-01-23 with application number 2026100902412) is constructed through the following steps:

[0082] Input a dataset containing the chemical formulas of materials and their historical performance values;

[0083] For each performance metric in the dataset, calculate its multi-dimensional statistical characteristics, including but not limited to the mean, variance, skewness, kurtosis, and coefficient of variation.

[0084] By combining the variability of material composition, statistical characteristics are fused and corrected to generate a quantitative sensitivity score for the performance index. The preset threshold range for the quantitative sensitivity score is: high sensitivity ≥ 0.7, medium sensitivity 0.4~0.7, and low sensitivity < 0.4.

[0085] Based on the preset threshold range in which the quantified sensitivity score falls, the sensitivity level of the performance index is determined, including high sensitivity, medium sensitivity, and low sensitivity.

[0086] By statistically analyzing the distribution of historical data for this performance indicator, we can obtain its historical typical value range.

[0087] The output includes structured records containing performance indicator names, quantified sensitivity scores, sensitivity levels, and historical typical value ranges, which are then compiled into a knowledge base.

[0088] Sensitivity levels include high sensitivity, medium sensitivity, and low sensitivity. Each level is assigned a quantified sampling number adjustment factor. The high sensitivity level corresponds to a sampling number adjustment factor of 1.5, which means that the sampling number needs to be increased by 50% compared to the baseline. The medium sensitivity level corresponds to a factor of 1.0 (the baseline). The low sensitivity level corresponds to a factor of 0.8, which can reduce the sampling number by 20%.

[0089] Target performance indicators include thermoelectric figure of merit (ZT), power factor (PF), Seebeck coefficient, oxygen evolution onset potential (onset), Tafel slope, melting point (Tm), permittivity, contact resistance (Rc), superconducting critical temperature (SC_copper / SC_traditional), and thermal conductivity.

[0090] S3. Element Combination Complexity Calculation: Analyze the composite elements in the element list, extract the 5-dimensional element features of each element, and quantify and calculate the element combination complexity score based on feature diversity, number of atom types and number of composite elements.

[0091] The five-dimensional characteristics of elements specifically include atomic number, electronegativity, atomic radius, group, and periodicity;

[0092] The analytical process for composite elements is as follows: It supports the analysis of composite elements (such as AlO3), decomposing them into basic atomic components (such as Al and O). Weights are determined based on the proportion of each atom in the composite element. A weighted average of the five-dimensional eigenvectors of each atomic component is then calculated based on these weights to obtain the five-dimensional eigenvector of the composite element. For example, if AlO3 contains 1 Al atom and 3 O atoms, then the weight of Al is 1 / 4, and the weight of O is 3 / 4. This weighting ratio is used to calculate the weighted average five-dimensional eigenvector of the composite element, solving the problem that traditional methods cannot handle composite components.

[0093] The calculation process for the element combinatorial complexity score is as follows:

[0094] S31. Constructing the feature matrix: Combining the basic elements and composite elements into a 5-dimensional feature matrix. , where n is the number of elements and m=5 is the feature dimension;

[0095] S32. Feature Diversity Calculation: Calculate the standard deviation of each dimension of the feature matrix along the column direction. Standard deviation Reflecting each element in the first The degree of discreteness on the dimensional features, for example:

[0096] If all elements have similar electronegativity, then a small standard deviation in electronegativity dimension indicates low feature diversity in that dimension.

[0097] If the electronegativity of elements differs greatly, the standard deviation will be large, indicating high characteristic diversity.

[0098] Standard deviation The calculation formula is:

[0099] ;

[0100] in, For the first The element in the first... eigenvalues ​​of dimension For the first The mean of the dimensional features;

[0101] Standard deviation Divide by the feature mean of the corresponding dimension to obtain the normalized standard deviation normalized_std, which reflects the intrinsic differences between elements and avoids the influence of dimensionality;

[0102] S33. Atom type number adjustment: Calculate the number of unique atom types after deduplication (unique_atoms) to obtain the atom type number adjustment factor A= To prevent high-atomic-number systems from excessively increasing complexity;

[0103] S34. Composite Element Adjustment: Calculate the composite element adjustment factor B based on the number of composite elements (compound_count), using the following formula:

[0104] B = 1.0 + 0.2 × compound_count, where 0.2 is the compound element bonus, which introduces additional uncertainty and increases the weight by 0.2 times;

[0105] S35. Complexity Synthesis: Multiply the mean normalized standard deviation of each dimension, the atomic type adjustment factor, and the composite element adjustment factor to obtain a complexity score between 0 and 1. The calculation formula is as follows:

[0106] ;

[0107] in The mean of the normalized standard deviation;

[0108] S4. Adaptive Sampling Strategy Selection and Sampling Quantity Allocation: Based on the number of elements, sensitivity level, and complexity score, select one of the following sampling methods as the optimal sampling strategy: precise adaptive sampling, Dirichlet optimization sampling, or hierarchical clustering sampling. Simultaneously, based on the preset basic sampling quantity, complexity score, and sampling quantity adjustment factor according to the number of elements, calculate and allocate the sampling quantity using a preset formula that includes complexity-related terms and sensitivity factors. The sampling quantity shall not exceed the preset maximum sampling quantity limit for the corresponding number of elements.

[0109] The specific logic for selecting the optimal sampling strategy is as follows:

[0110] If the number of composite elements is less than 3, then select exact adaptive sampling and use a fixed step size grid search.

[0111] If the number of composite elements is ≥3 and the target performance index is either high sensitivity level or complexity score >0.3, then stratified clustering is selected. Stratified clustering is suitable for high sensitivity or high complexity scenarios and ensures the representativeness of the distribution based on feature space clustering.

[0112] In addition to the two cases mentioned above, Dirichlet-optimized sampling is selected, and probability distribution sampling is used to improve efficiency.

[0113] The number of samples is calculated using the following formula:

[0114] ;

[0115] in: The base sampling size, the two key parameters 0.8 and 1.5, originate from:

[0116] Experimental optimization determined that: through systematic sampling experiments and distribution quality assessments of more than 50 typical material systems (including binary, ternary and composite element systems), it was found that when the complexity is close to 0, the sampling amount should still be 80% of the basic amount (i.e., parameter 0.8) to cover the basic feature space.

[0117] Complexity sensitivity adjustment: Parameter 1.5 is used to amplify the impact of complexity on the sampling rate, ensuring that when the complexity is close to 1, the increase in sampling rate does not exceed 1.5 times the base rate. This guarantees sufficient sampling for high-complexity systems while avoiding combinatorial explosion. By comparing the sampling coverage and computational efficiency under different coefficients (1.0, 1.5, 2.0), it was found that 1.5 can maintain high coverage (>95%) while keeping the sampling rate within a reasonable range, achieving the best balance between efficiency and quality.

[0118] Advantages: The combined effect of these two parameters allows the sampling amount to be smoothly and reasonably adjusted according to the system complexity, taking into account both the efficiency of simple systems and the coverage requirements of complex systems, and forming a synergistic optimization closed-loop system with the subsequent independent "distributed quality verification" method.

[0119] Based on the preset number of elements, specifically:

[0120] When the number of elements is 2, the corresponding basic sampling quantity is 1000;

[0121] When the number of elements is 3, the corresponding basic sampling quantity is 5000;

[0122] When the number of elements is 4, the corresponding basic sampling quantity is 15000;

[0123] When the number of elements is 5, the corresponding basic sampling quantity is 30000;

[0124] For every 1 increase in the number of elements, the base sampling size increases by a fixed gradient of 15000.

[0125] The complexity score calculated in step S3;

[0126] This is the sampling quantity adjustment factor obtained in step S2;

[0127] The sampling amount does not exceed the preset maximum sampling amount limit for the corresponding number of elements, that is:

[0128] The maximum sampling size is 5000 when the number of elements is 2;

[0129] The maximum sampling size is 20000 when the number of elements is 3;

[0130] The maximum sampling size is 50,000 when the number of elements is 4;

[0131] The maximum sampling size is 100,000 when the number of elements is 5;

[0132] For every 1 increase in the number of elements, the maximum sampling size increases by a fixed gradient of 50,000.

[0133] When the optimal sampling strategy is Dirichlet-optimized sampling, its implementation process is as follows:

[0134] For each element, its Pauling scale electronegativity is determined by the formula... Calculate the Dirichlet distribution parameter;

[0135] in, Let be the Dirichlet distribution parameters of the i-th element. Let $i$ be the Pauling scale electronegativity of the $i$-th element. The higher the electronegativity, the higher the electronegativity. The smaller the value, the more evenly the element is distributed in the sampling; conversely, the larger the value, the lower the electronegativity. The larger the value, the more concentrated the proportion of that element.

[0136] pass make sure A cutoff function of not less than 0.5, based on the properties of the Dirichlet distribution, when When <0.5, the distribution tends to produce extreme proportions near the boundary value;

[0137] Based on the adjusted The parameter vector generates a random proportion of the final sample size group.

[0138] For any combination where the proportion of any element is ≤0.001, round to 3 decimal places and finely adjust the sum of the proportions of each element in each combination to 1.0; Note: formula: proportions = np.round(Dirichlet distribution sample size group random proportion, 3);

[0139] proportions[:, -1] = 1.0 - np.sum(proportions[:, :-1], axis=1) # Recalculate the last column to ensure that the sum of the proportions in each row is exactly equal to 1.0;

[0140] In the formula, 3.0 is the electronegativity normalization benchmark value, determined based on statistical analysis and parameter tuning experiments of 80 common elements in the Pauling electronegativity scale, ensuring... The parameter distribution is reasonable and conforms to the chemical affinity rules of elements. Statistical data shows that the electronegativity of about 90% of common elements falls between 0.7 and 3.0. Therefore, choosing 3.0 as the benchmark can achieve the following optimization effects:

[0141] make The value distribution is reasonable: when the electronegativity of an element is close to 3.0, Approaching 0.5 (the lower limit of the Dirichlet distribution) makes the proportion of the element in the chemical formula more uniform and avoids extreme values;

[0142] Maintaining the trend of chemical affinity: Elements with electronegativity higher than 3.0 (such as O and F) correspond to smaller electronegativity values. This reflects the bonding tendency caused by its strong electronegativity. Its proportion will be arranged to be more "active" and more varied in virtual combinations in order to explore its diverse bonding possibilities.

[0143] Experimental verification of advantages: Through comparative experiments on 30 different types of material systems (including metal alloys, oxides, and semiconductors), the baseline value of 3.0, compared with 2.5 or 3.5, improves the "chemical rationality score" of the generated chemical formula by an average of about 18%, and has higher calculation stability.

[0144] This setting makes the Dirichlet sampling process not only a mathematical distribution sampling, but also incorporates the chemical laws between elements, improving the physical interpretability of the generated combinations and their usability in actual material research and development, making the generated chemical formulas more consistent with the chemical affinity between elements, and improving the sampling effectiveness.

[0145] When the optimal sampling strategy is precise adaptive sampling, a fixed step size (e.g., 0.001–0.1) is used to traverse all ratio combinations to ensure full coverage. The implementation process is as follows:

[0146] Step size calculation: The adaptive step size is calculated using the formula step size = 1.0 / (recommended sampling amount - 1), and the step size is normalized to an integer multiple of 0.001. The recommended sampling amount is the number of samples determined in step S4.

[0147] Mesh enumeration: Based on the normalized step size, traverse all combinations that satisfy the sum of the proportions of the elements being 1.0 to generate a complete mesh sampling combination;

[0148] Chemical formula construction: Generate the corresponding chemical formula string based on the element ratio of each grid combination;

[0149] When the optimal sampling strategy is hierarchical clustering sampling, its implementation process is as follows:

[0150] Candidate sample generation: Generate candidate samples five times the target sampling size, with an upper limit of 200,000. The candidate samples are generated using the Dirichlet optimization sampling method.

[0151] Feature extraction: Extract a multi-dimensional feature vector for each candidate sample, including the proportion of each element in each chemical formula, statistical features (proportion mean, standard deviation, maximum value, minimum value), and weighted average of element features (weighted average of atomic number, electronegativity, and atomic radius).

[0152] Dimensionality Reduction and Clustering: Multidimensional feature vectors are reduced to 3 dimensions using PCA, and K-means clustering is performed, resulting in a cluster size of [number missing]. ;

[0153] Stratified sampling: Samples are drawn uniformly from each cluster, and the number of samples drawn is the quotient of the target sample size and the number of clusters. If the total number of samples drawn is less than the target sample size, the remaining candidate samples are randomly supplemented.

[0154] S5. Chemical Formula Generation: Based on the optimal sampling strategy and the determined sampling quantity, generate a list of chemical formula combinations for the materials, and remove duplicates from the list of chemical formula combinations.

[0155] The deduplication process specifically involves: performing a consistency check on the generated candidate chemical formula list, removing identical chemical formula entries, and ensuring that each entry in the final output target chemical formula list is unique; specifying 3 decimal places, that is, determining whether there is a duplicate when the element ratio in the chemical formula is accurate to the thousandths place;

[0156] S6. Output and Storage of Results: Output a list of chemical formula combinations and save the sampling strategy, calculation parameters and metadata for subsequent traceability and analysis.

[0157] Implementation Case 1: Hierarchical Clustering Sampling with High Sensitivity Performance (ZT, Thermoelectric Figure of Merit) and High Input Element Complexity

[0158] Input elements: ["Cu", "Fe", "AlO3"]

[0159] Detailed steps:

[0160] 1. Performance Sensitivity Analysis:

[0161] - Knowledge base query: ZT's performance sensitivity is "High"

[0162] - Sensitivity factor: 1.5

[0163] 2. Calculation of element combination complexity:

[0164] - Analyzing the composite element: AlO3 → [Al:1, O:3], normalized Al weight = 1 / 4 = 0.25, O weight = 3 / 4 = 0.75

[0165] - Feature extraction: After removing duplicate atoms, the list is: Cu, Fe, Al, O → set(all_atoms) = {'Cu', 'Fe', 'Al', 'O'}, to obtain the feature of each atom:

[0166] Cu: [Atomic number 29, electronegativity 1.90, atomic radius 145, group 11, period 4]

[0167] Fe: [Atomic number 26, electronegativity 1.83, atomic radius 156, group 8, period 4]

[0168] Al: [Atomic number 13, electronegativity 1.61, atomic radius 118, group 13, period 3]

[0169] O: [Atomic number 8, electronegativity 3.44, atomic radius 48, group 16, period 2]

[0170] - Complexity calculation:

[0171] a. Characteristic standard deviation: [8.746, 0.7267, 42.02, 2.915, 0.829]

[0172] b. Normalized standard deviation: [0.4603, 0.3312, 0.3599, 0.2429, 0.2551]

[0173] c. Mean normalized standard deviation: 0.32988

[0174] d. Adjustment factor (number of atom types):

[0175] Number of heavy atoms removed: 4 (Cu, Fe, Al, O)

[0176] min(1.0, len(set(all_atoms)) / 5.0) = min(1.0, 4 / 5) = 0.8

[0177] Complexity × 0.8 = 0.32988 × 0.8 ≈ 0.2639

[0178] e. Consider the additional complexity of composite elements:

[0179] Number of composite elements: 1 (AlO3), i.e., compound_count = 1

[0180] Additional factor = 1.0 + 0.2 * compound_count = 1.0 + 0.2 × 1 = 1.2

[0181] f. Final complexity: Complexity × 1.2 = 0.2639 × 1.2 ≈ 0.31668

[0182] 3. Sampling strategy selection:

[0183] - Number of elements: 4

[0184] - Exhibits high sensitivity performance: Yes

[0185] - Complexity > 0.3: Yes (0.317 > 0.3)

[0186] - Select method: stratified_clustering

[0187] 4. Calculate the recommended number of samples:

[0188] - Base sample size (base_samples):

[0189] Base sample size lookup table: base_samples = {2:1000, 3:5000, 4:15000, 5:30000,...}, with 4 elements → base sample size base = 15000

[0190] - Complexity adjustment factor (complexity_factor):

[0191] complexity_factor = 0.8 + complexity * 1.5

[0192] complexity_factor = 0.8 + 0.31668 * 1.5 ≈ 1.275

[0193] - Sensitivity Factor: Querying the sensitivity level of performance ZT, the corresponding sensitivity factor is "High", with a sensitivity factor of 1.5.

[0194] - Recommended sampling size: adjusted = int(base × complexity_factor × sensitivity_factor)

[0195] adjusted = int(15000 × 1.275 × 1.5) = 28688

[0196] - Upper limit control:

[0197] The maximum sample size (max_samples) corresponding to 4 elements is found in the following lookup table:

[0198] max_samples = {2:5000, 3:20000, 4:50000, 5:100000, ...};

[0199] → Maximum allowed = 50,000

[0200] → Calculation result 28,688 < 50,000 → Limit not triggered

[0201] The final recommended sampling size for ZT performance is approximately 28,688.

[0202] 5. Hierarchical Clustering Sampling Execution (Module E) - S5.1 Generate a large number of candidate samples 1) The number is 5 times the target sample size (or up to 200,000):

[0203] candidate_samples = min(target_samples × 5, 200000)

[0204] = min(28688 × 5, 200000)

[0205] ≈ 143,440

[0206] In practice, 143,440 candidate samples were used.

[0207] 2) Generate candidate samples using an optimized Dirichlet distribution:

[0208] Element list: ["Cu", "Fe", "AlO3"]

[0209] AlO3 composition: Al: 0.25, O: 0.75 (normalized)

[0210] Adjust the α parameter:

[0211] Cu: Electronegativity 1.90 → α = max(0.5, 3.0 - 1.90) = 1.10

[0212] Fe: Electronegativity 1.83 → α = max(0.5, 3.0 - 1.83) = 1.17

[0213] AlO3: Weighted average electronegativity = 1.61 × 0.25 + 3.44 × 0.75 ≈ 2.98

[0214] α_AlO3 = max(0.5, 3.0 - 2.98) = max(0.5, 0.02) = 0.5

[0215] Vector α = [1.10, 1.17, 0.5]

[0216] Generate 143,440 sets of random proportions (rounded to 3 decimal places).

[0217] Construct a set of candidate chemical formulas, such as the chemical formula string: "Cu0.333Fe0.333AlO30.334"

[0218] - S5.2 Feature Engineering

[0219] Extract feature vectors for each candidate chemical formula:

[0220] 1) Basic proportional characteristics: the proportion of each element, such as the proportion values ​​of Cu, Fe, and AlO3 (3-dimensional).

[0221] 2) Statistical characteristics: proportion mean, standard deviation, maximum value, minimum value (4 dimensions)

[0222] 3) Weighted average of elemental characteristics:

[0223] For each proportional component, calculate a weighted average (3-dimensional) of its atomic number, electronegativity, and atomic radius.

[0224] For example, for the Cu, Fe, and AlO3 composition ratios [0.3, 0.4, 0.3], the weighted electronegativity is calculated as follows:

[0225] The electronegativity of Cu is 1.90 × 0.3 = 0.57

[0226] The electronegativity of Fe is 1.83 × 0.4 = 0.732

[0227] Weighted electronegativity of AlO3 = (Al electronegativity × 0.25 + O electronegativity × 0.75) × 0.3

[0228] = (1.61×0.25 + 3.44×0.75) × 0.3

[0229] ≈ (0.4025 + 2.58) × 0.3

[0230] ≈ 0.89475

[0231] The total = 0.57 + 0.732 + 0.89475 ≈ 2.19675

[0232] 4) The final feature vector dimension = 3 + 4 + 3 = 10 dimensions

[0233] - S5.3 PCA Dimensionality Reduction

[0234] Due to the high feature dimension (10 dimensions), PCA was used to reduce it to 3 dimensions while preserving the principal variance.

[0235] - S5.4 K-means clustering

[0236] n_clusters = min(50, target_samples / / 10)

[0237] = min(50, 28688 / / 10)

[0238] = min(50, 2868)

[0239] = 50

[0240] - S5.5 Stratified Sampling

[0241] Uniformly sample from each cluster:

[0242] samples_per_cluster = target_samples / / n_clusters

[0243] = 28688 / / 50

[0244] ≈ 573

[0245] Approximately 573 samples were drawn from each cluster, for a total of approximately 50 × 573 = 28,650 samples.

[0246] - S5.6 Supplemental Sampling

[0247] If the total number of samples is less than 28,688, the remaining samples will be randomly supplemented.

[0248] - S5.7 Chemical Degreasing Treatment

[0249] The list of all chemical formula strings obtained through stratified sampling and supplemental sampling is deduplicated to remove identical chemical formulas, ensuring that each entry in the final output set of chemical formulas is unique. The total number of samples after deduplication is recorded as 26982.

[0250] 6. Result Output and Storage

[0251] - Output format (first 5 lines of the example):

[0252] formula

[0253] Cu 0.250 Fe 0.250 AlO3 0.500

[0254] Cu 0.100, Fe 0.700, AlO3 0.200

[0255] Cu0.333Fe0.333AlO30.334

[0256] Cu 0.050 Fe 0.150 AlO3 0.800

[0257] Cu 0.400, Fe 0.400, AlO3 0.200

[0258] - Metadata records:

[0259] {

[0260] "input_elements": ["Cu", "Fe", "AlO3"],

[0261] "performance_target": "ZT",

[0262] "sensitivity_level": "high",

[0263] "complexity_score": 0.31668,

[0264] "selected_method": "stratified_clustering",

[0265] "target_samples": 28688,

[0266] "unique_samples_after_dedup": 26982,

[0267] "candidate_samples": 143440,

[0268] "pca_components": 3,

[0269] "clusters": 50,

[0270] "sampling_date": "2025-12-05T10:30:00Z",

[0271] "version": "1.0"

[0272] }

[0273] in conclusion:

[0274] While ensuring good detection capability for high-sensitivity performance (ZT, thermoelectric figure of merit), this invention reduces the sampling quantity from approximately 500,000 in the traditional exhaustive method to approximately 27,000 by varying the ratio of the three elements in increments of 0.001, thereby improving the computational efficiency by approximately 17 times and enabling minute-level computation. At the same time, the feature space hierarchical strategy ensures the representativeness and reasonable distribution of sampling points, resulting in high spatial coverage and excellent capture of sensitive areas.

[0275] Implementation Case 2: Dirichlet-optimized sampling for low-sensitivity performance (Onset, oxygen evolution initiation potential)

[0276] Input elements: ["Bi", "Te", "Se"]

[0277] Detailed steps:

[0278] 1. Performance Sensitivity Analysis:

[0279] - Knowledge base query: Onset performance sensitivity is "low"

[0280] - Sensitivity factor: 0.8

[0281] 2. Calculation of element combination complexity:

[0282] - No composite elements, all are single elements.

[0283] - Feature extraction:

[0284] * Bi: [Atomic number 83, electronegativity 2.02, atomic radius 143, group 15, period 6]

[0285] * Te: [Atomic number 52, electronegativity 2.10, atomic radius 140, group 16, period 5]

[0286] * Se: [Atomic number 34, electronegativity 2.55, atomic radius 10³, group 16, period 4]

[0287] - Complexity calculation:

[0288] a. Characteristic standard deviation: [20.238, 0.233, 18.190, 0.471, 0.816]

[0289] b. Normalized standard deviation: [0.359, 0.105, 0.141, 0.030, 0.163]

[0290] c. Mean normalized standard deviation: (0.359 + 0.105 + 0.141 + 0.030 + 0.163) / 5 = 0.1596

[0291] d. Adjustment factor (number of atom types):

[0292] Number of heavy atoms removed: 3 (Bi, Te, Se)

[0293] min(1.0, len(set(all_atoms)) / 5.0) = min(1.0, 3 / 5) = 0.6

[0294] Complexity × 0.6 = 0.1596 × 0.6 ≈ 0.0958

[0295] e. Consider the additional complexity of composite elements:

[0296] Number of composite elements: 0

[0297] Additional factor = 1.0 + 0.2 × 0 = 1.0

[0298] f. Final complexity:

[0299] Complexity = 0.0958 × 1.0 = 0.0958 ≈ 0.096

[0300] 3. Sampling strategy selection:

[0301] - Number of elements: 3

[0302] - High sensitivity performance exists: No (Onset sensitivity is "low")

[0303] - Complexity > 0.3: No (0.096 < 0.3)

[0304] - Selection method: dirichlet_optimized

[0305] 4. Calculate the recommended number of samples:

[0306] - Base sample size (base_samples):

[0307] Base sample size lookup table: base_samples = {2:1000, 3:5000, 4:15000, 5:30000,...},

[0308] Number of elements: 3 → Base sample size: 5000

[0309] - Complexity adjustment factor (complexity_factor):

[0310] complexity_factor = 0.8 + complexity × 1.5

[0311] complexity_factor = 0.8 + 0.096 × 1.5= 0.944

[0312] - Sensitivity factor:

[0313] The sensitivity level for query performance onset is "low", corresponding to a sensitivity_factor of 0.8.

[0314] - Recommended sampling size:

[0315] adjusted = int(base × complexity_factor × sensitivity_factor)

[0316] adjusted = int(5000 × 0.944 × 0.8) = 3776

[0317] - Upper limit control:

[0318] The maximum sample size (max_samples) corresponding to 3 elements is found in the following lookup table:

[0319] max_samples = {2:5000, 3:20000, 4:50000, 5:100000, ...}

[0320] → Maximum allowed = 20,000

[0321] → Calculation result 3,776 < 20,000 → Limit not triggered

[0322] The final recommended sampling size for Onset performance is 3776.

[0323] 5. Dirichlet optimization sampling execution:

[0324] - Adjust the α parameter of the Dirichlet distribution:

[0325] Element list: ["Bi", "Te", "Se"]

[0326] Bi: Electronegativity 2.02 → α_Bi = max(0.5, 3.0 - 2.02) = max(0.5, 0.98) = 0.98

[0327] Te: Electronegativity 2.10 → α_Te = max(0.5, 3.0 - 2.10) = max(0.5, 0.90) = 0.90

[0328] Se: Electronegativity 2.55 → α_Se = max(0.5, 3.0 - 2.55) = max(0.5, 0.45) = 0.50

[0329] Vector α = [0.98, 0.90, 0.50]

[0330] - Generate sampling ratio:

[0331] 3,776 random proportions were generated using the Dirichlet distribution (rounded to 3 decimal places).

[0332] Generation logic: proportions = np.random.dirichlet(αvector, size=3776)

[0333] - Constructing the chemical formula:

[0334] For each proportion [p_Bi, p_Te, p_Se], construct the chemical formula string:

[0335] For example: "Bi0.334Te0.333Se0.333"

[0336] Filter out any combinations where the proportion of any element is ≤0.001.

[0337] - Chemical degreasing treatment

[0338] The total number of duplicate samples recorded is 3657.

[0339] 6. Output Results:

[0340] - Output format (first 5 lines of the example):

[0341] formula

[0342] Bi0.334Te0.333Se0.333

[0343] Bi0.150Te0.700Se0.150

[0344] Bi0.050Te0.050Se0.900

[0345] Bi0.400Te0.300Se0.300

[0346] Bi0.250Te0.500Se0.250

[0347] - Metadata record:

[0348] {

[0349] "input_elements": ["Bi", "Te", "Se"],

[0350] "performance_target": "onset",

[0351] "sensitivity_level": "low",

[0352] "complexity_score": 0.096,

[0353] "selected_method": "dirichlet_optimized",

[0354] "target_samples": 3776, "unique_samples_after_dedup": 3657,

[0355] "alpha_parameters": [0.98, 0.90, 0.50],

[0356] "sampling_date": "2025-12-05T14:30:00Z",

[0357] "version": "1.0"

[0358] }

[0359] Conclusion:

[0360] For systems with low sensitivity performance (onset, oxygen evolution initiation potential), this invention employs a Dirichlet-optimized sampling strategy, adaptively adjusting the α parameter through electronegativity to make the sampling more closely approximate the chemical affinity between elements. In the Bi-Te-Se ternary system, the traditional exhaustive method (step size 0.001) requires generating approximately 500,000 combinations, while this method only requires generating approximately 3,657 samples, improving computational efficiency by more than 130 times. The sampling process is completed in seconds while maintaining reasonable coverage of the chemical space, achieving an effective balance between efficient allocation of computational resources and sampling quality.

[0361] Implementation Case 3: Precise Adaptive Sampling of Moderate Sensitivity Performance (Tm, Melting Point)

[0362] Input elements: ["Al", "Mg"]

[0363] Detailed steps:

[0364] 1. Performance Sensitivity Analysis:

[0365] - Query the performance sensitivity knowledge base: Tm (melting point) performance sensitivity is "medium".

[0366] - Sensitivity factor: 1.0

[0367] 2. Calculation of element combination complexity:

[0368] - No composite elements, all are single elements.

[0369] - Feature extraction:

[0370] Al: [Atomic number 13, electronegativity 1.61, atomic radius 118, group 13, period 3]

[0371] Mg: [Atomic number 12, electronegativity 1.31, atomic radius 145, group 2, period 3]

[0372] - Complexity calculation:

[0373] a. Characteristic standard deviation: [0.5, 0.15, 13.5, 5.5, 0.0]

[0374] b. Normalized standard deviation: [0.04, 0.1027, 0.1027, 0.7333, 0]

[0375] c. Mean normalized standard deviation: (0.04 + 0.1027 + 0.1027 + 0.7333 + 0) / 5 ≈ 0.19574

[0376] d. Adjustment factor (number of atom types):

[0377] Number of heavy atoms removed: 2 (Al, Mg)

[0378] min(1.0, len(set(all_atoms)) / 5.0) = min(1.0, 2 / 5) = 0.4

[0379] Complexity × 0.4 = 0.19574 × 0.4 ≈ 0.0783

[0380] e. Consider the additional complexity of composite elements:

[0381] Number of composite elements: 0

[0382] Additional factor = 1.0 + 0.2 × 0 = 1.0

[0383] f. Final complexity:

[0384] Complexity = 0.0783 × 1.0 = 0.0783

[0385] 3. Sampling strategy selection:

[0386] - Number of elements: 2

[0387] - High sensitivity performance exists: No (Tm sensitivity is "medium")

[0388] - Complexity > 0.3: No (0.0783 < 0.3)

[0389] - Selection method: exact_adaptive (select exact adaptive sampling if the number of elements is ≤3)

[0390] 4. Calculate the recommended number of samples:

[0391] - Base sample size (base_samples):

[0392] Base sample size table: base_samples = {2:1000, 3:5000, 4:15000, ...},

[0393] The number of elements is 2 → base = 1000

[0394] - Complexity adjustment factor (complexity_factor):

[0395] complexity_factor = 0.8 + complexity × 1.5

[0396] complexity_factor = 0.8 + 0.0783 × 1.5 ≈ 0.91745

[0397] - Sensitivity factor:

[0398] The sensitivity level for query performance Tm is "Medium", corresponding to a sensitivity factor of 1.0.

[0399] - Recommended sampling size:

[0400] adjusted = int(base × complexity_factor × sensitivity_factor)

[0401] adjusted = int(1000 × 0.91745 × 1.0) = 917

[0402] - Upper limit control:

[0403] The maximum sample size (max_samples) corresponding to a number of elements = 2 can be found in the following table:

[0404] max_samples = {2:5000, 3:20000, 4:50000, 5:100000, ...}

[0405] → Maximum allowed = 5,000

[0406] → Calculation result 917 < 5,000 → Limit not triggered

[0407] The final recommended sampling size for Tm performance is 917.

[0408] 5. Calculate the adaptive step size:

[0409] The step size is calculated in reverse based on the recommended sampling size of 917:

[0410] Step size = 1.0 / (Recommended sampling size - 1) = 1.0 / 916 ≈ 0.001092

[0411] Normalize to multiples of 0.001: round(0.001092, 3) = 0.001

[0412] Final step size: 0.001

[0413] 6. Precise adaptive sampling execution:

[0414] Step size = 0.001

[0415] Number of steps = int(1.0 / 0.001) + 1 = 1001

[0416] Proportional sequence = [0.000, 0.001, 0.002, ..., 1.000]

[0417] Enumerate all combinations:

[0418] Iterate through all combinations of (Al ratio, Mg ratio) such that Al ratio + Mg ratio = 1.0.

[0419] When the Al ratio is 0.000, the Mg ratio is 1.000.

[0420] When the Al ratio is 0.001, the Mg ratio is 0.999. ...

[0422] When the Al ratio is 1.000, the Mg ratio is 0.000.

[0423] Generate chemical formula strings:

[0424] For example: Al ratio = 0.334, Mg ratio = 0.666 → "Al 0.334 Mg 0.666"

[0425] Total sample size = 1001 (from Al0.000Mg1.000 to Al1.000Mg0.000)

[0426] Chemical degreasing treatment

[0427] Record the total number of duplicate samples: 1001

[0428] Output results:

[0429] Output format (first 10 lines of the example):

[0430] formula

[0431] Al 0.000 Mg 1.000

[0432] Al 0.001 Mg 0.999

[0433] Al 0.002 Mg 0.998

[0434] Al 0.003 Mg 0.997

[0435] Al0.004Mg0.996

[0436] Al0.005Mg0.995

[0437] Al0.006Mg0.994

[0438] Al0.007Mg0.993

[0439] Al0.008Mg0.992

[0440] Al0.009Mg0.991

[0441] Metadata record:

[0442] {

[0443] "input_elements": ["Al", "Mg"],

[0444] "performance_target": "Tm",

[0445] "sensitivity_level": "medium",

[0446] "complexity_score": 0.0783,

[0447] "selected_method": "exact_adaptive",

[0448] "target_samples": 917,

[0449] "step_size": 0.001,

[0450] "total_samples": 1001,

[0451] "unique_samples_after_dedup": 1001,

[0452] "sampling_date": "2025-12-05T16:45:00Z",

[0453] "version": "1.0"

[0454] }

[0455] Conclusion:

[0456] For Al-Mg binary systems with moderate sensitivity performance (Tm) and only two elements, this invention employs a precise adaptive sampling strategy, achieving full-coverage enumeration of the chemical space through adaptive step size control (0.001). Traditional exhaustive methods (fixed step size 0.001) require generating 1001 combinations, while this method dynamically adjusts complexity and sensitivity, recommending a sampling size of 917, and actually generating 1001 samples (slightly increased due to step size normalization). The computational efficiency is close to that of traditional exhaustive methods, but the intelligent decision-making mechanism ensures the systematic nature and interpretability of the sampling process. This strategy retains full-space detection capability in low-dimensional systems while providing high-precision, unbiased input data for subsequent performance prediction, demonstrating the invention's ability to balance computational resources and sampling accuracy in simple systems.

[0457] The intelligent sampling strategies of this invention (such as hierarchical clustering and Dirichlet optimization) reduce the sampling volume by 1-2 orders of magnitude, improve the computational efficiency of high-complexity systems by about 17 times, and improve the efficiency of low-sensitivity systems by more than 130 times; the response time is reduced from hours to seconds or minutes, which is fully adapted to real-time interaction and high-throughput computing scenarios.

[0458] Establish a "performance sensitivity-sampling factor" mapping mechanism, where high-sensitivity performance indicators correspond to more sampling resources, and low-sensitivity performance indicators reduce the sampling volume, thereby achieving "dense sampling in high-value areas and efficient simplification in low-value areas", avoiding resource waste and improving resource utilization efficiency;

[0459] For highly sensitive or complex systems, PCA dimensionality reduction, K-means clustering, and stratified sampling are used to ensure that sampling points are evenly distributed in chemical space, focusing on covering performance-sensitive areas; at the same time, key detailed features are preserved, significantly improving the accuracy of subsequent material screening and performance analysis.

[0460] This pioneering atomic-level analysis and weighted feature fusion technology for composite elements can decompose composite elements such as AlO3 into atomic components and calculate average features (atomic number, electronegativity, etc.) by weighting according to stoichiometric ratios. This solves the problem that traditional methods cannot handle composite components, improves the accuracy of chemical formula analysis and feature extraction, and achieves second-level / minute-level calculation response through simplified sampling and efficiency improvement, completely solving the response latency problem of traditional methods. It also supports structured output and metadata traceability, adapts to practical application scenarios such as WebAPI, and significantly improves user experience and system usability.

[0461] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0462] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for generating material chemical formulas based on performance-sensitivity adaptive hierarchical sampling, characterized in that: Includes the following steps: S1. Input element list: Input a list of elements that make up the material, which includes basic elements and composite elements; S2. Performance Sensitivity Analysis: Query the preset performance sensitivity mapping knowledge base to obtain the sensitivity level corresponding to the target performance index, and determine the corresponding sampling quantity adjustment factor based on the sensitivity level; S3. Calculation of element combination complexity: Analyze the composite elements in the element list, extract the multi-dimensional features of each element, and calculate the element combination complexity score based on feature diversity, number of atom types and number of composite elements. The multi-dimensional features are 5-dimensional element features, specifically including atomic number, electronegativity, atomic radius, group and period. The analytical process of the composite element is as follows: the composite element is decomposed into basic atomic components, the weights are determined according to the proportion of each atom in the composite element, and the five-dimensional feature vectors of each atomic component are weighted and averaged based on the weights to obtain the five-dimensional feature vector of the composite element. The calculation process for the element combination complexity score is as follows: S31. Constructing the feature matrix: Combining the basic elements and composite elements into a 5-dimensional feature matrix. , where n is the number of elements and m=5 is the feature dimension; S32. Feature Diversity Calculation: Calculate the standard deviation of each dimension of the feature matrix along the column direction. Standard deviation Reflecting each element in the first The degree of dispersion on the dimensional feature is calculated using the following formula: ； in, For the first The element in the first... eigenvalues ​​of dimension For the first The mean of the dimensional features; The standard deviation Divide by the feature mean of the corresponding dimension to obtain the normalized standard deviation normalized_std; S33. Atom Type Count Adjustment: Calculate the atom type count unique_atoms to obtain the atom type count adjustment factor A= To prevent high-atomic-number systems from excessively increasing complexity; S34. Composite Element Adjustment: Calculate the composite element adjustment factor B based on the number of composite elements (compound_count), using the following formula: B = 1.0 + 0.2 × compound_count; S35. Complexity Synthesis: Multiply the mean normalized standard deviation of each dimension, the atomic type adjustment factor, and the composite element adjustment factor to obtain a complexity score between 0 and 1. The calculation formula is as follows: ； in The mean of the normalized standard deviation; S4. Adaptive Sampling Strategy Selection and Sampling Quantity Allocation: Based on the number of elements, the sensitivity level, and the complexity score, select one of the following sampling methods as the optimal sampling strategy: precise adaptive sampling, Dirichlet optimized sampling, or hierarchical clustering sampling. Simultaneously, based on the preset basic sampling quantity according to the number of elements, the complexity score, and the sampling quantity adjustment factor, calculate and allocate the sampling quantity using a preset calculation formula that includes complexity-related terms and sensitivity factors. The sampling quantity shall not exceed the preset maximum sampling quantity limit for the corresponding number of elements. When the optimal sampling strategy is hierarchical clustering sampling, its implementation process is as follows: Candidate sample generation: Generate candidate samples five times the target sampling amount, with an upper limit of 200,000. The candidate samples are generated using the Dirichlet optimization sampling method. Feature extraction: Extract a multi-dimensional feature vector for each candidate sample, including the composition ratio of each element in each chemical formula, statistical features, and weighted average of element features; Dimensionality Reduction and Clustering: Multidimensional feature vectors are reduced to 3 dimensions using PCA, and K-means clustering is performed, resulting in a cluster size of [number missing]. ; Stratified sampling: Samples are drawn uniformly from each cluster, and the number of samples drawn is the quotient of the target sample size and the number of clusters. If the total number of samples drawn is less than the target sample size, the remaining candidate samples are randomly supplemented. S5. Chemical formula generation: Based on the optimal sampling strategy and the determined sampling quantity, generate a list of chemical formula combinations for the materials, and remove duplicates from the list of chemical formula combinations. S6. Result Output and Storage: Output the list of chemical formula combinations and save the sampling strategy, calculation parameters and metadata for subsequent traceability and analysis.

2. The material chemical formula generation method based on performance sensitivity adaptive hierarchical sampling according to claim 1, characterized in that: In step S2, the performance sensitivity mapping knowledge base comes from a preset material performance sensitivity structured knowledge base. The sensitivity levels include high sensitivity, medium sensitivity, and low sensitivity, where the high sensitivity level corresponds to a sampling quantity adjustment factor of 1.5, the medium sensitivity level corresponds to a factor of 1.0, and the low sensitivity level corresponds to a factor of 0.

8. The target performance indicators include thermoelectric figure of merit, oxygen evolution initiation potential, and melting point.

3. The material chemical formula generation method based on performance sensitivity adaptive hierarchical sampling according to claim 2, characterized in that: The selection logic for the optimal sampling strategy in step S4 is as follows: If the number of composite elements is less than 3, then precise adaptive sampling is selected; If the number of composite elements is ≥3 and the target performance index is either high sensitivity level or complexity score >0.3, then hierarchical clustering sampling is selected. Except for the two cases mentioned above, Dirichlet optimization sampling is selected.

4. The material chemical formula generation method based on performance sensitivity adaptive hierarchical sampling according to claim 1, characterized in that: The number of samples in step S4 is calculated using the following formula: ； in: The base sampling size is preset based on the number of elements, specifically as follows: When the number of elements is 2, the corresponding basic sampling quantity is 1000; When the number of elements is 3, the corresponding basic sampling quantity is 5000; When the number of elements is 4, the corresponding basic sampling quantity is 15000; When the number of elements is 5, the corresponding basic sampling quantity is 30000; For every 1 increase in the number of elements, the base sampling size increases by a fixed gradient of 15000. The complexity score calculated in step S3; This is the sampling quantity adjustment factor obtained in step S2; The sampling amount does not exceed the maximum sampling amount limit preset for the corresponding number of elements, that is: The maximum sampling size is 5000 when the number of elements is 2; The maximum sampling size is 20000 when the number of elements is 3; The maximum sampling size is 50,000 when the number of elements is 4; The maximum sampling size is 100,000 when the number of elements is 5; For every 1 increase in the number of elements, the maximum sampling size increases by a fixed gradient of 50,000.

5. The material chemical formula generation method based on performance sensitivity adaptive hierarchical sampling according to claim 1, characterized in that: When the optimal sampling strategy in step S4 is Dirichlet-optimized sampling, its implementation process is as follows: For each element, its Pauling scale electronegativity is determined by the formula... Calculate the Dirichlet distribution parameter; in Let be the electronegativity of the i-th element; Based on the adjusted The parameter vector generates a random proportion of the final sample size group. For any combination where the proportion of any element is ≤0.001, round to 3 decimal places and fine-tune to ensure that the sum of the proportions of all elements in each combination is 1.

0.

6. The material chemical formula generation method based on performance sensitivity adaptive hierarchical sampling according to claim 1, characterized in that: When the optimal sampling strategy in step S4 is precise adaptive sampling, its implementation process is as follows: Step size calculation: The adaptive step size is calculated using the formula step size = 1.0 / (recommended sampling amount - 1), and the step size is normalized to an integer multiple of 0.

001. The recommended sampling amount is the number of samples determined in step S4. Mesh enumeration: According to the normalized step size, traverse all combinations that satisfy the sum of the proportions of the elements being 1.0 to generate a complete mesh sampling combination; Chemical formula construction: Generate the corresponding chemical formula string based on the element ratio of each grid combination.

7. The material chemical formula generation method based on performance sensitivity adaptive hierarchical sampling according to claim 1, characterized in that: The deduplication process in step S5 specifically involves: performing a consistency check on the generated candidate chemical formula list, removing identical chemical formula entries, and ensuring that each entry in the final output target chemical formula list is unique.

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