Prediction method and prediction system for superconducting critical temperature

Abstract

The invention provides a superconducting critical temperature prediction method and prediction system. According to the method, N descriptor sets of a target superconductor are obtained, each descriptor set comprises M descriptors representing the target superconductor, and the N descriptor sets are input into an HNN model to predict the critical temperature of the target superconductor; wherein the HNN model comprises multiple layers of sub-models, the N descriptor sets serve as the input of the first layer of sub-model, the output of the ith layer of sub-model is the input of the (i + 1) th layer of sub-model, the output of the last layer of sub-model is the critical temperature of the target superconductor, and N, M and i are integers larger than or equal to 1.

Description

Technical Field

[0001] This specification relates to the field of artificial intelligence applications, and in particular to a method and system for predicting superconducting critical temperature. Background Art

[0002] The superconducting critical temperature has important implications for applications such as power transmission, rail transport, nuclear fusion, strong magnetic fields for medical imaging, and quantum computing. It is one of the most attractive material properties. How to predict its value is an urgent problem to be solved.

[0003] The content of the background technology section is only the information known to the inventor personally, and does not mean that the above information has entered the public domain before the application date of this disclosure, nor does it mean that it can become the prior art of the present disclosure. Summary of the invention

[0004] The present specification provides a method and system for predicting superconducting critical temperature. For some superconductors, the predicted critical temperature has a smaller average absolute percentage error than the experimental value, and can be extended to predict the critical temperature of other superconductors.

[0005] In a first aspect, the present specification provides a method for predicting a superconducting critical temperature, comprising: obtaining N descriptor sets of a target superconductor, each descriptor set comprising M descriptors characterizing the target superconductor, wherein N and M are both integers greater than or equal to 1; and inputting the N descriptor sets into an HNN model to predict the critical temperature of the target superconductor; wherein the HNN model comprises multiple layers of sub-models, the N descriptor sets serving as inputs to the first layer of sub-models, the output of the i-th layer of sub-models serving as inputs to the i+1-th layer of sub-models, and the output of the last layer of sub-models serving as the critical temperature of the target superconductor, wherein i is an integer greater than or equal to 1.

[0006] In a second aspect, the present specification also provides a prediction system, comprising: at least one storage medium storing at least one instruction set for predicting the superconducting critical temperature; and at least one processor communicatively connected to the at least one storage medium, wherein the at least one processor reads the at least one instruction set when running, and implements the prediction method as described in the first aspect according to the instructions of the at least one instruction set.

[0007] Other functions of the prediction method and prediction system of superconducting critical temperature provided in this specification will be partially listed in the following description. The creative aspects of the prediction method and prediction system of superconducting critical temperature provided in this specification can be fully explained by practicing or using the methods, devices and combinations described in the following detailed examples. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] In order to more clearly illustrate the technical solutions in the embodiments of this specification, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this specification. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0009] Figure 1 The superconducting critical temperature according to the present specification varies with the doping content;

[0010] Figure 2 shows the results of the GA provided according to the present specification;

[0011] Figure 3 A hierarchical neural network algorithm provided according to this specification is shown;

[0012] Figure 4 The learning results of different models provided in this specification are shown;

[0013] Figure 5 shows predictions for HEAs provided in accordance with this specification;

[0014] Figure 6 shows the relationship between the five key descriptors provided in this specification and the Tc value;

[0015] Figure 7 The results of studies based on different models provided in this specification are shown;

[0016] Figure 8 shows a periodic table of elements provided according to this specification;

[0017] Fig. 9 A flow chart of a method for predicting superconducting critical temperature according to the present specification is shown; and

[0018] Fig.10 The hardware structure diagram of the system provided in this specification is shown. DETAILED DESCRIPTION

[0019] The following description provides specific application scenarios and requirements of this specification, with the purpose of enabling those skilled in the art to make and use the contents of this specification. Various local modifications to the disclosed embodiments will be apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments and applications without departing from the spirit and scope of this specification. Therefore, this specification is not limited to the embodiments shown, but to the widest scope consistent with the claims.

[0020] The terms used herein are only used for the purpose of describing specific example embodiments and are not restrictive. For example, unless the context clearly indicates otherwise, as used herein, the singular forms "a", "an" and "the" may also include plural forms. When used in this specification, the terms "include", "comprise" and / or "contain" mean that the associated integers, steps, operations, elements and / or components exist, but do not exclude the existence of one or more other features, integers, steps, operations, elements, components and / or groups or that other features, integers, steps, operations, elements, components and / or groups may be added in the system / method.

[0021] In view of the following description, these and other features of the present specification, as well as the operation and function of the related elements of the structure, and the economy of the combination and manufacture of the parts can be significantly improved. Reference is made to the accompanying drawings, all of which form a part of this specification. However, it should be clearly understood that the drawings are for illustration and description purposes only and are not intended to limit the scope of this specification. It should also be understood that the drawings are not drawn to scale.

[0022] The flowcharts used in this specification illustrate the operations implemented by the system according to some embodiments in this specification. It should be clearly understood that the operations of the flowcharts may not be implemented in sequence. On the contrary, the operations may be implemented in reverse order or simultaneously. In addition, one or more other operations may be added to the flowchart. One or more operations may be removed from the flowchart.

[0023] The superconducting critical temperature is one of the most intriguing material properties because of its important implications for applications such as power transmission, rail transport, nuclear fusion and strong magnetic fields for medical imaging, quantum computing, etc. The ability to predict its value has been a relentless pursuit for condensed matter physicists. We developed a new hierarchical neural network (HNN) AI algorithm to address the contradiction between the large number of descriptors and the small number of datasets that neural network AI methods often face in materials science. Using this new HNN-based AI model, we significantly increased the number of common descriptors for inorganic compounds to 909 and thoroughly cleaned up the database of traditional superconductors, ultimately achieving test R 2 The newly developed HNN model accurately predicted the T values ​​of 45 new high-entropy alloy superconductors. c , with an average absolute percentage error of less than 6% compared to experimental data, demonstrating significant potential for predicting the properties of other inorganic materials.

[0024] Superconducting materials have shown great potential in a wide range of applications, including power transmission, rail transportation, nuclear fusion and strong magnetic fields for medical imaging, quantum computing, etc. The critical temperature (T) of a superconductor c), the temperature below which zero resistance and perfect diamagnetism occur, is the most critical factor affecting its practicality. Therefore, accurate prediction of T c The famous Bardeen-Cooper-Schrieffer (BCS) theory effectively explains the properties of many superconductors, especially conventional or low-temperature superconductors. However, it has limited success in accurately predicting T c and limited ability to identify new superconductors.

[0025] In recent years, neural network artificial intelligence (AI) models have been applied to study the T c According to previous reports, the descriptors used in AI models can be divided into three categories: the chemical composition of materials, the structure of materials, and the basic properties of the elements that make up the materials. Among them, the descriptors based on chemical formulas are limited by the lack of material property parameters; the corresponding model prediction capabilities are limited. The model corresponding to the descriptor based on structural information cannot predict the T of materials with unknown structures. c In contrast, elemental property-based descriptors are readily available and act as universal descriptors across all inorganic materials. Therefore, we chose to use elemental property-based descriptors.

[0026] However, due to the mismatch between the small dataset and the high-dimensional descriptor, the neural network model proposed by Logan et al. using a 145-element descriptor cannot accurately predict T c In this paper, we introduce a novel hierarchical neural network (HNN) algorithm that uses T c data to address this problem. In addition, we use a new set of 909 descriptors, a significant increase over the 145 descriptors introduced by Logan et al. The predictions of the final model are in R 2 The new AI method could have a profound impact on the development of superconducting materials, highlighting the huge benefits of the collaboration between artificial intelligence and materials science.

[0027] AI Workflow

[0028] Generally speaking, AI work involves the following steps: data collection and cleaning, descriptor (feature) construction, descriptor selection, and model building using a specific algorithm (in this case, a hierarchical neural network framework).

[0029] (1) Data collection and cleaning

[0030] To ensure the reliability of machine learning, it is crucial to have a robust and extensive dataset. In this paper, we used data from the SuperCon database, which contains T in published journals on experimental studies of known superconducting materials. c Information. Notably, as the largest database of its kind, the SuperCon database contains more than 14,794 records on conventional superconductors. However, these data have several flaws that hinder their direct application in AI:

[0031] 1. Lack of T c In some cases, the composition information of the material exists in the database, but the corresponding T c The missing information makes the dataset incomplete. Therefore, we cleaned 3052 such data points.

[0032] 2. The composition is unclear. 1 Nb 2 O z For materials like , the proportion of oxygen atoms 'z' is difficult to determine, making it impossible for the computer to discern. Therefore, we cleaned up 24 such data points.

[0033] 3. Data redundancy. This problem has two different forms. First, the same component has different T c For example, Nb 3 Pt 1 T c 8.1K and 11K respectively. Secondly, the ratio of elements in the material is adjusted by multiples, or the order of elements is modified. For example, Ga 7 Pt 3 (C 1.35 Ti 0.1 Y 0.9 ) and Ga 0.7 Pt 0.3 (Y 1.8 Ti 0.2 C 2.7 ) represent the same material, albeit with different chemical symbols. The first case introduces too much noise and may affect the accuracy of the model. The second case hinders accurate evaluation of the model because the same material may exist in both the training set and the test set, leading to severe overestimation by the model. Therefore, we cleaned up 6505 such data points.

[0034] After cleaning 9581 data points through these steps, we obtained 5213 reliable data for conventional superconductors. We also considered including high-temperature superconductors in our dataset. However, as mentioned above, the SuperCon database is only a basic compilation, and even for conventional superconductors, a large amount of inappropriate data must be deleted. The situation for high-temperature superconductors is more complicated.

[0035] Figure 1 The graph shows the variation of superconducting critical temperature with doping content: a) corresponding to La 2-x Sr x CuO 4 System; b) corresponding to Bi 2 Sr 2 CaCu 2 O y system.

[0036] In cuprate superconductors, the superconducting T c It varies with the carrier density introduced by doping. Usually, T c The phase diagram with doping shows a dome-shaped feature, indicating the emergence of superconductivity in a specific doping range, e.g. Figure 1 a. However, it is well known that oxygen content is difficult to measure accurately, that is, the doping level due to changes in oxygen content cannot be determined unless independent doping level measurements are performed. This has raised concerns about the accuracy of the cuprate superconductor data in the SuperCon database. Figure 1 As shown in a and 1b, La 2-x Sr x CuO 4 The system data shows a dome-shaped feature, and Bi 2 Sr 2 CaCu 2 O y This is not the case for the 2000 MHz and 5000 MHz systems, as the oxygen content was not accurately determined. There are many other similar examples of inaccuracies, with data showing confusion and not consistent with expected trends. This suggests that the data for high-temperature superconductors has not been rigorously cleaned and contains many unreliable records. Before applying machine learning to high-temperature superconductors, reliable data must be investigated from the literature in the future. In addition, there is still an ongoing discussion on whether conventional superconductors and high-temperature superconductors share the same basic mechanisms. Therefore, we decided not to include high-temperature superconductors in this specification.

[0037] (2) Descriptor construction

[0038] In previous studies, researchers chose specific descriptors designed only for certain material properties. However, in predicting the formation energy and T of superconductors, cIn their study, Logan et al. used 22 elemental properties to develop 145 universal descriptors. Here, we follow the approach of Logan et al. and use a set of universal elemental descriptors covering a wide range of inorganic materials properties. This strategy is expected to promote the development of comprehensive AI models in the future, which integrate a large number of specialized models in materials science. In this specification, we extracted key thermodynamic, physical, and crystallographic data from databases and literature, increasing the total number of elemental properties from 22 to 53, as listed in Table 1.

[0039] Table 1. Properties of the fifty-three elements

[0040]

[0041] In addition, we follow the approach of Logan et al. and further develop the descriptor construction rules shown in Table 2. We add the calculation of configurational entropy (CE), valence electron occupation state, and ionicity. We also add weights to the minimum, maximum, and range values ​​in the rules. In addition, we also incorporate the Absolute Percentage (AP) that reflects the change in atomic size and the electronegativity that significantly affects the structure and properties of the material. Finally, based on these properties and rules, we construct a comprehensive set of descriptors, increasing the total number of universal descriptors from 145 to 909.

[0042] Table 2. Construction rules of 909 descriptors

[0043]

[0044] (3) Descriptor selection

[0045] Due to the limited data in materials science, it is impractical to train a single neural network with all 909 descriptors. For example, an artificial neural network (ANN) with two hidden layers and 909 input descriptors would require more than a billion hyperparameters. In principle, a considerable amount of data is required to determine these hyperparameters through AI training, which poses a huge challenge to solving materials science problems. In previous studies, researchers believed that too many descriptors would be harmful to machine learning models. To address this problem, Holland developed a genetic algorithm (GA) to simplify the dimensionality of descriptors (feature extraction) in the ANN-based machine learning process.

[0046] exist Figure 2 In the above example, the x-axis represents the descriptor dimension d and the y-axis represents the test R. 2 When d = 49, the accuracy of our Convolutional Neural Network (CNN) model reaches a turning point, and the test R 2 The score saturates at 0.92. In addition, as shown in Table 3, the five main descriptors MD1 to MD5 appear 1055, 960, 944, 914, and 902 times, respectively, while the other descriptors appear less than 500 times, which shows the importance of the main descriptors.

[0047] Figure 2 Results of GA are shown: descriptor dimension and test R 2 Relation to GA iterative algebra.

[0048] (4) HNN construction

[0049] Based on extensive testing, we found that multiple combinations of descriptors with reduced dimensionality can produce high-performance CNN models. This suggests that each set of descriptors carries information related to the superconducting critical temperature. Therefore, we conclude that Figure 2 The turning point effect shown in derives from the limited ability of a given amount of data to determine the hyperparameters of a given neural network architecture, rather than from the fact that certain descriptors are harmful in AI learning, as discussed earlier.

[0050] Therefore, we realized that it was necessary to design an ensemble statistical algorithm to absorb all the knowledge from the entire set of 909 descriptors. Traditional ensemble algorithms include bagging, boosting, and stacking. Bagging and boosting algorithms simply take a geometric average of the output of each model. We previously used a stacking algorithm to statistically average the descriptor inputs of different machine learning algorithms. However, given the differences in performance of clusters of different descriptor sets, a simple geometric average cannot effectively capture all valuable insights.

[0051] Table 3. Five main descriptors of conventional superconductors

[0052] Descriptor Name Abbreviation Frequency AP_ave_BCCfermi MD1 1055 ave_FirstIonizationEnergy MD2 960 AP_min_GSestBCClatcnt MD3 944 ave_NValance MD4 914 AP_min_thermal_conductivity MD5 902

[0053] To address this challenge, we developed an ensemble algorithm called Hierarchical Neural Network (HNN) that statistically ensembles a large number of individual clusters (sub-models) with different weighting factors by training the hyperparameters of the HNN. Figure 3 As shown, the small dashed box represents the predicted T cANN / CNN sub-models of output values. Sub-models with the same horizontal position belong to the same cluster layer. Each sub-model is represented as where b and c represent the layer number and the number of sub-models in the same cluster layer, respectively. The input of the HNN sub-model is the given dataset and the simplified dimension of the basic neural network structure (49).

[0054] Importantly, multiple sets of 49 descriptors are used as input to the first layer of the HNN. Among these descriptors, some provide common basic information about the superconducting Tc, such as the five main descriptors mentioned in Table 3. The remaining 44 descriptors are randomly selected from the other 904 descriptors through a combination algorithm. The diversity of descriptors leads to a variety of sub-models, which enhances the generalization ability of the final HNN model. The input of the next layer is the output of the previous layer, which means that each subset has a trainable weight. The HNN model reduces the possibility of overfitting by integrating sub-models with different combinations of simplified descriptors as input.

[0055] Figure 3 A hierarchical neural network (HNN) algorithm is shown. A detailed description is given in the text.

[0056] Results and Discussion

[0057] To verify the effectiveness of the descriptors and HNN algorithm proposed in this paper, we used a cleaned dataset consisting of 5213 data points to train different AI models. The input includes 145 descriptors proposed by Logan et al., 909 descriptors introduced in this paper, and a set of 49 descriptors out of the 909 descriptors screened by GA (including the main descriptor) ( Figure 2 ). AI techniques include ANN, CNN, XGBoost ANN / CNN and HNN ensemble ANN / CNN. XGBoost is widely regarded as a powerful and popular ensemble learning based algorithm. It uses the power of multiple regression tree models to improve prediction performance, and the final output is a simple sum of the predictions of the individual trees. In total, we built 13 models, named 49-ANN, 909-HNN (CNN), etc. These models have a R 2 Value Figure 4 c. Press R 2 From low to high order, the models are 49-ANN, 145-ANN, 49-XGBoost, 145-CNN, 145-XGBoost, 145-HNN(ANN), 145-HNN(CNN), 49-CNN, 909-ANN, 909-XGBoost, 909-HNN(ANN), 909-CNN, and 909-HNN(CNN). In order to show the overfitting effect, Figure 4c also includes the R of the training and test datasets for these models 2 The difference between the values ​​is defined as ΔR 2 .

[0058] Figure 4 The learning results of different models are shown. a) 145-ANN; b) 909-HNN (CNN); c) Test R of 13 models 2 (blue) and training and testing R 2 The difference between 2 ,red).

[0059] from Figure 4 Five important conclusions can be drawn from this study. First, Figure 4 As shown in a, when T c When the number of descriptors is greater than 20K, the ANN model with 145 descriptors shows a large error on the training set, indicating that it is underfitting and that these 145 descriptors are incomplete. In contrast, the model with HNN and 909 descriptors has almost no error, as shown in Figure 4 b. Secondly, compared with the single model, the HNN model significantly enhanced the predictive ability of the model, and the test R 2 The score improved from 0.830 to 0.956. Third, the CNN model outperformed the fully connected ANN. Fourth, the performance of the HNN model improved with the increase in the number of individual clusters in the input layer and subsequent integration layers. This effect saturated after the third layer, as shown in Figure 7 Fifth, when the number of descriptors is reduced from 909 to 49, although the ΔR 2 Decline, but test R 2 This suggests that dimensionality reduction alleviates the overfitting effect, but may miss some c Compared with these models, the HNN model not only achieves a higher test R 2 , and also reduced overfitting (lower ΔR 2 ).

[0060] To further demonstrate the capabilities of the 909-HNN(CNN) model, we decided to use high-entropy alloys (HEAs) for testing because they share several common features with conventional superconductor data in SuperCon. First, HEAs are metals, which are similar to conventional superconductors in conductivity. Usually, candidate materials for superconductors must first be conductors. However, conventional superconductors in SuperCon cover almost all known conductive materials. As far as we know, possible new conductors mainly come from two categories: amorphous alloys and high entropy alloys (HEAs). Given that the long-range disordered atomic structure of amorphous alloys may have different superconducting mechanisms, we chose high entropy alloys as our new test database outside the SuperCon database. Second, the Tc of HEAs is typically below 10K, well below the so-called McMillan limit of about 40K. This means that the superconducting pairing mechanism in HEAs is consistent with the mechanism in conventional superconductors. Last but not least, the elements that make up HEAs are all included in the materials in SuperCon (see Figure 8 ). In addition, the cleaned SuperCon database contains 216 materials with more than 4 elements, which are similar to HEAs in terms of the number of elements (see Table 5, see Appendix: Supplementary Materials). This suggests that our model should have the ability to predict the T of multi-element materials in HEAs. c ability.

[0061] After extensive research, we identified 45 novel molecules with experimentally measured T c Therefore, we used the 13 models we constructed previously to predict the T of these 45 materials. c The results are as follows Figure 5 b. The R2 values ​​of 49-ANN, 145-ANN, 49-XGBoost, 145-CNN, 145-XGBoost, 145-HNN(ANN), 145-HNN(CNN), 49-CNN, 909-ANN, 909-XGBoost, 909-HNN(ANN), 909-CNN, and 909-HNN(CNN) are 0.72, 0.162, 0.67, 0.502, 0.512, 0.563, 0.694, 0.764, 0.53, 0.585, 0.81, 0.651, and 0.92, respectively. These results are consistent with our analysis based on the test dataset ( Figure 4 c). It is worth noting that although these HEAs are not included in our superconductor database, the test R 2 From 0.956 to 0.92, such as Figure 5a, indicating that overfitting is negligible. In contrast, the R 2 The decrease is more significant. For 145-ANN, R 2 It dropped from 0.891 to 0.162, indicating very serious overfitting.

[0062] Figure 5 Predictions for HEAs are shown. a) Experimental T values ​​for 45 HEAs in the literature c With prediction T c b) R of 45 HEAs in 13 models 2 (blue) and training and testing R 2 The difference between (ΔR' 2 , red); c) Experiment T c The distribution of (blue) and the distribution of the number of material elements (red) in relation to the number of constituent elements.

[0063] also, Figure 5 c shows the T in our collection of conventional superconductors c Distribution, classified by number of elements, with a distribution diagram. It was found that 215 materials contained 5 elements and 1 material contained 6 elements, which are listed in Table 5. Usually the highest T c The number of elements of the materials with the highest value is between 2 and 4. Due to the lack of multi-element (more than 4) data in the database, the model's predictions for higher-order systems may not be as accurate as those for lower-order systems. Among the 45 HEAs, 23 are quinary systems containing 5 elements and 22 are senary systems containing 6 elements, as shown in Table 4 (see Appendix: Supplementary Materials). For these higher-order systems, our 909-HNN (CNN) model exhibits mean absolute percentage errors of 5.3% and 6.1%, respectively, with an overall mean absolute percentage error of 5.7%.

[0064] These results clearly demonstrate the robustness of our AI model, showing that the fundamental associations between descriptors and key physical properties can be effectively captured in two steps. First, we train a large number (more than 10 3 ) individual clusters, each using a different combination of input descriptors but the same dataset. Secondly, the aggregated knowledge of these diverse clusters is integrated and further refined by the HNN algorithm. This approach exploits the overlapping and unique information in different clusters, ultimately achieving superior integration results.

[0065] In summary, in this specification, we developed a new machine learning framework for predicting Tc of metallic inorganic materials. First, we generated a high-quality dataset screened from the SuperCon database, eliminating past sources of significant overestimation due to data redundancy. We then created a hierarchical neural network statistical ensemble model to overcome the contradiction between the large number of descriptors and the small number of datasets faced by previous neural network AI methods in materials science. After overcoming this obstacle, we significantly expanded the number of elemental property-based descriptors from 145 to 909. We found that the hierarchical neural network ensembled individual convolutional neural networks that used 49 descriptors selected from the 909 descriptors ultimately obtained a high test R of 95.6%. 2 We applied this new model to the T c Among these alloys, we extensively searched the recent literature for the Tc of 45 alloys (not included in the SuperCon database). We found that the predicted Tc c The average absolute percentage error compared to experimental values ​​was less than 6%. This success reveals new directions for advancing materials science and accelerates the development of new materials tailored for various applications.

[0066] Appendix: Supplementary Materials

[0067] (1) Key descriptors and T c

[0068] To further illustrate the relationship between the descriptor and T c The relationship between us Figure 6 AP_ave_BCCfermi, ave_FirstIonizationEnergy(eV), ave_NValance, AP_min_GSestBCClatcnt(Angstrom, Angstrom) and AP_min_thermal_conductivity(W / m*K) vs. T are plotted in c The correlation between them.

[0069] Figure 6 Five key descriptors are shown with T c The relationship between the values ​​of a) AP_ave_BCCfermi, b) ave_FirstIonizationEnergy, c) ave_NValance, d) AP_min_GSestBCClatcnt and e) AP_min_thermal_conductivity.

[0070] (2) Model evaluation indicators

[0071] The most commonly used indicator in evaluating regression models is the coefficient of determination (R 2 ) and mean absolute percentage error (MAPE). MAPE and R 2 The calculation formulas for are shown in equations (1) and (2), respectively.

[0072]

[0073] In the equation, N represents the sample size, y i represents the attribute value of the i-th sample, represents the average attribute value of the sample, F(x i ) represents the predicted value of the i-th sample predicted by the AI ​​model. A higher R 2 A higher value and a lower MAPE value indicate that the AI ​​model performs better, meaning the predictions are more accurate.

[0074] (3) Results of different AI models

[0075] We used 145-ANN, 145-HNN(ANN), 145-CNN, 145-HNN(CNN), 909-ANN, 909-HNN(ANN), 909-CNN, and 909-HNN(CNN) models to train and test the data, where the numbers represent the number of descriptors and the abbreviations represent the machine learning techniques. Figure 7 shown.

[0076] Figure 7 Results of different models are shown. a) 145-ANN; b) 145-HNN(ANN); c) clustering layer of 145-HNN(ANN); d) 145-CNN; e) 145-HNN(CNN); f) clustering layer of 145-HNN(CNN); g) 909-ANN; h) 909-HNN(ANN); i) clustering layer of 909-HNN(ANN); j) 909-CNN; k) 909-HNN(CNN); l) clustering layer of 909-HNN(CNN).

[0077] Prediction results of 45 high entropy alloys

[0078] Table 4 shows the superconducting critical temperatures of 45 high entropy alloys (HEAs) reported in the literature and the T values ​​predicted by the 909-HNN (CNN) model. c .

[0079] Table 4: Experimental T values ​​of 45 HEAs in the literature c and predict T c .

[0080]

[0081]

[0082] Common features of SuperCon and 45 HEAs

[0083] Figure 8 The periodic table is shown, visually categorized according to their inclusion in the SuperCon database and the HEAs database. It was found that all elements of the 45 HEAs are included in the SuperCon training data.

[0084] Figure 8 The periodic table is shown as follows: Light red: Elements included only in the SuperCon database. Light blue: Elements included in both the SuperCon and HEAs databases. Blank: Elements not included in the SuperCon and HEAs databases.

[0085] Table 5: Materials containing 5 and 6 elements, extracted from the cleaned SuperCon database.

[0086]

[0087]

[0088] Table 5: Continue

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[0090]

[0091] Table 5: Continue

[0092]

[0093]

[0094] Table 5: Continue

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[0097] Table 5: Continue

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[0100] Table 5: Continue

[0101] formula <![CDATA[Experimental T c (K)]]> <![CDATA[B 44.4444 Sc 2.7778 AND 8.3333 Rh 4.4444 Go 40.0000 ]]> 2.92 <![CDATA[B 33.3333 C 16.6667 Ni 33.3333 Dy 10.0000 Tm 6.6667 ]]> 5.77 <![CDATA[B 33.3333 C 16.6667 Ni 33.3333 La 1.3333 Lu 15.3333 ]]> 13.6 <![CDATA[B 33.3333 C 16.6667 Neither 21.6667 Y 16.6667 Pd 11.6667 ]]> 12.1 <![CDATA[B 32.2581 C 16.1290 Co 6.4516 Ni 29.0323 Sun 16.1290 ]]> 2.6 <![CDATA[B 25.0000 C 25.0000 Ni 20.0000 Cu 5.0000 Sun 25.0000 ]]> 3.38 <![CDATA[B 33.3056 C 16.6528 What 0.1665 No 33.2223 Dy 16.6528 ]]> 4.1 <![CDATA[B 32.4149 C 16.2075 Co 5.5105 Ni 29.6596 Sun 16.2075 ]]> 3.8

[0102] Fig. 9 A flow chart of a method for predicting superconducting critical temperature provided in this specification is shown. Fig. 9 The illustrated prediction method P100 comprises the following steps:

[0103] S110: Obtain N descriptor sets of a target superconductor, each descriptor set including M descriptors characterizing the target superconductor, wherein both N and M are integers greater than or equal to 1.

[0104] S120: Input the N descriptor sets into the HNN model to predict the critical temperature of the target superconductor; wherein the HNN model includes multiple layers of sub-models, the N descriptor sets serve as inputs of the first layer of sub-models, the output of the i-th layer of sub-models serves as inputs of the i+1-th layer of sub-models, and the output of the last layer of sub-models serves as the critical temperature of the target superconductor, where i is an integer greater than or equal to 1.

[0105] In some embodiments, the M descriptors include m 1 primary descriptors and m2 non-primary descriptors, with m in each descriptor set. 1 The main descriptors are the same, the m 2 =Mm 1 .

[0106] In some embodiments, the m 1 is 5, the m 2 It is 44.

[0107] The construction and training methods of the HNN model refer to the above description.

[0108] Fig.10 A hardware structure diagram of a system 600 provided according to an embodiment of this specification is shown.

[0109] like Fig.10 As shown, the system 600 may include at least one storage medium 630 and at least one processor 620. In some embodiments, the system 600 may further include a communication port 650 and an internal communication bus 610. In addition, the system 600 may further include an I / O component 660.

[0110] The internal communication bus 610 can connect different system components. For example, the internal communication bus 610 can connect the storage medium 630, the processor 620, the communication port 650 and the I / O component 660.

[0111] I / O component 660 supports input / output between system 600 and other components.

[0112] The communication port 650 is used for data communication between the system 600 and the outside world. For example, the communication port 650 can be used for data communication between the system 600 and the network 400. The communication port 650 can be a wired communication port or a wireless communication port.

[0113] The storage medium 630 may include a data storage device. The data storage device may be a non-temporary storage medium or a temporary storage medium. For example, the data storage device may include one or more of a disk 632, a read-only storage medium (ROM) 634, or a random access storage medium (RAM) 636. The storage medium 630 also includes at least one instruction set stored in the data storage device. The instruction set may include a computer program code, and the computer program code may include a program, a routine, an object, a component, a data structure, a process, a module, etc. for executing the method for predicting the superconducting critical temperature and the method for training the HNN model provided in this specification.

[0114] The processor 620 may be in communication with the storage medium 630. The processor 620 is used to execute the at least one instruction set. When the system 600 is running, the processor 620 reads the at least one instruction set and executes the superconducting critical temperature prediction method and the HNN model training method provided in this specification according to the instructions of the at least one instruction set.

[0115] The processor 620 may be in the form of one or more processors, and in some embodiments, the processor 620 may include one or more hardware processors, such as a microcontroller, a microprocessor, a reduced instruction set computer (RISC), an application-specific integrated circuit (ASIC), an application-specific instruction set processor (ASIP), a central processing unit (CPU), a graphics processing unit (GPU), a physical processing unit (PPU), a microcontroller unit, a digital signal processor (DSP), a field programmable gate array (FPGA), an advanced RISC machine (ARM), a programmable logic device (PLD), any circuit or processor capable of performing one or more functions, etc., or any combination thereof.

[0116] For illustration purposes only, only one processor 620 is shown in the system 600 in the accompanying drawings. However, it should be noted that the system 600 in this specification may also include multiple processors, and therefore, the operations and / or method steps disclosed in this specification may be performed by one processor as described in this specification, or may be performed jointly by multiple processors. For example, if the processor 620 of the system 600 in this specification performs step A and step B, it should be understood that step A and step B may also be performed jointly or separately by two different processors 620 (e.g., the first processor performs step A, the second processor performs step B, or the first and second processors perform steps A and B together).

[0117] This specification also provides a computer-readable non-transitory storage medium, storing at least one set of executable instructions for training HNN models and predicting superconducting critical temperature. When the executable instructions are executed by the processor, the executable instructions instruct the processor to implement the steps of the method for predicting superconducting critical temperature and the method for training HNN models described in this specification. In some possible implementations, various aspects of this specification can also be implemented in the form of a program product, which includes program code. When the program product is run on system 600, the program code is used for system 600 to execute the training method and prediction method steps described in this specification. The program product for implementing the above method can use a portable compact disk read-only memory (CD-ROM) to include program code and can be run on system 600. However, the program product of this specification is not limited to this. In this specification, the readable storage medium can be any tangible medium containing or storing a program, which can be used by the instruction execution system or used in combination with it. The program product can use any combination of one or more readable media. The readable medium can be a readable signal medium or a readable storage medium. The readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination thereof. More specific examples of readable storage media include: an electrical connection with one or more conductors, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. The computer-readable storage medium may include a data signal propagated in a baseband or as part of a carrier wave, wherein a readable program code is carried. Such propagated data signals may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. The readable storage medium may also be any readable medium other than a readable storage medium, which may send, propagate, or transmit a program for use by or in combination with an instruction execution system, device, or device. The program code contained on the readable storage medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical cable, RF, etc., or any suitable combination thereof. Program code for performing the operations of the present specification may be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, etc., and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the system 600, partially on the system 600, as a stand-alone software package, partially on the system 600 and partially on a remote computing device, or entirely on a remote computing device.

[0118] The term “plurality” mentioned in this specification shall mean two or more than two unless otherwise stated.

[0119] The above is a description of a specific embodiment of the present specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in an order different from that in the embodiments and still achieve the desired results. In addition, the processes depicted in the drawings do not necessarily require a specific order or a continuous order to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0120] In summary, after reading this detailed disclosure, those skilled in the art will appreciate that the foregoing detailed disclosure may be presented only by way of example and may not be limiting. Although not explicitly stated herein, those skilled in the art will appreciate that this specification requires various reasonable changes, improvements and modifications to the embodiments. These changes, improvements and modifications are intended to be proposed by this specification and are within the spirit and scope of the exemplary embodiments of this specification.

[0121] In addition, certain terms in this specification have been used to describe embodiments of this specification. For example, "one embodiment", "an embodiment" and / or "some embodiments" mean that a particular feature, structure or characteristic described in conjunction with the embodiment may be included in at least one embodiment of this specification. Therefore, it can be emphasized and should be understood that two or more references to "an embodiment" or "one embodiment" or "an alternative embodiment" in various parts of this specification do not necessarily refer to the same embodiment. In addition, specific features, structures or characteristics may be appropriately combined in one or more embodiments of this specification.

[0122] It should be understood that in the foregoing description of the embodiments of this specification, in order to help understand a feature and for the purpose of simplifying this specification, this specification combines various features in a single embodiment, figure or its description. However, this does not mean that the combination of these features is necessary. When reading this specification, it is entirely possible for a person skilled in the art to mark out some of the devices as separate embodiments. In other words, the embodiments in this specification can also be understood as the integration of multiple secondary embodiments. This is also true when the content of each secondary embodiment is less than all the features of a single aforementioned disclosed embodiment.

[0123] Each patent, patent application, publication of patent applications, and other materials, such as articles, books, specifications, publications, documents, articles, etc., cited herein, except to the extent that it is inconsistent or conflicting with this document or that has a limiting effect on the broadest scope of the claims, may be incorporated herein by reference and used for all purposes now or hereafter associated with this document. In addition, in the event of any inconsistency or conflict between the description, definition, and / or use of a term in any material and the description, definition, and / or use of a term in this document, the term in this document shall prevail.

[0124] Finally, it should be understood that the embodiments of the application disclosed herein are explanations of the principles of the embodiments of this specification. Other modified embodiments are also within the scope of this specification. Therefore, the embodiments disclosed in this specification are only used as examples and not as limitations. Those skilled in the art can adopt alternative configurations according to the embodiments in this specification to implement the applications in this specification. Therefore, the embodiments of this specification are not limited to the embodiments accurately described in the application.

Claims

1. A method for predicting superconducting critical temperature, comprising: Obtaining N descriptor sets of a target superconductor, each descriptor set including M descriptors characterizing the target superconductor, wherein both N and M are integers greater than or equal to 1; as well as Inputting the N descriptor sets into the HNN model to predict the critical temperature of the target superconductor; The HNN model includes multiple layers of sub-models, the N descriptor sets serve as inputs to the first layer of sub-models, the output of the i-th layer of sub-models serves as inputs to the i+1-th layer of sub-models, the output of the last layer of sub-models serves as the critical temperature of the target superconductor, and i is an integer greater than or equal to 1.

2. The method according to claim 1, wherein: The M descriptors include m1 primary descriptors and m2 non-primary descriptors, the m1 primary descriptors in each descriptor set are the same, and m2=M-m1.

3. The method according to claim 2, wherein: The m1 is 5, and the m2 is 44.

4. A prediction system comprising: At least one storage medium storing at least one instruction set for predicting superconducting critical temperature; as well as At least one processor is communicatively connected to the at least one storage medium, wherein the at least one processor reads the at least one instruction set when running, and executes the method as described in any one of claims 1-3 according to the instructions of the at least one instruction set.

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