Hydrogen-based superconductor critical transition temperature prediction model based on electron state density integral and sign regression

Abstract

The invention relates to a symbol regression-based hydrogen-based superconductor critical transition temperature prediction method. Aiming at the problems of insufficient physical interpretability, limited generalization ability and the like of an existing hydrogen-based superconductor prediction method, the method innovatively introduces electronic state density integral characteristics near Fermi level, and constructs an explicit superconducting critical transition temperature prediction formula through a symbolic regression algorithm. By comprehensively considering the training of 343 samples and the fitting effect of 74 independent verification samples, the model shows excellent prediction precision (the training set RMSE is 20.15 K, and the verification set is 34.72 K), and is suitable for high-throughput screening of hydrogen-based superconducting materials.

Description

Technical Field

[0001] This invention relates to the field of computational design technology for superconducting materials, specifically to a method for predicting the critical transition temperature of hydrogen-based superconductors based on first-principles electronic structure calculation and symbolic regression machine learning algorithms. Background Art

[0002] Superconducting materials have attracted widespread attention in recent years due to their broad applications in power transmission, quantum computing, and magnetic resonance imaging. Hydride materials, with their high phonon frequencies and strong electron-phonon coupling, are considered important candidate systems for achieving high-temperature superconductivity. In particular, under high pressure conditions, many hydrides have been experimentally found to have superconducting transition temperatures above room temperature, sparking a research boom.

[0003] However, the search space for hydrogen-based superconductors is vast, and experimental synthesis conditions are stringent, making methods relying on blind experimentation extremely inefficient. Therefore, establishing reliable theoretical prediction methods to estimate the superconducting critical transition temperature of candidate materials using electronic structure information is a crucial means to accelerate the discovery of superconducting materials.

[0004] Existing methods for predicting the superconducting critical transition temperature can be broadly categorized into two types: one type is based on density functional theory combined with the McMillan formula or its modified form, calculating the superconducting critical transition temperature by measuring the electronic density of states, phonon spectrum, and electron-phonon coupling constant. However, this method is computationally expensive and unsuitable for high-throughput screening. The other type utilizes machine learning techniques, starting from the material structure, electronic structure, or elemental composition, and obtaining a superconducting critical transition temperature prediction model through model training. This method offers higher efficiency and scalability. However, existing machine learning-based superconducting critical transition temperature prediction models generally suffer from the following problems:

[0005] First, the input features are mostly general properties such as lattice constants and pressures, lacking physical quantities that accurately reflect the intrinsic mechanism of superconductivity, resulting in poor physical interpretability and generalization ability of the models. Second, most prediction models are black boxes, making the output results difficult to analyze and hard to guide subsequent material design or theoretical development. Finally, the limited number of samples in the training set means that without evaluation of external data, the models may overfit, thus reducing their effectiveness in practical applications.

[0006] Therefore, there is an urgent need to develop a rapid prediction method for the superconducting critical transition temperature that combines low computational cost, clear physical meaning, and strong generalization ability, in order to promote the discovery of practical hydrogen-based superconductors. Summary of the Invention

[0007] This invention provides a prediction model for hydrogen-based superconductor materials based on electronic structure characteristics, aiming to address the problems of weak physical correlation, poor interpretability, and insufficient generalization ability in existing prediction models for hydrogen-based superconductor materials. The technical effects of this invention include: (1) High prediction accuracy: The root mean square error on 343 training samples is 20.15K, and the root mean square error on 74 independent validation samples is 34.72K, which meets the requirements for high-throughput screening. (2) Improved computational efficiency: Compared with the traditional density functional theory combined with the McMillan formula, the computation time is greatly shortened, making it suitable for high-throughput material screening. (3) Strong physical interpretation: The explicit prediction formula obtained through symbolic regression has a clear physical meaning, providing guidance for the improvement of material design and theory.

[0008] To achieve the above objectives, the present invention proposes a critical transition temperature prediction model for hydrogen-based superconductors, the core technical solution of which includes:

[0009] The critical transition temperature data and crystal structure of hydrogen-based superconductors were obtained. The superconducting critical transition temperature data and corresponding crystal structures obtained by uniform parameter calculation EPC using QE were obtained from public databases, totaling 957 data samples.

[0010] The data was cleaned, for example, removing samples with outliers in the superconducting transition temperature and samples with negative frequencies in the phonon density of states, resulting in 343 samples used as the training set.

[0011] Subsequently, based on unified calculation parameters, VASP was used to perform first-principles calculations on the structure to obtain its electronic structure;

[0012] In addition to conventional structural and external pressure characteristics, this invention innovatively incorporates the integral of the electron density of states near the Fermi surface into the feature set. Compared to the traditional method that only examines the electron density of states of hydrogen at the Fermi surface, the integral of the electron density of states near the Fermi surface directly corresponds to the "number of electrons," making its physical meaning clearer. Test results of this invention show that the "proportion of the integral of the electron density of states near the Fermi surface of hydrogen" exhibits higher robustness than the traditional "proportion of the electron density of states at the Fermi surface of hydrogen" under parameter fluctuation scenarios.

[0013] By integrating the electronic density of states within a set integration window, the integral characteristics of the density of states of effective carriers near the Fermi surface are constructed. The present invention compares and finds that there is no significant difference between different electronic density of states integration ranges. In order to improve the repeatability of the present invention, the energy range is selected as (-1, +1) eV.

[0014] The integral features of the electronic density of states near the Fermi surface (including the total density of states and projected density of states of hydrogen, and normalized using the total density of states, the integral of the electronic density of states of non-hydrogen elements, the number of hydrogen atoms, volume, etc.) are combined with structural parameters (such as atomic density, the proportion of hydrogen atoms, and applied pressure) as features for symbolic regression.

[0015] To prevent the model from overfitting to the training set, this invention constructs an explicit critical temperature prediction formula in batches based on the feature sign regression method. At the same time, a total of 74 samples are collected from the published literature as a validation set. The optimal critical temperature prediction model is selected by comprehensively considering the root mean square error of the test set and the training set.

[0016] Meanwhile, to verify its robustness, this invention also collected theoretical calculation articles on cage-like hydrogen-based superconductors from the published literature, and compared the EPC calculation results in these articles with the model prediction results to evaluate the model's generalization ability and accuracy on cage-like hydrogen-based superconductors.

[0017] Furthermore, the prediction model uses a feature-symmetric regression algorithm to establish a mathematical expression, which can be directly used in the high-throughput material prediction process.

[0018] This model can be deployed on a computing platform that predicts the structure of hydrogen-based superconductors. After receiving the material structure input, it uses DFT to calculate the electronic structure and outputs the corresponding superconducting critical transition temperature. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the overall process of the method for predicting the critical transition temperature of hydrogen-based superconductors according to the present invention. It includes five main processing stages. Figure 2 A comparison of the distribution of the electronic density of states integral under different integration windows. Figure 3 This is a comparison of the stability of the integral characteristic of the electronic density of states near the Fermi surface of hydrogen and the traditional Fermi surface density of states under different computational settings. Figure 4 This is a critical temperature prediction model established through feature sign regression. Figure 5 The fitting effect of the critical temperature prediction model on cage-like hydrogen-based superconductors. Detailed Implementation

[0020] To more clearly illustrate the technical solution of the present invention, the present invention will be described in detail below with reference to typical embodiments of the test set screening process. Those skilled in the art should understand that the following embodiments are for illustrative purposes only and do not constitute a limitation thereof.

[0021] This embodiment provides a method for predicting the critical transition temperature of hydrogen-based superconductors based on electronic structure characteristics and a symbolic regression model. The overall construction process is as follows: Figure 1 As shown, it includes five stages: data construction, feature extraction, regression modeling, test set selection, and candidate material prediction.

[0022] First, 957 material samples with hydrogen-based superconductor properties were collected from public databases. Each sample included its crystal structure and the superconducting critical transition temperature calculated using first-principles calculations with uniform parameters. After data cleaning (removing abnormal superconducting critical transition temperatures, unreasonable structures such as those containing negative frequency phonons), 343 high-quality data points were obtained as the training set.

[0023] Subsequently, electronic structure calculations were performed on the sample structure using VASP software under uniform parameter settings. A PAW pseudopotential and a PBE functional were employed, with a plane wave cutoff energy of 1000 eV and a k-point grid density of approximately [value missing].

[0024] In the feature construction process, this invention proposes to introduce the "electronic density of states integral near the Fermi surface" as an innovative electronic structure descriptor. For electronic density of states data, see [link to relevant documentation]. Figure 2 The choice of integration window has almost no impact on the features. To improve the repeatability and convenience of this invention, we select ±1 eV symmetric around the Fermi level as the integration window. Within a reasonable range, this feature can be used in the superconducting critical temperature prediction model proposed in this invention.

[0025] To demonstrate the robustness of the novel features of this invention, see [link to relevant documentation]. Figure 3 The comparative results show that the "integral proportion of the electron density of states of hydrogen near the Fermi surface" has higher robustness than the "proportion of the hydrogen Fermi surface density of states" under parameter fluctuation scenarios. Furthermore, if you wish to use the results of this invention, please use the standard H pseudopotential for hydrogen.

[0026] In addition, the number of hydrogen atoms (N) was also extracted. H atomic density (ρ) at The structural and macroscopic physical characteristics, such as applied pressure (P) and total volume (V), are considered. To enhance model stability, these characteristics are normalized and standardized to form a feature vector.

[0027] The model is trained using a feature-signed regression method. Using the training set as input, a series of explicit candidate prediction formulas with physical interpretability are generated.

[0028] To prevent the model from overfitting to the training set, this invention collected relevant research on hydrogen-based superconductor materials from publicly available literature, extracting 74 material samples that were not used in the training as an independent validation set. Candidate prediction formulas were tested one by one on this validation set, and their root mean square error (RMSE) was calculated. The errors from both the training and validation sets were considered as the selection criterion. The results are as follows... Figure 4As shown, the final selected model achieved an RMSE of 20.15K on the training set and 34.72K on the test set, demonstrating good generalization ability. The predicted critical transition temperature of the hydrogen-based superconductor obtained by the symbolic regression algorithm in this invention is shown in Equation 1: in This represents the integral of the electronic density of states of the p orbitals of hydrogen in the energy range of (-1, 1), and uses N0... H Normalize (number of hydrogen atoms); This means that the integral of the density of electronic states of hydrogen in the energy range of (-1, 1) is divided by the integral of the total density of electronic states, that is, the density of states of hydrogen is normalized by using the total density of states. This represents the electronic density of states integral of all elements except hydrogen in the energy range of (-1, 1).

[0029] This invention was compared with data from cage-like hydrogen-based superconductors in published literature. The test set exhibits a novel structure and a significantly higher atomic count than the training set of this invention (the largest sample in the training set has 20 atoms, while the test set samples even reach 200 atoms). See [link to relevant documentation]. Figure 5 As can be seen, most samples are distributed near the diagonal, indicating that the feature sign regression model has good generalization ability.

[0030] The method of this invention can be embedded into a materials prediction platform to form a complete hydrogen-based superconductor screening system. The system receives material structure input files, automatically performs electronic structure calculations, feature extraction, superconducting critical transition temperature prediction, and outputs results, making it suitable for high-throughput screening and evaluation of hydrogen-based materials.

[0031] In summary, this embodiment demonstrates the application process and technical effects of the hydrogen-based superconductor critical temperature prediction method based on electronic structure integral features and symbolic regression model proposed in this invention in the screening of actual test sets and material prediction, fully proving that this invention has good feasibility and industrial application value.

Claims

1. A method for predicting the critical transition temperature of a hydrogen-based superconductor, characterized in that, include: (1) Obtain the crystal structure data and corresponding critical transition temperature data of hydrogen-based superconductors, and construct the original dataset; (2) The original dataset is subjected to stability screening. Based on the phonon density of states calculation results, dynamically stable crystal structures are selected to form a training dataset. (3) Additionally, crystal structure data and corresponding critical transition temperature data from publicly available literature were collected as a validation set; (4) Perform first-principles electronic structure calculations on the crystal structures in the training dataset and the validation set to obtain electronic state density distribution data; (5) Integrate the electronic density of states within a preset energy window and extract the integral features of the electronic density of states; (6) Using the integral features of the electronic density of states and the structural features as inputs, the explicit critical transition temperature prediction formula is obtained by training with the symbolic regression algorithm. (7) The critical transition temperature of the hydride to be predicted is predicted using the prediction formula.

2. The method according to claim 1, characterized in that: The symmetric energy window is ±1 eV centered on the Fermi level, and adjusting the integral window within a certain range has no significant impact on the prediction accuracy.

3. The method according to claim 1, characterized in that: The integral features include the total electronic density of states integral and the projected electronic density of states integral (s orbital or p orbital) of hydrogen, and are new features obtained after normalization.

4. The method according to claim 1, characterized in that, Step (6) involves using a symbolic regression algorithm to train an explicit critical transition temperature prediction formula, which specifically includes: (1) Generate multiple candidate prediction formulas using the symbolic regression algorithm; (2) Construct a validation set independent of the training dataset; (3) Apply each candidate prediction formula to the training set and the validation set respectively, and calculate the corresponding prediction error; (4) Based on the combined performance of the training set and validation set errors, the prediction formula that takes into account both prediction ability and generalization ability is selected as the final prediction formula for the critical transition temperature of hydrogen-based superconductors.

5. A system for predicting the critical transition temperature of a hydrogen-based superconductor, characterized in that, include: (1) Structural data acquisition module, used to acquire crystal structure data of hydrides; (2) Electronic structure calculation module, used to perform first-principles calculations to obtain the electronic state density distribution; (3) Feature acquisition module, used to integrate the electronic density of states and extract features within a preset energy window; (4) Prediction module, used to calculate the critical transition temperature based on the prediction formula constructed by the symbolic regression algorithm.

6. A device for predicting the structure of a hydrogen-based superconductor, characterized in that, include: (1) Structure input interface, used to receive hydride crystal structure files generated by structure prediction software, including but not limited to USPEX software; (2) Superconducting critical transition temperature prediction module, executes the hydrogen-based superconductor critical transition temperature prediction system as described in claim 5, and obtains the predicted superconducting critical transition temperature of the hydride. (4) Result output input module, used to output prediction results in batches and feed back the structure to the structure prediction software.

7. A high-throughput screening device for hydrogen-based superconductors, characterized in that, include: (1) Structure generation module: Use element substitution or generative large model to obtain a large number of hydride structures; (2) Superconducting critical temperature screening module, which executes the hydrogen-based superconductor critical transition temperature prediction system of claim 5, for large-scale prediction of superconducting critical transition temperature.

8. The high-throughput screening device according to claim 7, characterized in that: It further includes a stability assessment module, which uses a machine learning-based dynamic stability prediction algorithm to screen candidate crystal structures and then passes the screened structures to the superconducting critical temperature prediction module to achieve high-throughput search.

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