An ABO 3-δ Method and system for online prediction of oxygen ionic conductivity of abo-type perovskite electrolytes

Abstract

The application provides an ABO 3‑δ The application provides an online prediction method and system for perovskite electrolyte oxygen ion conductivity, and relates to the technical field of solid oxide fuel cell materials, material informatics and machine learning cross technology. The method realizes full-automatic serial execution of solidification model prediction through a B / S architecture Web platform, avoids invalid input by combining three-level stoichiometric verification closed loop with A / B bit doped element number hard constraint, quantifies feature contribution weight by multi-algorithm explainability analysis, and simultaneously satisfies compliance candidate components of doping restriction and charge balance by fixed time sequence inverse design screening output, effectively solving the problems of long cycle in traditional research and development, high threshold of existing offline tools, and insufficient physical reliability of screening results, and having the advantages of significantly shortening material research and development cycle, reducing synthesis and characterization experiment cost, improving prediction accuracy and material structure-activity relationship result explainability.

Description

Technical Field

[0001] This application belongs to the interdisciplinary fields of solid oxide fuel cells, materials informatics, and machine learning, specifically relating to an ABO... 3-δ An online prediction method and system for oxygen ion conductivity of perovskite electrolytes. Background Technology

[0002] Solid oxide fuel cells (SOCs) are highly efficient and clean energy conversion devices, with oxygen ion-type ABOs being the most common type. 3-δ The oxygen ion conductivity of perovskite electrolytes directly restricts the energy conversion efficiency of batteries. The ion conductivity of these materials is intricately influenced by the combination of A-site and B-site doping elements, doping ratios, oxygen vacancy concentration, and sintering temperature, among other process parameters. Traditional research and development relies heavily on trial-and-error experiments: repeated adjustments to element ratios, optimization of synthesis processes, and sample preparation and characterization are required, resulting in long development cycles, high experimental costs, and low screening efficiency. In recent years, machine learning technology has been applied to predict the performance of these materials, but existing technologies have significant shortcomings. Current prediction tools are mostly offline code or simple web interfaces, requiring users to manually configure the environment and execute calculations step by step, creating a high technical barrier for researchers. They lack a full-chain, decoupled online web service architecture, making it impossible to achieve zero-dependency, fully automated online prediction and batch screening. In the input processing stage, a three-level serial verification logic for A-site doping ratio, B-site doping ratio, and oxygen vacancy charge balance is not established, failing to identify and intercept inputs that do not conform to stoichiometric rules. Abnormal data still participates in subsequent calculations, generating a large number of physically meaningless prediction results. The computational modules are fragmented, with chemical formula verification, descriptor calculation, conductivity prediction, feature parsing, and reverse screening belonging to independent code units. Users need to manually switch scripts and manually pass intermediate data. The lack of a fully automated pipeline architecture with unified backend timing scheduling makes it impossible to achieve one-click, fully automated computation from input to reverse design. At the model interpretation level, existing technologies only provide a single numerical output of conductivity, failing to quantify the positive or negative contribution of each feature to conductivity performance. Conventional single-algorithm feature analysis is susceptible to data distribution interference and has poor conclusion stability. The lack of a reliable discrimination mechanism for parallel and cross-validation of multiple independent algorithms makes it difficult to support scientific decisions regarding the directional doping modification of materials. In the reverse design stage, while existing solutions attempt to divide high and low conductivity sample intervals using Fisher's discrimination and refine the constraint range using two-dimensional contour maps, they lack a complete constraint system including pre-filtering of A / B site doping types, fixed-time step-by-step reverse solving, and secondary charge verification of candidate components. The screening conditions are lenient, easily outputting invalid components with charge imbalances and unstable structures, severely reducing the accuracy and practicality of reverse design.

[0003] To address the aforementioned issues, existing technologies urgently need improvement. Summary of the Invention

[0004] This application provides an ABO 3-δ An online prediction method and system for the oxygen ion conductivity of perovskite electrolytes is proposed. This method offers significant advantages, including shortening the material development cycle, reducing experimental costs, and improving prediction accuracy and interpretability.

[0005] Firstly, this application provides an ABO 3-δ An online prediction method for the oxygen ion conductivity of perovskite electrolytes is presented, executed fully automatically and serially by a B / S architecture web platform. This web platform contains a pre-trained prediction model with fixed parameters, which is executed offline before deployment. Only inference operations are performed online; the model is not retrained, and samples are not re-divided. The method includes the following steps: S1, ABO (Application Programming Interface) for receiving user input in the front-end visual interface. 3-δ The chemical formula of the perovskite and three process parameters, namely sintering temperature, pre-sintering temperature and test temperature, are encapsulated in JSON format and sent to the backend. S2. The backend performs a three-level serial chemometric verification closed loop on the input chemical formula: The chemical formula is parsed, and the following are verified sequentially: ① The sum of the doping ratios of all cations at position A equals 1; ② The sum of the doping ratios of all cations at position B equals 1; ③ The oxygen vacancy content determined by the valence state of the doped ions satisfies ABO. 3-δ Perovskite charge balance constraint range; if any level of verification fails, the backend generates a message carrying an exception type identifier and sends it back to the frontend, indicating the corresponding exception item, and the process flows back to S1 for re-entry; after all three levels of verification pass, it enters S3; S3. The backend retrieves the built-in elemental property database, calculates atomic-level descriptors by weighting the doping ratio of each element at position A and position B, calculates structural-level descriptors based on fixed chemical formulas, extracts the input process parameters, integrates them to form 48 initial multi-source descriptors, and then obtains 8 key descriptors through a two-level feature screening process that is preset by the platform and cannot be customized. S4. Input the 8 key descriptors into the pre-trained SVR-RBF model, and output the natural logarithm of oxygen ion conductivity lnσ and the converted actual conductivity σ; the hyperparameters of the SVR-RBF model are determined and permanently fixed in the offline training stage through 10-fold cross-validation grid search: regularization parameter C=81, insensitive loss ε=0.01, kernel coefficient γ=1.3, and the fixed model can be directly called online to complete inference; S5. Simultaneously run three independent interpretable algorithms: SHAP analysis, permutation importance analysis, and one-way ANOVA. Using the eight key descriptors and the prediction results of the SVR-RBF model as input, quantify the positive and negative contribution weights of each key descriptor to conductivity, and perform consistency cross-verification on the feature importance ranking results obtained by the three algorithms to output a feature contribution visualization spectrum. S6. The two-level linkage reverse design screening is performed, and the following three steps cannot be changed in the order of operation: S61. Receive the user-defined target conductivity threshold, first eliminate invalid ratios with more than 3 types of A-site doped cations or more than 2 types of B-site doped cations according to the hard constraint of the number of component doping, and then divide the remaining samples into high and low conductivity categories by Fisher discrimination model with lnσ=-5.0 as the dividing value. After two-dimensional projection, delineate the rectangular coarse selection feature interval where high conductivity samples are concentrated. S62. Based on the pairwise coupling of the eight key descriptors, a two-dimensional contour map is generated, which is further compressed to a narrow constrained subspace of lnσ > -3.0 on the basis of Fisher's coarse selection of feature intervals. S63. The narrow-constrained subspace is projected back into the eight-dimensional feature space in reverse. Based on the calculation formulas corresponding to the eight key descriptors, the types of A-site elements, the types of B-site elements, the A / B-site doping ratio, and the oxygen vacancy content are solved in reverse step by step to generate candidate components in batches. Chemometric verification is performed again on each group of candidate components to remove charge imbalance components and output only the set of perovskite candidate components that fall within the high conductivity feature range and are chemometrically compliant. S7 provides a unified visual display of chemical formula verification results, all multi-source descriptor values, conductivity prediction results, feature contribution maps, two-dimensional contour constraint maps, Fisher discriminant clustering maps, and candidate component parameters obtained through reverse deduction. It also supports users selecting any group of candidate components to automatically backfill parameters and jump to S1 to re-execute the forward conductivity prediction. The Web platform backend uses the Python Flask framework to uniformly encapsulate and schedule all computing functions. Each computing subroutine only exchanges data through the backend master control program, and the frontend and backend achieve standardized data interaction through JSON messages.

[0006] Optionally, the two-step feature screening process in step S3 is as follows: First, the platform's built-in exclusive feature sorting rules are used to sort the importance of the 48 initial multi-source descriptors, and high-redundancy features with an absolute value of Pearson correlation coefficient greater than 0.95 are removed, leaving 34 non-redundant descriptors; Second, the platform's fixed iterative logic feature selection is performed on the 34 non-redundant descriptors using the maximization of the 5-fold cross-validation determination coefficient as the screening criterion, and finally, 8 key descriptors are selected, namely: oxygen vacancy fraction, A-site electron affinity, average ionic radius, tolerance factor deviation, average ionization energy, sintering temperature, pre-sintering temperature, and natural logarithm of test temperature.

[0007] Optionally, in step S2, after analyzing the chemical formula, the elemental property parameters are weighted and summed according to the doping ratio of each element to obtain the average property parameters of the A-site and B-site; in the third-level verification, the total positive charge of the cations in the system is calculated based on the valence of the doped ions at the A-site and B-site; the verification is deemed to pass only when the oxygen vacancy content can balance the positive and negative charges of the system and the oxygen vacancy content is within a preset reasonable range; the third-level verification is executed serially, and if the previous level verification fails, the process is terminated and the corresponding abnormality type identifier is output, and the next level verification is not executed.

[0008] Optionally, in step S5: the SHAP analysis quantifies the marginal contribution of each key descriptor to a single prediction based on cooperative game theory and outputs a global importance ranking; the permutation importance analysis quantifies the importance of a descriptor by the decrease in the coefficient of determination of the model after shuffling a single key descriptor; the one-way ANOVA determines the significance of the conductivity difference between different values ​​of each key descriptor by the significance level p-value; when the top-ranked important descriptors obtained by the three algorithms are consistent, the conclusion on the importance of the feature is reliable.

[0009] Optionally, the rectangular coarse selection feature interval mentioned in step S61 is the Fisher two-dimensional rectangle optimal interval with a high conductivity sample ratio of 98%; the two-dimensional contour map mentioned in step S62 is generated by pairing four sets of key descriptors, namely: oxygen vacancy fraction and average ionization energy, A-site electron affinity and average ionic radius, sintering temperature and tolerance factor deviation, and pre-sintering temperature and natural logarithm of test temperature.

[0010] Optionally, the reverse step-by-step solution in step S63 is as follows: first, determine the combination of A-site and B-site elements that satisfy the hard constraint of doping quantity within the value range corresponding to the narrow constraint subspace; then, solve the doping ratio of each element so that the calculated values ​​of the 8 key descriptors fall into the narrow constraint subspace; finally, determine the oxygen vacancy content based on the valence charge balance of the doped ions; the chemometric verification includes: calculating the total positive charge of cations and the total negative charge of oxygen ions of the candidate components, and retaining only the components that can achieve charge compensation and overall charge balance through reasonable oxygen vacancy content.

[0011] Optionally, the content displayed on the front end in step S7 includes 18 atomic-level derivation descriptors, 15 complete values ​​of the constituent derivation descriptors, and multi-level inverse design constraint interval parameters; the automatic backfill jump specifically means that when the user clicks on any candidate component in the Fisher discriminant clustering diagram, two-dimensional contour constraint map, or candidate component list on the front end, the front end extracts the unique identifier of the candidate component and sends it to the back end.

[0012] Secondly, this application also provides an ABO 3-δ An online prediction system for the oxygen ion conductivity of perovskite electrolytes, employing a four-layer B / S architecture, including: Front-end interaction layer: A visual webpage for Vue.js, implementing parameter input, error message pop-ups, full data and graph visualization, and single-point backfilling jump function for candidate components; Flask backend API scheduling layer: Deploys Python Flask master control API service, uniformly encapsulates chemical formula verification module, multi-source descriptor calculation module, conductivity prediction module, multi-algorithm interpretability analysis module, and two-level inverse design screening module. There is no direct data interaction between the modules. They only use the master control API for serial scheduling and data transfer. After receiving the front-end JSON request, it schedules the serial operation of each module according to a fixed time sequence and sends the structured operation data back to the front-end. Data storage layer: includes MySQL database and local file storage. The MySQL database stores standard element property library, historical prediction records, and candidate component data. The local file stores pre-trained SVR-RBF model files, Fisher discriminant model files, and SHAP interpreter files. Operations and maintenance deployment management layer: Deployed on a public cloud server, configured with regular data backup, concurrent request distribution and automatic restart mechanism for service failures; The modules of the system work together to execute the online prediction method described in any one of claims 1 to 7.

[0013] Optionally, the two-level inverse design screening module has an built-in irreversible timing lock, which fixes the serial operation order of first Fisher discrimination to coarsely divide the interval, then two-dimensional contour map compression to narrow the constraint subspace, and finally eight-dimensional feature inverse mapping to solve the composition and perform chemometric verification; the chemical formula verification module has a built-in three-level serial chemometric verification logic, which can automatically parse multi-doped perovskite chemical formulas, calculate the weighted average physical property parameters of A / B sites and determine the charge balance state. If a single-level verification is abnormal, the operation will be terminated immediately and an abnormality flag will be returned.

[0014] Thirdly, this application also provides a computer-readable storage medium having a computer program stored thereon, characterized in that, when the computer program is executed by a processor, it implements the method described above.

[0015] In summary, this application utilizes a B / S architecture web platform to automatically and serially execute fixed model predictions. It combines a three-level stoichiometric verification closed loop with hard constraints on the number of dopant elements at A / B sites to avoid invalid inputs, multi-algorithm interpretability analysis to quantify feature contribution weights, and fixed-time inverse design to screen compliant candidate components that simultaneously meet doping constraints and charge balance. This effectively solves the problems of lengthy cycles, high barriers to entry for existing offline tools, and insufficient physical reliability of screening results in traditional R&D. It has the advantages of significantly shortening the material R&D cycle, reducing the cost of synthesis and characterization experiments, improving prediction accuracy, and enhancing the interpretability of material structure and property results. Attached Figure Description

[0016] Figure 1 This application is ABO 3-δ A schematic flowchart of the first embodiment of the online prediction method for oxygen ion conductivity of perovskite electrolytes; Figure 2 This application is ABO 3-δ A structural block diagram of the first embodiment of an online prediction system for the oxygen ion conductivity of perovskite electrolytes. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of this application.

[0018] Traditional ABO 3-δ The development of perovskite electrolytes relies heavily on trial and error experiments, resulting in long development cycles, high costs, and low screening efficiency. Existing machine learning prediction tools suffer from drawbacks such as high programming barriers, lack of an integrated web service architecture, lack of standardized chemical formula pre-verification loops, independent computational functions, poor interpretability of model prediction results, and imperfect reverse design constraints. Consequently, they cannot achieve zero-environment dependence, fully automated, and highly reliable forward prediction and reverse component screening of materials.

[0019] In response, this application provides an ABO (Abbreviated Name) implementation. 3-δ An online prediction method for the oxygen ion conductivity of perovskite electrolytes, referring to... Figure 1 .

[0020] The online prediction method provided in this embodiment includes the following steps: Step S1: The front-end visual interface receives ABO data input from the user. 3-δ The perovskite chemical formula and three process parameters—sintering temperature, pre-sintering temperature, and test temperature—are encapsulated in a JSON format request and sent to the backend. Step S2: The backend performs a three-level serial chemometric verification closed loop on the input chemical formula: parse the chemical formula and verify in sequence: ① the sum of the doping ratios of all cations at position A is equal to 1; ② the sum of the doping ratios of all cations at position B is equal to 1; ③ the oxygen vacancy content determined by the valence state of the doped ions satisfies ABO. 3-δ Perovskite charge balance constraint range; if any level of verification fails, the backend generates a message with an exception type identifier and sends it back to the frontend to prompt the corresponding exception item. The process flows back to S1 for re-entry and does not proceed to subsequent calculations; after all three levels of verification pass, it proceeds to S3. Step S3: The backend retrieves the built-in elemental property database, calculates atomic-level descriptors by weighting the doping ratio of each element at position A and position B, calculates structural-level descriptors based on fixed chemical formulas, extracts the input process parameters, integrates them to form 48 initial multi-source descriptors, and then obtains 8 key descriptors through a two-level feature screening process that is preset by the platform and cannot be customized. Step S4: Input the 8 key descriptors into the pre-trained SVR-RBF model, and output the natural logarithm of oxygen ion conductivity lnσ and the converted actual conductivity σ; the hyperparameters of the SVR-RBF model are determined and permanently fixed in the offline training stage through 10-fold cross-validation grid search: regularization parameter C=81, insensitive loss ε=0.01, kernel coefficient γ=1.3. Online, only the fixed model is called to complete steady-state inference, and no model retraining or sample re-split is performed; Step S5: Simultaneously run three independent interpretability algorithms: SHAP analysis, permutation importance analysis, and one-way ANOVA. Using the eight key descriptors and the prediction results of the SVR-RBF model as input, quantify the positive and negative contribution weights of each key descriptor to conductivity, perform consistency cross-verification on the feature importance ranking results of the three algorithms, and output a feature contribution visualization spectrum. Step S6: Perform a two-level linked sequential inverse design screening with strong data dependencies and an invariable execution order. The following three steps cannot be changed in order: Step S61: Receive the user-defined target conductivity threshold. First, eliminate invalid ratios with more than 3 types of A-site doped cations or more than 2 types of B-site doped cations according to the hard constraint of the number of component doping. Then, use lnσ=-5.0 as the dividing value to divide the remaining samples into high and low conductivity categories through the Fisher discriminant model. After two-dimensional projection, delineate the rectangular coarse selection feature interval where high conductivity samples are concentrated. Step S62: Generate a two-dimensional contour map by pairwise coupling of the eight key descriptors, and further compress it to a narrow constrained subspace of lnσ > -3.0 based on Fisher's coarsely selected feature interval; Step S63: Project the narrow-constrained subspace back into the eight-dimensional feature space in reverse. Based on the calculation formulas corresponding to the eight key descriptors, solve the types of A-site elements, types of B-site elements, A / B-site doping ratio and oxygen vacancy content in reverse step by step to generate candidate components in batches. Perform stoichiometric verification on each group of candidate components again, remove components with charge imbalance, and output only the set of perovskite candidate components that fall within the high conductivity feature range and comply with stoichiometric requirements. Step S7: The front end provides a unified visual display of the chemical formula verification results, all multi-source descriptor values, conductivity prediction results, feature contribution maps, two-dimensional contour constraint maps, Fisher discriminant clustering maps, and candidate component parameters obtained through reverse deduction. It also supports users selecting any group of candidate components to automatically backfill parameters and jump to S1 to re-execute the forward conductivity prediction. The Web platform backend uses the Python Flask framework to uniformly encapsulate and schedule all computing functions. Each computing subroutine only interacts with data through the backend master control program. The frontend and backend achieve standardized data interaction through JSON messages.

[0021] For ease of understanding, the following explains some key terms in this embodiment: Oxygen ion type ABO 3-δ Type A perovskite electrolyte is a material system used as an electrolyte in [material name - likely a specific process or application], with the general chemical formula ABO. 3-δ The A and B sites can be occupied by different metal cations, and δ represents the oxygen vacancy content. The oxygen ion conductivity of this material directly determines the energy conversion efficiency of the fuel cell.

[0022] B / S architecture web platform is a software architecture based on browser / server mode. Users access applications on the server through a web browser without the need for local deployment. It features zero environment dependency, easy deployment, easy maintenance, and online stable service.

[0023] The SVR-RBF prediction model is a support vector regression model based on radial basis function kernel function. It learns the nonlinear structure-property relationship between features and conductivity through offline datasets, and performs fixed inference online without retraining to predict oxygen ion conductivity.

[0024] The chemometric verification closed loop is a step-by-step serial verification mechanism. Through three levels of verification—A-site doping ratio, B-site doping ratio, and oxygen vacancy charge balance—illegal inputs that do not conform to chemical rules or have no physical meaning are intercepted, ensuring the validity of downstream calculation data.

[0025] Multi-source descriptors are a parameter system for quantitatively characterizing the composition, structure, and process features of materials, including atomic-level, structural-level, and process parameter features. After redundant features are removed by the platform's fixed screening rules, key descriptors that have a significant impact on conductivity are obtained, which serve as the core input for model inference.

[0026] Interpretable algorithms, including SHAP analysis, permutation importance analysis, and one-way ANOVA, are used to quantify the positive and negative contributions of each feature, cross-validate the conclusions of feature importance, and solve the black box problem of machine learning models.

[0027] Two-stage linked inverse design screening is a design method that starts with the target performance and works backward to deduce the material composition. This method uses multi-stage constraints and screening to progressively narrow down the material composition space, efficiently identifying candidate materials with the desired performance. Specifically, the Fisher discriminant model is used to classify samples into different performance categories, while two-dimensional contour maps are used to visualize the performance distribution in the feature space.

[0028] JSON requests and JSON messages are data exchange formats based on JavaScript object representation. This format stores and transmits data in text form, and is characterized by its lightweight nature, ease of reading and writing, and machine parsing capabilities. It is commonly used for data exchange between front-end and back-end systems.

[0029] The Python Flask framework is a lightweight web application framework used to uniformly encapsulate and schedule various computing modules in a time sequence, achieving subroutine isolation, central control transfer, and fully automated scheduling.

[0030] The online prediction method in this embodiment specifically includes the following steps: In step S1, the front-end visual interface is configured to receive user input via ABO. 3-δ The perovskite chemical formula and three process parameters—sintering temperature, pre-sintering temperature, and testing temperature—are standardized and encapsulated into a JSON request message and uploaded to the backend to complete the frontend parameter access.

[0031] In step S2, the backend performs a three-level serial chemometric verification closed loop on the received chemical formula: First, it parses the chemical formula, identifies the types of doping elements and their corresponding doping ratios, and performs A-position doping ratio normalization verification, B-position doping ratio normalization verification, and oxygen vacancy charge balance verification level by level. If any level of verification fails, a corresponding error flag is immediately generated and sent back to the frontend, the process flows back to S1 for re-entry, and subsequent calculations are terminated; the process only proceeds to S3 when all three levels of verification are compliant. For example, if the sum of the A-position doping ratios entered by the user is 0.9, the first-level verification fails, the system will prompt an error and require re-entry.

[0032] In step S3, the backend retrieves the built-in elemental property database to obtain the physicochemical properties of each element. Atomic-level descriptors are calculated based on the weighted doping ratios of each element at positions A and B, and structural-level descriptors are solved using fixed chemical formulas. Additionally, process parameters such as sintering temperature, pre-sintering temperature, and testing temperature are extracted from user input. These atomic-level descriptors, structural-level descriptors, and process parameters are integrated to form 48 initial multi-source descriptors. Redundant features are progressively eliminated through a platform-defined two-level feature screening process, ultimately resulting in eight key descriptors that significantly impact electrical conductivity performance.

[0033] In step S4, the eight key descriptors obtained above are used as inputs and fed into the pre-trained SVR-RBF model. This model is used to output the natural logarithm lnσ of oxygen ion conductivity and the converted actual conductivity σ. The hyperparameters of this SVR-RBF model, such as the regularization parameter C, the insensitive loss ε, and the kernel coefficient γ, have been optimized and fixed offline through multi-fold cross-validation combined with grid search. In the online running phase, only the fixed model is called to complete the inference calculation, without the need for secondary training and parameter fine-tuning.

[0034] In step S5, three independent interpretable algorithms—SHAP analysis, permutation importance analysis, and one-way ANOVA—are run simultaneously in parallel. Using eight key descriptors and model prediction results as unified input, the positive and negative contribution weights of each feature to conductivity are quantified. Cross-validation of feature ranking results from multiple algorithms enhances the credibility of the mechanistic analysis. Finally, a visual graph of feature contributions is output, intuitively demonstrating the influence patterns of each descriptor.

[0035] In step S6, a two-level linkage inverse design with a fixed execution timing is performed to filter the following three steps of operation logic, which are fixed and cannot be changed in order: In step S61, the system receives the user-defined target conductivity threshold and firstly eliminates invalid ratios of more than 3 types of cations at A site and more than 2 types of cations at B site by hard constraint of doping quantity; using lnσ=-5.0 as the dividing value and classification threshold, the system divides high and low conductivity samples by Fisher discrimination model, and locks the rectangular coarse selection feature interval where high conductivity samples are densely distributed by two-dimensional projection.

[0036] In step S62, a two-dimensional contour map is constructed based on the pairwise coupling of the eight key descriptors to visualize the correlation between the feature combination and conductivity. Based on the coarse selection interval, the constraint range is further narrowed to obtain a high-precision narrow constraint subspace with lnσ > -3.0.

[0037] In step S63, the aforementioned narrow-constrained subspace is projected back into the eight-dimensional feature space. Based on the calculation formulas corresponding to the eight key descriptors, the element types, doping ratios, and oxygen vacancy parameters are deduced step-by-step in reverse to generate a series of candidate components. Subsequently, the stoichiometry and charge balance of all derived components are verified, and invalid ratios with unstable structures and charge imbalances are eliminated, ultimately outputting a set of high-conductivity, compliant, and valid perovskite candidate components.

[0038] In step S7, the front end provides a centralized visual display of the chemical formula verification results, multi-source descriptor values, conductivity prediction results, feature contribution maps, two-dimensional contour constraint maps, Fisher discriminant clustering maps, and candidate component parameters obtained through reverse deduction. Furthermore, the front end allows users to select any group of candidate components; the system will automatically fill in the parameters of that component to the input interface and then jump to S1 to re-execute the forward conductivity prediction process.

[0039] The backend of this web platform uses the Python Flask framework to uniformly encapsulate and schedule all computational functions. Subroutines such as chemical formula verification, descriptor calculation, and conductivity prediction are decoupled from each other, with data interaction and timing scheduling handled solely by the backend master control program. Standardized data interaction between the frontend and backend is achieved through JSON messages, ensuring the standardization and efficiency of data exchange.

[0040] The online prediction method in this embodiment achieves fully automated serial execution through a B / S architecture web platform, effectively solving the problems of long trial-and-error experimental cycles, high costs, and low efficiency in traditional R&D models. Its built-in chemometric verification closed-loop intercepts illegal inputs, ensuring the physical validity of the prediction results. Unified encapsulated backend scheduling enables seamless integration of various computational functions, improving computational efficiency. Multi-algorithm interpretability analysis provides quantitative evidence for the directional doping modification of materials. Two-stage linked reverse design screening, combined with pre-filtering and final verification, improves the effectiveness and screening accuracy of candidate components, thereby accelerating ABO (Absolute Booster) analysis. 3-δ The development progress of perovskite electrolytes.

[0041] If the initial feature selection mechanism is imperfect and cannot effectively remove redundant and noisy features, it will lead to redundant input dimensions of the model, decreased fitting accuracy, and increased online computational burden. To address this issue, all feature selection logic in this application is an offline solidification process before model deployment. The specific two-step selection rule is as follows: First, the mRMR method is used to sort the 48 initial multi-source descriptors. Using the absolute value of the Pearson correlation coefficient of 0.95 as the redundancy threshold, highly collinear features are removed, and 34 non-redundant descriptors are retained. Second, based on the criterion of maximizing the 5-fold cross-validation determination coefficient, forward iterative selection is performed on the non-redundant features, resulting in 8 exclusive key descriptors obtained offline solidification: oxygen vacancy fraction, A-site electron affinity, average ionic radius, tolerance factor bias, average ionization energy, sintering temperature, pre-sintering temperature, and natural logarithm of test temperature.

[0042] Specifically, this application employs an offline dual-constraint feature optimization mechanism, relying on the mRMR algorithm to balance the correlation between features and conductivity with low redundancy among features, accurately eliminating invalid features with high information overlap, avoiding model collinearity issues, and completing the initial round of feature denoising. Unlike dynamic filtering architectures, this application does not deploy the feature filtering program to a web platform; instead, it uses the optimal feature subset after offline filtering as a fixed input to the model, effectively avoiding computational fluctuations and result uncertainties caused by online dynamic filtering.

[0043] Meanwhile, this application uses an offline 5-fold cross-validation iterative selection method to iteratively select features with the goal of achieving the best model fit, and determines the appropriate AB matching. 3-δ Eight key descriptors for perovskite electrolyte systems. This set of features combines high performance relevance and low dimensional redundancy, making it the optimal fixed feature combination for the conductivity prediction model in this application, ensuring the professionalism and adaptability of the model input dimensions.

[0044] Through the aforementioned offline solidification and screening scheme, this application completes feature denoising, dimensionality reduction, and optimal feature subset determination in advance. During the online operation phase of the Web platform, only the fixed 8-dimensional feature input solidification model is called, eliminating the need for real-time feature calculation and screening iteration. This ensures the accuracy, stability, and generalization ability of the prediction model, simplifies the backend online computing chain, reduces server computing power overhead, and achieves efficient and stable response for online prediction on the platform.

[0045] For multi-element doped ABO 3-δ For perovskite systems, precise oxygen vacancy charge balance verification and efficient process control are crucial for ensuring accurate predictions and improving system response speed. Existing verification methods suffer from issues such as coarse property integration, vague charge determination criteria, and high redundancy in invalid calculations, easily resulting in the output of components that do not conform to physicochemical laws.

[0046] To address this, this embodiment adds standardized verification logic in step S2: After the chemical formula analysis is completed, the average physical property parameters of sites A and B are calculated weighted according to the doping ratio to accurately quantify the overall characteristics of the multi-doped system; the third-level verification calculates the total positive charge of the system based on the ion valences of sites A and B, and the verification is deemed compliant only when the oxygen vacancy content can achieve overall charge balance and is within a reasonable range. Simultaneously, the three-level verification adopts a serial short-circuit execution mechanism; if any level of verification fails, the process is immediately terminated, the corresponding abnormal flag is returned, and subsequent calculations are no longer executed, effectively reducing invalid calculations and improving the system's verification accuracy and response efficiency.

[0047] Existing machine learning prediction models suffer from the black box problem, resulting in weak interpretability of prediction results and an inability to quantify the influence weight of each parameter on conductivity, which is detrimental to material modification and optimization.

[0048] To address this, this embodiment, after conductivity prediction, simultaneously runs three independent interpretable algorithms in parallel: SHAP analysis, substitution importance analysis, and one-way ANOVA. Using eight key descriptors and prediction results as input, it quantifies the positive and negative contribution weights of each feature and cross-verifies the results through multi-algorithm ranking to output a reliable feature contribution visualization. Specifically, SHAP analysis quantifies the marginal contribution of a single feature, substitution importance analysis assesses the impact of features on model accuracy, and one-way ANOVA determines the significance of differences in feature values; the analysis results are only accepted when the importance conclusions of multiple algorithms are consistent. In this system, oxygen vacancy fraction can be identified as the core influencing factor; this conclusion is limited to the sample system of this application and does not constitute a general rule. This scheme effectively solves the model black box problem, improves prediction reliability, and provides a quantitative basis for the targeted doping design of materials.

[0049] Traditional inverse design suffers from vague coarse selection intervals and arbitrary feature pairings, which can easily lead to problems such as missing high-quality components, excessive screening space, and low screening accuracy.

[0050] To address this, this embodiment precisely defines the reverse design screening process: In S61, the Fisher coarse selection interval is limited to the optimal two-dimensional rectangular interval with 98% of high-conductivity samples, maximizing coverage of highly active components while compressing ineffective intervals; In S62, the two-dimensional contour map uses four sets of fixed preferred feature pairings: oxygen vacancy fraction and average ionization energy, A-site electron affinity and average ionic radius, sintering temperature and tolerance factor deviation, and pre-sintering temperature and the natural logarithm of the test temperature. This fixed pairing method is constructed based on physicochemical mechanisms and big data patterns, which can accurately capture parameter coupling correlations, effectively refine the high-conductivity narrow-constraint subspace, and significantly improve the accuracy of reverse screening.

[0051] Traditional reverse engineering lacks a fixed solution timing and post-charge verification, making it prone to generating invalid components with charge imbalance and structural instability in batches.

[0052] To address this, this embodiment limits the irreversible step-by-step solution sequence in step S63: It prioritizes screening combinations of A and B elements that meet the hard constraint on doping quantity, then iteratively solves for the optimal doping ratio to ensure characteristic parameters fall within a narrow constraint range, and finally determines the oxygen vacancy content based on ion valence equilibrium. Simultaneously, a post-charge balance final verification is added to all candidate components. By calculating the total charge of cations and anions, only compliant components that can achieve charge compensation through reasonable oxygen vacancies and maintain structural stability are retained. This step-by-step solution + secondary verification mechanism significantly eliminates invalid ratios, improving the effectiveness and synthesizability of reverse-engineered components.

[0053] Traditional platforms only support single positive predictions. Users need to manually enter parameters if they need to fine-tune, reproduce, or iteratively optimize. This is cumbersome, has low iteration efficiency, and is prone to introducing human error.

[0054] To address this, this embodiment improves the front-end visualization and interactive iteration functions in S7: the front-end fully displays 18 atomic-level descriptors, 15 composition descriptors, and multi-level inverse design constraint parameters; it supports users to select components with one click in cluster maps, contour maps, and candidate lists for automatic parameter backfilling; the front-end captures the unique identifier of each component and requests complete parameter data from the back-end, automatically filling in chemical formulas and process parameters, and automatically restarting the entire process iteration prediction from S1 to S6. This function enables rapid iterative calculation of material components, eliminating manual input steps, avoiding operational errors, and greatly improving the efficiency of material screening and modification optimization.

[0055] In specific implementation, the core calculation formula in this embodiment includes: 1) Oxygen vacancy fraction O SVF = In the formula, δ represents ABO 3-δ The oxygen nonstoichiometry in the sample is calculated from the valence charge balance of the doped ions at sites A and B.

[0056] 2) Goldschmidt tolerance factor and tolerance factor bias In the formula , These are the average ionic radii at the A and B sites, respectively, in pm. 140 pm is O 2- Ionic radius; 3) Average ionic radius at sites A and B 4) Test temperature natural logarithm Input the test temperature for the user, in °C, convert it to Kelvin, and then take the natural logarithm.

[0057] 5) SVR-RBF model prediction formula , For support vectors and unknown vectors, n and These represent the number of support vectors and their Lagrange multipliers, respectively.

[0058] Furthermore, embodiments of this application also propose a computer-readable storage medium storing ABO information. 3-δA program for online prediction of the oxygen ion conductivity of perovskite electrolytes; when the processor executes this program, it implements all the steps of the online prediction method described above.

[0059] Reference Figure 2 , Figure 2 For this application ABO 3-δ A structural block diagram of the first embodiment of an online prediction system for the oxygen ion conductivity of perovskite electrolytes. (See diagram below.) Figure 2 As shown, this system is divided into four layers: Front-end interaction layer: A visual webpage for Vue.js, implementing parameter input, error message pop-ups, full data and graph visualization, and single-point backfilling and interactive features for candidate components; Flask backend API scheduling layer: Deploys PythonFlask master control API service, which uniformly encapsulates chemical formula verification module, multi-source descriptor calculation module, conductivity prediction module, multi-algorithm interpretability analysis module, and two-level inverse design screening module. Each calculation subroutine is isolated from each other and has no direct data interaction. Data is only exchanged through the master control API service. After receiving the front-end JSON request, the master control API service schedules the serial operation of each module according to a fixed time sequence and sends the structured operation data back to the front end. Data storage layer: includes MySQL database and local file storage. The MySQL database stores standard element property library, historical prediction records, and candidate component data. The local file stores pre-trained SVR-RBF model files, Fisher discriminant model files, and SHAP interpreter files. Operations and maintenance deployment management layer: Deployed on a public cloud server, configured with regular data backup, concurrent request distribution and automatic restart mechanism for service failures; The two-level inverse design screening module is configured with execution timing locks. The process is constrained to be executed serially through the backend state machine / task queue synchronization mechanism, and steps cannot be swapped or skipped: first, the high conductivity interval is coarsely divided by Fisher discrimination, then the narrow constraint subspace is obtained by compression of the two-dimensional contour map, and finally the components are solved by inverse mapping to the eight-dimensional feature space. The output components are then chemometrically verified to avoid invalid calculations caused by step disorder.

[0060] The chemical formula verification module is equipped with a three-level serial metrological verification logic, which automatically parses multi-element doped chemical formulas and calculates the average physical property parameters of A and B sites according to the doping ratio. The third level of verification calculates the total charge of anions and cations in the system, and only determines compliance when the oxygen vacancy content meets the charge balance and is within a reasonable range. The verification adopts a short-circuit mechanism. If any level of verification fails, the operation is terminated immediately, and an abnormal message with an identifier is sent back to the front end to prevent invalid data from flowing into the subsequent calculation process.

[0061] The aforementioned layered architecture, timing locks, and three-level verification mechanism work together to ensure that the reverse design process is logically rigorous, the input components conform to the physical laws, reduce redundant calculations, and improve system stability and the practicality of the output components.

[0062] Existing offline prediction tools require users to configure their own Python runtime environment, which presents a high barrier to entry. This solution encapsulates the complete prediction chain into an executable program, integrating all functional module instruction sets. After the program runs, it automatically completes the entire process, including JSON request reception, three-level chemometric verification, descriptor solving, conductivity prediction of the solidified model, parallel operation of three types of interpretable algorithms, time-constrained reverse screening, and visualization result feedback. The entire program is integrated into a B / S web platform and can be directly accessed through a browser after deployment to the server, eliminating the need for user-configured development environments. This significantly lowers the barrier to material screening and shortens the R&D cycle of perovskite electrolytes.

[0063] The above are merely preferred embodiments of this application and are not intended to limit the technical solution of this application. Those skilled in the art can flexibly adjust the configuration according to actual needs. The process described herein is only for illustration. In actual applications, all or part of the steps can be selected as needed to implement this solution. Technical details not described in detail can be referred to the online prediction method embodiments above, and will not be repeated here.

[0064] It should be noted that the terms "including", "comprising", and similar variations in this document are non-exclusive. Including the listed elements may also include other elements not listed or inherent to the scheme; "including one" does not exclude the coexistence of other elements of the same kind.

[0065] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0066] Those skilled in the art will understand that this solution can be implemented using software in conjunction with a general-purpose hardware platform, with the software solution being the preferred embodiment. The core content of this application that makes innovative contributions to the prior art can be packaged into a software product and stored in readable storage media such as ROM, RAM, disk, and optical disc. The instructions stored in the media can drive computers, servers, and other terminals to execute all the method steps of this application. The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. An ABO 3-δ A method for online prediction of oxygen ion conductivity of perovskite electrolytes, characterized in that, The method is executed fully automatically and serially by a B / S architecture web platform. This web platform has a built-in prediction model that has been trained offline and has its parameters fixed before deployment. During online execution, the model is not retrained and the samples are not re-divided. The method includes the following steps: S1, ABO (Application Programming Interface) for receiving user input in the front-end visual interface. 3-δ The chemical formula of the perovskite and three process parameters, namely sintering temperature, pre-sintering temperature and test temperature, are encapsulated in JSON format and sent to the backend. S2. The backend performs a three-level serial chemometric verification closed loop on the input chemical formula: The chemical formula is parsed, and the following are verified sequentially: ① The sum of the doping ratios of all cations at position A equals 1; ② The sum of the doping ratios of all cations at position B equals 1; ③ The oxygen vacancy content determined by the valence state of the doped ions satisfies ABO. 3-δ Perovskite charge balance constraint range; if any level of verification fails, the backend generates a message with an exception type identifier and sends it back to the frontend to prompt the corresponding exception item. The process flows back to S1 for re-entry and does not proceed to subsequent calculations; after all three levels of verification pass, it proceeds to S3. S3. The backend retrieves the built-in elemental property database, calculates atomic-level descriptors by weighting the doping ratio of each element at position A and position B, calculates structural-level descriptors based on fixed chemical formulas, extracts the input process parameters, integrates them to form 48 initial multi-source descriptors, and then obtains 8 key descriptors through a two-level feature screening process that is preset by the platform and cannot be customized. S4. Input the 8 key descriptors into the pre-trained SVR-RBF model, and output the natural logarithm of oxygen ion conductivity lnσ and the converted actual conductivity σ; the hyperparameters of the SVR-RBF model are determined and permanently fixed in the offline training stage through 10-fold cross-validation grid search: regularization parameter C=81, insensitive loss ε=0.01, kernel coefficient γ=1.3, and the fixed model can be directly called online to complete inference; S5. Simultaneously run three independent interpretable algorithms: SHAP analysis, permutation importance analysis, and one-way ANOVA. Using the eight key descriptors and the prediction results of the SVR-RBF model as input, quantify the positive and negative contribution weights of each key descriptor to conductivity, and perform consistency cross-verification on the feature importance ranking results obtained by the three algorithms to output a feature contribution visualization spectrum. S6. Perform a two-level linked inverse design screening with a fixed execution sequence. The following three steps cannot be changed in the order of operation: S61. Receive the user-defined target conductivity threshold, first eliminate invalid ratios with more than 3 types of A-site doped cations or more than 2 types of B-site doped cations according to the hard constraint of the number of component doping, and then divide the remaining samples into high and low conductivity categories by Fisher discrimination model with lnσ=-5.0 as the dividing value. After two-dimensional projection, delineate the rectangular coarse selection feature interval where high conductivity samples are concentrated. S62. Based on the pairwise coupling of the eight key descriptors, a two-dimensional contour map is generated, which is further compressed to a narrow constrained subspace of lnσ > -3.0 on the basis of Fisher's coarse selection of feature intervals. S63. The narrow-constrained subspace is projected back into the eight-dimensional feature space in reverse. Based on the calculation formulas corresponding to the eight key descriptors, the types of A-site elements, the types of B-site elements, the A / B-site doping ratio, and the oxygen vacancy content are solved in reverse step by step to generate candidate components in batches. Chemometric verification is performed again on each group of candidate components to remove charge imbalance components and output only the set of perovskite candidate components that fall within the high conductivity feature range and are chemometrically compliant. S7 provides a unified visual display of chemical formula verification results, all multi-source descriptor values, conductivity prediction results, feature contribution maps, two-dimensional contour constraint maps, Fisher discriminant clustering maps, and candidate component parameters obtained through reverse deduction. It also supports users selecting any group of candidate components to automatically backfill parameters and jump to S1 to re-execute the forward conductivity prediction. The Web platform backend uses the Python Flask framework to uniformly encapsulate and schedule all computing functions. Each computing subroutine only exchanges data through the backend master control program, and the frontend and backend achieve standardized data interaction through JSON messages.

2. The ABO according to claim 1 3-δ A method for online prediction of oxygen ion conductivity in perovskites, characterized in that, The two-step feature screening process described in step S3 is as follows: First, the platform's built-in exclusive feature sorting rules are used to sort the importance of the 48 initial multi-source descriptors, and high-redundancy features with an absolute value of Pearson correlation coefficient greater than 0.95 are removed, leaving 34 non-redundant descriptors; Second, the platform's fixed iterative logic is used to select features from the 34 non-redundant descriptors by maximizing the 5-fold cross-validation determination coefficient, and finally, 8 key descriptors are selected, namely: oxygen vacancy fraction, A-site electron affinity, average ionic radius, tolerance factor deviation, average ionization energy, sintering temperature, pre-sintering temperature, and natural logarithm of test temperature.

3. The ABO according to claim 1 3-δ A method for online prediction of oxygen ion conductivity in perovskites, characterized in that, In step S2, after analyzing the chemical formula, the elemental property parameters are weighted and summed according to the doping ratio of each element to obtain the average property parameters of the A-site and B-site. In the third-level verification, the total positive charge of the cations in the system is calculated based on the valence of the doped ions at the A-site and B-site. The verification is considered successful only when the oxygen vacancy content can balance the positive and negative charges of the system and the oxygen vacancy content is within a preset reasonable range. The third-level verification is executed serially. If the previous level verification fails, the process is terminated and the corresponding abnormality type is output. The next level verification is not executed.

4. The ABO according to claim 1 3-δ A method for online prediction of oxygen ion conductivity in perovskites, characterized in that, In step S5: the SHAP analysis quantifies the marginal contribution of each key descriptor to a single prediction based on cooperative game theory and outputs a global importance ranking. The permutation importance analysis quantifies the importance of a descriptor by the decrease in the coefficient of determination of the model after shuffling a single key descriptor; the one-way ANOVA determines the significance of the difference in conductivity between different levels of each key descriptor by the p-value. When the importance descriptors obtained by the three algorithms are consistent, the conclusion on the importance of the feature is reliable.

5. The ABO according to claim 1 3-δ A method for online prediction of oxygen ion conductivity in perovskites, characterized in that, The rectangular coarse selection feature interval mentioned in step S61 is the Fisher two-dimensional rectangle optimal interval with a high conductivity sample ratio of 98%; the two-dimensional contour map mentioned in step S62 is generated by pairing four sets of key descriptors, namely: oxygen vacancy fraction and average ionization energy, A-site electron affinity and average ionic radius, sintering temperature and tolerance factor deviation, and pre-sintering temperature and natural logarithm of test temperature.

6. The ABO according to claim 1 3-δ A method for online prediction of oxygen ion conductivity in perovskites, characterized in that, The reverse step-by-step solution in step S63 is as follows: first, determine the combination of A-site and B-site elements that satisfy the hard constraint of doping quantity within the value range corresponding to the narrow constraint subspace; then, solve the doping ratio of each element so that the calculated values ​​of the 8 key descriptors fall into the narrow constraint subspace; finally, determine the oxygen vacancy content based on the valence charge balance of the doped ions; the chemometric verification includes: calculating the total positive charge of cations and the total negative charge of oxygen ions of the candidate components, and retaining only the components that can achieve charge compensation and overall charge balance through reasonable oxygen vacancy content.

7. The ABO according to claim 1 3-δ A method for online prediction of oxygen ion conductivity in perovskites, characterized in that, In step S7, the front-end displays 18 atomic-level derivation descriptors, 15 compositional derivation descriptors with complete numerical values, and multi-level inverse design constraint interval parameters. The automatic backfill jump is as follows: the user clicks on any candidate component in the Fisher discriminant clustering diagram, two-dimensional contour constraint spectrum, or candidate component list on the front end. The front end extracts the unique identifier of the candidate component and sends it to the back end. The back end returns the complete stoichiometric data of the candidate component. The front end automatically backfills its chemical formula and process parameters to the input interface and re-executes steps S1 to S6.

8. An ABO 3-δ An online prediction system for the oxygen ion conductivity of perovskite electrolytes, characterized in that, It adopts a four-layer B / S architecture, including: Front-end interaction layer: A visual webpage for Vue.js, implementing parameter input, error message pop-ups, full data and graph visualization, and single-point backfilling jump function for candidate components; Flask backend API scheduling layer: Deploys PythonFlask master control API service, which uniformly encapsulates chemical formula verification module, multi-source descriptor calculation module, conductivity prediction module, multi-algorithm interpretability analysis module, and two-level inverse design screening module. Each calculation subroutine is isolated from each other and has no direct data interaction. Data is only exchanged through the master control API service. After receiving the front-end JSON request, the master control API service schedules the serial operation of each module according to a fixed time sequence and sends the structured operation data back to the front end. Data storage layer: includes MySQL database and local file storage. The MySQL database stores standard element property library, historical prediction records, and candidate component data. The local file stores pre-trained SVR-RBF model files, Fisher discriminant model files, and SHAP interpreter files. Operations and maintenance deployment management layer: Deployed on a public cloud server, configured with regular data backup, concurrent request distribution and automatic restart mechanism for service failures; The modules of the system work together to execute the online prediction method described in any one of claims 1 to 7.

9. The ABO according to claim 8 3-δ An online prediction system for the oxygen ion conductivity of perovskite, characterized in that, The two-level inverse design screening module has a built-in execution timing lock, which fixes the serial operation order of Fisher discrimination coarse division interval, two-dimensional contour map compression narrowing constraint subspace, and finally eight-dimensional feature inverse mapping to solve the composition and perform chemometric verification. The chemical formula verification module has a built-in three-level serial metrometric verification logic, which automatically identifies multi-element doped chemical formulas, calculates the weighted average physical property parameters of A-site and B-site and determines the charge balance compliance. If any level of verification fails, the subsequent operation is terminated and the abnormal type identifier is returned.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the ABO as described in any one of claims 1 to 7. 3-δ An online prediction method for oxygen ion conductivity of perovskite electrolytes.

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