Neural network-based functional ceramic material doping performance prediction method, system and medium

Abstract

The application discloses a function ceramic material doping performance prediction method and system based on a neural network, a medium, and the like. A pre-constructed doping process and performance baseline prediction model is called first, a virtual doping component space covering a full effective interval is generated based on a target matrix doping prediction boundary parameter set, each group of virtual doping formulas in the virtual doping component space is classified and arranged, embedding coding is performed, doping element type characteristics and doping concentration characteristics are extracted and fused to generate a unified feature tensor, all unified feature tensors corresponding to the virtual doping formulas are input into a deep feedforward neural network model in batches, and a function ceramic performance prediction result corresponding to a batch of to-be-predicted doping formulas is output. The function ceramic performance prediction result is subjected to multi-objective optimization to obtain a Pareto optimal doping scheme set. The application realizes accurate prediction of function ceramic doping performance and intelligent optimization of a doping formula, and improves the efficiency and reliability of doping formula design.

Description

Technical Field

[0001] This invention relates to the field of performance prediction technology for functional ceramic materials, and in particular to a method, system, and medium for predicting the doping performance of functional ceramic materials based on neural networks. Background Technology

[0002] As the market demands higher comprehensive performance from functional ceramic materials, single properties and functions are no longer sufficient to meet practical application needs. Element doping modification, as a key means to achieve breakthroughs in the performance of functional ceramics, can significantly control the microstructure and macroscopic properties of materials by adding trace amounts of rare earth elements, transition metal elements, and other doping elements to the matrix.

[0003] However, the current research and development of functional ceramic doping modification still relies on the traditional trial-and-error mode. The doping mechanism is complex and unpredictable. The impact of doping elements on material properties and their occupancy in the crystal lattice are difficult to predict. Traditional experience cannot accurately quantify the interaction of various factors, which easily leads to misjudgment and further increases the difficulty and cost of research and development.

[0004] Furthermore, in the scenario of functional ceramic doping prediction, due to the large doping combination space, the existing technology lacks sufficient sample support, and the extrapolation prediction reliability of the neural network model is insufficient. It is easy to get trapped in local optima and it is difficult to accurately determine the optimal doping element type and ratio. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method, system, and medium for predicting the doping performance of functional ceramic materials based on neural networks. Specifically, it designs a batch formulation performance prediction method, which can accurately predict the performance of selected specific doping formulations that meet boundary conditions, and efficiently search a vast doping combination space to accurately recommend the optimal doping scheme. This improves the accuracy of predicting the doping performance of functional ceramics, shortens the R&D cycle, and reduces R&D costs.

[0006] In a first aspect, the present invention provides a method for predicting the doping properties of functional ceramic materials based on neural networks, specifically including: By calling the pre-built prediction model of doping process and performance baseline, the target matrix material system information of functional ceramics is matched, retrieved and verified by mechanism to obtain the target matrix doping prediction boundary parameter set; Based on the target matrix doping prediction boundary parameter set, a virtual doping composition space covering the entire effective range is generated. Each virtual doping formula in the virtual doping composition space is structurally classified and coded. The doping element type features and doping concentration features are extracted and fused to generate a unified feature tensor. The unified feature tensors corresponding to all virtual doping formulas are batch-input into a deep feedforward neural network model, and the functional ceramic performance prediction results corresponding to the batch doping formulas to be predicted are output. The functional ceramic performance prediction results are multi-objective optimized to obtain the Pareto optimal doping scheme set. The Pareto optimal doping scheme set was experimentally verified, and the experimental verification results were fed back as new data to the deep feedforward neural network model for model optimization.

[0007] It should be noted that this invention deeply couples the experimental verification stage with the model training stage. It can rapidly complete feature encoding, dual-channel feature fusion, and neural network performance prediction for a single set of existing doping formulations. Combined with known formulations, it can quickly evaluate the accuracy of the deep feedforward neural network model. Based on the verified model, a virtual doping component space is constructed within the effective boundary. Feature processing and parallel prediction are performed on a massive number of virtual formulations in batches. Then, a Pareto-optimal doping scheme set is output through multi-objective optimization. Furthermore, the Pareto-optimal doping scheme can be used to re-optimize the deep feedforward neural network model based on actual experiments, forming a closed-loop prediction and model optimization mechanism.

[0008] In one embodiment, the pre-built doping process and performance baseline prediction model further includes: Based on small-scale, high-quality experimental sample data, with dopant element type, doping concentration, and preparation process parameters as input features, and with the mechanical, electrical, and microstructure properties of functional ceramics as target properties, partial least squares regression was used to screen dopant elements and process conditions that are significantly linearly correlated with the target properties. The nonlinear importance weights of the influence of each screened dopant element and process condition on the target performance were calculated using a random forest model. The partial least squares regression results and the random forest feature importance results were cross-validated in two directions to screen out the key influencing factors of robustness. By combining crystal field theory and defect chemistry principles, the mechanism of the key factors affecting robustness is analyzed, the effective concentration range of each key dopant element and the optimization range of core preparation process parameters are defined, and the space of invalid components that exceed the solid solution limit and are prone to generating impurities is eliminated. This can effectively avoid the problems of blind trial and error and many invalid experiments in traditional R&D from the source.

[0009] Based on the aforementioned key robustness influencing factors and defined parameter ranges, the partial least squares regression model parameters are optimized to construct a prediction model for doping process and performance baseline. This prediction model not only defines a compliant and effective parameter boundary range for subsequent neural network predictions but also provides a performance prediction baseline reference, improving the rationality and accuracy of subsequent feature construction, virtual screening, and performance prediction, reducing redundant calculations, and enhancing the overall efficiency of doping formulation optimization.

[0010] It should be noted that this invention uses partial least squares regression combined with bidirectional cross-validation of random forests, taking into account both linear correlation and nonlinear feature contributions, to accurately screen out the robust key influencing factors affecting the doping performance of functional ceramics, thus avoiding the problems of one-sided feature screening and low reliability of single algorithm.

[0011] In one embodiment, the construction steps of the deep feedforward neural network model include: A deep feedforward neural network with a multilayer perceptron structure is constructed, and batch normalization layers and dropout layers are sequentially set in each hidden layer. Taking the unified feature tensor as input and the functional ceramic performance as output target, a mean squared error loss function with L2 regularization term is adopted. The gradient of the loss function with respect to the weights of each layer of the network is calculated by backpropagation algorithm, which can effectively suppress network overfitting, alleviate internal covariate bias, and enhance model stability and robustness.

[0012] Furthermore, the deep feedforward neural network model is trained by using the AdamW optimizer combined with a cosine annealing learning rate scheduling strategy. This allows for dynamic adaptive adjustment of the learning rate, accelerating model convergence, avoiding training from getting stuck in local optima, and improving training efficiency and fitting accuracy.

[0013] Finally, cross-validation and multiple performance metrics were used to evaluate the trained deep feedforward neural network model. If the model's generalization ability was insufficient, a domain adversarial neural network was used to fine-tune the model until the model's prediction accuracy and generalization ability reached the preset threshold, thus obtaining a pre-trained deep feedforward neural network model. This effectively improved the model's cross-domain adaptability in different functional ceramic matrix systems, significantly enhanced the model's overall prediction accuracy, generalization ability, and engineering applicability, and provided highly reliable model support for the performance prediction of subsequent single-formulation and batch virtual doping formulations.

[0014] In this embodiment, within one cycle or when calling the model for prediction, the method further includes: acquiring a single set of doping formula data and preparation process parameters of the functional ceramic to be predicted that conform to the target matrix doping prediction boundary parameter set, and structuring and classifying them according to the target matrix material system; embedding and encoding the doping formula data and preparation process parameters after structuring and classifying them, and extracting the doping element type features and doping concentration features respectively using category adaptive normalization, and fusing the two types of features to generate a unified feature tensor; inputting the unified feature tensor into a deep feedforward neural network model, outputting the functional ceramic performance prediction results corresponding to the doping formula to be predicted, and comparing the prediction results with the collected experimental data. If the results are consistent, the accuracy verification of the model is completed.

[0015] In one embodiment, training the deep feedforward neural network model using the AdamW optimizer combined with a cosine annealing learning rate scheduling strategy includes: With an initial learning rate of 1e -3 Starting from this point, the learning rate is periodically adjusted according to a cosine function after each round of training, with a minimum learning rate of no less than 1e. -5 During training, an early stopping strategy is implemented based on validation set loss, and the deep feedforward neural network model is trained using a pre-built structured database. In other words, this application employs a cosine annealing learning rate scheduling strategy, limiting the training interval with a fixed initial learning rate and a minimum learning rate, and dynamically adjusting the learning rate periodically according to a cosine function. This allows for rapid convergence and accelerated parameter optimization in the early stages of training, while also enabling precise approximation of the optimal solution in the later stages, effectively preventing the model from getting stuck in local optima. Simultaneously, the early stopping strategy based on validation set loss can promptly terminate ineffective training processes, effectively suppressing model overfitting. This ensures the prediction accuracy of the deep feedforward neural network model while improving training efficiency and model generalization ability.

[0016] In one embodiment, training the deep feedforward neural network model includes: training the deep feedforward neural network model using a pre-built structured database; the step of acquiring the structured database includes: using the robust key influencing factors as the retrieval basis, batch acquiring charts and images from functional ceramics-related literature, and performing standardized preprocessing on the charts and images sequentially to avoid redundant collection of irrelevant data and improve the targeting and efficiency of data acquisition.

[0017] Furthermore, the first 5 layers of the VGG16 network are used as the feature extraction backbone. The pre-trained weights are frozen and the convolution kernel parameters are fine-tuned. The pre-processed charts and images are digitally recognized. The material composition, performance and process information are extracted and fused by combining optical character recognition and natural language processing models. This enables automatic parsing, association and fusion of multimodal literature information, thus overcoming the drawbacks of traditional manual data processing, which is inefficient, labor-intensive and prone to errors.

[0018] Furthermore, missing values ​​are filled in the extracted data. For randomly missing numerical data such as doping concentration and process parameters, the K-nearest neighbor algorithm is used in combination with the data distribution law to fill in the missing values. For performance missing values ​​related to the physical field distribution, the Poisson equation is used to construct a physical constraint model to solve and fill in the missing values. This not only conforms to the statistical law of the data, but also fits the physical mechanism of the material, ensuring that the database data is complete, true and reasonable, and finally a structured database is obtained.

[0019] In one embodiment, the process of embedding and encoding the structured and categorized doping formulation data and preparation process parameters, and using category adaptive normalization to extract doping element type features and doping concentration features respectively, and fusing the two types of features to generate a unified feature tensor, includes: The doping formulation data and preparation process parameters were grouped according to the target matrix material system, and each group of data was encoded into learnable embeddings. Each set of data is standardized using adaptive categorical normalization. The mean and variance of the adaptive categorical normalization are obtained independently based on the data of the corresponding target matrix material system. The discrete dopant element types are encoded by the embedding layer to generate type feature vectors, and the continuous dopant concentration parameters are mapped by the fully connected layer to generate concentration feature vectors. The type feature vector and the concentration feature vector are fused by feature concatenation or attention-weighted fusion to generate a unified feature tensor.

[0020] It should be noted that this invention performs structured classification and embedding encoding of doping formulation data and process parameters. It uses a dual-channel adaptive normalization method to extract the characteristics of doping element type and doping concentration respectively and fuses them to generate a unified feature tensor. This can accurately characterize the coupling influence of discrete element type and continuous doping concentration on ceramic performance. Compared with the traditional single feature input method, the feature characterization is more in line with the intrinsic mechanism of material doping and effectively improves the accuracy of model prediction.

[0021] In one embodiment, the step of performing multi-objective optimization on the predicted performance results of the functional ceramics to obtain a Pareto-optimal doping scheme set includes: By employing the optimal Latin hypercube sampling method, a set of virtual doping formulations covering the entire effective range is generated within the range defined by the target matrix doping prediction boundary parameter set, thus forming a virtual doping composition space. This allows for uniform and full coverage of the entire effective parameter range with a small number of samples, resulting in good sampling distribution uniformity and strong representativeness. It avoids random sampling redundancy or omission of local intervals, significantly improving the efficiency and completeness of high-throughput virtual screening.

[0022] With the mechanical properties, electrical properties and doping cost of functional ceramics as optimization objectives, and with the constraints of doping concentration not exceeding the solid solution limit and no impurity phase generation as constraints, the non-dominated sorting genetic algorithm NSGA-II is used to perform multi-objective optimization on the performance prediction results of all doping formulations to be predicted, and outputs a Pareto optimal doping scheme set.

[0023] It should be noted that this invention uses the NSGA-II non-dominated sorting genetic algorithm to carry out multi-objective optimization, which can achieve balanced optimization among multiple mutually constraining optimization objectives, avoid the one-sidedness of single-objective optimization, automatically converge and output the Pareto optimal doping scheme set; it eliminates the need for manual comparison and screening of a large number of doping combinations, and efficiently completes the intelligent recommendation of the optimal doping element type and ratio.

[0024] The prediction method of the present invention further includes: Target schemes are selected from the Pareto-optimal doping scheme set for experimental verification to obtain measured performance data. This allows for the verification of the true effectiveness of the optimal doping scheme, timely correction of model prediction biases, and improvement of the scheme's practicality. The measured performance data, along with the corresponding doping formulations and preparation process parameters, are used as new samples to update the structured database. The pre-trained deep feedforward neural network model is incrementally trained using a mixture of new and historical samples. Simultaneously, the doping process and performance baseline prediction model are iteratively optimized, thereby constructing a closed-loop R&D system encompassing virtual prediction, experimental verification, data updates, and model iteration. This system enables self-learning and continuous optimization. As the number of iterations increases, the accuracy of doping performance prediction and the reliability of formulation recommendations continuously improve, thereby reducing R&D trial-and-error costs and shortening the iterative R&D cycle of new materials in the long term.

[0025] In a second aspect, the present invention also provides a neural network-based system for predicting the doping properties of functional ceramic materials, the system being used to execute the neural network-based method for predicting the doping properties of functional ceramic materials as described in the first aspect, the system comprising: The prediction boundary processing module is used to call the pre-built doping process and performance baseline prediction model, match and retrieve the target matrix material system information of functional ceramics and verify the mechanism to obtain the target matrix doping prediction boundary parameter set; The batch prediction module generates a virtual doping composition space covering the entire effective range based on the target matrix doping prediction boundary parameter set. It performs structured classification and organization of each virtual doping formula in the virtual doping composition space, embeds and encodes it, extracts and fuses the doping element type features and doping concentration features to generate a unified feature tensor, and inputs the unified feature tensors corresponding to all virtual doping formulas into a deep feedforward neural network model in batches. It outputs the functional ceramic performance prediction results corresponding to the batch doping formulas to be predicted, and performs multi-objective optimization on the functional ceramic performance prediction results to obtain the Pareto optimal doping scheme set. The model optimization module performs experimental verification based on the Pareto optimal doping scheme set and feeds the experimental verification results back to the deep feedforward neural network model as new data for model optimization. The model validation module acquires a single set of doped ceramic formulation data and preparation process parameters that conform to the target matrix doping prediction boundary parameter set within one cycle or when calling the model for prediction. These data are then structured and categorized according to the target matrix material system. The structured doped formulation data and preparation process parameters are embedded and encoded. Adaptive category normalization is used to extract doping element type features and doping concentration features, respectively. These two types of features are then fused to generate a unified feature tensor. This unified feature tensor is input into a deep feedforward neural network model, which outputs the predicted performance results of the functional ceramic corresponding to the doped formulation. The prediction results are compared with the collected experimental data. If the results are consistent, the accuracy of the model is verified.

[0026] Thirdly, the present invention also provides a computer storage medium storing a computer program, which, when executed by a processor, implements the neural network-based method for predicting the doping properties of functional ceramic materials as described in the first aspect.

[0027] Compared with the prior art, the present invention has the following advantages and beneficial effects: 1. This invention first uses a pre-constructed doping process and performance baseline prediction model to match and verify the target matrix material system, delineate the target matrix doping prediction boundary parameter set, and eliminate invalid doping ranges that exceed the solid solution limit and are prone to generating impurity phases in advance. This avoids the drawbacks of blindly trying a large number of doping combinations in traditional trial-and-error R&D, effectively reduces the number of experimental trials, and significantly reduces the R&D cost and R&D cycle of functional ceramic doping modification. At the same time, it overcomes the R&D uncertainty caused by the complexity of element doping mechanisms and the difficulty in predicting performance effects.

[0028] 2. This invention provides a virtual space high-throughput batch prediction mode, which calls the real-time optimal model to generate a virtual doping composition space within a limited effective parameter range, thereby realizing batch parallel prediction of doping formulations across the entire range.

[0029] 3. This invention relies on a deep feedforward neural network model to complete performance prediction, and combines multi-objective optimization to solve the Pareto optimal doping scheme set for batch prediction results. Under multiple performance constraints, it automatically outputs the balanced optimal candidate doping formula. It overcomes the shortcomings of existing neural networks in terms of insufficient reliability of extrapolation prediction in small sample and large space scenarios and easy to get trapped in local optima. It can quickly and accurately determine the optimal doping element type and ratio, and provide reliable theoretical formula support for the research and development of functional ceramic doping modification. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of a method for predicting the doping properties of functional ceramic materials based on neural networks.

[0031] Figure 2 This is a schematic diagram of a neural network-based system for predicting the doping properties of functional ceramic materials. Detailed Implementation

[0032] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention. It should be noted that relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations.

[0033] Example 1 This invention provides a method for predicting the doping properties of functional ceramic materials based on neural networks (see [link]). Figure 1 First, the doping prediction boundary parameter set of the target matrix is ​​verified by a pre-constructed doping process and performance baseline prediction model. Then, high-throughput batch prediction in virtual space is provided to generate a virtual doping composition space within a limited effective parameter range, so as to realize batch parallel prediction of doping formulations in the whole range.

[0034] In one embodiment, the specific implementation process of the neural network-based method for predicting the doping properties of functional ceramic materials is as follows: By calling the pre-built prediction model of doping process and performance baseline, the target matrix material system information of functional ceramics is matched, retrieved and verified by mechanism to obtain the target matrix doping prediction boundary parameter set; Based on the target matrix doping prediction boundary parameter set, a virtual doping composition space covering the entire effective range is generated. Each virtual doping formula in the virtual doping composition space is structurally classified and coded. The doping element type features and doping concentration features are extracted and fused to generate a unified feature tensor. The unified feature tensors corresponding to all virtual doping formulas are batch-input into a deep feedforward neural network model, and the functional ceramic performance prediction results corresponding to the batch doping formulas to be predicted are output. The functional ceramic performance prediction results are multi-objective optimized to obtain the Pareto optimal doping scheme set. The Pareto optimal doping scheme set was experimentally verified, and the experimental verification results were fed back as new data to the deep feedforward neural network model for model optimization.

[0035] In one embodiment, the target matrix material system information of the functional ceramic is matched, retrieved, and validated mechanistically to obtain a set of predicted boundary parameters for target matrix doping. Specifically, the complete information of the target matrix material system of the functional ceramic to be developed is input into the baseline prediction model. The model first performs a matching retrieval operation on the input target matrix material system information, matching corresponding or similar matrix systems from the built-in functional ceramic matrix mechanism knowledge base and the baseline database to extract basic doping characteristic information. Subsequently, combined with the built-in crystal field theory and defect chemistry rules, the extracted basic doping characteristic information is validated mechanistically in multiple dimensions. Taking into account physical constraints such as the material solid solution limit, phase stability conditions, ion radius matching, and charge compensation mechanism, the basic doping characteristics are dynamically corrected and screened to define the range of legal doping parameters corresponding to the current target matrix. Finally, a standardized set of predicted boundary parameters for target matrix doping is output. Through this pre-mechanistic constraint step, invalid doping parameter ranges that are prone to generating impurities, exceed the solid solution limit, or have unstable crystal structures can be completely eliminated from the source, ensuring that all subsequent prediction operations are performed within a physically feasible range.

[0036] In one embodiment, when performing batch formulation performance prediction, based on the target matrix doping prediction boundary parameter set obtained in the aforementioned steps, the effective doping element types, upper and lower limits of each element concentration, multi-element co-doping ratio constraints, and core preparation process parameter ranges defined by this parameter set are used as the unique legal boundaries. The optimal Latin hypercube sampling method is employed to perform uniform sampling across the entire domain, generating a massive number of virtual doping formulations in batches, thus constructing a virtual doping composition space covering all effective parameter ranges. Secondly, for each set of virtual doping formulations and corresponding process parameters in the virtual doping composition space, a standardized processing procedure completely consistent with that for single-formula prediction is executed: structured classification and organization according to the target matrix material system, unifying data formats and field specifications; learnable embedding encoding and adaptive category normalization processing are performed on the structured data; discrete doping element type features and continuous doping concentration and process parameter features are extracted separately through a dual-channel independent feature extraction mechanism; the two heterogeneous features are integrated through feature splicing or attention-weighted fusion to generate a batch unified feature tensor with uniform dimensions. By inputting the batch of unified feature tensors corresponding to all virtual doping formulations into a pre-trained deep feedforward neural network model in parallel, and relying on the powerful parallel computing and nonlinear fitting capabilities of the deep feedforward neural network, the performance prediction of a massive number of virtual doping formulations is completed in one go, and the prediction results of multi-dimensional key performances such as mechanical properties, electrical properties and microstructure properties of functional ceramics corresponding to all the formulations under test are output in batches.

[0037] In one embodiment, the specific implementation process of the neural network-based method for predicting the doping properties of functional ceramic materials is as follows: Based on the obtained target matrix doping prediction boundary parameter set, and with the doping element types, doping concentration ranges and preparation process parameter ranges defined by the parameter set as constraints, full-domain sampling is carried out within the reasonable parameter value range to generate a virtual doping composition space that can completely cover all effective doping ranges. This avoids missing the optimal doping ratio and avoids invalid doping combinations that exceed the solid solution limit and are prone to generating impurity phases.

[0038] For each virtual doping formulation in the virtual doping composition space, a structured classification is uniformly organized according to the standard of the target matrix material system. The organized virtual doping formulation data are then embedded and encoded sequentially. Using a category adaptive normalization method, the discrete dimension doping element type features and the continuous dimension doping concentration features are extracted independently. The two types of features are then fused to generate a unified feature tensor corresponding to each virtual doping formulation.

[0039] The unified feature tensor corresponding to all virtual doping formulations is input into the trained deep feedforward neural network model in batch parallel mode. By utilizing the powerful nonlinear fitting capability of the deep feedforward neural network, the intrinsic relationship between doping formulations, process parameters and various properties of functional ceramics is learned and mapped in batches. The prediction results of multiple properties of functional ceramics, such as mechanical properties and electrical properties, corresponding to all batches of virtual doping formulations are output at one time.

[0040] Further optimization objectives were set for high mechanical properties, high electrical properties, and low doping cost of functional ceramics. Physical constraints included doping concentration not exceeding the solid solution limit of the matrix and no impurity phase precipitation. A multi-objective optimization algorithm was used to perform non-dominated sorting and optimal selection of batch performance prediction results. The Pareto optimal doping scheme set under multi-objective constraints was obtained, providing a multi-dimensional selection of optimal formulation combinations for the research and development of doping modification of functional ceramic materials.

[0041] In one embodiment, the present invention specifies in detail the construction process of the pre-constructed doping process and performance baseline prediction model: Based on small-scale, high-quality experimental sample data, this study uses the type and concentration of doping elements and preparation process parameters as input features, and the mechanical, electrical, and microstructure properties of functional ceramics as target properties. Partial least squares regression is used to screen doping elements and process conditions that are significantly linearly correlated with the target properties. Specifically, the small-scale, high-quality experimental sample data includes measured sample data of functional ceramic doping modification with a moderate sample size, controllable experimental conditions, complete data records, and reliable test results. Examples include basic information on the matrix material, doping formulation parameters, preparation process parameters, performance test data, and data quality constraints, but are not limited to these.

[0042] The nonlinear importance weights of the influence of each screened dopant element and process condition on the target performance were calculated using a random forest model. The partial least squares regression results and the random forest feature importance results were cross-validated in two directions to screen out the key influencing factors of robustness. By combining crystal field theory and defect chemistry principles, the mechanism of the key factors affecting robustness is analyzed, the effective concentration range of each key dopant element and the optimization range of core preparation process parameters are defined, and the space of invalid components that exceed the solid solution limit and are prone to generating impurities is eliminated. This can effectively avoid the problems of blind trial and error and many invalid experiments in traditional R&D from the source.

[0043] Based on the aforementioned key robustness influencing factors and defined parameter ranges, the partial least squares regression model parameters are optimized to construct a prediction model for doping process and performance baseline. This prediction model not only defines a compliant and effective parameter boundary range for subsequent neural network predictions but also provides a performance prediction baseline reference, improving the rationality and accuracy of subsequent feature construction, virtual screening, and performance prediction, reducing redundant calculations, and enhancing the overall efficiency of doping formulation optimization.

[0044] In one embodiment, within one cycle or when calling the model for prediction, the method further includes: verifying the accuracy of the deep feedforward neural network model. Specifically, this involves acquiring a single set of doping formulation data to be predicted and corresponding preparation process parameters that fall entirely within the range of the doping prediction boundary parameter set. The data is then standardized and structurally categorized according to the target matrix material system, unifying the data format and field specifications. A learnable embedding encoding operation is performed on the structured doping formulation data and preparation process parameters, converting the original engineering parameters into a digital vector form that the model can process. Simultaneously, a category-adaptive normalization method is used to standardize the encoded data. This method independently calculates the mean and variance based on the data distribution of different matrix systems, relying solely on the real data of the system to complete the standardization scaling, fully preserving the unique doping control rules of different material systems. Based on this, a dual-channel independent feature extraction mechanism is used to extract discrete doping element type features and continuous doping concentration and process parameter features, respectively. These two heterogeneous features are then integrated through direct feature concatenation or attention-weighted fusion to generate a unified feature tensor with unified dimensions, complete information, and clear physical semantics. Finally, the constructed unified feature tensor is directly input into the trained deep feedforward neural network model to predict the performance of the functional ceramics corresponding to the doped formulation and output the results. The prediction results are compared with the collected experimental data; if the results are consistent, the accuracy of the model is verified.

[0045] In one embodiment, the partial least squares regression method described in this invention for screening doping elements and process conditions that are significantly linearly correlated with the target performance is as follows: Based on the collected small-scale high-quality experimental sample data, the types of doping elements, doping concentrations, and preparation process parameters are constructed as independent variable matrices, and the mechanical properties, electrical properties, and microstructure properties of functional ceramics are constructed as dependent variable matrices. The components of both the independent and dependent variable matrices are extracted simultaneously using partial least squares regression to screen out the principal components that can simultaneously maximize the explanation of the variation information of the independent variables and have the strongest correlation with the target performance. The regression coefficients and related significance indicators of each doping element and each process parameter on each target performance are solved sequentially. Based on the magnitude of the coefficients and the significance test results, the types of doping elements, doping concentration ranges, and key preparation process conditions that have a high degree of linear correlation with the mechanical properties, electrical properties, and microstructure properties of functional ceramics and make significant contributions are identified. Redundant elements and process parameters with weak linear effects and no obvious effect on performance regulation are eliminated, completing the preliminary linear screening of key characteristics.

[0046] In one embodiment, the present invention employs a random forest model to calculate the nonlinear importance weights of the influence of each screened dopant element and process condition on the target performance. The partial least squares regression results are then cross-validated with the random forest feature importance results to screen out robust key influencing factors. Specifically: Using doping elements, doping concentrations, and preparation process conditions initially screened through partial least squares regression as input features, and the mechanical, electrical, and microstructure properties of functional ceramics as model output labels, a random forest model is constructed. By analyzing the information gain and Gini impurity reduction of the split nodes in multiple decision trees within the model, the nonlinear contribution and importance weight of each feature to the target performance are quantitatively calculated, characterizing the complex nonlinear coupling relationship between various doping factors and performance. Furthermore, the ranking of linear significant features obtained from partial least squares regression is compared and cross-validated with the ranking of nonlinear feature importance weights output by the random forest. Features that rank highly in both linear correlation and nonlinear contribution and have a stable regulatory effect on material properties are retained, while spurious influencing factors that are only considered significant by a single algorithm but have weak actual regulatory effects are eliminated. This avoids the shortcomings of a single linear model failing to characterize nonlinear laws and a single machine learning model lacking physical and statistical basis.

[0047] In one embodiment, the present invention combines crystal field theory and defect chemistry principles to perform mechanistic analysis on the key influencing factors of robustness, defining the effective concentration range of each key dopant element and the optimization range of core preparation process parameters, specifically as follows: For the key doping elements and core process parameters identified through screening, we first analyzed the changes in valence state, ionic radius, electronic configuration, and orbital splitting energy of dopants based on crystal field theory. This determined the occupancy preference of dopants in the functional ceramic matrix lattice, the degree of lattice distortion, and the variation law of crystal field stability energy, clarifying the regulatory mechanism of different doping elements on the matrix crystal stability and microstructure symmetry. Simultaneously, relying on the principles of defect chemistry, we analyzed the generation mechanism and concentration variation law of intrinsic or intriguing defects such as substitutional defects, interstitial defects, and oxygen vacancies introduced by doping, elucidating the intrinsic relationship between doping element type, doping concentration, defect evolution, and charge compensation mechanism.

[0048] Based on the above mechanism analysis and combined with the solid solution characteristics of the ceramic matrix, the effective concentration range of each key dopant element that can be stably dissolved is quantitatively defined. At the same time, the optimal process window of the core preparation process parameters such as sintering temperature, holding time, and heating rate is matched to ensure that the dopant ions can be uniformly dissolved in the matrix lattice, the defect structure is controllable, and the lattice distortion is in a stable range.

[0049] Furthermore, based on the solid solution limit threshold and phase stability conditions, the entire doping parameter space is screened and eliminated. Parameter combinations with doping concentrations exceeding the matrix solid solution limit, prone to causing lattice mismatch, stress concentration, second phase precipitation, and impurity phase formation are identified as invalid components and eliminated entirely. Only effective doping parameter ranges with stable crystal structure, controllable defects, no impurities, and the ability to achieve positive performance regulation are retained. This ensures the scientific validity and effectiveness of subsequent model training, virtual sampling, and performance prediction from a physical mechanism perspective.

[0050] In one embodiment, the deep feedforward neural network model of the present invention includes: This invention uses a multilayer perceptron as the basic network architecture to build a deep feedforward neural network. To address the problems of complex dimensions of ceramic doped data, strong parameter coupling, and the tendency of traditional networks to have internal data shifts and overfitting, batch normalization layers and Dropout layers are set sequentially in each hidden layer. Furthermore, during the model training phase, the unified feature tensor obtained through dual-channel feature extraction and fusion is used as the sole input variable of the network. Multiple key performance indicators, such as the mechanical properties, electrical properties, and microstructure properties of the functional ceramics, are used as the model's regression prediction output. Simultaneously, this invention employs a mean squared error loss function with L2 regularization as the loss constraint for model training. L2 regularization attenuates the network weight parameters, preventing overfitting caused by excessively large weight parameters. Combined with the backpropagation algorithm, the gradient of the loss function relative to the weights and bias parameters of each layer of the network is calculated layer by layer, enabling iterative updates of the network parameters and accurately fitting the complex nonlinear mapping relationship between doping formulations, process parameters, and ceramic properties.

[0051] Among them, the batch normalization layer can standardize the output features of each layer, effectively alleviate the internal covariate shift problem during network training, ensure the stability of data distribution in each layer, and accelerate network convergence; the dropout layer can randomly deactivate some neurons during training, weaken the co-dependency between neurons, suppress model overfitting from the structural level, and significantly improve the overall stability and robustness of the network.

[0052] To further optimize training performance and improve model fitting accuracy, this invention employs the AdamW optimizer to iteratively update network parameters. Compared to traditional optimizers, the AdamW optimizer decouples weight decay and gradient updates, effectively improving the accuracy of parameter updates and avoiding parameter redundancy accumulation. Simultaneously, a cosine annealing learning rate scheduling strategy is used, allowing the learning rate to be dynamically adjusted periodically according to a cosine law with each training epoch. A high learning rate is maintained in the early stages of training, enabling rapid coarse convergence of parameters and improving training efficiency; in the later stages, the learning rate decays smoothly, allowing for fine-tuning of network parameters, effectively avoiding the problem of the model getting trapped in local optima and significantly improving the overall model fitting accuracy.

[0053] After model training, this invention employs cross-validation combined with multiple ceramic performance evaluation indicators to comprehensively assess the model's prediction accuracy, stability, and generalization ability. This addresses the issues of poor cross-matrix system adaptability and insufficient generalization ability discovered during the evaluation process.

[0054] In one embodiment, the present invention employs a two-level cross-validation method combined with multi-dimensional performance indicators to comprehensively evaluate the trained model: 5-fold cross-validation within the same matrix is ​​used to evaluate the model's prediction accuracy and stability on known matrices, while leave-one-matrix cross-validation is used to specifically evaluate the model's cross-matrix generalization ability; simultaneously, four indicators, including the coefficient of determination R² and mean absolute error (MAE), are used to quantify the prediction performance. To address the poor cross-matrix adaptability issue discovered during the evaluation, targeted optimization is performed by supplementing a small number of high-quality samples from the target system, employing domain adversarial fine-tuning techniques, and optimizing the parameters of the class adaptive normalization layer, ensuring that the model possesses both high prediction accuracy and good cross-matrix generality.

[0055] In one embodiment, further iterative fine-tuning continues until the model's prediction accuracy and generalization performance both reach preset thresholds, ultimately obtaining a trained deep feedforward neural network model. This model possesses extremely strong nonlinear fitting ability, anti-overfitting ability, and cross-domain generalization ability, enabling it to accurately adapt to scenarios of single-set doping formulation point prediction and massive virtual formulation batch prediction, providing stable and reliable model support for the intelligent and high-precision prediction of functional ceramic doping performance.

[0056] In one embodiment, training the deep feedforward neural network model using the AdamW optimizer combined with a cosine annealing learning rate scheduling strategy includes: Starting with an initial learning rate of 1e-3, the learning rate is periodically adjusted according to a cosine function after each training round, with a minimum learning rate not lower than 1e-5. During training, an early stopping strategy is implemented based on the validation set loss, and the deep feedforward neural network model is trained using a pre-built structured database. In other words, this application adopts a cosine annealing learning rate scheduling strategy, which limits the training interval with a fixed initial and minimum learning rate and dynamically adjusts the learning rate periodically according to a cosine function. This strategy can achieve rapid convergence and accelerate parameter optimization in the early stage of training, and can also finely approximate the optimal solution in the later stage, effectively avoiding the model training from getting stuck in local optima. At the same time, combined with the early stopping strategy based on the validation set loss, ineffective training processes can be terminated in time, effectively suppressing the model overfitting problem. While ensuring the prediction accuracy of the deep feedforward neural network model, it improves training efficiency and model generalization ability.

[0057] In one embodiment, the present invention trains the deep feedforward neural network model, including: training the deep feedforward neural network model using a pre-built structured database. The specific process is as follows: the structured database is randomly divided into a training set, a validation set, and a test set in an 8:1:1 ratio, and uniformly converted into a feature tensor format recognizable by the model. A deep feedforward neural network with a multilayer perceptron architecture is constructed, and batch normalization layers and Dropout layers are sequentially set after each hidden layer to suppress overfitting and accelerate convergence. During the training phase, a mean squared error loss function with added L2 regularization is used, and the network parameters are updated through the backpropagation algorithm; the AdamW optimizer combined with a cosine annealing learning rate scheduling strategy is used to dynamically adjust the learning rate, and an early stopping strategy based on the validation set loss is introduced, terminating training when the validation set loss does not decrease for five consecutive rounds. Finally, the model is comprehensively evaluated using a test set to verify its prediction accuracy and generalization ability; after achieving the target, a pre-trained deep feedforward neural network model is obtained.

[0058] The steps for acquiring the structured database include: using the robust key influencing factors as the retrieval basis, acquiring charts and images from functional ceramics-related literature in batches, and performing standardized preprocessing on the charts and images sequentially to avoid redundant collection of irrelevant data and improve the targeting and efficiency of data acquisition.

[0059] In this embodiment, the charts and images are preprocessed in sequence to standardize the data. This includes image noise reduction, resolution unification, background removal, region segmentation, size normalization, and removal of invalid watermarks and interference information. This eliminates problems such as blurriness, noise, inconsistent scale, and clutter in the original document images, standardizes the format and quality of all image data, ensures the accuracy of subsequent feature extraction and data recognition, and provides high-quality raw data support for subsequent multimodal data analysis and information extraction.

[0060] In one embodiment, the present invention uses the first 5 layers of the VGG16 network as the feature extraction backbone, freezes the pre-trained weights and fine-tunes the convolution kernel parameters, performs digital recognition on the pre-processed charts and images, and combines optical character recognition and natural language processing models to extract and fuse material composition, performance and process information, so as to realize the automatic parsing, association and fusion of multimodal literature information, and get rid of the disadvantages of traditional manual literature data processing which is inefficient, labor-intensive and error-prone.

[0061] In one embodiment, the present invention fills in missing values ​​in the extracted data. Specifically, for randomly missing numerical data such as doping concentration and process parameters, the K-nearest neighbor algorithm is used in combination with the data distribution law to fill in the missing values. For performance missing values ​​related to the physical field distribution, the Poisson equation is used to construct a physical constraint model to solve and fill in the missing values. This not only conforms to the statistical law of the data, but also fits the physical mechanism of the material, ensuring that the database data is complete, true and reasonable, and finally a structured database is obtained.

[0062] In one embodiment, the present invention embeds and encodes the structured and classified doping formulation data and preparation process parameters, and uses category adaptive normalization to extract doping element type features and doping concentration features respectively, and fuses the two types of features to generate a unified feature tensor, including: The doping formulation data and preparation process parameters are grouped according to the target matrix material system. Doping components, concentration parameters, and sintering process parameters under the same matrix system are grouped into the same data group to ensure that the material system background and physical rules of each group are consistent, avoiding interference from the mixed distribution of data from different matrices to feature extraction. After grouping, learnable embedding encoding is performed on each group of structured data to convert the manually structured tabular parameter data into a digital latent vector form that the model can iteratively learn, realizing the mapping transformation of the original engineering parameters to a high-dimensional feature space.

[0063] This application employs category-adaptive normalization to standardize each data set. It's important to note that this method differs from global uniform normalization; instead, it independently calculates the mean and variance of the data for each target matrix material system, relying solely on the actual data distribution of that system for standardization scaling. This approach effectively adapts to the differences in material properties and data distribution characteristics of different functional ceramic matrices, preserving the unique characteristics and control rules of doping parameters under different matrix systems. It avoids the problem of global normalization smoothing out system differences and causing distortion of feature information, significantly improving the specificity and accuracy of feature characterization.

[0064] Based on this, the present invention employs a dual-branch independent feature extraction strategy to obtain two types of core features: for discrete doping element type data, a dedicated embedding layer is used to complete the encoding mapping, converting the disordered and discrete element category information into a category feature vector with unified dimensions and learnable semantics, accurately representing the intrinsic attribute differences of different doping elements; for continuous doping concentration and preparation process parameters, a fully connected layer is used to perform nonlinear feature mapping, mining the correlation between concentration gradient, process parameter changes and material properties, generating continuous and smooth concentration and process feature vectors, and realizing the effective extraction of deep features of continuous parameters.

[0065] Finally, the extracted feature vectors of dopant element types and dopant concentrations are efficiently fused. The fusion method can be either direct feature concatenation or attention-weighted fusion, depending on the training scenario. Feature concatenation preserves all effective information from both sets of features, adapting to conventional prediction scenarios; attention-weighted fusion automatically assigns weights to different features, strengthening key features and weakening redundant interference features, adapting to prediction scenarios with complex doping formulations across multiple systems. By integrating the two heterogeneous features into a unified feature tensor with consistent dimensions, complete information, and clear physical semantics, this tensor serves as the standard input data for the deep feedforward neural network model, providing high-quality feature support for subsequent high-precision performance prediction.

[0066] It should be noted that this invention performs structured classification and embedding encoding of doping formulation data and process parameters. It uses a dual-channel adaptive normalization method to extract the characteristics of doping element type and doping concentration respectively and fuses them to generate a unified feature tensor. This can accurately characterize the coupling influence of discrete element type and continuous doping concentration on ceramic performance. Compared with the traditional single feature input method, the feature characterization is more in line with the intrinsic mechanism of material doping and effectively improves the accuracy of model prediction.

[0067] In one embodiment, the present invention performs multi-objective optimization on the predicted performance results of the functional ceramics to obtain a Pareto optimal doping scheme set, so as to achieve high-throughput, high-precision, and comprehensive intelligent optimization of functional ceramic doping formulations. The specific implementation process is as follows: First, based on the target matrix doping prediction boundary parameter set defined by the previous baseline model, and using the effective dopant element types, doping concentration ranges, and compliant preparation process parameter ranges defined by this parameter set as constraints, the optimal Latin hypercube sampling method is used to conduct full-domain sampling, generating a large number of virtual doping formulation sets in batches, and constructing a virtual doping composition space covering all effective parameter ranges. Compared with traditional random sampling methods, optimal Latin hypercube sampling has excellent spatial uniformity distribution characteristics, enabling uniform and full coverage of the entire effective doping parameter range with a limited number of samples. It avoids the problems of sampling redundancy and data duplication in local parameter ranges, and also completely avoids the defect of missing the optimal doping ratio range. While significantly reducing the number of invalid samples and improving the efficiency of high-throughput virtual screening, it ensures the integrity and representativeness of the virtual formulation space, providing a comprehensive and balanced sample foundation for subsequent global optimal formulation optimization.

[0068] After constructing the virtual doping composition space and obtaining the performance prediction results of all virtual formulations in batches through a deep feedforward neural network model, this invention establishes a multi-objective optimization system that fits engineering practice, clarifying the optimization objectives and physical constraints. This invention takes the excellent mechanical properties, superior electrical properties, and lowest doping preparation cost of functional ceramics as its three core optimization objectives, balancing material performance with the economic viability of industrial applications. Simultaneously, it sets hard constraints based on the material's physical mechanisms, strictly limiting the doping concentration in all optimization processes to not exceeding the solid solution limit of the target matrix, ensuring that the system structure corresponding to all virtual doping formulations is free of impurity phase precipitation and second-phase formation, guaranteeing that all optimized schemes meet the basic requirements of stable crystal structure and compliant physical mechanisms, and preventing the output of theoretically feasible but practically unfeasible or structurally unstable ineffective doping schemes.

[0069] Based on the aforementioned multiple optimization objectives and physical constraints, this invention employs the NSGA-II non-dominated sorting genetic algorithm to iteratively optimize the performance prediction results of batch virtual formulations. This algorithm effectively handles complex optimization problems involving multiple mutually constrained and coupled objectives. Through rapid non-dominated sorting, crowding calculation, and an elite retention strategy, it performs hierarchical selection of massive virtual doping formulations, continuously eliminating inferior formulations with poor performance, high cost, and failure to meet constraints, while retaining superior doping formulations with balanced and excellent performance, controllable cost, and stable structure. After multiple rounds of iterative convergence, it finally outputs a set of Pareto-optimal doping schemes without any mutual dominance relationships.

[0070] In one embodiment, the present invention employs the NSGA-II non-dominated sorting genetic algorithm to iteratively optimize the performance prediction results of batch virtual recipes. The specific process is as follows: Using all virtual doping formulations and their corresponding performance predictions as the initial population, each individual in the population represents a complete combination of doping formulations and process parameters. First, a fast non-dominated sort is performed on the initial population, dividing the population into different levels of non-dominated fronts according to the dominance relationship between individuals. At the same time, all invalid individuals that do not meet the solid solution limit and the constraint of no impurity phase precipitation are removed.

[0071] Crowding density is calculated for individuals at the same frontier to measure their distribution density in the target space, ensuring population diversity. A tournament selection strategy is adopted, prioritizing dominant individuals with high non-dominance levels and high crowding density as parents; offspring populations are generated through simulated binary crossover and polynomial mutation operations.

[0072] The parent and offspring populations are merged, and non-dominated sorting and crowding calculation are performed again. An elite retention strategy is used to select the best individuals to form the new generation population. The above iterative process is repeated until the preset maximum number of iterations is reached or the population converges. Finally, all individuals corresponding to the first non-dominated front are output, which is the Pareto optimal doping scheme set that takes into account mechanical performance, electrical performance, and doping cost.

[0073] This invention employs the NSGA-II non-dominated sorting genetic algorithm for multi-objective optimization, which can achieve balanced optimization among multiple mutually constraining optimization objectives, avoid the one-sidedness of single-objective optimization, automatically converge and output a Pareto optimal doping scheme set; it eliminates the need for manual comparison and screening of a large number of doping combinations, and efficiently completes the intelligent recommendation of the optimal doping element type and ratio.

[0074] In one embodiment, the prediction method of the present invention further includes: experimentally verifying the Pareto optimal doping scheme set, and feeding the experimental verification results back to the deep feedforward neural network model as new data for model optimization. Specifically, this includes: after obtaining the Pareto optimal doping scheme set, selecting the target doping scheme that best suits the engineering application scenario and balances performance and cost from the optimal scheme set according to actual R&D needs, conducting physical preparation experiments and performance testing verification, and accurately obtaining the measured mechanical properties, electrical properties, and microstructure properties of the functional ceramics corresponding to the doping formula. Through physical experimental verification, the feasibility and practicality of the optimal doping scheme output by the model can be effectively verified, the deviation between the model prediction data and the measured data can be directly compared, and the model prediction error can be identified and corrected in a timely manner. After completing the experimental verification, the high-precision measured performance data obtained in this experiment, as well as the corresponding optimal doping formula parameters and the complete set of preparation process parameters, are standardized and organized into standardized structured sample data, and incorporated as new valid samples into a pre-constructed structured database to complete the real-time iterative update of the database. After the database update is completed, the newly added measured samples and the original historical samples are combined to form a hybrid training dataset, and incremental training is carried out on the pre-trained deep feedforward neural network model.

[0075] Example 2 This invention also provides a neural network-based system for predicting the doping properties of functional ceramic materials (see [link]). Figure 2 This system is used to implement the entire process of the aforementioned neural network-based method for predicting the doping performance of functional ceramic materials. The system adopts a loosely coupled modular architecture design, with each module deployed independently, logically connected, and data interconnected, meeting the needs of different stages of functional ceramic doping research and development. Specifically, the system includes: The prediction boundary processing module is used to call a pre-built prediction model for doping processes and performance baselines to match and verify the target matrix material system information of functional ceramics, thereby obtaining a set of predicted boundary parameters for the target matrix doping. This module calls the pre-built prediction model for doping processes and performance baselines, receives complete information about the target matrix material system of the functional ceramic to be developed, and first performs a multi-dimensional precise matching search on the target matrix information. It matches corresponding or highly similar matrix systems from the built-in functional ceramic matrix mechanism knowledge base and baseline database, extracting the basic doping characteristic information of the system. Then, combining the built-in crystal field theory and defect chemistry rule base, it sequentially performs multi-dimensional mechanism verification on the basic doping characteristic information, including ion radius matching verification, valence charge compensation verification, dynamic correction of solid solution limit, and phase stability verification. By comprehensively considering physical constraints such as the material's solid solution limit, phase stability conditions, and lattice distortion threshold, it dynamically corrects and defines the legal doping parameter range corresponding to the current target matrix, and finally outputs a standardized set of predicted boundary parameters for the target matrix doping, thoroughly eliminating invalid doping parameter ranges that are prone to generating impurities, exceed the solid solution limit, or have unstable lattice structures from the source.

[0076] The batch prediction module generates a virtual doping composition space covering the entire effective range based on the target matrix doping prediction boundary parameter set. It performs structured classification and organization of each virtual doping formula in the virtual doping composition space, embeds and encodes it, extracts and fuses the doping element type features and doping concentration features to generate a unified feature tensor, and inputs the unified feature tensors corresponding to all virtual doping formulas into a deep feedforward neural network model in batches. It outputs the functional ceramic performance prediction results corresponding to the batch doping formulas to be predicted, and performs multi-objective optimization on the functional ceramic performance prediction results to obtain the Pareto optimal doping scheme set. The model optimization module performs experimental verification based on the Pareto optimal doping scheme set and feeds the experimental verification results back to the deep feedforward neural network model as new data for model optimization. The model validation module acquires a single set of doped ceramic formulation data and preparation process parameters that conform to the target matrix doping prediction boundary parameter set within one cycle or when calling the model for prediction. These data are then structured and categorized according to the target matrix material system. The structured doped formulation data and preparation process parameters are embedded and encoded. Adaptive category normalization is used to extract doping element type features and doping concentration features, respectively. These two types of features are then fused to generate a unified feature tensor. This unified feature tensor is input into a deep feedforward neural network model, which outputs the predicted performance results of the functional ceramic corresponding to the doped formulation. The prediction results are compared with the collected experimental data. If the results are consistent, the accuracy of the model is verified.

[0077] In this embodiment, the batch prediction module performs multi-objective optimization by using the NSGA-II non-dominated sorting genetic algorithm to iteratively optimize the batch prediction results.

[0078] Example 3 The present invention also provides a computer storage medium storing a computer program, which, when executed by a processor, implements the neural network-based method for predicting the doping properties of functional ceramic materials in the foregoing embodiments.

[0079] All content not described in detail in this specification is prior art known to those skilled in the art, and the model parameters of each electrical appliance are not specifically limited; conventional equipment can be used. Electrical control components not mentioned in this technical solution are not shown in the figures because they are prior art, and will not be described further here.

[0080] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the doping properties of functional ceramic materials based on neural networks, characterized in that, Includes the following steps: By calling the pre-built prediction model of doping process and performance baseline, the target matrix material system information of functional ceramics is matched, retrieved and verified by mechanism to obtain the target matrix doping prediction boundary parameter set; Based on the target matrix doping prediction boundary parameter set, a virtual doping composition space covering the entire effective range is generated. Each virtual doping formula in the virtual doping composition space is structurally classified and coded. The doping element type features and doping concentration features are extracted and fused to generate a unified feature tensor. The unified feature tensors corresponding to all virtual doping formulas are batch-input into a deep feedforward neural network model, and the functional ceramic performance prediction results corresponding to the batch doping formulas to be predicted are output. The functional ceramic performance prediction results are multi-objective optimized to obtain the Pareto optimal doping scheme set. The Pareto optimal doping scheme set was experimentally verified, and the experimental verification results were fed back as new data to the deep feedforward neural network model for model optimization.

2. The method for predicting the doping properties of functional ceramic materials based on neural networks according to claim 1, characterized in that, The steps for constructing the doping process and performance baseline prediction model include: Based on small-scale, high-quality experimental sample data, with dopant element type, doping concentration, and preparation process parameters as input features, and with the mechanical, electrical, and microstructure properties of functional ceramics as target properties, partial least squares regression was used to screen dopant elements and process conditions that are significantly linearly correlated with the target properties. The nonlinear importance weights of the influence of each screened dopant element and process condition on the target performance were calculated using a random forest model. The partial least squares regression results and the random forest feature importance results were cross-validated in two directions to screen out the key influencing factors of robustness. Combining crystal field theory and defect chemistry principles, the mechanism of the key factors affecting robustness is analyzed, the effective concentration range of each key dopant element and the optimization range of core preparation process parameters are defined, and the space of ineffective components that exceed the solid solution limit and are prone to generating impurity phases is eliminated. Based on the aforementioned key factors affecting robustness and the defined parameter range, the parameters of the partial least squares regression model are optimized to construct a prediction model for doping process and performance baseline.

3. The method for predicting the doping properties of functional ceramic materials based on neural networks according to claim 2, characterized in that, The construction steps of the deep feedforward neural network model include: Construct a deep feedforward neural network with a multilayer perceptron structure, and set batch normalization layer and Dropout layer in each hidden layer in sequence; Using the unified feature tensor as input and the functional ceramic performance as output target, the mean squared error loss function containing L2 regularization term is adopted, and the gradient of the loss function with respect to the weights of each layer of the network is calculated through the backpropagation algorithm. The deep feedforward neural network model was trained using the AdamW optimizer combined with a cosine annealing learning rate scheduling strategy. Cross-validation and multiple performance metrics are used to evaluate the trained deep feedforward neural network model. If the model's generalization ability is insufficient, a domain adversarial neural network is used to fine-tune the model until the model's prediction accuracy and generalization ability reach the preset threshold, thus obtaining a pre-trained deep feedforward neural network model. The process includes, within one cycle or when calling the model for prediction, the following steps: acquiring a single set of doping formula data and preparation process parameters for the functional ceramic to be predicted that conform to the target matrix doping prediction boundary parameter set, and structuring and classifying them according to the target matrix material system; embedding and encoding the structuring and classifying doping formula data and preparation process parameters, and using category adaptive normalization to extract the doping element type features and doping concentration features respectively, and fusing the two types of features to generate a unified feature tensor; inputting the unified feature tensor into a deep feedforward neural network model, outputting the functional ceramic performance prediction results corresponding to the doping formula to be predicted, and comparing the prediction results with the collected experimental data. If the results are consistent, the accuracy verification of the model is completed.

4. The method for predicting the doping properties of functional ceramic materials based on neural networks according to claim 3, characterized in that, The training of the deep feedforward neural network model using the AdamW optimizer combined with a cosine annealing learning rate scheduling strategy includes: With an initial learning rate of 1e -3 Starting from this point, the learning rate is periodically adjusted according to a cosine function after each round of training, with a minimum learning rate of no less than 1e. -5 During training, an early stopping strategy is implemented based on the validation set loss. The deep feedforward neural network model is trained using a pre-built structured database.

5. The method for predicting the doping properties of functional ceramic materials based on neural networks according to claim 4, characterized in that, The steps for obtaining the structured database include: Based on the aforementioned key influencing factors of robustness, charts and images from functional ceramics-related literature are retrieved in batches, and the charts and images are then preprocessed in a standardized manner. The first 5 layers of the VGG16 network are used as the feature extraction backbone. The pre-trained weights are frozen and the convolution kernel parameters are fine-tuned. The pre-processed charts and images are digitally recognized. The material composition, performance and process information are extracted and fused by combining optical character recognition and natural language processing models. Missing values ​​were filled in the extracted data. For randomly missing numerical data such as doping concentration and process parameters, the K-nearest neighbor algorithm was used to fill in the missing values ​​based on the data distribution. For missing performance values ​​related to the physical field distribution, the Poisson equation was used to construct a physical constraint model to fill in the missing values, resulting in a structured database.

6. The method for predicting the doping properties of functional ceramic materials based on neural networks according to claim 5, characterized in that, The structured and categorized doping formulation data and preparation process parameters are embedded and encoded. Category adaptive normalization is used to extract doping element type features and doping concentration features respectively. These two types of features are then fused to generate a unified feature tensor, including: The doping formulation data and preparation process parameters were grouped according to the target matrix material system, and each group of data was encoded into learnable embeddings. Each set of data is standardized using adaptive categorical normalization. The mean and variance of the adaptive categorical normalization are obtained independently based on the data of the corresponding target matrix material system. The discrete dopant element types are encoded by the embedding layer to generate type feature vectors, and the continuous dopant concentration parameters are mapped by the fully connected layer to generate concentration feature vectors. The type feature vector and the concentration feature vector are fused by feature concatenation or attention-weighted fusion to generate a unified feature tensor.

7. The method for predicting the doping properties of functional ceramic materials based on neural networks according to claim 6, characterized in that, The multi-objective optimization of the predicted performance results of the functional ceramics to obtain the Pareto optimal doping scheme set includes: Using the optimal Latin hypercube sampling method, a set of virtual doping recipes covering the entire effective range is generated within the range defined by the target matrix doping prediction boundary parameter set, thus forming a virtual doping composition space; With the mechanical properties, electrical properties and doping cost of functional ceramics as optimization objectives, and with the constraints of doping concentration not exceeding the solid solution limit and no impurity phase generation as constraints, the non-dominated sorting genetic algorithm NSGA-II is used to perform multi-objective optimization on the performance prediction results of all doping formulations to be predicted, and outputs a Pareto optimal doping scheme set.

8. The method for predicting the doping properties of functional ceramic materials based on neural networks according to claim 7, characterized in that, Also includes: Target schemes were selected from the Pareto optimal doping scheme set to conduct experimental verification and obtain measured performance data; The measured performance data and the corresponding doping formulations and preparation process parameters are used as new samples to update the structured database; The pre-trained deep feedforward neural network model is incrementally trained using a mixture of new and historical samples, while the doping process and performance baseline prediction model are iteratively optimized.

9. A neural network-based system for predicting the doping properties of functional ceramic materials, characterized in that, The system is used to execute the neural network-based method for predicting the doping properties of functional ceramic materials as described in any one of claims 1 to 8, the system comprising: The prediction boundary processing module is used to call the pre-built doping process and performance baseline prediction model, match and retrieve the target matrix material system information of functional ceramics and verify the mechanism to obtain the target matrix doping prediction boundary parameter set; The batch prediction module generates a virtual doping composition space covering the entire effective range based on the target matrix doping prediction boundary parameter set. It performs structured classification and organization of each virtual doping formula in the virtual doping composition space, embeds and encodes it, extracts and fuses the doping element type features and doping concentration features to generate a unified feature tensor, and inputs the unified feature tensors corresponding to all virtual doping formulas into a deep feedforward neural network model in batches. It outputs the functional ceramic performance prediction results corresponding to the batch doping formulas to be predicted, and performs multi-objective optimization on the functional ceramic performance prediction results to obtain the Pareto optimal doping scheme set. The model optimization module performs experimental verification based on the Pareto optimal doping scheme set and feeds the experimental verification results back to the deep feedforward neural network model as new data for model optimization. The model validation module acquires a single set of doped ceramic formulation data and preparation process parameters that conform to the target matrix doping prediction boundary parameter set within one cycle or when calling the model for prediction. These data are then structured and categorized according to the target matrix material system. The structured doped formulation data and preparation process parameters are embedded and encoded. Adaptive category normalization is used to extract doping element type features and doping concentration features, respectively. These two types of features are then fused to generate a unified feature tensor. This unified feature tensor is input into a deep feedforward neural network model, which outputs the predicted performance results of the functional ceramic corresponding to the doped formulation. The prediction results are compared with the collected experimental data. If the results are consistent, the accuracy of the model is verified.

10. A computer storage medium, characterized in that, The computer storage medium stores a computer program, which, when executed by a processor, implements the method for predicting the doping properties of functional ceramic materials based on neural networks as described in any one of claims 1 to 8.

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