Material digital representation-oriented feature learning method based on dimension reduction and dimension rise and application thereof in machine learning prediction of material performance

Abstract

The invention provides a material digital characterization-oriented feature learning method based on dimension reduction and dimension rise and application thereof in machine learning prediction of material performance, and relates to the technical field of material science. The method comprises the steps of firstly obtaining original features and properties of a material sample, calculating expansion features and generating labels; multiple machine learning feature selection algorithms are used in parallel to evaluate importance, normalized scores are aggregated to obtain a comprehensive score, and feature subsets are screened; and then high-dimensional transformation is carried out on the dimension reduction features through deep embedded nonlinear dimension raising mapping, and final features with more information are obtained through pre-training based on physical information and a fine-tuning transfer learning process guided by target properties. The method has robust feature selection and depth nonlinear representation of multiple algorithms, overcomes the problems of traditional one-sidedness and insufficient information, provides high-quality input for a subsequent model, and improves the accuracy of material property prediction.

Description

Technical Field

[0001] The present invention relates to the field of materials science and technology, and in particular to a feature learning method based on dimensionality reduction and dimensionality increase for digital characterization of materials and its application in machine learning prediction of material properties. Background Art

[0002] Traditional materials design methods rely primarily on trial-and-error experiments based on expert experience and theoretical calculations under simplified conditions, resulting in a series of challenges such as long lead times, high costs, poor precision, and low efficiency. Recent advances in computational materials science and high-throughput experimental techniques have provided new tools for materials design, but they still face challenges such as the vast space of candidate element types and composition ratios, as well as the complexity, cost, and time-consuming optimization process. Data-driven AI-powered materials design and development is a key emerging frontier in the era of artificial intelligence (AI). Developing efficient and accurate machine learning-based material property prediction methods is a core technology. With the rise of high-throughput computational and experimental techniques in recent years, materials science has entered a new data-driven paradigm. Initiatives such as the Materials Genome Initiative (MGI) and AI-enabled Materials Science (AI4Mat) have significantly accelerated the discovery of new materials. By combining advanced computational simulations with automated high-throughput experiments, researchers are generating vast amounts of materials data at an unprecedented rate. However, effectively extracting valuable information from this high-dimensional, complex, and heterogeneous multi-source materials data and applying it to guide the design and optimization of new materials presents a new challenge.

[0003] In particular, when using artificial intelligence technologies such as machine learning and deep learning to process material data, feature engineering and representation learning play a vital role. In machine learning methods in the field of materials, the feature engineering link is the key to determining the upper limit of prediction accuracy. The essence of feature engineering in the field of materials informatics is a feature construction method for digital characterization of materials. Traditional feature construction methods still have shortcomings such as simple form, incomplete information, unclear importance and correlation, and construction methods that rely too much on experience and are too random. The performance of materials is often determined by multiple factors such as their composition, structure, and process, which constitute a high-dimensional feature space. Existing data-driven methods face the following challenges:

[0004] First, feature redundancy and screening difficulties: Raw material data features are high-dimensional and contain a large amount of redundant, noisy, and even irrelevant features. Directly using them for model training not only increases the computational burden but can also reduce model performance and generalization capabilities. Currently, there is a lack of a systematic, efficient feature screening mechanism that can integrate multiple evaluation criteria to identify key features.

[0005] Second, simple feature screening (dimensionality reduction) can miss important key features, as well as nonlinear relationships and high-order interactions between features, which are crucial for accurately predicting complex material properties. Traditional machine learning models have specific requirements for feature representation. While deep learning models hold great potential, designing effective network structures to achieve deep, nonlinear representation of material characteristics (dimensionality increase) remains an ongoing research challenge.

[0006] Third, model adaptability and R&D efficiency: Different machine learning models have varying sensitivities to the type, distribution, and dimensionality of input features. How to process features to better adapt downstream predictive models is a pressing issue. Furthermore, current methods often focus on a single step (such as predicting a single property) and lack a comprehensive optimization approach that integrates feature processing, model training, performance prediction, and other steps, resulting in limited improvements in overall R&D efficiency. Summary of the Invention

[0007] In order to overcome the shortcomings of the existing technology, the purpose of the present invention is to provide a feature learning method based on dimensionality reduction and dimensionality increase for digital characterization of materials and its application in machine learning prediction of material properties, aiming to address the challenges of low R&D efficiency caused by the difficulty of feature redundancy screening, insufficient feature characterization capabilities and poor model adaptability in existing material data processing.

[0008] To achieve the above object, the present invention provides the following solutions:

[0009] A feature learning method based on dimensionality reduction and dimensionality increase for digital representation of materials, including:

[0010] Obtaining a sample data set of an initial material; the data set includes original input features characterizing the initial material sample and corresponding target material properties;

[0011] Calculating extended features based on the original input features and generating label data for pre-training and prediction;

[0012] Applying at least three different machine learning feature selection algorithms in parallel to perform importance assessment on the sample data set to generate an importance score for each of the original input features, and normalizing the importance scores to obtain a set of normalized score vectors in a uniform interval;

[0013] Aggregating all the normalized score vector sets, calculating the comprehensive importance score of each of the original input features, and selecting a feature subset according to a preset screening rule and the comprehensive importance score;

[0014] A nonlinear dimensionality-increasing mapping module is constructed to perform a nonlinear transformation on the feature subset after dimensionality reduction through the nonlinear dimensionality-increasing mapping module to generate a final high-dimensional feature representation.

[0015] Preferably, it also includes:

[0016] A prediction module is constructed, and the high-dimensional feature representation is input into the prediction module to obtain the predicted target property.

[0017] Preferably, it also includes:

[0018] Based on the feature subset and the target property value, end-to-end training or fine-tuning is performed on a deep neural network composed of a nonlinear dimensionality-increasing mapping module embedded with the physical information and the prediction module to obtain a trained target property prediction model;

[0019] The input features of the new sample are processed and input into the target property prediction model to obtain the predicted value of the target property.

[0020] Preferably, after obtaining the sample data set of the initial material, the method further comprises:

[0021] The initial material is cleaned to obtain a cleaned sample data set; the data cleaning process includes: processing missing data points, identifying and processing outliers, and performing data formatting.

[0022] Preferably, before constructing the prediction module, the method further includes:

[0023] Designing an auxiliary prediction task embedded with physical information matching the label data to construct a temporary network; the temporary network includes a nonlinear dimensionality-increasing mapping module and a temporary prediction head adapted to the auxiliary task;

[0024] Using target property-oriented labeled data as a supervisory signal to train the temporary network to optimize parameters of the nonlinear dimensionality-increasing mapping module;

[0025] After the training is completed, the parameters learned by the nonlinear dimensionality-increasing mapping module are saved to obtain a pre-trained nonlinear dimensionality-increasing mapping module.

[0026] Preferably, the original input features include the inherent attribute features of the central atom and the statistical features related to the local environment around the site where the central atom is located.

[0027] Preferably, the extended features are obtained by calculating or extracting a set of initial features that may contain redundant information through a preset automatic feature generation tool.

[0028] Preferably, the feature subset is selected according to the preset screening rules and the comprehensive importance score, including:

[0029] Sorting the original input features in descending order according to the calculated comprehensive importance score to obtain a sorted list;

[0030] Selecting the final feature subset from the sorted list according to predefined screening rules;

[0031] The preset screening rule includes any one of the first rule and the second rule;

[0032] The steps of the first rule include:

[0033] Select the features ranked in the top N positions in the sorted list;

[0034] Select the features whose comprehensive importance scores are higher than a preset threshold; or select all features in the sorted list before the score curve has a descending inflection point, to obtain the feature subset;

[0035] The second rule includes

[0036] Dividing each of the original input features into at least two mutually exclusive or overlapping feature groups based on prior knowledge or feature attributes of the material field;

[0037] Within each of the feature groups, multiple algorithms are independently applied to perform scoring, normalization, aggregation, and sorting, and the preferred features of each group are screened according to preset intra-group rules;

[0038] The preferred features screened out from all the feature groups are merged to form a final feature subset.

[0039] Preferably, the nonlinear dimensionality-raising mapping module is composed of a multi-layer perceptron; or when processing discretized features, the nonlinear dimensionality-raising mapping module includes one or more embedding layers.

[0040] Preferably, when processing discretized features, the method further includes:

[0041] A preselected bucketing algorithm is applied to the continuous features in the feature subset to perform feature processing to obtain a processed feature subset.

[0042] An application of the above-mentioned feature learning method based on dimensionality reduction and dimensionality increase for digital representation of materials in machine learning prediction of material properties.

[0043] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0044] The present invention provides a feature learning method based on dimensionality reduction and dimensionality increase for digital characterization of materials, comprising: obtaining a sample data set of initial materials; the data set includes original input features characterizing the initial material sample and corresponding target material properties; calculating extended features based on the original input features, and generating label data for pre-training and prediction; applying at least three different machine learning feature selection algorithms in parallel to evaluate the importance of the sample data set, generating an importance score for each of the original input features, and normalizing the importance scores to obtain a set of normalized score vectors in a uniform interval; aggregating all the normalized score vector sets, calculating a comprehensive importance score for each of the original input features, and selecting a feature subset based on preset screening rules and the comprehensive importance score; constructing a nonlinear dimensionality increase mapping module to perform a nonlinear transformation on the feature subset after dimensionality reduction through the nonlinear dimensionality increase mapping module to generate a final high-dimensional feature representation. The present invention systematically integrates multiple machine learning feature screening technologies to obtain robust feature importance evaluation, and combines an innovative deep embedded neural network architecture to achieve nonlinear dimensionality increase and deep representation learning of features. This effectively solves the one-sidedness and lack of representation ability of existing methods in feature selection, and can provide higher quality and more informative feature inputs for downstream machine learning models. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0046] Figure 1 A flow chart of a method provided by an embodiment of the present invention;

[0047] Figure 2 A schematic diagram of the technical route provided for an embodiment of the present invention. DETAILED DESCRIPTION

[0048] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0049] The purpose of this invention is to provide a feature learning method based on dimensionality reduction and dimensionality increase for digital characterization of materials and its application in machine learning prediction of material properties, aiming to improve the quality and applicability of material data features, provide a prerequisite for building high-quality machine learning prediction models, and thus accelerate data-driven material characterization learning and the entire chain R&D process efficiently and at low cost.

[0050] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] Figure 1 A flow chart of the method provided in the embodiment of the present invention is shown in FIG. Figure 1 As shown, the present invention provides a feature learning method based on dimensionality reduction and dimensionality increase for digital characterization of materials, comprising:

[0052] S100: Obtaining a sample data set of an initial material; the data set includes original input features characterizing the initial material sample and corresponding target material properties;

[0053] S200: Calculate extended features based on the original input features and generate label data for pre-training and prediction;

[0054] S300: Apply at least three different machine learning feature selection algorithms in parallel to perform importance evaluation on the sample data set, generate importance scores for each original input feature, and normalize the importance scores to obtain a set of normalized score vectors with a uniform interval;

[0055] S400: Aggregate all normalized score vector sets, calculate the comprehensive importance score of each original input feature, and select a feature subset based on preset screening rules and the comprehensive importance score;

[0056] S500: Construct a nonlinear dimensionality-increasing mapping module to perform a nonlinear transformation on the feature subset after dimensionality reduction through the nonlinear dimensionality-increasing mapping module to generate a final high-dimensional feature representation.

[0057] Specifically, such as Figure 2 As shown, the technical route of this embodiment includes the following steps:

[0058] S1: Obtain an initial material sample dataset from one or more sources (the sources include but are not limited to public literature databases, material property databases such as the Materials Project or AFLOW, theoretical calculation software output, and high-throughput experimental platform records). The dataset contains multiple material samples, each of which consists of a set of original input features and at least one corresponding target material property value or category label. Perform data cleaning operations on the dataset, which may include processing missing data points, identifying and processing outliers, and performing data formatting operations to ensure data consistency and compatibility with subsequent processing.

[0059] S2: Based on the material composition information (e.g., element types and their stoichiometric ratios) in the data set obtained in step S1, use an automated feature generation tool (e.g., an integrated material informatics library such as XenonPy or Magpie) to calculate or extract a set of initial, possibly redundant, extended features. Optionally, composite features are defined and calculated based on prior knowledge in the field of materials, where the composite features are mathematical or logical combinations of the original features. At the same time, label data for subsequent model training is collated or generated, and the label data may include auxiliary category labels for pre-training (e.g., crystal structure classification, specific atomic occupancy information such as substitution site coordinates) and / or target material property values for final performance prediction. The generated extended features and label data are stored in a structured manner.

[0060] S3: For the feature set generated in step S2 (or the original feature set in step S1), a set of machine learning feature selection algorithms based on at least three different principles is applied in parallel and independently. The algorithm set may include, but is not limited to: statistical-based methods (such as variance threshold method, Pearson correlation coefficient method, F-test regression), information-theoretic-based methods (such as mutual information method), model-based embedded methods (such as L1 regularization coefficient, feature importance ranking based on random forest, feature importance ranking based on XGBoost), and wrapper methods (such as recursive feature elimination (RFE). The purpose is to evaluate the relevance and importance of each feature to the target property or auxiliary label from multiple different perspectives.

[0061] S4: For each feature selection algorithm applied in step S3, an initial importance score or ranking is generated for each feature in the feature set based on its internal mechanism. Subsequently, the set of scores generated by each algorithm (or scores based on the ranking transformation) are independently normalized, using a normalization method such as min-max normalization (mapping the scores to the interval [0, 1]) or Z-score normalization. The output of this step is a set of normalized score vectors with the same number of algorithms applied, a length equal to the number of features, and values within a uniform and comparable range.

[0062] S5: First, for each feature in the feature set, aggregate its normalized scores obtained from all different algorithms in step S4 to calculate a single comprehensive importance score. The aggregation method can be the arithmetic mean, weighted average (the weights can be equal or set according to the reliability of the algorithm), median or other aggregation functions. Then, all features are sorted in descending order according to the calculated comprehensive importance score. Finally, the final feature subset is selected from the sorted list according to predefined screening rules, such as: select the features ranked in the top N; select features with a comprehensive score higher than a preset threshold; or select all features before the score curve in the sorting graph shows a significant drop (inflection point). This step outputs the feature subset for subsequent modeling.

[0063] S6: Provide an optional feature grouping screening strategy that can replace or supplement step S5. This step includes: first, based on the prior knowledge or feature attributes of the material field, divide the original feature set (or generated in step S2) into at least two mutually exclusive or overlapping feature groups (for example, the central atom feature group and the local environment feature group). Then, within each feature group, independently repeat the core logic of steps S3 to S5 (or only steps S3-S4 and sorting within the group), that is, apply multiple algorithms, scoring, normalization, aggregation (optional), sorting, and screen out the preferred features of each group according to the rules within the group (for example, select the Top M features in each group). Finally, merge the features screened from all groups (for example, take the union) to form the final feature subset.

[0064] S7: Design and instantiate a deep neural network model architecture. The architecture logically contains at least two core modules: a nonlinear dimensionality increase mapping module and a prediction module. The nonlinear dimensionality increase mapping module is responsible for receiving the input features (from step S5 or S6, which may be processed by step S8) and nonlinearly mapping them to a dense vector representation (embedding vector) of a preset dimension (for example, 64, 128 or higher). The nonlinear dimensionality increase mapping module can be composed of a multi-layer perceptron (containing several fully connected layers and nonlinear activation functions), or, when processing discretized features, it can contain one or more embedding layers (Embedding Layer). The prediction module receives the embedding vector generated by the nonlinear dimensionality increase mapping module as input, and predicts the final target material property value through one or more subsequent layers (usually also an MLP structure). The output layer design of the prediction module needs to match the prediction task (for example, linear activation is used for regression tasks and Softmax activation is used for classification tasks).

[0065] S8: Conditional execution, executed when and only when the deep embedding network model constructed in step S7 (especially its nonlinear dimensionality increasing mapping module) is expected to receive discretized input. This step includes: applying a preselected discretization algorithm to the continuous features in the feature subset screened out in step S5 or S6. The algorithm is, for example, an equal-width bucketing method or an equal-frequency bucketing method, which divides the value range of each continuous feature into a preset number of K intervals (buckets) and maps each feature value to a unique index of the interval to which it belongs. The output of this step is the discrete bucket index representation after the original continuous feature is converted.

[0066] S9 is an optional pre-training step that aims to optimize the initial state of the nonlinear dimensionality increasing mapping module by utilizing the rich auxiliary information that may exist in the data set. This step includes: using the auxiliary label information prepared in step S2 (for example, material structure classification labels, atomic placeholder labels) to design an auxiliary prediction task that matches the information (for example, a multi-classification task or a self-supervised learning task). Construct a temporary network (usually containing the nonlinear dimensionality increasing mapping module designed in step S7 and a temporary prediction head adapted to the auxiliary task), and use the auxiliary labels as supervisory signals to train the network, focusing on optimizing the parameters (weights) of the nonlinear dimensionality increasing mapping module. After the training is completed, the parameters learned by the nonlinear dimensionality increasing mapping module are saved for initialization of the main task model in step S10.

[0067] S10: Using the feature subset selected in step S5 or S6 (or the discretized representation if S8 was performed) as input and the target material property values defined in step S1 as supervisory labels, perform end-to-end supervised learning training on the complete deep embedding network model (nonlinear dimensionality increase mapping module + prediction module) constructed in step S7. During training, a loss function suitable for the target task is selected (for example, mean squared error loss for regression tasks). A gradient descent optimization algorithm (such as the Adam optimizer) is used to update the network parameters. If pre-training in step S9 was performed, this step is fine-tuning: first, the nonlinear dimensionality increase mapping module weights saved in step S9 are loaded as initialization, and then training is performed. At this time, different learning rate strategies can be set for the nonlinear dimensionality increase mapping module and the prediction module (usually randomly initialized from scratch) (for example, a lower learning rate for the former and a higher learning rate for the latter). The training process can include data batching, multi-cycle iterations, monitoring performance using a validation set, and applying an early stopping strategy.

[0068] S11: Use the deep embedding network model trained and solidified in step S10 to perform inference prediction. For one or more new material samples that are not included in the training set, first obtain their original input features and apply a feature processing process that is completely consistent with the training data, including performing feature screening in step S5 or S6 (and possible S7 grouping basis judgment), and performing feature discretization in step S8 (if used in training). Then, input the processed features into the trained model, and obtain the predicted values of the target material properties of these new samples through the forward propagation calculation of the model. These predicted values can be used for subsequent material evaluation, screening or design optimization.

[0069] Example 1:

[0070] As an optional embodiment, the intelligent feature processing method of the present invention is used to predict the substitution phase energy and structural changes of Nb-Si alloys. This example is used to illustrate the intelligent feature processing method for material data proposed by the present invention, specifically applied to the Nb-Si alloy system. By feature processing the data obtained by DFT calculation, three target properties are predicted: single-point substitution energy (SSE), double-point substitution energy (DSE), and average bond length change (Δd). The steps are as follows:

[0071] S1 uses first-principles DFT calculations to obtain simulation data for Nb-Si alloys with different compositions and atomic occupancy. The dataset used in this case contains 3528 samples. Each sample contains 40 original input features: 20 of which are intrinsic properties of the central atom (the replaced site), and the other 20 are statistical features related to the local environment surrounding the site, as shown in Table 1. The features shown in Table 1 include both central and environmental categories.

[0072] Table 1 Center environment characteristics and English

[0073] Feature Name English atomic number Atomicnumber Number of cycles Periodic number Atomic weight Atomicweight Effective nuclear charge Charge,nucleareffective(Clementi) density Density Core electron spacing Distance,coreelectron(Schubert)Molar Valence electron spacing Distance,valenceelectron(Schubert)Moment electronegativity Electronegativity Cohesive energy Energy, cohesive Brewer First ionization energy Energyofionization,first Melting enthalpy Enthalpy of melting

[0074]

[0075] S2 directly uses the 40 features defined in S1 as the initial feature set for subsequent processing. SSE (single-site substitution energy), DSE (double-site substitution energies), and Δd (average bond length change) are used as the target properties for final prediction. 23 categories of 2-label data are prepared for the pre-training task in the subsequent step S9. This 23-category labeled data is shown in Table 2.

[0076] Table 2 Various label data

[0077]

[0078]

[0079] S3 independently and concurrently applies 10 different machine learning feature selection algorithms to evaluate the importance of the 40 original input features obtained from S1. These algorithms include: variance selection, Pearson correlation coefficient, mutual information, F regression, VIF (to assess collinearity, score is 1 / VIF), recursive feature elimination (RFE), L1 regularization (Lasso), random forest feature importance, XGBoost feature importance, and information gain.

[0080] For each feature selection algorithm applied in S3, S4 generates initial importance scores for each of the 40 original input features based on its evaluation criteria. These 40 scores generated by each algorithm are then subjected to min-max scaling, mapping all scores to the [0, 1] interval to facilitate cross-algorithm comparison and aggregation.

[0081] For each feature, S5 calculates the arithmetic mean of the normalized scores from all 10 algorithms in S4 to obtain the final comprehensive importance score of the feature. The 40 features are sorted in descending order according to the comprehensive importance score to form the "global screening feature subset".

[0082] S6 directly uses the global screening feature subset of S5 as the subsequent features

[0083] S7 designed and built two deep neural network models for comparison:

[0084] Continuous Lifting Model (CLM): This model uses a multi-layer perceptron (MLP) to receive features as input, consists of several fully connected layers (the hidden layer dimension is set to 128, using the ReLU activation function), and finally connects to an output layer (3 neurons, linear activation) for predicting SSE, DSE, and Δd.

[0085] Discrete Dimensionality Lifting Model (DLM): This model first discretizes the input features as described in S8, and then includes an embedding layer (which maps the bucket index of each feature to a dense vector with the same 128-dimensional dimension as the continuous dimensionality lifting model). After concatenating or aggregating the embedding vectors of all features, it is input into the subsequent fully connected layer (MLP structure, lifted to 128 dimensions) and the final prediction output layer (3 neurons).

[0086] S8 is specific to the bucketed embedding model. Before inputting the features into the network, it applies an equal-frequency bucketing algorithm to the selected continuous features (a subset of features from S5 or S6, or all features from S1), mapping each continuous feature value to one of 30 discrete bucket indices. The MLP model uses the original (continuous) feature values directly.

[0087] S9 performed an optional pretraining step. Using the 23-category, 2-label site information prepared by S2 as auxiliary labels, a multi-label classification task was designed. The embedding modules of the continuous and discrete dimensionality-raising models were pretrained to learn feature representations related to site classification. The effectiveness of pretraining was evaluated using the F1 score of the classification task, and the weights of the pretrained model (primarily the embedding module) were saved. The formula for the F1 score is shown in Formulas 1-3, and the results are shown in Table 3.

[0088] For each label l = {1, ..., L}, first calculate its precision and recall:

[0089]

[0090] Among them, TP l , FP l , FN l They represent the number of true positives, false positives, and false negatives for label l, respectively. Based on this, the F1 score for each label is calculated as follows:

[0091]

[0092] Finally, the F1 scores of all labels are averaged to get the F1 score of the task.

[0093] Table 3 F1 score of each model

[0094] Model F1 score Continuous Dimensionality Model (CLM) 0.783 Discrete Dimensionality Model (DLM) 0.994

[0095] S10 uses all 40 features of S1 as input and outputs SSE, DSE, and Δd as targets. Two training strategies are used to train the MLP and bucket embedding models constructed in S7:

[0096] Training from Scratch (FS): End-to-end training using randomly initialized weights.

[0097] Pre-training-fine-tuning (PF): Load the pre-trained weights saved in S9 to initialize the embedding module (or corresponding layer), and then perform end-to-end training. At this time, a smaller learning rate is set for the embedding module and a larger learning rate is set for the prediction module.

[0098] The training uses mean square error (MSE) as the loss function and Adam as the optimizer, and the training set and test set are divided into training set and test set for model performance evaluation.

[0099] S11 evaluated the prediction performance of all model combinations (model architecture x training strategy) on the test set, with the main evaluation indicators being the root mean square error (RMSE) and the coefficient of determination (R 2 ), and the two formulas are shown in Formula 4-5. The results are shown in Table 4.

[0100]

[0101] Table 4 Evaluation index scores

[0102] SSERMSE DSERMSE ΔdRMSE <![CDATA[SSER 2 ]]> <![CDATA[DSER 2 ]]> <![CDATA[ΔdR 2 ]]> CLM-FS 0.493 0.757 0.221 0.849 0.858 0.513 DLM-FS 0.433 0.757 0.188 0.883 0.858 0.645 CLM-PF 0.701 1.137 0.247 0.694 0.679 0.388 DLM-PF 0.412 0.706 0.194 0.894 0.876 0.624

[0103] The results show that in this embodiment, DLM predicts the three properties best in the pre-training-fine-tuning training mode. In most cases, the prediction accuracy of DLM (lower RMSE, R 2 Higher) outperforms CLM, especially when combined with a pre-training-fine-tuning strategy (for example, DLM-PF performs well on SSE and DSE). The pre-training-fine-tuning strategy significantly improves the performance of DLM, but has little effect on the CLM model in this case, or even slightly degrades it.

[0104] Example 2:

[0105] This example illustrates the intelligent feature processing method for material data proposed in this invention, specifically applied to the Nb-Si alloy system. By performing feature processing on the data obtained from DFT calculations, three target properties are predicted: single-point substitution energy (SSE), double-point substitution energy (DSE), and average bond length change (Δd). This step is essentially the same as in Example 1, with the following differences:

[0106] The top 16 features with the highest comprehensive scores were selected from S5 and S6 to form a "global screening feature subset". As a comparison and supplement, a group screening strategy was implemented. First, the 40 original features were divided into two groups: a central feature group (20) and an environmental feature group (20). Within each feature group, S3 (application of 10 algorithms), S4 (scoring and normalization), and part of the logic of S5 (aggregate scoring and sorting) were repeated independently. The top 8 features with the highest comprehensive scores were selected from each group. The top 8 features selected from the two groups were merged to form a "group screening feature subset" containing 16 features. This subset has similarities and differences with the global subset, with 11 features overlapping.

[0107] In S7, in order to adapt to the feature dimensions after dimensionality reduction, certain dimensional adjustments are made to both CLM and DLM so that the model can process the data after dimensionality reduction.

[0108] In S10, the global screening feature subset (16) obtained in S5 and the group screening feature subset (16) obtained in S6 are used as inputs, and SSE, DSE, and Δd are used as output targets. The same two training strategies are used for training.

[0109] S11 evaluated the prediction performance of all model combinations (feature set x model architecture x training strategy) on the test set, and the main evaluation indicators were root mean square error (RMSE) and coefficient of determination (R 2 ). The prediction performance is shown in Table 5.

[0110] Table 5 Evaluation index scores

[0111] SSERMSE DSERMSE ΔdRMSE <![CDATA[SSER 2 ]]> <![CDATA[DSER 2 ]]> <![CDATA[ΔdR 2 ]]> Global-CLM-FS 0.558 0.9 0.235 0.806 0.799 0.449 Group-CLM-FS 0.559 0.85 0.224 0.805 0.821 0.496 Global-DLM-FS 0.451 0.802 0.204 0.873 0.84 0.582 Group-DLM-FS 0.49 0.832 0.2 0.851 0.828 0.601 Global-CLM-PF 0.697 1.149 0.255 0.697 0.672 0.349 Group-CLM-PF 0.745 1.148 0.25 0.654 0.673 0.376 Global-DLM-PF 0.44 0.78 0.2 0.88 0.849 0.598 Group-DLM-PF 0.479 0.806 0.204 0.857 0.839 0.583

[0112] Using the 16 filtered features (either globally or in groups) shows little performance degradation on DLM (even some indicators on CLM are improved) compared to using all 40 features, and significantly reduces the feature dimension (by 60%), demonstrating the effectiveness of the feature screening method of the present invention.

[0113] Example 3:

[0114] This example illustrates the intelligent feature processing method for material data proposed in this invention, specifically applied to the Nb-Si alloy system. By performing feature processing on data obtained from DFT calculations, three target properties are predicted: single-point substitution energy (SSE), double-point substitution energy (DSE), and average bond length change (Δd). This step is essentially the same as in Example 2, with the following differences:

[0115] The S7 model directly uses the random forest model for property prediction

[0116] No bucketing is required in S8

[0117] No pre-training required in S9

[0118] In S11, global features and filtered features are used for prediction respectively, and the prediction results are shown in Table 6.

[0119] Table 6 Evaluation index scores

[0120] SSERMSE DSERMSE ΔdRMSE <![CDATA[SSER 2 ]]> <![CDATA[DSER 2 ]]> <![CDATA[ΔdR 2 ]]> All-RF 0.427 0.723 0.163 0.886 0.87 0.735 Global-RF 0.383 0.73 0.169 0.909 0.868 0.714 Group-RF 0.417 0.708 0.165 0.892 0.876 0.727

[0121] It can be found that random forest is particularly outstanding in predicting Δd, and feature screening significantly improves the prediction effect of RF. This embodiment successfully demonstrates the intelligent feature processing method proposed by the present invention. By integrating multiple algorithms for feature screening and combining deep embedding networks (especially pre-trained bucket embedding networks) for feature representation learning, it is possible to effectively process the complex feature data of the Nb-Si alloy system and establish a high-precision multi-objective property prediction model, verifying the beneficial effects of the present invention in improving the efficiency and accuracy of material data modeling.

[0122] Example 4:

[0123] Predicting the tensile strength of polymer composites using the intelligent feature processing method of the present invention. This example illustrates the application of the intelligent feature processing method proposed in this invention to another material system: polymer composites. The goal is to predict tensile strength, one of the composite's key mechanical properties, based on its compositional information, matrix and filler properties, and preparation process parameters.

[0124] S1: By integrating public literature reports, internal experimental databases, and relevant material properties manuals, a dataset containing a variety of polymer composite samples was constructed. The dataset covers different polymer matrices (such as polypropylene PP, polyethylene PE, epoxy resin, etc.), different types of fillers (such as glass fiber, carbon nanotubes, talc, etc.), and different filler contents and treatment methods. Each sample contains original input features, such as: basic properties of the polymer matrix (such as molecular weight, melt index, glass transition temperature), filler type, size, aspect ratio, type of surface treatment agent, volume fraction of filler, and key preparation process parameters (such as molding temperature, pressure, shear rate, etc.). Each sample corresponds to a target material property value: experimentally measured tensile strength (unit: MPa). The data was cleaned, missing values were handled (for example, using the mean or median to fill), and categorical features (such as filler type) were numerically encoded (such as One-Hot Encoding).

[0125] S2: Based on the original features of S1, extended features are further calculated or extracted. For example, the interface interaction parameters between the matrix and the filler (based on literature models or empirical formulas), the quantitative index of the dispersion of the filler in the matrix (if obtained by image analysis, etc.), and the combined effect index of different process parameters are calculated. The experimentally measured tensile strength is used as the target (label) data for model training. No auxiliary labels are used for pre-training in this embodiment.

[0126] S3: For the combined feature set generated by S1 and S2 (containing a total of 80 features), at least five different machine learning feature selection algorithms were applied in parallel, including but not limited to: filter-based random forest importance ranking (Permutation Importance), model-based LASSO regression coefficient, statistics-based analysis of variance (ANOVAF-value), mutual information (Mutual Information), and feature importance evaluation built into the gradient boosting machine (such as LightGBM).

[0127] S4: For each of the 80 features, an initial importance score was generated based on each algorithm applied in S3. Each set of scores was Z-score normalized to a mean of 0 and a standard deviation of 1 to eliminate the impact of the range and distribution of scores from different algorithms.

[0128] S5: Calculate the average Z-score of each feature across all algorithms to obtain a comprehensive importance score. Sort the 80 features in descending order based on the comprehensive score, and select the top 25 features to form the feature subset after global screening.

[0129] S6: To simplify the explanation, the group screening strategy is not implemented separately; only the global screening results from S5 are used. However, in actual applications, group screening can be performed based on feature sources, such as matrix features, filler features, and process features.

[0130] S7: We designed a deep embedding network based on an attention mechanism. The network first performs a preliminary linear transformation or passes a small MLP on the 25 filtered input features. It then introduces a self-attention mechanism to learn the interdependencies and weights between different features, generating context-aware feature representations. The output of the attention module is then fed into a subsequent fully connected layer for further nonlinear transformation and dimensionality increase (e.g., mapping to a 64-dimensional embedding space), and finally connected to a prediction module (an MLP with two hidden layers, which ultimately outputs a node predicting the tensile strength).

[0131] S8: Since the network designed in S7 directly processes continuous input and learns interactions through the attention mechanism, the feature discretization step is not used in this embodiment.

[0132] S9: No pre-training step was performed due to the lack of suitable auxiliary labels and the main reliance on the attention mechanism.

[0133] S10: Use the 25 features selected in S5 as input and the tensile strength in S1 as the output target. Perform end-to-end supervised learning training on the deep embedding network based on the attention mechanism constructed in S7. The training uses the mean absolute error (MAE) as the loss function, the AdamW optimizer, and k-fold cross-validation (for example, k = 5) to evaluate the model's generalization performance.

[0134] S11: After training, the model can be used to predict the tensile strength of polymer composites with new components or process parameter combinations. Expected effect: Through the application of the method of the present invention, the core feature combination that is most critical to the tensile strength of polymer composites is first identified through the feature screening steps (S3-S5) of multi-algorithm integration. Subsequently, through the designed deep embedding network (S7) based on the attention mechanism, the complex and nonlinear interactions between these key features (for example, the synergistic effect of filler properties and process parameters) can be effectively captured to generate high-quality feature representations. Compared with traditional linear models or methods that only use simple MLP to process original or simple screening features, it is expected that the model constructed in this embodiment can provide more accurate and robust tensile strength predictions. This demonstrates the potential of the method of the present invention to improve the performance of prediction models through intelligent feature engineering when processing data of complex material systems (such as composite materials with multi-component and multi-scale influencing factors), and is suitable for guiding the optimization of new formulas or processes.

[0135] This example demonstrates that the method can be applied to different materials (polymer composites), different properties (tensile strength), and can be combined with different deep learning architectures (such as attention mechanisms) and feature processing strategies.

[0136] Example 5:

[0137] The intelligent feature processing method of the present invention is used to predict the selectivity of supported metal nanocatalysts. This example aims to illustrate the application of the intelligent feature processing method proposed in the present invention in the field of catalytic science. The specific goal is to predict the product selectivity of supported metal nanocatalysts in specific chemical reactions (for example, selective hydrogenation reactions) based on the composition, structural characteristics and reaction conditions of the supported metal nanocatalysts.

[0138] S1: Constructed by integrating published research papers, patent literature, and possibly in-house high-throughput catalytic testing experimental data in the field of heterogeneous catalysis. The dataset contains a variety of supported metal nanocatalyst samples. Each sample contains the original input features covering:

[0139] Active metal component: metal type (such as Pd, Pt, Ru, etc., or bimetallic combinations such as PdAu, PtNi), metal loading (wt%), average nanoparticle size, size distribution width, morphology descriptor (such as spherical, cubic, rod-shaped, to be coded).

[0140] Carrier information: carrier material type (such as Al2O3, SiO2, CeO2, activated carbon, etc.), specific surface area, pore size, pore volume, surface acidity and alkalinity index.

[0141] Preparation method related parameters: precursor type, reducing agent, reduction temperature, calcination conditions, etc. (need to be classified and coded or key parameters extracted).

[0142] Reaction conditions: reaction temperature, pressure, raw material concentration, solvent type (if any), space velocity or reaction time.

[0143] Each sample corresponds to a target material property value: the selectivity (%) of the primary target product measured under specific reaction conditions. The data was cleaned and standardized, and categorical / textual features (such as metal type, support type, and morphological descriptors) were appropriately coded (e.g., target encoding, label encoding, or dummy variables).

[0144] S2: Based on the original features from S1, extended features were calculated. For example, possible indicators of strong metal-support interaction (SMSI) were calculated (based on the metal, support, and processing conditions), estimates of the geometric exposed surface ratio (based on size and morphology), metal d-band centers (if estimated through simplified models or literature correlation), and descriptors related to the adsorption energies of reactants / products on the support (if theoretical calculation data is available). The selectivity (%) of the target product was used as the target (label) data for model training.

[0145] S3: For the combined feature set generated by S1 and S2 (containing a total of 120 features), at least six different feature selection techniques were applied in parallel, such as: correlation-based filtering (such as Spearman rank correlation coefficient, which is more suitable for nonlinear relationships), tree model-based feature importance (such as ExtraTrees, CatBoost), stability-based selection methods (such as Stability Selection combined with LASSO), mutual information maximization method, and variable projection importance (VIP) scoring based on principal component analysis (PCA) or partial least squares (PLS) commonly used in the field.

[0146] S4: For each of the 120 features, an initial importance score or ranking was generated based on each algorithm applied in S3. Each set of scores was rank-transformed and normalized (e.g., the ranking was converted to a score in the interval [0, 1], with higher rankings giving higher scores) to account for differences in the output form (scores vs. rankings) of the different algorithms and to unify the scale.

[0147] S5: Calculate the weighted average normalized score of each feature across all algorithms (weights can be assigned based on the algorithm's adaptability or stability to catalysis data) to obtain a comprehensive importance score. Sort the 120 features in descending order based on the comprehensive score, and select the top 35 features to form the feature subset after global screening.

[0148] S6: To simplify the explanation, we assume that the global screening results of S5 are mainly used. However, in practice, group screening can be performed based on metal-related characteristics, support-related characteristics, preparation method characteristics, and reaction condition characteristics.

[0149] S7: A deep MLP embedding network with residual connections is designed. The network receives 35 features selected by S5 as input. The embedding module is composed of multiple residual blocks stacked together. Each residual block contains two to three fully connected layers, batch normalization, activation functions (such as GeLU), and skip connections. This design helps to train deeper networks and capture more complex interactions between features. The embedding module ultimately outputs an embedding vector of a fixed dimension (for example, 128 dimensions). The prediction module is a simple MLP that receives a 128-dimensional embedding vector and outputs a node that predicts selectivity (the output value can be constrained to the range of 0-100% by the Sigmoid function, or directly predict an unconstrained value).

[0150] S8 and S9 do not use discretized features and do not perform pre-training and fine-tuning.

[0151] S10: Use the 35 features selected in S5 as input and the target product selectivity in S1 as the output target. Perform end-to-end supervised learning training on the deep embedding network with residual connections constructed in S7. Training uses the modified Huber loss (more robust to outliers) or Beta distribution regression loss (if the selectivity data has a unique distribution) as the loss function. The Adam optimizer is used with a learning rate decay strategy. Model performance is evaluated using either holdout or cross-validation.

[0152] S11: After training, the model can be used to predict the product selectivity of supported nanocatalysts with novel metal components, supports, preparation methods or under different reaction conditions. This embodiment can identify the key feature combination (which may include metal electronic structure, particle geometry, support surface properties and their coupling with reaction conditions) that plays a decisive role in catalytic selectivity from a large number of potential influencing factors through multi-algorithm integrated screening. The designed deep residual embedding network (S7) can effectively learn the highly nonlinear dependencies between these key features and generate an information-rich catalyst "fingerprint" representation. It is expected that the model constructed in this embodiment can more accurately predict catalytic selectivity compared to the traditional descriptor engineering plus shallow model method, especially when exploring new and structurally complex catalyst systems. This proves that the method of the present invention can be applied to complex catalytic material systems, and the modeling capability of the structure-activity relationship is improved through advanced feature processing technology, providing a powerful tool for the rational design of highly selective catalysts.

[0153] The beneficial effects of the present invention are as follows:

[0154] (1) The present invention improves upon the limitations of existing technologies in material data processing: In current data-driven material research and development, feature engineering often relies on manual selection, single dimensionality reduction techniques, or simple linear representations, making it difficult to effectively process the high dimensionality, strong coupling, and nonlinear characteristics of material data. This results in problems such as feature information loss, key information flooding, low quality of machine learning model input, and limited prediction accuracy and generalization capabilities. The present invention proposes an intelligent feature processing method for material data, which systematically integrates multiple machine learning feature screening technologies to obtain robust feature importance assessments, and combines innovative deep embedding neural network architectures to achieve nonlinear dimensionality enhancement and deep representation learning of features. This effectively addresses the one-sidedness of existing methods in feature selection and the shortcomings in representation capabilities, and can provide higher quality and more informative feature inputs for downstream machine learning models.

[0155] (2) The present invention improves the efficiency and accuracy of data-driven material research and development: The present invention combines intelligent feature dimensionality reduction screening with dimensionality increase characterization to more accurately identify key factors affecting material properties and capture complex nonlinear relationships between features. This directly improves the accuracy, robustness and interpretability of machine learning-based material performance prediction models (through feature importance analysis). Compared with using original features or simply processed features, this method enables the model to learn on a smaller, more information-intensive feature subset or in a better representation space, which may reduce the computing resources and time required for model training and improve the model's convergence and generalization capabilities. By improving the key link of material data processing, the present invention helps to accelerate the entire data-driven material research and development process, screen potential candidate materials more quickly, and reduce research and development costs.

[0156] (3) The present invention has broad applicability and scalability: Although the present invention may use a specific material system (such as Nb-Si alloy) as an implementation case, the design principle of the proposed intelligent feature processing method is universal. The method does not depend on a specific material type or specific target properties. In principle, it is applicable to any material system that can obtain structured feature data and target properties through calculation or experiment, such as metal materials, ceramic materials, polymer materials, composite materials, etc., as well as the prediction of various properties such as mechanics, thermal, electrical, and optical. Therefore, the present invention has broad application prospects and good scalability in the fields of materials informatics and computational materials science.

[0157] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0158] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A feature learning method based on dimensionality reduction and dimensionality increase for digital representation of materials, characterized by: include: Obtaining a sample data set of an initial material; the data set includes original input features characterizing the initial material sample and corresponding target material properties; Calculating extended features based on the original input features and generating label data for pre-training and prediction; Applying at least three different feature selection algorithms in parallel to perform importance evaluation on the sample data set to generate an importance score for each of the original input features, and normalizing the importance scores to obtain a set of normalized score vectors in a uniform interval; Aggregating all the normalized score vector sets, calculating the comprehensive importance score of each of the original input features, and selecting a feature subset according to a preset screening rule and the comprehensive importance score; A nonlinear dimensionality-increasing mapping module is constructed to perform a nonlinear transformation on the feature subset after dimensionality reduction through the nonlinear dimensionality-increasing mapping module to generate a final high-dimensional feature representation.

2. The feature learning method based on dimensionality reduction and dimensionality increase for digital representation of materials according to claim 1, characterized in that: Also includes: A prediction module is constructed, and the high-dimensional feature representation is input into the prediction module to obtain the predicted target property.

3. The feature learning method based on dimensionality reduction and dimensionality increase for digital representation of materials according to claim 2, characterized in that: Also includes: Based on the feature subset and the target property value, end-to-end training or fine-tuning is performed on a deep neural network composed of a nonlinear dimensionality-increasing mapping module embedded with the physical information and the prediction module to obtain a trained target property prediction model; The input features of the new sample are processed and input into the target property prediction model to obtain the predicted value of the target property.

4. The feature learning method based on dimensionality reduction and dimensionality increase for digital representation of materials according to claim 3, characterized in that: Before building the prediction module, also include: Designing an auxiliary prediction task embedded with physical information matching the label data to construct a temporary network; the temporary network includes a nonlinear dimensionality-increasing mapping module and a temporary prediction head adapted to the auxiliary task; Using target property-oriented labeled data as a supervisory signal to train the temporary network to optimize parameters of the nonlinear dimensionality-increasing mapping module; After the training is completed, the parameters learned by the nonlinear dimensionality-increasing mapping module are saved to obtain a pre-trained nonlinear dimensionality-increasing mapping module.

5. The feature learning method based on dimensionality reduction and dimensionality increase for digital representation of materials according to claim 1, characterized in that: The original input features include the inherent attribute features of the central atom and the statistical features related to the local environment around the site where the central atom is located.

6. The feature learning method based on dimensionality reduction and dimensionality increase for digital representation of materials according to claim 1, characterized in that: The extended features are obtained by calculating or extracting a set of initial features that may contain redundant information using a preset automatic feature generation tool.

7. The feature learning method based on dimensionality reduction and dimensionality increase for digital representation of materials according to claim 1, characterized in that: A feature subset is selected based on the preset screening rules and the comprehensive importance score, including: Sorting the original input features in descending order according to the calculated comprehensive importance score to obtain a sorted list; Selecting the final feature subset from the sorted list according to predefined screening rules; The preset screening rule includes any one of the first rule and the second rule; The steps of the first rule include: Select the features ranked in the top N positions in the sorted list; Select the features whose comprehensive importance scores are higher than a preset threshold; or select all features in the sorted list before the score curve has a descending inflection point, to obtain the feature subset; The second rule includes Based on prior knowledge or feature attributes of the material field, each of the original input features is divided into at least two mutually exclusive or overlapping feature groups; Within each of the feature groups, multiple algorithms are independently applied to perform scoring, normalization, aggregation, and sorting, and the preferred features of each group are screened according to preset intra-group rules; The preferred features screened out from all the feature groups are merged to form a final feature subset.

8. The feature learning method based on dimensionality reduction and dimensionality increase for digital representation of materials according to claim 1, characterized in that: The nonlinear dimensionality-raising mapping module is composed of a multi-layer perceptron; or when processing discretized features, the nonlinear dimensionality-raising mapping module includes one or more embedding layers.

9. The feature learning method based on dimensionality reduction and dimensionality increase for digital representation of materials according to claim 1, characterized in that: When dealing with discretized features, this also includes: A preselected bucketing algorithm is applied to the continuous features in the feature subset to perform feature processing to obtain a processed feature subset.

10. Application of the feature learning method based on dimensionality reduction and dimensionality increase for digital characterization of materials as claimed in any one of claims 1 to 9 in machine learning prediction of material properties.

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