Performance prediction and reverse design method and device for multi-component glass material

Abstract

The invention discloses a performance prediction and reverse design method and device for a multi-component glass material, and the method comprises the steps: obtaining a component vector of a multi-component glass sample and corresponding physical performance data, carrying out the preprocessing, and dividing the multi-component glass sample into a training set and a test set; determining the structure and training hyper-parameters of the neural network by adopting Bayesian optimization, performing global optimization on the connection weight and / or threshold of the neural network by adopting a genetic algorithm to obtain initialization parameters, and training the neural network based on the training set and the test set to obtain a prediction model; generating a candidate formula according to target physical performance given by a user and a component index set allowed to be allocated; predicting the physical performance corresponding to the candidate formula by using the prediction model, and calculating the target deviation of the candidate formula; and selecting a plurality of optimal formulas as reverse design results according to the target deviation and the comprehensive score of the similarity of the candidate formulas and the samples in the training set in the component space. The method has the advantages of high prediction accuracy, high inverse design efficiency and the like.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of material intelligent design, and particularly relates to a performance prediction and reverse design method and device for multi-component glass materials. BACKGROUND

[0002] Fluoride glass is an amorphous material composed of fluoro-beryllate, fluoro-aluminate and fluoro-zirconate, etc. Due to its unique optical properties, fluoride glass has broad prospects in the fields of infrared optical fiber, window material, multi-spectral instrument, etc.

[0003] The light transmission range of fluoride glass covers ultraviolet to mid-infrared band (200 nm-10 μm), and it has low phonon energy and low nonlinear refractive index, making it an ideal matrix material for mid-infrared optical fiber. Especially in the 3-5 μm atmospheric transmission window band, fluoride optical fiber (such as ZBLAN optical fiber) can realize low-loss laser transmission, and has been used in mid-infrared laser, super-continuum light source, etc.

[0004] ‌The wide light transmission window and high infrared transmittance of fluoride glass make it suitable for manufacturing infrared optical windows for infrared imaging, thermal imaging systems, etc. For example, the component design of fluoro-zirconate glass can enhance the thermal stability and chemical stability, and is suitable for large-size infrared window materials.‌ Such materials can effectively transmit mid-infrared radiation, meeting the needs of high-precision sensing and detection.

[0005] In multi-spectral instruments (such as spectrometers, sensors), the wide-band light transmission characteristics of fluoride glass help to realize multi-wavelength detection at the same time.‌ For example, fluoride glass matrix can be used as a gain material for mid-infrared lasers to generate fluorescence at key wavelengths such as 3.5 μm, expanding the application of instruments in the fields of gas monitoring, biomedical imaging, etc.‌ Therefore, there is an urgent need for an efficient method and formula system for developing multi-component fluoride glass formula. However, traditional development mainly relies on experience and repeated trial and error, which is time-consuming and costly, and it is difficult to quickly provide an implementable candidate scheme under the coexistence of multiple targets and multiple constraints.

[0006] Although the existing design methods using statistical regression or neural networks can fit the mapping from components to performance to some extent, there are generally the following problems: the hyperparameters and initial weights are sensitive, manual parameter tuning is time-consuming and easy to fall into local optimum; overfitting is significant under the condition of few samples, and the training and verification / testing performances are inconsistent; the data distribution drift and noise robustness are insufficient, and the extrapolation ability is limited; the feasible region and similarity constraints are lacking in the reverse design link, and only sorting by target deviation can easily obtain a formula far from the training domain, and the preparation and success rate are difficult to guarantee.

[0007] Furthermore, the reverse engineering problem of glass formulations is inherently ambiguous and ill-posed: the same target property often corresponds to multiple formulation combinations. Without constraints and penalties based on historical sample distribution and process feasibility domain, the resulting solutions are difficult to reproduce in actual preparation.

[0008] Based on the above pain points, there is an urgent need for a comprehensive method and system that combines automated hyperparameter optimization, global weight search, regularization adaptation, data augmentation robustness, and similarity weighting for reverse selection, in order to improve prediction accuracy and stability, and significantly improve the feasibility and first-time hit rate of candidate formulations in the reverse design stage. Summary of the Invention

[0009] This invention provides a method and apparatus for performance prediction and reverse design of multi-component glass materials. This invention significantly improves prediction accuracy and stability, and significantly enhances the feasibility and first-time success rate of candidate formulations in the reverse design stage.

[0010] The technical solution of the present invention is as follows: A method for performance prediction and reverse design of multi-component glass materials includes the following steps: (1) Obtain the component vectors and corresponding physical performance data of multi-component glass samples, preprocess them, and divide them into training and test sets; (2) Construct a neural network, use Bayesian optimization to determine the structure and training hyperparameters of the neural network, and use a genetic algorithm to globally optimize the connection weights and / or thresholds of the neural network to obtain the initial parameters; (3) The feedforward neural network is configured using the obtained training hyperparameters and initialization parameters, and the neural network is trained based on the training set and the test set to obtain the prediction model; (4) Based on the set of allowed ingredient indices given by the user, randomly generate candidate recipes that satisfy the feasible domain constraint; The prediction model is used to predict the physical properties of the candidate formulations, and the target deviation of the candidate formulations is calculated based on the target physical properties given by the user and the predicted physical properties. Calculate the similarity between candidate formulations and samples in the training set in the component space; The target deviation and the similarity are weighted and fused to obtain a comprehensive score. Several preferred formulations are selected as reverse design results based on the comprehensive score.

[0011] In step (1), the component vector is a multi-component formulation ratio vector with dimension D, which is used as input; the physical property data is density and / or refractive index, which is used as output. Stack the component vectors of the M samples column-wise into a matrix. Stack the physical performance data of M samples column-wise into a matrix. .

[0012] Preferably, in step (1), the preprocessing includes data cleaning and consistency processing, and normalization processing.

[0013] The data cleaning and standardization processes are performed in the following order: (a1) Missing component handling: If a component is missing, it is filled with 0 or a robust statistic based on the same batch of data; if a physical property is missing, the corresponding sample is not included in supervised modeling. (a2) Unit uniformity: Physical properties are corrected according to uniform dimensions; unit transformations retain an accuracy of no less than three decimal places; (a3) Outlier detection: If a single point deviates significantly but is within the physical allowable range, it is marked as a "weak outlier" and its training weight is reduced; if it obviously violates the physical rationality of the material, it is marked as a "strong outlier" and the corresponding sample is removed. (a4) Sample deduplication: Samples with completely identical components and physical performance differences below a set threshold are merged into one sample; (a5) Consistency of summation: enforced for each component vector ,in For the first Percentage of each component.

[0014] The normalization process includes: For matrix and Perform linear normalization separately: ; in, This represents the normalized value; Represents the original eigenvalues; This represents the minimum value of a feature in the training set; This represents the maximum value of the feature in the training set; Indicates the upper and lower bounds of the normalization interval; save and As a normalized configuration.

[0015] In the subsequent inference phase, the same mapping is applied to the input, and denormalization is performed on the output to restore the physical magnitude.

[0016] Preferably, in step (1), the preprocessing further includes data augmentation; the data augmentation includes: (b1) Select two samples randomly from the training set and perform linear interpolation with random weights to obtain candidate samples; (b2) Apply Gaussian noise of a first amplitude to the input side of the candidate sample and Gaussian noise of a second amplitude to the output side of the candidate sample, wherein the first amplitude is greater than the second amplitude, to obtain an enhanced sample; (b3) Enhanced samples must simultaneously satisfy: a) each component is non-negative, b) the sum of components is consistent with the original sample, c) the normalization domain is relaxed, and d) it does not violate known process incompatibilities rules; qualified enhanced samples are incorporated into the training set, and the number of enhanced samples is controlled to be 10%-150% of the number of original samples.

[0017] Furthermore, step (b1) includes: Two samples were randomly selected from the training set. With random weights Candidate samples are obtained through linear interpolation: ; in, This represents the generated interpolation candidate samples; Indicates from the interval Random numbers obtained through uniform sampling; This represents the component vectors of the two original training samples; This represents the property vectors of two original training samples.

[0018] Furthermore, step (b2) includes: Input side of candidate samples Superimposed Gaussian noise of the first amplitude on the output side of the candidate sample By superimposing a second-amplitude Gaussian noise, an enhanced sample is obtained. ; The first amplitude of Gaussian noise is zero-mean Gaussian noise with a standard deviation of 0.05 to 0.20; The second amplitude of Gaussian noise is zero-mean Gaussian noise with a standard deviation of 0.005 to 0.02.

[0019] In step (b3), relaxing the normalization domain boundary means relaxing the normalization domain boundary to [-0.2, 1.2].

[0020] Interpolation and perturbation data augmentation and validity screening are more robust to noise and slight distribution drift.

[0021] In step (2), the constructed neural network is a three-layer feedforward regression network consisting of two hidden layers and one output layer; the input dimension of the neural network is... D The number of neurons in the first and second hidden layers are respectively and The output dimension is 2.

[0022] Preferably, the two hidden layers employ hyperbolic tangent activation to enhance nonlinear representation, and the output layer employs linear activation to adapt to continuous real-valued output.

[0023] Bayesian optimization was used to determine the structure and training hyperparameters of the neural network, with the mean square error of the validation set samples as the optimization objective. ; in, To determine the mean squared error of the validation set samples; Indicates the number of samples in the validation set; Indicates the first The actual output of each validation sample; Indicates the first The model's predicted output for each validation sample; Represents the Euclidean norm; the optimization process is to find the norm that makes the Euclidean norm... The smallest combination of hyperparameters.

[0024] In a further preferred embodiment, in step (2), the search space for Bayesian optimization includes at least: the number of neurons in the first hidden layer, the number of neurons in the second hidden layer, the learning rate, and the number of training rounds, with the optimization objective being the minimization of the prediction error.

[0025] Further optimized, the specific search range for Bayesian optimization is: 10–100 neurons in the first hidden layer, 10–50 neurons in the second hidden layer, and a learning rate of 1×10⁻⁶. -4 ~1×10 -1 The number of training rounds is 50 to 500.

[0026] In a further preferred embodiment, in step (2), the genetic algorithm uses real number encoding, with the training / verification error as the fitness function, and generates offspring through selection, crossover and mutation to determine the initial weights and / or thresholds of the neural network.

[0027] In a further preferred embodiment, during the mutation operation, a subtle, directional perturbation is applied to the random gene, and the mutation intensity is set as a function that decreases with the number of generations: ; in, for Random numbers sampled uniformly from the top. For the current algebra, For the largest algebra, This is the variation intensity factor.

[0028] Preferably, in step (3), the training uses a gradient optimization algorithm of momentum or Gauss-Newton type, and sets the "upper limit of the number of rounds in the validation set that have not been improved" as the early stopping threshold.

[0029] Preferably, in step (3), training the neural network includes: introducing an L2 regularization term under mean squared error loss, and adaptively adjusting the regularization strength according to the relationship between the training error and the validation error, and training until the model converges.

[0030] Furthermore, the loss function is based on the mean squared error (MSE), with a weight decay term added: ; in, Indicates the number of training samples; They represent the first The actual output and predicted output of each training sample; Represents the coefficient of the L2 regularization term; Denotes the Frobenius norm. Indicates the first Layer weight matrix.

[0031] Furthermore, the adaptive adjustment of regularization strength includes: increasing the regularization strength when the training error decreases while the validation error increases; and decreasing the regularization strength when both the training error and the validation error decrease simultaneously, until the preset convergence or early stopping conditions are met.

[0032] Preferably, after obtaining the predictive model, the method further includes an evaluation and diagnostic visualization step, including: outputting error indices of density and refractive index on the test set, and generating a predictive-actual control and residual distribution for diagnosis; the diagnostic visualization includes: (a) Plot the predicted and actual values ​​of density and refractive index as scatter plots and overlay the identity lines; (b) Plot the residual histogram and fit it to a normal distribution; (c) Output the mean absolute error and mean square error.

[0033] Preferably, the diagnostic visualization further includes feature-directed influence visualization: applying a small positive perturbation to a single feature in the normalized input space, calculating the average change in density and refractive index to obtain and visualize the directional influence of each feature.

[0034] The visualization of diagnostic features, such as residual distribution and directional influence of features, enhances interpretability and makes the entire process of modeling, diagnosis, selection, and export engineering-friendly and accessible.

[0035] In step (4), the number of candidate formulations generated is 100 to 100,000; preferably 5,000 to 10,000, in order to balance computational cost and coverage.

[0036] In step (4), candidate formulations that satisfy the feasible region constraint are randomly generated based on the set of allowed ingredient indices provided by the user, including: (4-1i) Based on the set of allowed ingredient indices provided by the user. K ,exist Random sampling of nonnegative vectors in dimensional space and normalization ; (4-1ii) will Embedding length is D vector ,in ; Vectors that satisfy engineering constraints Add to the candidate pool; (4-1iii) to The normalization configuration in step (1) is normalized to obtain .

[0037] The engineering constraints include upper and lower limits for single components, prohibited pairings, compatibility rules, and upper limits for total impurities.

[0038] Furthermore, in step (4), the physical properties corresponding to the candidate formulation are predicted using the aforementioned prediction model, and the target deviation of the candidate formulation is calculated, including: (4-2i) will Input the aforementioned prediction model to obtain Then, it is reverted to the predicted value of physical properties. ; (4-2ii) Calculate the target deviation of the candidate formulation based on the target physical properties and predicted physical properties given by the user.

[0039] Furthermore, in step (4), the similarity between the candidate formulation and the samples in the training set in the component space is calculated, including: calculating the distance between the candidate formulation and the samples in the training set in the component space, and taking the minimum value as the similarity of the candidate formulation. : ; in, This represents the component vector of the candidate formulation. Indicates the first training set The component vector of each sample, This represents the Euclidean distance.

[0040] Furthermore, in step (4), the comprehensive score includes a density single-objective score Score1, a refractive index single-objective score Score2, and a dual-objective score Score3: ; ; ; in, , where is the weighting coefficient; Indicates the predicted density; Indicates user target density; Indicates the predicted density; This indicates the user's target density.

[0041] Sort all candidate recipes in ascending order of score and output the Top-k as the preferred recipes.

[0042] Preferably, the method of the present invention further includes user interaction: providing a graphical user interface for receiving a set of target density, target refractive index and composition index, and outputting a preferred formulation, predicted physical properties and the index of the closest training sample.

[0043] Based on the same inventive concept, this invention also provides a performance prediction and reverse design system for multi-component glass materials, comprising: The data acquisition and processing module obtains the composition vectors and corresponding physical performance data of multi-component glass samples, performs preprocessing, and divides them into training and testing sets. The model building module constructs a neural network, uses Bayesian optimization to determine the structure and training hyperparameters of the neural network, and uses a genetic algorithm to globally optimize the connection weights and / or thresholds of the neural network to obtain the initial parameters. The model training module uses the obtained training hyperparameters and initialization parameters to configure the neural network, and trains the neural network based on the training set and test set to obtain the prediction model; The reverse design module randomly generates candidate formulations that satisfy the feasible region constraint based on the user-provided set of allowed component indices; it uses the prediction model to predict the physical properties corresponding to the candidate formulations, and calculates the target deviation of the candidate formulations based on the user-provided target physical properties and the predicted physical properties; it calculates the similarity between the candidate formulations and the samples in the training set in the component space; it weights and fuses the target deviation and the similarity to obtain a comprehensive score, and selects several preferred formulations as the reverse design results based on the comprehensive score.

[0044] Preferably, the device of the present invention further includes a user interaction module: providing a graphical user interface for receiving a set of target density, target refractive index and composition index, and outputting a preferred formulation, predicted physical properties and the index of the closest training sample.

[0045] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention uses a feedforward neural network as the core predictor, combined with Bayesian optimization to automate the search for network structure and training hyperparameters, and employs a genetic algorithm to globally optimize network weights and thresholds (and optional structural elements). During the training phase, an adaptive adjustment mechanism with L2 regularization and early stopping control are introduced to suppress overfitting. In the design phase, a comprehensive scoring criterion based on "target bias + training domain similarity" is constructed to achieve target-oriented reverse engineering of the formulation. Simultaneously, it provides visualization of the directional influence of features and a graphical user interface, realizing an end-to-end closed loop from data preparation, modeling, diagnosis to component design and derivation.

[0046] This invention significantly reduces the sensitivity to initial values ​​and parameter tuning through a multi-level optimization process, suppressing overfitting, improving convergence, and enhancing generalization. A comprehensive evaluation criterion is introduced into the reverse design process, balancing performance achievement with consistency with historical samples, significantly improving fabrication feasibility and first-time success rate. Candidate formulation generation and similarity calculation are vectorized and employ a two-stage screening process to balance accuracy and efficiency. The solution naturally supports multiple objectives and constraints such as process / incompatible materials, is easily transferable to other glass and multi-component material systems, and exhibits good synergy with experimental procedures, risk warnings, and full traceability. It is independent of specific languages ​​or libraries, facilitating integration with continuous optimization strategies such as active learning and ensemble learning. In industrial applications, it reduces trial and error, shortens development cycles, and balances cost and environmental goals, demonstrating significant technological advancement and broad applicability.

[0047] This invention has the advantages of high prediction accuracy, strong reverse design efficiency, and user-friendly interface, and has broad application prospects in fields such as optical material design and functional glass development. Attached Figure Description

[0048] Figure 1 This is the overall flowchart of the glass performance prediction method in Example 1; Figure 2 A flowchart illustrating the data augmentation process; Figure 3 This is a schematic diagram illustrating the construction and training process of a BP neural network. Figure 4 A schematic diagram of the Bayesian optimization process for model hyperparameters; Figure 5 This is a schematic diagram of the dynamic L2 regularization training process; Figure 6 This is a schematic diagram of the reverse design process and comprehensive scoring for Example 2. Detailed Implementation

[0049] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be noted that the embodiments described below are intended to facilitate the understanding of the present invention and do not limit it in any way.

[0050] Example 1: Prediction of Glass Properties like Figure 1 As shown, the glass performance prediction method includes the following steps: 1. Data organization and retrieval (1-1) Data Source and Shape: Samples are stored in a spreadsheet, one sample per row. The data source consists of two parts: ① Input is the component data of each sample (including multi-component formulation ratio vector, dimension denoted as...). D (53 in the example); ② The output is the physical property data corresponding to the sample (including two physical property indicators, namely density). p With refractive index n ), merged into 2× M The matrix, where M This represents the number of sample records (816 in this example).

[0051] (1-2) After reading, stack the component data into a matrix by column. The physical property data are stacked into a matrix by columns. To avoid row / column misalignment, each column feature is assigned a uniform field name during the reading phase, and dimension consistency is checked: if a column is missing, misaligned, or empty, it is immediately recorded and the process is rejected from proceeding to the next step.

[0052] 2. Data cleaning and consistency (2-1) The cleaning process shall be carried out in the following order: (1) Missing component handling: If a component is missing, it is filled with 0 or a robust statistic (median / quantile) based on the same batch of data; if a property is missing, the sample will not be included in supervised modeling unless it is used for structured semi-supervised training.

[0053] (2) Unit uniformity: Density and refractive index are measured in a uniform dimension (e.g., g·cm). -3 Dimensionless correction; unit transformation retains an accuracy of no less than three decimal places.

[0054] (3) Outlier detection: Perform 3σ and IQR double tests on each feature dimension; if a single point deviates significantly but is within the physical allowable range, mark it as “weak outlier” and reduce its training weight; if it obviously violates the physical rationality of the material, mark it as “strong outlier” and remove it.

[0055] (4) Sample deduplication: Samples with completely identical components and physical property differences below the set threshold are merged into one and the source index is recorded for traceability.

[0056] (5) Consistency of summation: enforced for each component vector ,in For the first The percentage of each component is used to ensure the consistency of the physical meaning of the formulation. If the sum of the component vectors deviates from 100%, it is linearly scaled according to the relative proportion of each component to meet the consistency requirements, and the adjustment range is recorded.

[0057] (2-2) Unified Normalization and Invertible Mapping To improve numerical stability, the matrix is... and Perform linear normalization separately: ; in, This represents the normalized value. Represents the original feature values. This represents the minimum value of the feature in the training set. This represents the maximum value of the feature in the training set. Indicates the upper and lower bounds of the normalized interval (0 and 1 in this example), and saves... and As a normalization configuration, the same mapping is applied to the input in subsequent inference phases, and denormalization is performed on the output to restore the physical magnitude.

[0058] 3. Data Partitioning: The samples are randomly divided into training, validation, and test sets in an 80 / 10 / 10 ratio. The validation set is used only for model selection and early stopping, while the test set is used only for final generalization evaluation. If the samples have batch or time dependencies, a stratified batch hold-out method is used to ensure that the test set comes from unseen batches, avoiding information leakage.

[0059] 4. Data augmentation (optional, to improve robustness) like Figure 2 As shown, data augmentation includes the following steps: (4-1) Interpolation generation: Randomly select two samples from the training set With random weights Candidates were obtained through linear interpolation: ; in, This represents the generated interpolation candidate samples. Indicates from the interval Uniformly sampled random numbers, This represents the component vector and property vector of the original training sample.

[0060] (4-2) Abnormal amplitude disturbance: on the input side Superimposed with a relatively large small disturbance (in this example, zero-mean Gaussian noise with a standard deviation of 0.05–0.20), on the output side... By superimposing a small perturbation (in this example, zero-mean Gaussian noise with a standard deviation of 0.005–0.02) on the sample, an enhanced sample is obtained. .

[0061] (4-3) Validity screening: Enhanced samples must simultaneously meet the following conditions: a) Each component is non-negative; b) The sum of components is consistent with the original sample (in the example, the sum is 100% ± tolerance); c) The normalization domain boundary is relaxed (in the example, it is within [-0.2, 1.2]); d) It does not violate known process incompatibilities. Only qualified samples are included in the training set, and the actual number of valid samples added is counted to evaluate the enhancement quality.

[0062] (4-4) Augmentation ratio: The number of augmented samples should not be much larger than the original training samples, so as not to change the true distribution; empirically, it should be adjusted within 10%-150% of the original samples.

[0063] The construction and training process of a BP neural network is as follows: Figure 3 As shown, it includes the following steps: 5. Network Structure and Parameterization (5-1) Structure and Topology: Establish a three-layer feedforward regression network with two hidden layers and one output layer. Let the input dimension be... D The number of neurons in the first and second hidden layers are respectively and The output dimension is 2.

[0064] (5-2) Activation configuration: The two hidden layers use hyperbolic tangent activation (S-shaped or hyperbolic S-shaped activation function) to enhance nonlinear expression; the output layer uses linear activation to adapt to continuous real-valued output.

[0065] (5-3) Forward mapping: For any input sample The network calculation process is as follows: ; ; ; in, is the hidden layer nonlinear function (tansig in the example); This represents the weight matrix from the input layer to the first hidden layer, from the first hidden layer to the second hidden layer, and from the second hidden layer to the output layer. This represents the corresponding bias vector; This indicates the activation output of two hidden layers. This represents the final predicted physical property output vector.

[0066] (5-4) Training and Loss Function: A second-order approximation training function is used (Levenberg–Marquardt algorithm in the example), with mean squared error (MSE) as the main loss, which can be superimposed. Weight decay.

[0067] (5-5) Parameter initialization: Trigger the library's default layer / weight initialization before the first training to ensure that the hidden layer activation is not in the initial saturation region; then uniformly write the network size and training control terms such as iteration rounds selected in the hyperparameter optimization stage. If the learning rate field is used, its effect is only effective when the corresponding training function supports it (in the example, the damping / step size parameter is dominant).

[0068] 6. Global Initialization Based on Genetic Algorithm To reduce sensitivity to initial values ​​and the risk of getting trapped in local minima, an evolutionary global search is introduced before the formal long-term training to directly find a better starting point in the weight / threshold space. This stage is only for initialization and does not change the subsequent supervised training and early stopping / regularization process. The complete steps are as follows: (6-1) Chromosome coding (1) Expansion order: Expand by layer and block, and by column main order, as follows: ; ; ; (2) Boundary constraints: Set symmetric numerical boundaries for each gene (weight / threshold). This is to avoid hidden layer saturation or numerical explosion caused by excessively large initial values.

[0069] (3) Feasibility determination: Set a determination function to check whether the chromosome has crossed the boundary gene by gene; individuals that have crossed the boundary are handled by boundary pruning or resampling replacement strategy to ensure that the evolutionary process always evolves within the feasible domain.

[0070] (6-2) First generation and fitness (1) Initial generation: Within the above boundaries, each gene is independently and uniformly sampled to form an initial population of a given size.

[0071] (2) Fitness measurement: Decoding candidate chromosomes back to network parameters Reconstructing according to the chromosome coding order, performing short-range training on a unified training / validation partition, and calculating the supervision error as the fitness.

[0072] (6-3) Dual-objective consistent scoring: If both density and refractive index are used as objectives, the fitness is the weighted sum and / or vector norm of their errors in the normalized domain. Single-target tolerance: When only density (or refractive index) labels are available, the error term of the other target is ignored, and only the error of the valid target is scored, so that scenarios with incomplete data can still participate in the initial optimization.

[0073] (6-4) Reciprocal selection idea: Based on the principle of "the smaller the error, the higher the fitness", in order to avoid division by zero, the selection probability is constructed by "the bounded reciprocal of the error" to ensure that the better individuals have an advantage in selection without excessive monopolization.

[0074] (6-5) Selection, Crossover and Mutation Individual selection: A tournament or roulette wheel method is used to extract parent indices based on fitness probability, ensuring that the best are more likely to be selected, while retaining a certain degree of diversity.

[0075] Crossover operation: Single-point or multi-point crossover is performed at the chromosome scale, that is, the segments of the parent are exchanged at random positions to obtain two offspring; a feasibility check is performed immediately after crossover, and if it is not qualified, it is rolled back or crossover is performed again.

[0076] Mutation operation: Apply a directional, subtle perturbation to a random gene, with the mutation strength set as a function that decreases with generation: ; in, for Random numbers sampled uniformly from the top. For the current algebra, For the largest algebra, The mutation intensity factor gradually decreases with each iteration, resulting in a large exploration range in the early stages and a tendency towards convergence and stability in the later stages. This design ensures broad exploration in the early stages and stable convergence in the later stages. A feasibility check is performed after each mutation.

[0077] (6-6) Iteration and Termination Short-range retraining: Decode the offspring, train it briefly, evaluate it, and update its fitness. Convergence criterion: Termination occurs when the maximum number of generations is reached or when the overall improvement is insufficient for several consecutive generations; Optimal Extraction: Output the globally optimal chromosome and decode it as... , which serve as the initial weights and thresholds for subsequent long-term supervised training.

[0078] Connection: The parameters obtained from global initialization are directly loaded into the network, and then the regularized training and early stopping process begins.

[0079] 7. Hyperparameter Bayesian optimization The hyperparameter Bayesian optimization process of the model is as follows: Figure 4 As shown, it includes the following steps: Objective function: using the average sample value of the validation set Error is the optimization objective: ; in, Indicates the number of samples in the validation set. Indicates the first The actual output of a validation sample This represents the model's predicted output under the same input. Let represent the Euclidean norm. The optimization process is to find the combination of hyperparameters that minimizes this loss.

[0080] Search space: includes key hyperparameters such as the number of neurons in the two hidden layers, learning rate, and maximum number of training epochs; the learning rate is modeled using a logarithmic scale; the hidden layer size is taken as an integer domain.

[0081] Agent and Acquisition: Construct a Gaussian process agent and use acquisition strategies such as "Expected Improvement (EI)" to dynamically balance exploring new areas and mining prime areas. The number of evaluations is recommended to be 30-50 to balance search sufficiency and time cost.

[0082] Output: Produces the optimal combination of structure and training strategy (in the example, it is...) The optimal number of neurons in the first hidden layer. The optimal number of neurons in the second hidden layer. Optimal learning rate The optimal training rounds are determined and fixed as the subsequent modeling configuration.

[0083] 8. Regularized training and adaptive weight decay, such as Figure 5 As shown, it includes the following steps: Loss function: Based on mean squared error (MSE), with added weight decay terms: ; in, Represents the number of training samples. Indicates the first The actual output and predicted output of each sample Represents the coefficient of the L2 regularization term. The Frobenius norm is used to measure the magnitude of the weights. Indicates the first Layer weight matrix. The second term is used to suppress excessively large weights and reduce the risk of overfitting.

[0084] Adaptive rules: to train for optimal error Verification of optimal error Based on the relative change, dynamically adjust :like Decline Increase (overfitting occurs), amplify If both decrease simultaneously, the decrease will be slight. After each adjustment, a small round of retraining is performed, and the validation error is compared and a snapshot of the optimal validation model is retained.

[0085] Optimizer and early stopping: The Levenberg-Marquardt algorithm is adopted; the upper limit of the number of unimproved rounds in the validation set is set as the early stopping threshold to avoid excessively long training and oscillations.

[0086] 9. Visualization of Test Evaluation and Diagnosis Inference and Denormalization: After transforming the test set input according to the same normalization configuration, forward inference is performed to obtain... Then, return to the physical scale.

[0087] Evaluation metrics: Calculate the mean absolute error (MAE) and mean squared error (MSE) separately; additional metrics may be required. Correlation coefficient.

[0088] Scatter Consistency Plot: Draws a scatter plot comparing the actual and predicted values ​​during training / validation / testing, and overlays them. Identifier lines facilitate observation of the overall fit and deviation bands.

[0089] Residual distribution and fitting: A wider bin is used for the density residual (0.01 in the example), and a narrower bin is used for the refractive index residual (0.001 in the example). A normal fitting curve is then superimposed to observe the center offset and tail thickness, and to locate the source of systematic error.

[0090] Training logs: Includes optimal hyperparameters, learning rate, number of iterations, Adjustments to the trajectory, convergence curve, and time overhead are persistently saved along with the model to support reproducibility experiments and audit trails.

[0091] Example 2: Reverse formulation design like Figure 6 As shown, reverse engineering of recipes includes the following steps: 1. Task Definition and Input Given target physical properties (Can be single-target or dual-target) and a set of glass composition indices that can be adjusted. K (in the example) ).

[0092] Then select the prediction target; enter the target value; enter the set. K (This represents the set of ingredient indices that the user specifies as allowed to be mixed, i.e., which ingredients can be freely allocated in proportion among all glass components); Set the number of candidates (10,000 candidate formulations are generated in this instance) and the scoring weight.

[0093] 2. Candidate Generation and Feasible Region Constraints Non-negativity is consistent with summation: in Random sampling of nonnegative vectors in dimensional space ,vector That is, the component proportion vector of the generated candidate formulations within the set K, and normalized to make To obtain more uniform combinatorial diversity, Dirichlet distribution sampling was used.

[0094] Full-dimensional mapping: Embedding length is D (in the example) D The vector with =53) ,in ( for The complement represents components that cannot be mixed or remain fixed.

[0095] Engineering constraint stacking: Supports the following feasible domain restrictions: upper and lower limits for single components; forbidden pairings; compatibility rules; upper limit for total impurities, etc.

[0096] Candidates that do not meet the constraints are directly eliminated and supplemented to make the final candidate pool reach the target size.

[0097] 3. Unified Normalization and Forward Forecasting Normalization: for Applying the same normalization configuration as in Example 1, we obtain .

[0098] Prediction and Inverse Unity: The optimal verification model obtained from Example 1 is used to perform forward computation to obtain... Then return to one .

[0099] 4. Similarity Calculation To reduce the risk of extrapolation, for each candidate, the distance between it and all historical training samples in the original component space is calculated, and the minimum value is taken as the "proximity" metric for that candidate. ; in, This represents the component vector of a candidate formulation. Indicates the first training set The component vector of each sample, This represents the Euclidean distance. This distance reflects how closely the candidate formulation matches the training data; the smaller the distance, the closer it is to the historical experience region, and the higher its prefabrication potential.

[0100] 5. Comprehensive scoring and ranking for selection of the best. Single target density: ; in, Indicates the predicted density. Indicates user target density, This represents the weighting coefficient.

[0101] Single-object refractive index: ; in, Indicates the predicted density. Indicates user target density, Indicates the weighting coefficients. Bi-objective: ; in, This represents the weighting coefficient, which can be adjusted according to the usage scenario.

[0102] 6. Sorting and truncation: Sort all candidates in ascending order of score and output the Top-k (k=5 in this example) as the preferred recipes.

[0103] For each preferred recipe, output: ① In the set K The components are: ① the component proportion vector; ② the predicted density and refractive index; ③ the nearest neighbor training sample index and its summary information of the minimum distance Dist, as a reference.

[0104] The embodiments described above provide a detailed explanation of the technical solutions and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for performance prediction and reverse design of multi-component glass materials, characterized in that, Includes the following steps: (1) Obtain the component vectors and corresponding physical performance data of multi-component glass samples, preprocess them, and divide them into training and test sets; (2) Construct a neural network, use Bayesian optimization to determine the structure and training hyperparameters of the neural network, and use a genetic algorithm to globally optimize the connection weights and / or thresholds of the neural network to obtain the initial parameters; (3) The feedforward neural network is configured using the obtained training hyperparameters and initialization parameters, and the neural network is trained based on the training set and the test set to obtain the prediction model; (4) Based on the set of allowed ingredient indices given by the user, randomly generate candidate recipes that satisfy the feasible domain constraint; The prediction model is used to predict the physical properties of the candidate formulations, and the target deviation of the candidate formulations is calculated based on the target physical properties given by the user and the predicted physical properties. Calculate the similarity between candidate formulations and samples in the training set in the component space; The target deviation and the similarity are weighted and fused to obtain a comprehensive score. Several preferred formulations are selected as reverse design results based on the comprehensive score.

2. The method for performance prediction and reverse design of multi-component glass materials according to claim 1, characterized in that, In step (1), the component vector is a multi-component formulation ratio vector, which is used as input; the physical property data is density and / or refractive index, which is used as output.

3. The method for performance prediction and reverse design of multi-component glass materials according to claim 1, characterized in that, In step (1), the preprocessing further includes data augmentation; the data augmentation includes: (b1) Select two samples randomly from the training set and perform linear interpolation with random weights to obtain candidate samples; (b2) Apply Gaussian noise of a first amplitude to the input side of the candidate sample and Gaussian noise of a second amplitude to the output side of the candidate sample, wherein the first amplitude is greater than the second amplitude, to obtain an enhanced sample; (b3) Enhanced samples must simultaneously satisfy: a) each component is non-negative, b) the sum of components is consistent with the original sample, c) the normalization domain is relaxed, and d) it does not violate known process incompatibilities rules; qualified enhanced samples are incorporated into the training set, and the number of enhanced samples is controlled to be 10%-150% of the number of original samples.

4. The method for performance prediction and reverse design of multi-component glass materials according to claim 1, characterized in that, In step (2), the constructed neural network is a three-layer feedforward regression network consisting of two hidden layers and one output layer; the input dimension of the neural network is... D The number of neurons in the first and second hidden layers are respectively and The output dimension is 2; The two hidden layers employ hyperbolic tangent activation to enhance nonlinear representation, while the output layer employs linear activation to accommodate continuous real-valued output.

5. The method for performance prediction and reverse design of multi-component glass materials according to claim 4, characterized in that, The search space for Bayesian optimization includes at least the number of neurons in the first hidden layer, the number of neurons in the second hidden layer, the learning rate, and the number of training epochs. The optimization objective is to minimize the prediction error.

6. The method for performance prediction and reverse design of multi-component glass materials according to claim 1, characterized in that, In step (3), training the neural network includes: introducing an L2 regularization term under mean squared error loss, and adaptively adjusting the regularization strength according to the relationship between the training error and the validation error, and training until the model converges.

7. The method for performance prediction and reverse design of multi-component glass materials according to claim 6, characterized in that, Adaptive adjustment of regularization strength includes: increasing the regularization strength when the training error decreases while the validation error increases; and decreasing the regularization strength when both the training error and the validation error decrease simultaneously, until the preset convergence or early stopping conditions are met.

8. The method for performance prediction and reverse design of multi-component glass materials according to claim 1, characterized in that, It also includes user interaction: providing a graphical user interface for receiving a set of target density, target refractive index and composition indexes, and outputting the preferred formulation, predicted physical properties and the index of the closest training sample.

9. A performance prediction and reverse design system for multi-component glass materials, characterized in that, include: The data acquisition and processing module obtains the composition vectors and corresponding physical performance data of multi-component glass samples, performs preprocessing, and divides them into training and testing sets. The model building module constructs a neural network, uses Bayesian optimization to determine the structure and training hyperparameters of the neural network, and uses a genetic algorithm to globally optimize the connection weights and / or thresholds of the neural network to obtain the initial parameters. The model training module uses the obtained training hyperparameters and initialization parameters to configure the neural network, and trains the neural network based on the training set and test set to obtain the prediction model; The reverse design module randomly generates candidate formulations that satisfy the feasible region constraint based on the set of allowed component indices given by the user; it uses the prediction model to predict the physical properties corresponding to the candidate formulations, and calculates the target deviation of the candidate formulations based on the target physical properties given by the user and the predicted physical properties. Calculate the similarity between candidate formulations and samples in the training set in the component space; weight the target deviation and the similarity to obtain a comprehensive score, and select several preferred formulations as the reverse design results based on the comprehensive score.

10. The performance prediction and reverse design system for multi-component glass materials according to claim 9, characterized in that, It also includes a user interaction module: providing a graphical user interface for receiving a set of target density, target refractive index and composition indexes, and outputting the preferred formulation, predicted physical properties and the index of the closest training sample.

Images