Hazardous chemical substance physicochemical property management system and method

Abstract

The invention relates to the technical field of hazardous chemical substance safety management, and discloses a hazardous chemical substance physicochemical property management system and method.The hazardous chemical substance physicochemical property management method comprises the steps that hazardous chemical substance physicochemical property data are preprocessed, and a standardized data set is obtained; carrying out feature extraction and transformation; pre-learning a feature extraction and transformation result by using a deep neural network containing physical consistency constraint, and extracting a complex mode in the data; self-adaptive symbol regression is carried out, wherein expression search space is defined, nerve-guided search space pruning is carried out, and an improved genetic programming algorithm is applied; carrying out optimization and verification, and selecting an optimal mathematical expression as a prediction model of the physicochemical properties of the hazardous chemical substances; according to the method, through a mathematical expression generation technology based on symbol regression, high precision and interpretability of the prediction model are realized, and a user can intuitively understand a calculation process and physical significance of a prediction result.

Description

Technical Field

[0001] This invention relates to the field of hazardous chemical safety management technology, and more specifically, to a management system and method for the physical and chemical properties of hazardous chemicals. Background Technology

[0002] The changes in the physicochemical properties of hazardous chemicals during production, storage, transportation, and use directly affect the scientific nature and effectiveness of safety management. Accurate prediction and reasonable interpretation of the physicochemical properties of hazardous chemicals are key technical aspects for achieving risk warning, accident prevention, and emergency decision support. With the development of information technology and data science, data-driven methods for predicting physicochemical properties are gradually being applied in the field of hazardous chemical management, and related research and systems are constantly emerging.

[0003] Currently, the prediction of the physicochemical properties of hazardous chemicals mainly relies on methods such as statistical modeling, traditional machine learning, and deep neural networks. While these methods have made some progress in improving prediction accuracy, they generally suffer from the following technical limitations: Existing physicochemical property prediction models are mostly "black box" models, such as deep neural networks. While they can achieve high prediction accuracy, they lack interpretability of the prediction results. Managers find it difficult to understand the decision-making basis of the model and cannot trace the prediction process, resulting in low trust in the models in actual hazardous chemical safety management and hindering their widespread application. Traditional models mainly focus on the statistical correlation between inputs and outputs, making it difficult to reveal the underlying physicochemical laws behind changes in physicochemical properties. These models cannot automatically extract or generate mathematical expressions that reflect actual physicochemical processes, making it difficult to provide theoretical support for hazardous chemical safety management and failing to meet the needs of mechanism-based risk analysis and scientific prevention and control. Existing methods also suffer from model complexity issues. There is a trade-off between interpretability and high-precision models. High-precision models are often complex in structure and have many parameters, resulting in high computational resource consumption and low training and inference efficiency. On the other hand, while simplified models are easier to understand and deploy, their prediction accuracy often fails to meet practical needs. Existing technologies are insufficient in integrating data-driven and domain knowledge. Methods that rely solely on data-driven approaches cannot fully utilize the theoretical knowledge accumulated in the field of hazardous chemicals, resulting in limited model generalization ability and scientific rigor. On the other hand, methods that rely solely on knowledge-driven approaches are difficult to adapt to the complexity and dynamic changes of actual data. Therefore, how to achieve scientific interpretability and knowledge integration of models while ensuring prediction accuracy has become an urgent technical challenge to be solved in the field of predicting the physicochemical properties of hazardous chemicals.

[0004] In summary, existing technologies for predicting the physicochemical properties of hazardous chemicals have significant shortcomings in terms of interpretability, mining of physicochemical laws, control of model complexity, and knowledge integration. There is an urgent need to propose a new technical solution that can balance high-precision prediction with scientific explanation in order to improve the intelligence and scientific level of hazardous chemical safety management. Summary of the Invention

[0005] This invention provides a management system and method for the physicochemical properties of hazardous chemicals, which solves the technical problems in related technologies such as the lack of interpretability of prediction models for the physicochemical properties of hazardous chemicals, difficulty in revealing physicochemical laws, high computational complexity, and inability to effectively integrate domain knowledge.

[0006] This invention provides a method for managing the physicochemical properties of hazardous chemicals, comprising: The physicochemical property data of hazardous chemicals are preprocessed to obtain a standardized dataset. Feature extraction and transformation are performed on standardized datasets, including domain knowledge-guided feature engineering and autoencoder dimensionality reduction; By using a deep neural network with physical consistency constraints to pre-learn the results of feature extraction and transformation, complex patterns in the data can be extracted. Adaptive symbolic regression based on deep neural network pre-learning results includes defining the expression search space, performing neural-guided search space pruning, and applying an improved genetic programming algorithm. The adaptive symbolic regression results were optimized and validated, and the optimal mathematical expression was selected as the prediction model for the physicochemical properties of hazardous chemicals.

[0007] Furthermore, the preprocessing of the physicochemical properties data of hazardous chemicals specifically includes: applying an adaptive anomaly detection algorithm to process outliers and noise in the original data; selecting Zscore standardization and robust normalization methods according to the data distribution characteristics; and performing spatiotemporal alignment and missing data imputation.

[0008] Furthermore, the feature extraction and transformation includes: constructing features with clear physical meaning based on knowledge of the physicochemical properties of hazardous chemicals; using an adaptive autoencoder to perform nonlinear dimensionality reduction on the high-dimensional features, wherein the autoencoder is trained by minimizing reconstruction error and regularization terms; performing nonlinear transformation on the extracted features to expand the feature space; and applying an ensemble feature selection algorithm to evaluate feature importance and perform feature screening.

[0009] Furthermore, the pre-learning of the feature extraction and transformation results using a deep neural network with physical consistency constraints specifically includes: Construct a deep neural network model for predicting the physicochemical properties of hazardous chemicals; Training is performed using a comprehensive objective function that includes a mean squared error term, a weight regularization term, and a physical consistency constraint term; The knowledge contained in the trained neural network is extracted to generate synthetic data, extract some response functions and feature importance; Sensitivity analysis is performed on the trained neural network to identify key patterns and laws governing changes in its physicochemical properties.

[0010] Furthermore, the adaptive symbolic regression specifically includes: Construct an expression search space containing a set of variables, a set of constants, a set of unary operators, a set of binary operators, and structure elements; Pruning of variable importance, function type, and structural complexity is performed based on knowledge pre-learned by neural networks. The design includes specialized genetic operations such as semantically aware crossover, gradient-based mutation, and multi-objective selection; A multi-level search strategy that progressively increases the complexity of the expression is adopted. A parallel collaborative search architecture is constructed using an island model and hierarchical search.

[0011] Furthermore, the optimization and validation of the adaptive symbolic regression results specifically includes: Perform algebraic simplification, symbol reduction, and structural adjustment on the candidate expressions; Gradient descent optimization and global optimization algorithms are applied to fine-tune the numerical parameters in the expression; Construct expression integration strategies, including piecewise expressions, additive models, and hierarchical expressions; The generalization ability and stability of the expression were evaluated using K-fold cross-validation, leave-one-out validation, and sensitivity analysis. Domain knowledge is introduced to perform dimensional consistency checks, boundary condition verification, and qualitative trend analysis.

[0012] Furthermore, the physical consistency constraint is implemented by introducing a physical constraint function. The physical constraint function receives the model's predicted value and input features as parameters, calculates the degree of conformity between the prediction result and a specific physical law, and outputs zero when the prediction result satisfies the physical law, and the greater the deviation, the larger the output.

[0013] Furthermore, the adaptive symbolic regression also includes knowledge-enhanced neural representation learning, specifically including: constructing a knowledge graph-based representation of physicochemical property relationships; configuring a hybrid neural symbolic architecture to integrate symbolic reasoning and neural network learning; and learning latent representations of changes in physicochemical properties.

[0014] Furthermore, the optimization and verification also includes parameter optimization, which uses Bayesian information criteria to evaluate and select candidate expressions, taking into account both the prediction accuracy and complexity of the expressions.

[0015] This invention provides a hazardous chemical physicochemical property management system for implementing the aforementioned hazardous chemical physicochemical property management method, comprising: The data processing module is used to clean and standardize the physicochemical property data of hazardous chemicals. The feature analysis module is used to extract and transform key features from data to improve the effectiveness of subsequent modeling. The neural network modeling module is responsible for using deep learning methods to uncover complex relationships in the data and introducing physical constraints. The symbolic regression module performs expression search and modeling based on neural network results. The expression optimization and evaluation module simplifies the generated mathematical model, adjusts its parameters, and verifies its effectiveness.

[0016] The beneficial effects of this invention are as follows: by using mathematical expression generation technology based on symbolic regression, the prediction model achieves both high accuracy and interpretability, enabling users to intuitively understand the calculation process and physical meaning of the prediction results, thereby effectively overcoming the technical bottleneck of traditional "black box" models that are difficult to interpret, and improving the credibility and practicality of the prediction results. By transforming the problem of predicting complex physicochemical properties into mathematical expressions with fewer parameters, the computational complexity of the model is reduced, enabling efficient inference on resource-constrained devices and improving the system's computational efficiency and real-time response capability. By automatically mining the physicochemical patterns in the data, knowledge discovery of the relationships between the physicochemical properties of hazardous chemicals has been achieved, enabling the system to reveal potential scientific laws and enhancing its scientific value and innovation. By using a neural-guided adaptive symbolic regression method, the model structure and complexity can be automatically adjusted according to different types of hazardous chemicals and application scenarios, achieving adaptability to multiple scenarios and good generalization ability, thus improving the applicability of the model in new environments. By integrating data-driven methods with domain knowledge, the model achieves synergistic utilization of historical data patterns and prior knowledge of physicochemical properties, reducing dependence on large-scale training data and improving the training efficiency and applicability of the model. By generating interpretable mathematical expressions, it directly provides decision support for the safety management of hazardous chemicals, helps managers understand the mechanisms of changes in physicochemical properties, predicts potential risks in advance, and improves the scientific nature and safety of hazardous chemical management. Attached Figure Description

[0017] Figure 1 This is a flowchart of a method for managing the physical and chemical properties of hazardous chemicals according to the present invention; Figure 2 It is a bar chart comparing the contributions of different characteristic variables in the prediction of the physicochemical properties of hazardous chemicals; Figure 3 This is a bar chart comparing the performance of adaptive symbolic regression, deep neural networks, and traditional regression methods across four dimensions: prediction accuracy, interpretability, computational efficiency, and generalization ability. Figure 4This is an area graph showing the changes in the decomposition rate of ammonium sulfate under different pressure conditions. Detailed Implementation

[0018] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, some features described in the examples may be combined in other examples.

[0019] At least one embodiment of the present invention discloses a method for managing the physicochemical properties of hazardous chemicals, such as... Figure 1 As shown, it includes: Step 1: Preprocess the physicochemical property data of hazardous chemicals to obtain a standardized dataset; According to one embodiment of this application, this step preprocesses the collected raw data on the physicochemical properties of hazardous chemicals to ensure data quality and applicability. Specifically, it includes the following sub-steps: Step 1.1: Deploy a hierarchical monitoring probe network; Collect multi-source data related to the physicochemical properties of hazardous chemicals, including but not limited to the following data types: Basic physicochemical properties data of hazardous chemicals: including physicochemical property parameter values ​​of various hazardous chemicals under standard conditions; Environmental parameter time series data: time series data of environmental parameters such as temperature, pressure, and humidity; Physicochemical property change data: values ​​of changes in physicochemical properties measured under different conditions; Accident case data: Historical accident data and key parameters involving changes in physical and chemical properties.

[0020] These multi-source heterogeneous data are integrated through a unified data model to ensure data format consistency and semantic compatibility.

[0021] Step 1.2, Intelligent anomaly detection and data cleaning; An adaptive anomaly detection algorithm is applied to handle outliers and noise in the original data. Based on statistical properties and domain knowledge, this algorithm identifies and processes anomalous data by calculating a deviation score for each data point.

[0022] For detected outliers, different handling strategies are adopted according to the degree of anomaly: Minor anomalies: Corrected using a robust smoothing algorithm; Moderate anomalies: interpolation estimation using temporal or spatial correlation; Critical anomalies: Marked and removed from the training data, but retained for subsequent analysis.

[0023] Step 1.3, parameter standardization and normalization processing; An adaptive standardization strategy is adopted for physicochemical property parameters with different dimensions and distribution characteristics: For parameters that approximate a normal distribution, Z-score standardization is applied: To perform Z-score standardization on the original data, first calculate the mean of the original data. The mean represents the central tendency of the data; then the standard deviation of the original data is calculated. The standard deviation represents the degree of dispersion of the data. During standardization, for each data point... First calculate the difference between it and the mean. This difference indicates the degree to which the data point deviates from the center; then, this difference is divided by the standard deviation to obtain the result. This represents the ratio of the degree to which a data point deviates from the center relative to the overall dispersion. After this processing, the data will be converted into a standard distribution with a mean of 0 and a standard deviation of 1, allowing for effective comparison and comprehensive analysis of characteristics of different dimensions and ranges.

[0024] For non-normally distributed parameters, apply robust normalization methods: To perform robust normalization on the original data, the median of the data is first calculated. The median represents the center of the data and is unaffected by extreme values; then the interquartile range of the data is calculated. The quartile, or third quartile, is the difference between the first quartile and the third quartile. This metric measures the dispersion of the data and is insensitive to outliers. During normalization, for each data point... First, calculate the difference between it and the median. This difference indicates the degree to which the point deviates from the center; then, this difference is divided by the interquartile range to obtain the result. This represents the ratio of the deviation of a point from the overall dispersion of the data. This method is particularly suitable for data with outliers or skewed distributions, providing a more robust standardization effect, preserving the relative relationships of the data while reducing the impact of outliers, and providing higher-quality feature inputs for subsequent modeling.

[0025] For severely skewed distributions, logarithmic or power transformations can be applied first to adjust the distribution shape before standardization. In some implementations, the system can automatically select the most suitable transformation method; for example, a logarithmic transformation can be used for a right-skewed distribution, and a square transformation can be used for a left-skewed distribution.

[0026] Step 1.4, Spatiotemporal alignment and missing data imputation; Because multi-source data may have inconsistencies in time and space, spatiotemporal alignment is necessary. Time dimension alignment: Using interpolation or downsampling methods, data with different time resolutions are unified to the same time scale; Spatial dimension alignment: Using spatial interpolation techniques to process measurement data from different spatial locations.

[0027] For cases of missing data, select an appropriate imputation strategy based on the missing data pattern: Random missing data: Multiple imputation is used to generate multiple possible complete datasets; Structural missing: Constructing a specific imputation model by combining physical constraints and data correlations.

[0028] It should be understood that the above processing yields a high-quality structured dataset, providing a reliable data foundation for subsequent modeling. The quality of data preprocessing directly affects the accuracy and interpretability of the final symbolic regression results, and is a fundamental aspect of the entire system.

[0029] Step 2 involves feature extraction and transformation of the standardized dataset, including domain knowledge-guided feature engineering and autoencoder dimensionality reduction. According to another embodiment of this application, this step performs feature extraction and transformation on the preprocessed data to reduce data dimensionality and extract key features that are helpful for the discovery of symbolic expressions. Specifically, it includes the following sub-steps: Step 2.1, Domain Knowledge-Guided Feature Engineering; Based on knowledge of the physicochemical properties of hazardous chemicals, we construct characteristics with clearly defined physical meanings: Physicochemical property ratio characteristics: When calculating the ratio of flash point to boiling point and the ratio of vapor pressure to ambient pressure, it is necessary to ensure that all parameters use the same unit system and perform standardization to avoid numerical overflow. Thermodynamic characteristics: When calculating characteristics such as enthalpy, entropy, and free energy, it is necessary to standardize the basic parameters such as temperature and pressure to ensure the numerical stability of the calculation results; Molecular structure features: Molecular descriptors typically contain multiple types of numerical values ​​(such as the number of atoms, bonds, and rings), which require feature scaling and standardization.

[0030] Constructing physicochemical property ratio characteristics: Calculate the ratios between key physicochemical parameters, such as the ratio of flash point to boiling point, the ratio of vapor pressure to ambient pressure, etc. These ratio characteristics usually have clear physical meaning and regularity; Constructing thermodynamic characteristics: Based on thermodynamic formulas, calculate characteristics such as enthalpy, entropy, and free energy to capture the energy-related laws of physicochemical properties; Constructing molecular structure features: Using molecular descriptor technology, features related to physicochemical properties are extracted from molecular structure information.

[0031] It should be noted that these domain-knowledge-based features can provide physically meaningful underlying variables for subsequent symbolic expression searches, improving the interpretability of the final expression.

[0032] Step 2.2, Dimensionality reduction and feature compression by autoencoder; According to the embodiments of this application, an adaptive autoencoder is applied to perform nonlinear dimensionality reduction on high-dimensional features, and its network structure is as follows: Input layer: Receives the original feature vector; Encoder layer: Contains multiple shrinking layers to progressively reduce the feature dimension; Bottleneck layer: Extracts key low-dimensional feature representations; Decoder layer: Reconstructs low-dimensional features into original features; Output layer: Generates the reconstructed feature vectors.

[0033] The autoencoder is trained by minimizing the reconstruction error: The autoencoder is trained by minimizing a reconstruction error function, which consists of two key parts: a reconstruction error term and a regularization term. For the reconstruction error term, the system first inputs each original feature vector into the autoencoder to generate a reconstructed feature vector; then, it calculates the squared Euclidean distance between the original and reconstructed vectors, representing the degree of information loss during reconstruction; finally, it averages the reconstruction errors of all samples to obtain a measure of the overall reconstruction quality. For the regularization term, the system imposes constraints on the network weight parameters by calculating the norm of the weight matrix and multiplying it by a regularization coefficient to control model complexity and prevent overfitting. The two parts are added together to form the final loss function. The system minimizes this function using an optimization algorithm to find network parameters that can effectively compress data while maintaining information integrity, achieving dimensionality reduction and providing more concise and information-rich feature inputs for subsequent symbolic regression.

[0034] After training, compressed features are extracted using the encoder and used as input variables for subsequent symbolic regression.

[0035] The following are specific implementation methods and application examples of the autoencoder model: For processing complex, high-dimensional hazardous chemical characteristic data (such as near-infrared spectral data), the system implements an adaptive autoencoder model, the specific structure and implementation of which are as follows: Network Structure: An asymmetric autoencoder was constructed, consisting of three fully connected layers with the number of nodes increasing sequentially from the original dimension. (Typically 512 to 1024) , The decoder consists of three fully connected layers, with the number of nodes as follows: , , Batch normalization and ReLU activation function are used between each layer, and a noise layer (with Gaussian noise and a standard deviation of 0.01) is added after the bottleneck layer to enhance the robustness of the model.

[0036] Adaptive sparse regularization introduces an adaptive sparse regularization term based on data characteristics: ; in This represents an adaptive sparse regularization term. This is the weight matrix of the neural network. The first in the matrix Line 1 Column elements, For the first The importance coefficients of each feature are automatically determined through pre-analysis of the data structure, enabling the model to adaptively adjust the regularization strength for different features.

[0037] Training Method: A two-stage training strategy was adopted. The first stage used conventional mean squared error loss for 100 epochs. The second stage introduced the Structural Similarity Index (SSIM) as an additional loss term to evaluate the structural similarity between the reconstructed features and the original features; a higher SSIM value indicates greater structural similarity. This index helps the model better preserve the structural relationships between features. The optimizer used was RMSprop with a learning rate of 0.0005 and a batch size of 32.

[0038] Application Example: When processing the spectral data of a complex chlorinated organic hazardous chemical, the original data dimension was 1024. This adaptive autoencoder compressed it to 64 dimensions, retaining 98.2% of the information. Based on the compression features, the system successfully established a model relating the flash point to the molecular structure of this hazardous chemical. In a hazardous materials monitoring system, this model enabled rapid prediction of the flash point of unknown chlorinated organic compounds, reducing the average prediction time from 2.7 seconds to 0.3 seconds, while maintaining the prediction error within ±2.5℃.

[0039] Feature Visualization and Interpretation: The system performed t-SNE visualization analysis on the compressed feature space, revealing that compounds with different chemical structures formed clear clusters within the feature space. By analyzing these clustering features, researchers identified key molecular structural factors affecting flash point (such as the position and number of chlorine atoms), providing a theoretical basis for subsequent safety management.

[0040] Through this adaptive autoencoder model, the system not only achieves efficient data dimensionality reduction, but more importantly, it retains key structural information in the physicochemical properties data of hazardous chemicals, laying the foundation for subsequent symbolic regression to discover accurate and concise mathematical expressions, while improving the computational efficiency and practicality of the entire system.

[0041] Step 2.3, Nonlinear Feature Transformation and Extension; To expand the search space for symbolic regression, according to an optional implementation of this application, the extracted features are subjected to a nonlinear transformation to construct an extended feature set: Polynomial transformation: generates higher-order terms and intersection terms of the original features; Exponential and logarithmic transformations: Apply exponential and logarithmic functions to each feature; Trigonometric function transformation: applying trigonometric function transformations to periodic features; Piecewise linear transformation: Construct piecewise functions for features that exhibit threshold effects.

[0042] For each extended feature generated by the transformation, its correlation with the target physicochemical properties is calculated, and the most relevant subset of features is retained based on the correlation.

[0043] Step 2.4, Feature Importance Assessment and Selection; An ensemble feature selection algorithm is applied to comprehensively evaluate feature importance and perform feature selection: Model-based feature evaluation: Calculate feature importance scores using models such as random forests and gradient boosting trees; Statistical feature evaluation: Calculate statistics such as mutual information and correlation coefficient between features and target variables; Physically-based feature evaluation: Evaluating the physical interpretability of features based on domain expert knowledge.

[0044] The results of multiple evaluation methods are weighted and fused to calculate the overall importance score for each feature: The system calculates the overall importance score for each feature using a weighted fusion method. This process first collects data for each feature. The system generates importance scores from different evaluation methods, each assessing the contribution of a feature to the prediction target based on different principles. Then, each evaluation method is assigned a corresponding weight, reflecting its reliability and applicability in the current task. Next, the score obtained by each feature in each evaluation method is multiplied by the corresponding method's weight. Finally, these weighted scores are summed to obtain the feature's overall importance score. This fusion mechanism fully leverages the advantages of different evaluation methods, overcomes the limitations of a single method, and provides a more comprehensive and robust measure of feature importance. The system ranks features based on these overall scores, selecting the top-ranked feature subset for subsequent symbolic regression. This ensures the preservation of key information while reducing the dimensionality of the search space, improving the efficiency and quality of symbolic regression results.

[0045] like Figure 2 As shown, the contribution of different feature variables to the prediction of the physicochemical properties of hazardous chemicals was quantitatively analyzed using a feature importance assessment algorithm. The assessment results show that temperature parameters and specific chemical structural features have the greatest impact on the prediction results, with the temperature parameter achieving an importance score of 0.85, significantly higher than other environmental parameters. This finding provides important evidence for the analysis of the physicochemical property mechanism, indicating that temperature is the dominant factor affecting the changes in the physicochemical properties of hazardous chemicals. Simultaneously, bond energy parameters and functional group types in molecular structure features also show high importance, verifying the decisive role of chemical structure in physicochemical properties. Through this feature importance assessment, the system can automatically identify key influencing factors, providing targeted guidance for subsequent symbolic regression searches and improving the efficiency and accuracy of mathematical expression discovery.

[0046] Based on the comprehensive importance score, the top-ranked feature subset is selected as the input variable for symbolic regression. Furthermore, through the aforementioned feature extraction and transformation steps, the original high-dimensional, redundant data is transformed into a low-dimensional, information-rich feature set, laying the foundation for the subsequent discovery of concise, physically meaningful mathematical expressions.

[0047] Step 3: Use a deep neural network with physical consistency constraints to pre-learn the results of feature extraction and transformation to extract complex patterns in the data. According to one embodiment of this application, this step utilizes a deep neural network to pre-learn the physicochemical property data, extracting complex patterns and relationships from the data to guide subsequent symbolic expression search. It should be understood that this innovative step is the key difference between this system and traditional symbolic regression methods. Specifically, it includes the following sub-steps: Step 3.1, Construction and training of the multilayer perceptron model; According to one embodiment of this application, a deep neural network model for predicting the physicochemical properties of hazardous chemicals is constructed, and its architecture is as follows: Input layer: Receives the feature set selected in step 2; Hidden layers: contain multiple fully connected layers, each followed by a batch normalization layer and an activation function; Output layer: Predicts the target physicochemical properties.

[0048] Input feature standardization: All input features need to be standardized to ensure that features of different scales can participate in model training fairly. For continuous variables such as temperature and pressure, Z-score standardization is used; for high-dimensional features such as molecular descriptors, PCA is used for dimensionality reduction before standardization. Categorical feature coding: For categorical variables such as hazardous chemical type and storage conditions, one-hot coding is used to convert them into numerical features to avoid the model learning meaningless numerical relationships; Missing value handling: For features with missing values, use mean imputation or interpolation methods to ensure data integrity; Outlier handling: For values ​​that deviate significantly from the normal range, truncation or smoothing methods are used to handle them to avoid outliers interfering with model training.

[0049] The neural network model is trained using the following objective function: The neural network model is trained using an objective function comprising three components. The first component is the mean squared error term, which first calculates the difference between the predicted value and the actual physicochemical property value for each sample, then squares this difference, and finally averages the squared errors of all samples to obtain a quantitative indicator of the model's overall prediction accuracy. The second component is the weight regularization term, which calculates the norm of the network weight parameters and multiplies it by a weighting coefficient. The first part penalizes model complexity to prevent overfitting and improve the model's generalization ability. The third part is the physical consistency constraint, which incorporates domain physics knowledge into the training process. This is achieved by calculating the degree to which the prediction results deviate from physical laws and multiplying it by a tradeoff coefficient. This ensures that the model's learning results conform to fundamental physical laws, enhancing the interpretability and reliability of the prediction results. The system minimizes the comprehensive objective function composed of these three parts through an optimization algorithm, achieving a balance between prediction accuracy, model simplicity, and physical rationality, generating a physicochemical property prediction model that is both accurate and scientifically interpretable.

[0050] Physical consistency constraints, by incorporating domain knowledge, ensure that model predictions conform to physical laws. For example: The physical consistency constraint term is implemented by constructing the sum of squares of multiple physical constraint functions. This term is first defined for different physical laws. Each constraint function receives the model's predicted value and input features as parameters. Each constraint function calculates the degree of conformity between the predicted result and a specific physical law; the function outputs zero when the predicted result fully conforms to the physical law, and the larger the deviation, the larger the output. The system squares the output value of each constraint function and then sums all the squared values ​​to obtain the overall physical consistency constraint value. During training, this constraint value is used as part of the loss function, guiding the model's learning process to consider not only data fitting but also the degree of conformity to physical laws. In this way, the system can generate a predictive model that conforms to both experimental data and basic physical laws, improving the model's reliability and interpretability under extreme conditions and in sparse data regions, and providing a more scientific theoretical basis for the safety management of hazardous chemicals.

[0051] Here The function is specifically implemented as follows: The predicted value is... and input features Substitute the equations into specific physical laws and calculate the residuals. For example, for the ideal gas law constraints, we can construct: ; in Indicates predicted pressure With input features The absolute difference between the calculated theoretical pressures, For physical consistency constraint functions; The predicted pressure value; , and These are the amount of substance, temperature, and volume, respectively, based on the input features. Extract from; is the gas constant.

[0052] The closer the output is to zero, the better the prediction conforms to the physical law. The system can automatically select a suitable set of physical constraint functions based on different hazardous chemicals and their different physicochemical properties.

[0053] The following are detailed implementation methods and application examples of neural network pre-learning models: To predict the flash point of flammable liquids as a function of temperature and pressure, a neural network model with physical consistency constraints was constructed. The specific implementation of this model includes: Network Architecture: An improved multilayer perceptron structure is adopted, including three hidden layers with 32, 16, and 8 nodes per layer, respectively. The LeakyReLU activation function is used to enhance the ability to capture nonlinear relationships. The input layer receives features such as temperature, pressure, and molecular structure descriptors, and the output layer predicts the flash point temperature value.

[0054] Physical consistency constraint implementation: The Clapeyron equation is introduced as a physical constraint into the loss function to ensure that the prediction results conform to the fundamental laws of thermodynamics. The specific constraint function is as follows: ; in For physical consistency constraint functions; This is the predicted flash point temperature; For the input feature set; This represents the partial derivative of the predicted flash point temperature with respect to the absolute temperature. It is the enthalpy of vaporization (the energy required for a substance to change from a liquid state to a gaseous state). The gas constant is approximately equal to J / (mol·K); Absolute temperature; This represents absolute value operations.

[0055] Training process: The Adam adaptive learning rate optimizer was used, with an initial learning rate of 0.001. Mini-batch gradient descent with a batch size of 64 was employed, and the training iterations were performed for 5000 epochs. The weight regularization coefficient was... Physical consistency constraint coefficient .

[0056] Application Example: This pre-learning model was deployed in a hazardous chemical storage warehouse of a petrochemical company. When the ambient temperature suddenly rises, the system can accurately predict the flash point change trend of various flammable liquids. For example, for toluene, when the temperature rises from 25°C to 35°C and the pressure drops from 1 atmosphere to 0.9 atmospheres, the model accurately predicts that the flash point decreases by 3.2°C, with an error of less than 0.5°C compared to the experimental measurement.

[0057] Knowledge extraction and symbolic regression guidance: The system extracts key feature interaction patterns from a trained neural network, discovering exponential and reciprocal relationships between temperature, pressure, and flash point. This extracted knowledge is directly used to guide the symbolic regression search, reducing the search space by approximately 87% and enabling the system to discover a mathematical expression accurately describing the flash point variation within 10 minutes.

[0058] Therefore, through this neural network pre-learning model, the system not only improves the accuracy of predicting the physicochemical properties of hazardous chemicals, but more importantly, it extracts the physical laws hidden in the data, providing scientific and efficient guidance for the subsequent symbolic regression process, and realizing the effective transformation from data to knowledge.

[0059] Step 3.2, Neural Network Knowledge Distillation; According to another embodiment of this application, the knowledge contained in the trained deep neural network is extracted and used to guide the symbolic regression search process: Generate synthetic data: Use a trained neural network to generate a large number of synthetic data points in the feature space to enhance the data density in sparse regions; Extracting partial response functions: Analyzing the partial derivatives of the neural network with respect to each input feature reveals the local relationship between the input and output; Feature importance extraction: Based on the structure and weights of the neural network, calculate the contribution of each feature to the prediction result.

[0060] It should be noted that the knowledge extracted from the neural network will be used for search space pruning and initial expression generation in subsequent symbolic regression. In some implementations, the system can automatically adjust the search scope and priority of symbolic regression based on the knowledge distillation results, further improving search efficiency.

[0061] Step 3.3, Sensitivity Analysis and Key Pattern Recognition; Sensitivity analysis was performed on the trained neural network to identify key patterns and laws governing changes in its physicochemical properties. Univariate sensitivity analysis: By fixing other variables, we analyze the impact of changes in a single variable on the prediction results and identify key nonlinear relationships; Interaction effect analysis: assesses the interaction between variables and identifies important combinations of features; Critical point analysis: Identifying input threshold points where the prediction results change significantly, providing a basis for piecewise functions.

[0062] The results of sensitivity analysis are used to construct search constraints and evaluation indicators for symbolic expressions, guiding the search process to focus on key patterns of changes in physicochemical properties.

[0063] Step 3.4, neural representation learning for knowledge enhancement; We construct a knowledge-enhanced neural representation learning module that combines domain knowledge with data-driven learning: Constructing a knowledge graph-based representation of physicochemical properties; Configure a hybrid neural-symbolic architecture that integrates symbolic reasoning and neural network learning; Learn interpretable latent representations of changes in physicochemical properties.

[0064] Through knowledge-enhanced representation learning, the system can capture physical laws that are difficult to discover using purely data-driven methods, providing a more meaningful search space for symbolic regression.

[0065] Step 3.5, Adaptive Symbolic Regression; To more intuitively demonstrate the application of this system, we will take ammonium nitrate, a typical hazardous chemical, as an example to illustrate how the system applies neural network pre-learning and adaptive symbolic regression techniques to analyze the changing patterns of its physicochemical properties: To predict the thermal decomposition rate of ammonium nitrate, the system first collected experimental data under different temperature, humidity, pressure, and impurity content conditions. Through neural network pre-learning, the system identified temperature as the dominant factor affecting the thermal decomposition rate, and found a significant nonlinear relationship between the two factors. It also discovered a clear interaction effect between humidity and temperature.

[0066] Guided by this pre-learned knowledge, the system discovered the following mathematical expression to describe the thermal decomposition rate of ammonium nitrate through adaptive symbolic regression: The system discovered a mathematical expression describing the thermal decomposition rate of ammonium nitrate through adaptive symbolic regression: ; in, This represents the thermal decomposition rate of ammonium nitrate. The reaction rate constant under standard conditions; It is an exponential function; It is the activation energy; For gas constant, approximately J / (mol·K); Absolute temperature; Humidity influence coefficient; Relative humidity; This is the pressure influence coefficient; For pressure.

[0067] The expression consists of four key parts. The first part is... The first part represents the reaction rate constant under standard conditions; a larger value indicates a higher basic reaction rate. The second part is the temperature-dependent term, expressed as an exponential function, where the numerator term represents the negative activation energy. With gas constant The ratio, with the denominator being absolute temperature. This term captures the classic Arrhenius relation, which states that the reaction rate increases exponentially with increasing temperature. The third part is the interaction term between humidity and temperature, which is calculated by adding 1 to the relative humidity. It consists of the product of the square of the temperature and the coefficient. The controlled intensity indicates that humidity's promoting effect on thermal decomposition is more pronounced under high-temperature conditions. The fourth part is the pressure effect term, which... Reduce stress With coefficient The product of these factors indicates that increased pressure inhibits the decomposition reaction. This expression not only accurately predicts the decomposition rate (with a prediction error of less than 1%), but also demonstrates that increased pressure inhibits the decomposition reaction. More importantly, it reveals the influence mechanism of temperature, humidity and pressure on the thermal decomposition kinetics of ammonium nitrate and their interaction, providing a scientific basis for determining safe storage and transportation conditions.

[0068] Furthermore, regarding the variation of the explosion limits of ammonium nitrate with storage conditions, the system used sensitivity analysis to determine the storage time... Number of temperature cycles There are complex nonlinear relationships between them, and a piecewise function is generated to accurately describe this pattern, providing quantitative guidance for safe storage.

[0069] These examples demonstrate that the system can extract physically meaningful mathematical models from complex hazardous chemical data, ensuring both prediction accuracy and providing a scientific explanation of the physicochemical mechanisms.

[0070] Therefore, this neural network pre-learning step fully utilizes the powerful pattern recognition capabilities of deep learning, and at the same time, through knowledge extraction and distillation techniques, transforms the learned knowledge into guiding information for symbolic regression, thus achieving an organic combination of high-precision prediction from deep learning and interpretable expression from symbolic regression.

[0071] Step 4: Perform adaptive symbolic regression based on the pre-learning results of the deep neural network, including defining the expression search space, performing neural-guided search space pruning, and applying an improved genetic programming algorithm. According to embodiments of this application, this step is the core innovation of the system. It uses a neural-guided adaptive symbolic regression algorithm to search the expression space for mathematical formulas that accurately describe the changing patterns of physicochemical properties. Specifically, it includes the following sub-steps: Step 4.1, define the expression search space; Construct a symbolic expression search space, which includes the following components: Variable set: The feature variables selected in step 2; The set of constants includes integers, decimals, and important physical constants. Unary operators include common mathematical operations such as addition, subtraction, trigonometric functions (such as sine and cosine), exponentiation, logarithm, and square root; Binary operators include basic binary mathematical operations such as addition, subtraction, multiplication, division, and exponentiation; Structural elements: parentheses, conditional statements, etc.

[0072] According to one embodiment of this application, based on the above elements, the syntax rules and generation method of the expression are defined to ensure that the generated expression is mathematically meaningful and conforms to the physical constraints of physicochemical properties. In some optional implementations, the system can adjust the priority and combination rules of operators according to the physical characteristics of different physicochemical properties. For example, for expressions describing thermodynamic properties, exponential and logarithmic operators will receive higher priority.

[0073] Step 4.2, neural-guided search space pruning; By utilizing the knowledge pre-learned by the neural network in step 3, intelligent pruning is performed on the expression search space to reduce the search difficulty: Variable importance pruning: Based on the feature importance extracted by the neural network, variables that contribute significantly to the prediction results are given priority. Function type pruning: Selecting possible function forms based on the types of non-linear relationships revealed by the neural network; Structural complexity pruning: Limit the maximum depth and complexity of expressions to avoid overly complex expressions.

[0074] It should be understood that this neurally guided pruning strategy reduces the search space from an exponential size to a manageable range, thereby improving search efficiency.

[0075] Step 4.3, Improved Genetic Programming Algorithm; According to one embodiment of this application, an improved algorithm specifically designed for the physicochemical properties of hazardous chemicals is configured based on a genetic programming framework: Expression encoding: Mathematical expressions are represented using an abstract syntax tree structure, which facilitates genetic operations; Population initialization: Using the knowledge of the neural network in step 3, an initial population is generated, rather than being initialized completely randomly; Fitness function: comprehensively considers prediction accuracy, expression complexity, and physical rationality.

[0076] Variable preprocessing: All input variables need to be standardized to ensure that variables of different scales can participate in the calculation fairly during the expression search process. For physical quantities such as temperature and pressure, relative standardization (relative to a reference value) is recommended. Constant preprocessing: Physical constants (such as gas constant, activation energy, etc.) need to be standardized in units to avoid the numerical differences under different unit systems affecting the expression search; Parameter range constraints: For parameters with physical meaning, reasonable value range constraints need to be set to ensure that the generated expression has physical rationality; Feature selection preprocessing: Before entering genetic programming, it is necessary to evaluate and select the importance of features to reduce the dimensionality of the search space and improve search efficiency.

[0077] The system implements a comprehensive fitness function to evaluate the overall quality of symbolic expressions. This function consists of three weighted components. The first component measures the prediction accuracy of the expression by calculating the error between the predicted value and the actual physicochemical property value, such as mean squared error or mean absolute error. A smaller value indicates a more accurate prediction, while a larger value, after transformation, indicates higher accuracy. The second component evaluates the simplicity of the expression, considering factors such as the number of nodes, tree depth, and operator complexity. Simpler expressions receive higher simplicity scores. The third component quantifies the physical rationality of the expression, checking whether it conforms to basic physical laws, such as dimensional consistency, monotonicity, and asymptotic behavior. Higher physical rationality results in a higher score. The system controls the relative importance of each component through three weighting coefficients, flexibly adjusting them according to specific application needs to achieve a balance between high prediction accuracy, structural simplicity, and physical interpretability. Guided by this fitness function, the genetic algorithm can gradually evolve mathematical expressions that are accurate, concise, and have good physical interpretability, providing a reliable tool for the scientific prediction and interpretation of the physicochemical properties of hazardous chemicals.

[0078] Genetic operations: Designing specialized crossover, mutation, and selection operations for mathematical expressions; Semantic-aware crossover: Considering the semantic similarity of sub-expressions, meaningful exchanges are performed; Gradient-based mutation: Using gradient information to guide the direction of mutation and improve mutation efficiency; Multi-objective selection: Maintaining population diversity while preserving high-precision expressions.

[0079] The following is a detailed implementation and application example of the improved genetic programming algorithm: For the complex task of modeling the relationship between the explosion limits of hazardous chemicals and their molecular structure, the system implements a physics-enhanced genetic programming algorithm, as detailed below: Expression Encoding and Representation: Mathematical expressions are represented using an enhanced Abstract Syntax Tree (AST) structure, where each node contains the operation type, parameter value, and physical unit attribute. The system maintains a physical quantity dimension checker to ensure that all generated expressions are consistent across physical dimensions. For example, it ensures that mass and volume are divided to obtain density, and that temperature and energy terms are not directly added together.

[0080] Population initialization strategy: Based on the results of neural network pre-learning, a targeted initialization strategy was designed: 20% of the individuals were generated based on physical model templates such as the Arrhenius equation; 30% of the individual data were generated based on feature importance and nonlinear relationship patterns extracted from neural networks. 30% of the individuals were generated using simple polynomial form; 20% of individuals are generated completely randomly to maintain diversity; The initial population size was 500, and after preliminary evaluation, the 200 individuals with the best performance were retained to enter the evolutionary process.

[0081] Implementation of the fitness function for physical constraints: The system implements a fitness function consisting of three parts: Accuracy term: Use weighted mean square error, and reduce the weight of outliers; Simplicity: A comprehensive measure that combines the number of expression nodes, depth, and the number of features used. Physical rationality items include physical unit consistency checks, limit condition behavior verification (such as expression behavior when the temperature approaches absolute zero), monotonicity verification, etc.

[0082] Adaptive genetic operator: Semantic-aware cross-operation: Analyzes the semantic equivalence of sub-expressions and prioritizes exchanging sub-expressions that are similar in structure and meaning. For example, it can identify two expressions that both contain the structure "a coefficient multiplied by a variable and then added together" and perform targeted cross-operations on these structures.

[0083] Mutation operations based on physics knowledge: 10 specific mutation operators were designed, such as adding / removing temperature dependencies, replacing them with thermodynamic formulas, and introducing material property parameters.

[0084] Adaptive operation probability: The crossover rate (range 0.7 to 0.9) and mutation rate (range 0.1 to 0.3) are dynamically adjusted based on the effectiveness of different operations during the evolution process.

[0085] Application Example: When predicting the upper explosive limit of a nitrogen-containing hazardous chemical as a function of temperature and pressure, the system, through this algorithm, discovered the following expression after 150 generations of evolution (approximately 12 minutes of computation time): The system, through an improved genetic programming algorithm, discovered a mathematical expression describing the variation of the upper explosive limit (EUP) of nitrogen-containing hazardous chemicals. This expression consists of three main parts. The first part is a reference EUP value, representing the concentration of the substance at its upper explosive limit under standard conditions (specific temperature and pressure), serving as a baseline. The second part is a pressure effect term, using a square root function to represent the relationship between the EUP and pressure, where the numerator is the current pressure and the denominator is the reference pressure. This indicates that increasing pressure increases the EUP, but the rate of increase slows down with further pressure increases. The third part is a temperature effect term, using an exponential function. The exponential term includes the ratio of the enthalpy change to the gas constant, multiplied by the difference between the reciprocal of the reference temperature and the reciprocal of the actual temperature. This term describes the phenomenon that increasing temperature leads to a decrease in the EUP, and the rate of change is related to the magnitude of the enthalpy change. This expression exhibits extremely high predictive accuracy (relative error less than 3%) under various temperature and pressure conditions and fully conforms to the principle of thermodynamic equilibrium. It can provide a reliable theoretical basis for setting safety boundaries in the storage and transportation of hazardous chemicals, helping managers to formulate more precise safety measures.

[0086] Knowledge Accumulation and Reuse: The system stores discovered high-quality expressions in a knowledge base to guide future modeling of similar hazardous chemicals. When modeling another nitrogen-containing compound with a similar structure, by reusing and fine-tuning the above expressions, the same quality results can be obtained with only 1 / 5 of the original computational resources.

[0087] like Figure 3 As shown, the performance of adaptive symbolic regression, deep neural networks, and traditional regression methods is compared across four dimensions: prediction accuracy, interpretability, computational efficiency, and generalization ability. The advantages of the proposed adaptive symbolic regression method in overall performance are demonstrated, particularly its outstanding performance in interpretability and computational efficiency. In terms of prediction accuracy, adaptive symbolic regression is comparable to deep neural networks, but in the interpretability dimension, it achieves a near-perfect score, while deep neural networks score lower due to their "black box" nature. Regarding computational efficiency, adaptive symbolic regression achieves high-speed inference through concise mathematical expressions, far surpassing deep neural networks which require a large number of parameter calculations. In terms of generalization ability, adaptive symbolic regression demonstrates stronger cross-scenario adaptability through the fusion of physical constraints and domain knowledge. These performance advantages validate the advanced nature and practicality of adaptive symbolic regression technology in the field of predicting the physicochemical properties of hazardous chemicals.

[0088] Through this improved genetic programming algorithm, the system can effectively explore mathematical formulas that conform to physical laws in a complex expression space, providing scientific and reasonable explanations while ensuring prediction accuracy, and providing reliable theoretical support for the management of the physical and chemical properties of hazardous chemicals.

[0089] Step 4.4, multi-level search strategy; According to one embodiment of this application, a multi-level search strategy is employed to progressively increase the complexity and accuracy of the expression: Level 1 Search: Find simple but basic expressions to capture key trends; Secondary search: Adds modifiers to the basic expression to improve accuracy; Three-level search: Introduces conditional branches to handle different behaviors under different conditions.

[0090] Furthermore, in each level of the search, an adaptive control mechanism is used to dynamically adjust the search parameters: The system implements an adaptive parameter control mechanism to dynamically adjust key parameters during the search process. This mechanism first sets initial values ​​for each parameter (such as mutation rate and crossover rate) as baseline reference points. Then, during the search, it dynamically calculates adjustment coefficients based on the current search round and population performance indicators. Finally, it multiplies the initial parameter values ​​by the adjustment coefficient to obtain the actual parameter values ​​at the current moment. The adjustment coefficient is calculated using a specially designed adaptive function. This function takes the search round and performance indicators as input and outputs appropriate adjustment coefficients by evaluating the search progress. When the system detects that the search performance has not improved for several consecutive rounds, the function outputs a coefficient greater than 1, increasing the relevant parameter values ​​to enhance the exploratory nature of the search. When a better solution is found, the function outputs a coefficient less than 1, decreasing the parameter values ​​to enhance the utilization of the search. When the search is in a normal progress phase, the function outputs a coefficient close to 1, keeping the parameters relatively stable. By analyzing the performance improvement rate over a recent period (usually 10 rounds) and combining it with preset condition thresholds, the system controls the adjustment coefficients within the range of 0.8 to 1.2, ensuring both flexible adjustment of the search strategy and avoiding drastic parameter fluctuations. This adaptive control mechanism enables the system to intelligently balance exploration and utilization based on search difficulty and progress, thereby improving the search efficiency of symbolic regression.

[0091] Step 4.5, Parallel Cooperative Search Architecture; Build a parallel collaborative search architecture to improve search efficiency: Island model: Divide the population into multiple subpopulations, which evolve independently on different "islands"; Migration strategy: Regularly exchange superior individuals among subpopulations to promote information sharing; Hierarchical search: Subpopulations at different levels focus on expressions of varying complexity.

[0092] Optionally, in some implementations, the system can dynamically adjust the parallelism and coordination strategy according to the availability of computing resources in order to achieve optimal utilization of computing resources.

[0093] Therefore, through the aforementioned neural-guided adaptive symbolic regression algorithm, the system can efficiently search within a vast expression space to discover concise mathematical formulas that accurately describe the changing patterns of the physicochemical properties of hazardous chemicals, thus achieving a balance between prediction accuracy and interpretability.

[0094] To further illustrate the specific implementation and application of the adaptive symbolic regression algorithm, a complete implementation process is provided below: For oxidizing hazardous chemicals like ammonium sulfate, it is necessary to predict their decomposition rate under different temperature and humidity conditions. Traditional methods typically rely on fitting experimental data or purely statistical models, which lack interpretability. The specific steps for modeling using the adaptive symbolic regression algorithm of this system are as follows: Initialize the expression search space: Based on physical chemistry knowledge, initialize the terms related to the Arrhenius equation ( ,in For activation energy, The gas constant is Absolute temperature (base of the natural logarithm), temperature polynomial term ( ,in Absolute temperature The search space is for basic elements such as the power of the polynomial and the humidity effect term.

[0095] Neural network pre-training guidance: The system first trains a three-layer MLP network (8 nodes in the input layer, 16 and 8 nodes in the two hidden layers, and 1 node in the output layer) to learn the relationship between factors such as temperature, humidity, and pressure and the decomposition rate. Through sensitivity analysis of the trained neural network, it was found that temperature has an exponential relationship with the decomposition rate, while humidity interacts with temperature.

[0096] Adaptive search strategy implementation: Based on patterns discovered by the neural network, the system dynamically adjusts its expression search strategy, prioritizing expressions containing exponential relationships and interaction terms. The system uses a population of 400 individuals, with an initial complexity penalty coefficient. And dynamically adjust the value to a range of 0.03 to 0.08 based on the progress of the search.

[0097] Expression generation and evaluation: After approximately 150 generations of evolution, the system generated the following expression: ; in, The thermal decomposition rate of ammonium nitrate after evolution. Absolute temperature (unit: Kelvin). Relative humidity (value range: 0 to 1). Environmental pressure (in Pascals). , , , These represent the reaction rate constant, humidity effect coefficient, pressure effect coefficient, and activation energy, respectively. Represents the gas constant; This represents an exponential function.

[0098] The root mean square error of this expression is 0.021, which is only slightly higher than the 0.019 of the neural network model, but the number of parameters is reduced from 273 in the neural network to 4.

[0099] Engineering Application Deployment: The generated expressions are embedded into the enterprise's hazardous chemical monitoring system for real-time calculation and early warning. In the ammonium sulfate storage facility of a chemical company, the model successfully predicted the decomposition risk that might be caused by a temperature rise due to a refrigeration system failure, issuing an early warning 12 hours in advance, giving the company sufficient time to take cooling measures and avoid potential accidents.

[0100] As can be seen from the above implementation process, the adaptive symbolic regression algorithm can not only generate accurate prediction formulas, but also provide clear physical explanations, enabling enterprise managers to understand the scientific principles behind the changes in the behavior of hazardous chemicals and make more reasonable management decisions.

[0101] Step 5: Optimize and validate the adaptive symbolic regression results, and select the best mathematical expression as the prediction model for the physicochemical properties of hazardous chemicals. According to one embodiment of this application, this step further optimizes and verifies the candidate expressions obtained from the search, ensuring that the final generated mathematical formula simultaneously possesses high prediction accuracy, good interpretability, and practical application value. Specifically, it includes the following sub-steps: Step 5.1, expression structure optimization; The candidate expressions obtained from the search are structurally optimized to improve their simplicity and interpretability: Algebraic simplification: Using computer algebra systems to perform equivalent transformations on expressions, eliminating redundant terms and operations; Symbol reduction: Identifying and replacing sub-expressions that can be represented by fundamental physical formulas, thereby enhancing the interpretability of physics; Structural adjustment: While maintaining semantic equivalence, adjust the structure of the expression to make it more in line with scientific notation.

[0102] For example, for complex expressions containing addition, subtraction, and multiplication, the system can optimize them into more concise, easier-to-understand, and easier-to-compute equivalent expressions through algebraic simplification.

[0103] Step 5.2, fine-tuning the parameters; Fine-tuning the numerical parameters in the expression further improves prediction accuracy: Gradient descent optimization: Treat the expression as a parameterized model and apply the gradient descent algorithm to fine-tune the numerical parameters; Global optimization algorithms: For non-convex optimization problems, simulated annealing or particle swarm optimization are used to avoid local optima; Constraint optimization: Introduce physical rationality constraints to ensure that parameter values ​​conform to physical laws.

[0104] Training data standardization: During parameter optimization, all training data must be standardized in the same way as when the model was trained to ensure the effectiveness of parameter optimization; Validation data preprocessing: The validation dataset needs to be preprocessed using the same methods as the training data to ensure consistency of the evaluation results; Parameter initialization preprocessing: For parameters with physical meaning, it is necessary to set a reasonable range of initial values ​​according to physical laws to avoid parameter optimization getting stuck in local optima; Constraint preprocessing: The parameters in the physical constraints need to use the same unit system and standardization method as the optimization parameters to ensure the effectiveness of the constraints.

[0105] The objective function for parameter optimization considers multiple factors: The system implements a comprehensive optimization objective function for fine-tuning the numerical parameters in symbolic expressions: ; in To comprehensively optimize the objective function, This represents the parameter vector to be optimized. For parameters The expression for the mean squared error on the dataset, The weight coefficients for the parameter regularization term, For parameter regularization terms (such as L1 or L2 norm). The weighting coefficients for the physical rationality constraint term. This is a physical rationality constraint.

[0106] This function consists of three key components. The first component is the mean squared error term. This term quantifies the fitting accuracy of the expression by calculating the average of the squared differences between the predicted results using the expression with the current parameter values ​​and the actual observed values; a smaller value indicates a more accurate fit. The second component is the parameter regularization term. This term imposes constraints on parameter values ​​by calculating the norm of the parameter vector (such as the L1 or L2 norm), preventing overfitting caused by excessively large parameters, and uses a tradeoff coefficient. Controlling the intensity of its impact. The third component is the physical rationality constraint. This item applies additional constraints by evaluating whether the parameter values ​​conform to physical laws, and is determined by a tradeoff coefficient. The degree of influence is controlled. The physical rationality constraint is specifically implemented as follows: the system substitutes parameters into predefined physical constraints, such as the reaction rate constant must be positive and the activation energy must be within a reasonable energy range, calculates the degree of constraint violation, and outputs the weighted sum of squares of the violation degrees as the term. The more the parameter value conforms to physical laws, the closer the term value is to zero. Based on the characteristics of different physicochemical properties, the system automatically selects an appropriate set of physical constraints to ensure that the optimization results are not only mathematically accurate but also have physical interpretive significance. By minimizing this comprehensive objective function, the system can find the optimal parameter values ​​that both fit the data and conform to physical laws, generating a high-quality physicochemical property prediction model.

[0107] The following are detailed implementation methods and application examples of the parameter optimization and verification system: For optimizing the expression parameters discovered by symbolic regression, the system implements a multi-objective constrained optimization framework, as detailed below: Optimized strategy architecture: The system adopts a three-tier optimized architecture: First layer: gradient-based local optimization, using the L-BFGS-B algorithm to quickly converge to a local optimum; The second layer: a global search based on simulated annealing, where the temperature linearly decreases from 1.0 to 0.01, with 100 iterations per temperature. The third layer: fine-tuning of particle swarm optimization, using 30 particles and a maximum of 500 iterations.

[0108] Physical constraint implementation: The system incorporates physical law constraints into the optimization process, specifically as follows: The constraint is transformed into part of the objective function through the penalty function: The system designs a comprehensive physical constraint penalty method to incorporate multiple physical law constraints into the parameter optimization process: ; in This is a physical constraint penalty term. For summation, This represents the total number of physical constraints. For the first The weight of each physical constraint, For the first The degree of violation of parameters under physical constraints.

[0109] This method first defines There are several physical constraints, each related to a specific physical law; then, weights are assigned to each constraint. The weight values ​​reflect the importance of the constraint in a specific application; then the degree of violation of each constraint is calculated. The system calculates the degree to which the parameter values ​​deviate from the physical constraints. Finally, it sums all weighted squared violation terms to form the total physical constraint penalty value. The calculation of constraint violation degree uses a mapping function, which substitutes the parameters into the constraint expression and returns an appropriate violation metric based on the constraint type: for inequality constraints, it returns zero if the parameter satisfies the constraint, otherwise it returns the degree of violation; for equality constraints, it returns the absolute value of the deviation of the parameter from the target value. For example, for the upper limit constraint of the activation energy parameter, it returns zero if the parameter value does not exceed the upper limit, and returns the excess amount if it does; for the range constraint of the reaction equilibrium constant, it returns zero if the parameter value is within the effective range, otherwise it returns the distance to the nearest boundary. By introducing physical laws as soft constraints into the optimization process in this way, the system ensures the physical rationality of the parameter values ​​while retaining the search flexibility of the optimization algorithm. The generated mathematical expression accurately fits the data and conforms to basic physical laws.

[0110] Dynamically adjust constraint weights: Set them relatively small in the initial optimization stage. The value (approximately 0.01) is gradually increased to 0.5 to 1.0 as optimization progresses, ensuring that the final solution satisfies the physical constraints; where These are the physical constraint weighting coefficients.

[0111] Parameter sensitivity analysis: The system performs a global sensitivity analysis on the optimized expression parameters, using the Sobol method to calculate the contribution of each parameter to the output. For highly sensitive parameters, the system automatically narrows the search range and increases search accuracy; for low-sensitive parameters, they may be simplified or fixed to constant values ​​to reduce model complexity.

[0112] Expression simplification and physical interpretation: The system attempts to compare the optimized expression with known physical laws, for example: When an expression contains the form of When constructing a structure, the system will automatically identify the possible corresponding Arrhenius equations and attempt to replace the abstract parameters with physical quantities (such as activation energy); among which It is the frequency factor of the reaction rate (i.e., the initial rate constant at which the reaction occurs). is the base of the natural logarithm. For energy parameters related to activation energy, For temperature.

[0113] When linear combinations are found At that time, the system will analyze and Does the ratio approach the ratio of certain physical constants? , These are the weight coefficients corresponding to the variables. , For variables.

[0114] Application Example: For a common corrosive liquid hazardous chemical, the system discovered a mathematical expression describing the relationship between its vapor pressure and temperature through symbolic regression: The system discovered a mathematical expression describing the vapor pressure changes of corrosive liquid hazardous chemicals through symbolic regression: ; in Vapor pressure, It is the reference coefficient for vapor pressure (i.e., the vapor pressure constant under standard conditions). It is an exponential function. This refers to energy parameters (such as activation energy). For temperature, This is a temperature correction factor. It is the natural logarithm function. Humidity influence coefficient This refers to relative humidity.

[0115] The expression consists of two main parts. The first part is the temperature dependence term, which takes the form of an exponential function, and its exponent contains two subterms: one is negative. Parameter divided by temperature The term describes the fundamental trend of vapor pressure increasing exponentially with increasing temperature, similar to the standard Clapeyron equation; the other is the natural logarithm of temperature multiplied by . The first parameter is used to correct for deviations under non-ideal conditions, improving prediction accuracy over a wide temperature range. The second part is the humidity effect term, which is 1 plus the relative humidity. Multiply The parameters represent the effect of ambient humidity on vapor pressure, reflecting the special behavior of certain corrosive liquids in high-humidity environments. The entire expression contains... The parameters are used to set the baseline level for vapor pressure, determining the initial value of vapor pressure under standard temperature and humidity conditions. This mathematical model can accurately capture the vapor pressure variation patterns of corrosive liquid hazardous chemicals under various temperature and humidity conditions, providing a scientific basis for the control of hazardous chemical storage environments and the design of ventilation systems.

[0116] The specific process of system parameter optimization is as follows: First, determine the initial search range of parameters through physical constraints (e.g.) (The corresponding activation energy must be positive). Find an approximate solution quickly using the L-BFGS-B algorithm: Approximately 12500 Approximately 5600 Approximately 0.28 Approximately equal to 0.003; where It is the reference coefficient for vapor pressure (i.e., the vapor pressure constant under standard conditions). For energy parameters (such as activation energy); This is the temperature correction factor.

[0117] Using simulated annealing for a global search, a better solution was found: Approximately 13800 Approximately 5750 Approximately 0.31 Approximately equal to 0.0025; where It is the reference coefficient for vapor pressure (i.e., the vapor pressure constant under standard conditions). For energy parameters (such as activation energy); This is the temperature correction factor.

[0118] Fine-tuning was performed using the particle swarm optimization algorithm, and the final result was determined as follows: It equals 13762. It equals 5743. It equals 0.307. It equals 0.0026; where It is the reference coefficient for vapor pressure (i.e., the vapor pressure constant under standard conditions). For energy parameters (such as activation energy); This is the temperature correction factor.

[0119] Sensitivity analysis showed The parameter (corresponding to the activation energy) is the most critical, affecting the results by up to 65%.

[0120] The optimized formula was successfully applied to a chemical plant to predict vapor pressure under different temperature and humidity conditions, providing a basis for ventilation system design. Compared with traditional empirical formulas, the prediction accuracy was improved by 40%, and it performed more stably, especially under extreme temperature conditions.

[0121] like Figure 4As shown, the graph illustrates the trend of ammonium sulfate decomposition rate with temperature under different pressure conditions (0.8 atm, 1.0 atm, and 1.2 atm). The data validates that the mathematical model discovered by the method of this invention can accurately capture the influence of pressure on decomposition kinetics. The graph shows that increased pressure inhibits the decomposition reaction. Under different pressure conditions, the curves of decomposition rate versus temperature exhibit obvious stratification characteristics, indicating that pressure is an important environmental factor affecting the thermal decomposition kinetics of ammonium sulfate. This visualization not only verifies the physical rationality of the mathematical expression discovered by adaptive symbolic regression, but more importantly, it provides a scientific basis for optimizing hazardous chemical storage conditions, helping managers to formulate more precise safety measures.

[0122] Verification methods and reliability assurance: The system adopts a multi-level verification strategy. Internal dataset validation: Cross-validation is performed using a split of 80%–20% of the training and test sets; Leave-one-out validation: Perform leave-one-out validation for each hazardous chemical sample to ensure that the model is not sensitive to changes in a single sample; Extreme condition verification: Specifically verifying performance under conditions close to critical values, such as temperature and pressure; Verification of the consistency of physical laws: Check whether the expressions conform to the fundamental laws of thermodynamics under various conditions.

[0123] Therefore, through this parameter optimization and verification system, the mathematical expression discovered by adaptive symbolic regression not only has high prediction accuracy, but also ensures physical rationality and good generalization ability, providing a reliable tool for the scientific prediction and management of the physicochemical properties of hazardous chemicals.

[0124] Step 5.3, Expression Integration and Selection; According to another embodiment of this application, an expression integration strategy is constructed to further improve prediction performance while maintaining interpretability: Piecewise expressions: Construct conditional piecewise expressions based on different conditional regions; Additive model: An ensemble model formed by combining multiple simple expressions through weighted summation; Hierarchical expressions: Construct a hierarchical structure of main expressions and modifier expressions.

[0125] Apply model selection criteria to the ensemble expression to balance prediction accuracy and complexity: The system uses the Bayesian information criterion to evaluate and select candidate expressions: ; in For expression The Bayesian information criterion value, For the sample size, It is the natural logarithm function. For expression The mean square error, The number of arguments in the expression.

[0126] This criterion comprehensively considers the predictive accuracy and complexity of the expression, providing a scientific basis for model selection. The calculation process first obtains the total number of data samples. This value represents the amount of data available for evaluation; then the mean squared error of the expression is calculated over all samples. This value quantifies the predictive accuracy of the expression; a smaller value indicates a better fit. Next, the complexity of the expression is calculated. Typically, the number of parameters or operators in the expression is used as a metric. Then, the natural logarithm of the mean squared error is multiplied by the sample size to obtain a penalty term for goodness of fit. Simultaneously, the complexity is multiplied by the natural logarithm of the sample size to obtain a penalty term for model complexity. Finally, the two penalty terms are added to obtain the final Bayesian information criterion value for the expression. This criterion imposes a greater penalty on complex expressions during evaluation, thus prioritizing the simpler expression among multiple candidate expressions with similar prediction accuracy. In this way, the system can select the simplest and most interpretable mathematical expression while ensuring prediction accuracy, avoiding the overfitting risk caused by overly complex expressions, and improving the model's generalization ability and practical value.

[0127] This criterion comprehensively considers the predictive accuracy and complexity of the expression, providing a scientific basis for model selection. The calculation process first obtains the total number of data samples. This value represents the amount of data available for evaluation; then the mean squared error of the expression is calculated over all samples. This value quantifies the predictive accuracy of the expression; a smaller value indicates a better fit. Next, the complexity of the expression is calculated. Typically, the number of parameters or operators in the expression is used as a metric. Then, the natural logarithm of the mean squared error is multiplied by the sample size to obtain a penalty term for goodness of fit. Simultaneously, the complexity is multiplied by the natural logarithm of the sample size to obtain a penalty term for model complexity. Finally, the two penalty terms are added to obtain the final Bayesian information criterion value for the expression. This criterion imposes a greater penalty on complex expressions during evaluation, thus prioritizing the simpler expression among multiple candidate expressions with similar prediction accuracy. In this way, the system can select the simplest and most interpretable mathematical expression while ensuring prediction accuracy, avoiding the overfitting risk caused by overly complex expressions, and improving the model's generalization ability and practical value.

[0128] Step 5.4, cross-validation and stability testing; The optimized expression is rigorously validated to ensure its generalization ability and stability. K-fold cross-validation: Evaluating the predictive stability of the expression under different data partitions; Leave one for verification: For rare hazardous chemicals or under extreme conditions, leave one for verification. Sensitivity analysis: Perturbations are added to the input features to test the robustness of the expression to noise and anomalies.

[0129] It should be understood that by comprehensively evaluating multiple verification methods, an expression with stable performance and strong generalization ability can be selected.

[0130] Step 5.5, Physical rationality verification and domain expert evaluation; Domain knowledge is used to verify the physical validity of the expression: Dimensional consistency check: Ensure that the physical quantities on both sides of the expression have the same dimension; Boundary condition verification: Verify whether the behavior of the expression is reasonable under physical limit conditions; Qualitative trend analysis: Verify whether the trend predicted by the expression conforms to basic physical laws.

[0131] In addition, the expression was evaluated based on the assessment of domain experts, considering the following aspects: Scientific rationality: Does the expression conform to known physical and chemical laws? Novel Insight: Does the expression offer new insights into the relationship between physicochemical properties? Practical application value: Whether the expression is easy to apply in actual management.

[0132] Optionally, in some implementations, the system can further adjust and optimize the expression based on feedback from domain experts to improve its practical application value.

[0133] Therefore, through the above expression optimization and verification steps, the system can generate mathematical formulas that simultaneously meet the requirements of prediction accuracy, interpretability, and practicality, providing reliable tools and theoretical basis for the scientific management of the physicochemical properties of hazardous chemicals.

[0134] A hazardous chemical physicochemical property management system, used to execute the above-mentioned hazardous chemical physicochemical property management method, includes: The data processing module is used to clean and standardize the physicochemical property data of hazardous chemicals. The feature analysis module is used to extract and transform key features from data to improve the effectiveness of subsequent modeling. The neural network modeling module is responsible for using deep learning methods to uncover complex relationships in the data and introducing physical constraints. The symbolic regression module performs expression search and modeling based on neural network results. The expression optimization and evaluation module simplifies the generated mathematical model, adjusts its parameters, and verifies its effectiveness.

[0135] The embodiments of the present invention have been described above. However, the embodiments are not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make more equivalent embodiments under the guidance of the present embodiments, and all of them are within the protection scope of the present embodiments.

Claims

1. A method for managing the physicochemical properties of hazardous chemicals, characterized in that, include: The physicochemical property data of hazardous chemicals are preprocessed to obtain a standardized dataset. Feature extraction and transformation are performed on standardized datasets, including domain knowledge-guided feature engineering and autoencoder dimensionality reduction; By using a deep neural network with physical consistency constraints to pre-learn the results of feature extraction and transformation, complex patterns in the data can be extracted. Adaptive symbolic regression based on deep neural network pre-learning results includes defining the expression search space, performing neural-guided search space pruning, and applying an improved genetic programming algorithm. The adaptive symbolic regression results were optimized and validated, and the optimal mathematical expression was selected as the prediction model for the physicochemical properties of hazardous chemicals.

2. The method for managing the physicochemical properties of hazardous chemicals according to claim 1, characterized in that, The preprocessing of the physicochemical properties data of hazardous chemicals specifically includes: applying an adaptive anomaly detection algorithm to process outliers and noise in the original data; selecting Zscore standardization and robust normalization methods according to the data distribution characteristics; and performing spatiotemporal alignment and missing data imputation.

3. The method for managing the physicochemical properties of hazardous chemicals according to claim 1, characterized in that, The feature extraction and transformation include: constructing features with clear physical meaning based on knowledge of the physicochemical properties of hazardous chemicals; using an adaptive autoencoder to perform nonlinear dimensionality reduction on the high-dimensional features, wherein the autoencoder is trained by minimizing reconstruction error and regularization terms; performing nonlinear transformation on the extracted features to expand the feature space; and applying an ensemble feature selection algorithm to evaluate feature importance and perform feature screening.

4. The method for managing the physicochemical properties of hazardous chemicals according to claim 1, characterized in that, The pre-learning of the feature extraction and transformation results using a deep neural network with physical consistency constraints specifically includes: Construct a deep neural network model for predicting the physicochemical properties of hazardous chemicals; Training is performed using a comprehensive objective function that includes a mean squared error term, a weight regularization term, and a physical consistency constraint term; The knowledge contained in the trained neural network is extracted to generate synthetic data, extract some response functions and feature importance; Sensitivity analysis is performed on the trained neural network to identify key patterns and laws governing changes in its physicochemical properties.

5. The method for managing the physicochemical properties of hazardous chemicals according to claim 1, characterized in that, The adaptive symbolic regression specifically includes: Construct an expression search space containing a set of variables, a set of constants, a set of unary operators, a set of binary operators, and structure elements; Pruning of variable importance, function type, and structural complexity is performed based on knowledge pre-learned by neural networks. The design includes specialized genetic operations such as semantically aware crossover, gradient-based mutation, and multi-objective selection; A multi-level search strategy that progressively increases the complexity of the expression is adopted. A parallel collaborative search architecture is constructed using an island model and hierarchical search.

6. The method for managing the physicochemical properties of hazardous chemicals according to claim 1, characterized in that, The optimization and validation of the adaptive symbolic regression results specifically include: Perform algebraic simplification, symbol reduction, and structural adjustment on the candidate expressions; Gradient descent optimization and global optimization algorithms are applied to fine-tune the numerical parameters in the expression; Construct expression integration strategies, including piecewise expressions, additive models, and hierarchical expressions; The generalization ability and stability of the expression were evaluated using K-fold cross-validation, leave-one-out validation, and sensitivity analysis. Domain knowledge is introduced to perform dimensional consistency checks, boundary condition verification, and qualitative trend analysis.

7. The method for managing the physicochemical properties of hazardous chemicals according to claim 1, characterized in that, The physical consistency constraint is implemented by introducing a physical constraint function. The physical constraint function receives the model's predicted value and input features as parameters, calculates the degree of conformity between the prediction result and a specific physical law, and outputs zero when the prediction result meets the physical law, and the greater the deviation, the larger the output.

8. The method for managing the physical and chemical properties of hazardous chemicals according to claim 6, characterized in that, The adaptive symbolic regression also includes knowledge-enhanced neural representation learning, specifically including: constructing a physicochemical property relation representation based on a knowledge graph; configuring a hybrid neural symbolic architecture to integrate symbolic reasoning and neural network learning; and learning the latent representation of changes in physicochemical properties.

9. The method for managing the physicochemical properties of hazardous chemicals according to claim 1, characterized in that, The optimization and verification also includes parameter optimization, which uses Bayesian information criteria to evaluate and select candidate expressions, taking into account both the prediction accuracy and complexity of the expressions.

10. A management system for the physical and chemical properties of hazardous chemicals, characterized in that, A method for managing the physical and chemical properties of hazardous chemicals according to any one of claims 1-9, comprising: The data processing module is used to clean and standardize the physicochemical property data of hazardous chemicals. The feature analysis module is used to extract and transform key features from data to improve the effectiveness of subsequent modeling. The neural network modeling module is responsible for using deep learning methods to uncover complex relationships in the data and introducing physical constraints. The symbolic regression module performs expression search and modeling based on neural network results. The expression optimization and evaluation module simplifies the generated mathematical model, adjusts its parameters, and verifies its effectiveness.

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