Explanatable machine learning method and system for optimizing self-assembly monomolecular layer interface thermal conductivity, and medium

Abstract

The invention relates to an interpretable machine learning method and system for optimizing self-assembly monomolecular layer interface thermal conductivity, and a medium. The method comprises the following steps: acquiring an initial machine learning training feature data set, and performing feature engineering processing in combination with self-assembly monomolecular layer interface thermal conductivity to obtain key physical features beneficial to explaining a physical mechanism as a machine learning model training input set; aiming at the interface thermal conductivity of the self-assembled monomolecular layer and combining the physical characteristics obtained by filtering, building and training an interface thermal conductivity machine learning model; for the trained interface thermal conductivity machine learning model, SHAP feature interpretable analysis is carried out, and a symbol regression variable set is determined; and further obtaining interpretable physical screening indexes. Compared with the prior art, the method has the advantages that interpretable machine learning is carried out through feature engineering with physical meanings, independent and unassociated physical features are fused through a symbolic regression algorithm, and new interpretable physical screening indexes are created and used for reliable heat transport design of the self-assembled monomolecular layer.

Description

Technical Field

[0001] The present invention belongs to the field of material genetic engineering technology for new interface materials at the micro-nano scale, and in particular relates to an explainable machine learning method, system, and medium for optimizing the thermal conductivity of a self-assembled monolayer interface. Background Art

[0002] Self-assembled monolayers of organic molecules (abbreviated as SAMs) can form spontaneously by adsorption on the surface. At the thermodynamic level, its formation process can be understood through the interaction between the entropy of water, the associated surface tension and free energy. SAMs have a wide range of surface functionalization applications in micro-nano devices, evaporation and condensation, biomedicine and catalysts. Specifically, in applications such as electronic device cooling, solar thermal evaporation, nanofluids and nanoparticle-assisted photothermal therapy, the system size is at the nanometer or micrometer scale, which is comparable to the mean free path of phonons in the SAM. For this reason, phonon scattering plays an important role in the interfacial thermal resistance and overall heat transport of the SAM. Furthermore, it is a major challenge to control and regulate interfacial heat transport using SAMs. Due to the complex structural factors involved in the formation of SAMs, such as end groups, chain length and degree of mixing, the physical mechanism of optimizing the interfacial thermal conductivity of SAMs is extremely complex.

[0003] However, previous studies usually used the general formula X-(CH2) n -S-alkanethiolate self-assembled monolayers are prepared as single chains, where X represents the end group and n is usually used to control the chain length. In addition, X is often replaced by simple groups with different polarities (such as -CH3, -OH or -COOH) to study their effects on the heat transfer mechanism. In fact, the structural design flexibility of the end group is extremely great, which has hindered researchers from using self-assembled monolayers to predict and control interfacial thermal conductivity. In recent years, the application of machine learning-assisted self-assembled monolayer design has attracted widespread attention in fields such as biomedicine and interfacial lubrication. Nevertheless, due to the lack of simulation and experimental data on the interfacial thermal conductivity properties of self-assembled monolayers, this poses a challenge to the data-driven design of cross-interface heat transfer.

[0004] In view of this, conducting interpretable data-driven paradigm research on physical associations in small (few) sample data sets can effectively avoid the above problems. At present, there have been interpretable machine learning works developed for different materials and different target properties. Patent CN119808579A "An interpretable machine learning method for predicting rock shear strength parameters" discloses a machine learning prediction method for rock shear strength parameters in the field of mechanical performance testing; Patent CN117497099A "A method for predicting the melting point of energetic materials based on an interpretable machine learning model" adopts a variety of efficient feature engineering processing technologies to extract key features from the molecular structure of energetic materials and predict the melting point of energetic materials; Patent CN118053514A "Polyimide glass transition temperature prediction method based on interpretable machine learning" uses SHAP to explain the machine learning model and The experimental results were compared to achieve efficient prediction of the glass transition temperature of polyimide; Patent CN119479910A "Method for predicting the thermal expansion coefficient of polyimide based on an interpretable machine learning model" uses SHAP to interpret the model, which can explain the factors affecting related properties and provide guidance for the synthesis of new polyimide with low thermal expansion coefficient; Patent CN119833012A "A design method and preparation method for magnesium-air battery negative electrode components based on interpretable machine learning" uses an interpretable machine learning model and interpretable analysis, combined with multi-objective optimization, to design a magnesium alloy component that can simultaneously improve the discharge voltage and negative electrode efficiency.

[0005] In summary, interpretable machine learning is a reliable approach in the new paradigm of materials research and development. However, no relevant interpretable machine learning methods have been publicly reported for the interfacial thermal conductivity characteristics of self-assembled monolayers.

[0006] Therefore, for the control of interfacial thermal conductivity of self-assembled monolayers, an interpretable machine learning method that can assist in the design of self-assembled monolayers is urgently needed to assist researchers in carrying out new paradigm research. Summary of the Invention

[0007] The purpose of the present invention is to overcome the defect that there is still no interpretable machine learning method for regulating interfacial thermal conductivity in the current design of self-assembled monolayer structures, and to provide an interpretable machine learning method, system, and medium for predicting and optimizing the interfacial thermal conductivity of self-assembled monolayers. In view of the fact that existing experimental and computational data are very limited, the present invention uses molecular dynamics simulation to obtain relevant interfacial thermal transport data. To address the problem of small samples of interfacial thermal transport data, interpretable machine learning training is carried out through interpretable physical feature engineering, and independent and unrelated physical features are integrated through a symbolic regression algorithm to create a new interpretable physical screening indicator for reliable thermal transport design of self-assembled monolayers.

[0008] The purpose of the present invention can be achieved by the following technical solutions:

[0009] The first object of the present invention is to provide an interpretable machine learning method for optimizing the interfacial thermal conductivity of self-assembled monolayers, the method comprising the following steps:

[0010] 1) Obtain the physical correlation features related to thermal transport at the interface of self-assembled monolayers and the physical and chemical descriptor features of organic molecules, perform preliminary feature engineering processing for the training of the machine learning model of thermal conductivity at the interface of self-assembled monolayers, filter the features to retain the original physical meaning of the features, and obtain key physical features as the input set for subsequent interpretable machine learning training;

[0011] 2) Targeting the interfacial thermal conductivity of self-assembled monolayers, we build and train an interfacial thermal conductivity machine learning model based on the key physical features obtained through feature engineering filtering.

[0012] 3) Perform SHAP feature interpretability analysis on the trained interface thermal conductivity machine learning model to determine the set of symbolic regression variables;

[0013] 4) Based on the set of symbolic regression variables, obtain interpretable physical screening indicators, including the following process:

[0014] 4-1) Based on the symbolic regression variable set, perform symbolic regression grid formula search to generate a set of candidate interpretable physical indicators;

[0015] 4-2) The set of interpretable physical equations is screened through the Pareto frontier to obtain an interpretable physics screening index, that is, interpretable physical equations with higher fitting degree and simpler formula are identified through the Pareto frontier as interpretable physics screening indicators.

[0016] Furthermore, step 1) includes the following process:

[0017] 1-1) Obtaining physical correlation features related to thermal transport at the interface of self-assembled monolayers and physical and chemical descriptor features of organic molecules as an initial machine learning training feature dataset, performing preliminary feature engineering processing for training a machine learning model of thermal conductivity at the interface of self-assembled monolayers, and performing feature dimensionality reduction on the initial machine learning training feature dataset using low-variance filtering to obtain a low-variance filtered input training feature set;

[0018] 1-2) Comprehensive correlation screening is used to achieve feature dimensionality reduction of the input training feature set after low variance filtering, and a set of key physical features is obtained for machine learning model training while retaining the original physical meaning of the features.

[0019] Furthermore, in step 1), the calculated thermal conductivity of the self-assembled monolayer interface is regarded as the objective function Y, the calculated physical correlation characteristics related to the thermal transport of the self-assembled monolayer interface are used as the input dynamic training feature data set, and the physicochemical descriptor features obtained through the open source software RDKit are used as the input static training feature data set, and the input dynamic training feature data set and the input static training feature data set are used as the initial machine learning training feature data set.

[0020] Furthermore, the dynamic training feature data set, i.e., the physical correlation characteristics related to the thermal transport at the interface of the self-assembled monolayer, includes one or more of the interface action energy / force and its components, the energy and component information of the simulation system, the vibration spectrum information of the self-assembled monolayer such as the peak value, the vibration spectrum coupling strength between the self-assembled monolayer and the interface material, and the thickness of the self-assembled monolayer.

[0021] Furthermore, in step 1-1), low-variance features are removed from the input training features by setting a variance threshold. The reference formula is as follows (1):

[0022]

[0023] Among them S 2 The variance of the descriptor is set, and the cleaning threshold is set. The default value is 0.01. Descriptors below the cleaning threshold are excluded. D represents the physical feature set, j represents the j-th type of one-dimensional feature data, and i represents the i-th data of the one-dimensional feature data of this type.

[0024] Furthermore, in step 1-2), the process of implementing comprehensive correlation screening to reduce the dimension of the input training feature set after low variance filtering specifically includes the following steps:

[0025] Comprehensive feature filtering is performed by using three data statistical correlation indicators: linear (Pearson), monotonicity (Spearman), and nonlinearity (Distance). The three data correlation formulas are as follows: Formulas (2) to (4):

[0026]

[0027] Among them, R pearson 、R spearman 、R dist They represent the correlation coefficients of linearity, monotonicity, and nonlinearity respectively, D represents the set of physical features after low-variance feature filtering, Y represents the interface thermal conductivity, m represents the mth type of one-dimensional feature data, i represents the i-th data of this type of one-dimensional feature data, and n represents the amount of data of each type of one-dimensional data. The above filtering method can effectively avoid the loss of physical information caused by feature dimensionality reduction and retain the original physical meaning of the features.

[0028] Furthermore, in step 2), during the process of building the interface thermal conductivity machine learning model, the deployed machine learning models include a random forest regression model, an extreme gradient boosting regression model, and a gradient boosting regression model, and 10-fold cross validation is performed;

[0029] In step 2), during the process of building the interface thermal conductivity machine learning model, the global optimization tool Bayesian optimization package is used to adjust the hyperparameters of all machine learning models in each training to improve the prediction accuracy.

[0030] Furthermore, in step 3), for the trained interface thermal conductivity machine learning model, the SHAP toolkit is used to explain the relationship between the set of key physical features obtained after dimensionality reduction in steps 1-1) and 1-2) and the interface thermal conductivity, and the feature importance is evaluated based on the machine learning models ranked in the top 25% of the overall training performance. The SHAP value matrix of this type of trained interface thermal conductivity machine learning model is used for the interpretable work of machine learning, and finally the set of symbolic regression variables is determined.

[0031] Furthermore, in step 4-1), based on the set of symbolic regression variables, the symbolic regression formula construction strategy is incorporated into the simple screening descriptor creation process, and a symbolic regression grid formula search is performed and implemented in the gplearn software, where the Pearson coefficient is used as the fitness function of the symbolic regression of the interface thermal conductivity data, and new descriptors with higher linear correlation are generated as screening criteria, and finally a set of candidate interpretable physical indicators is generated.

[0032] Furthermore, in step 4-2), based on the formula complexity (formula length) of the interpretable physical indicator and the Pearson coefficient of linear correlation between it and the interface thermal conductivity, multiple interpretable physical screening indicator formulas with higher fit and simpler formulas are finally determined. These interpretable physical screening indicator formulas with higher fit and simpler formulas are all located on the global optimal Pareto frontier of formula complexity and linear correlation Pearson coefficient.

[0033] Furthermore, several interpretable physical screening index formulas with higher fitting degree and simpler formulas are determined, namely formulas (5) to (10), as follows:

[0034]

[0035] ln(1.02-E)-L(7)

[0036]

[0037] where E is the average interfacial interaction energy between the self-assembled monolayer and water, and L is the average chain length.

[0038] Furthermore, after step 4-2), perform the following step 4-3):

[0039] 4-3) Compare the final determined interpretable physical screening indicator with the screening results of a single physical indicator to confirm the screening effect of the interpretable physical screening indicator.

[0040] The method of the present invention, namely an interpretable machine learning method for optimizing the interfacial thermal conductivity of self-assembled monolayers, mainly includes four parts: feature engineering, machine learning model building, SHAP analysis and filtering, and symbolic regression feature creation.

[0041] In feature engineering, the interfacial thermal conductivity of the self-assembled monolayer is first calculated and regarded as the target function Y. The calculated physical correlation characteristics of the self-assembled monolayer, such as the interfacial interaction energy / force and its components, the energy and component information of the simulation system, the vibration spectrum information of the self-assembled monolayer, such as the peak value, the coupling strength of the vibration spectrum of the self-assembled monolayer (the ratio of the overlapping area of ​​the vibration spectrum), the thickness of the self-assembled monolayer (dynamic chain length), etc., are used as the input dynamic training feature data set. The physicochemical descriptor features obtained through the open source software RDKit are used as the input static training feature data set; then, low-variance feature removal is performed on the input training features; then, three data statistical correlation indicators, linear (Pearson), monotonicity (Spearman), and nonlinear (Distance), are used to perform feature filtering. The above filtering method can effectively avoid the loss of physical information caused by feature dimensionality reduction and retain the original physical meaning of the features.

[0042] In the machine learning model construction, three types of machine learning models were deployed: random forest (RF), extreme gradient boosting (XGB), and gradient boosting (GB) regression, with 10-fold cross-validation. Each model was trained 100 times to assess its robustness. During each training session, hyperparameters of all machine learning models were adjusted using the global optimization tool Bayesian Optimization package to improve prediction accuracy. During the hyperparameter optimization process, 20 pairs of random parameters were initially used to train the Gaussian process and acquisition function. After 100 optimization iterations, the ideal parameters for each machine learning model were determined.

[0043] In SHAP analysis filtering, to explain the association between the filtered set of physical features and the interfacial thermal conductivity, the SHAP toolkit was used to assess feature importance based on a machine learning model ranked by overall training performance. SHAP analysis is a method based on game-theoretic Shapley values ​​that explains the contribution of features to machine learning predictions.

[0044] In the symbolic regression feature creation, the present invention incorporates the symbolic regression formula construction strategy into the simple screening descriptor creation process and implements it in the gplearn software. Considering that symbolic regression is not applicable to high-dimensional data, only the key physical features determined after SHAP analysis are used as input variables. The Pearson coefficient is used as the symbolic regression fitness function applied to the interface thermal conductivity data, aiming to generate a new equation with higher linear correlation as a screening criterion. Based on this, a grid search strategy is adopted to generate mathematical equations. Finally, multiple equations identified by the density distribution method are determined on the Pareto front.

[0045] A second object of the present invention is to provide a system for optimizing the interfacial thermal conductivity of a self-assembled monolayer, comprising:

[0046] A memory, a processor, and computer instructions stored in the memory and running on the processor, wherein when the computer instructions are run by the processor, the explainable machine learning method for optimizing the thermal conductivity of the self-assembled monolayer interface is completed.

[0047] A third object of the present invention is to provide a storage medium comprising computer-executable instructions, which, when executed by a computer processor, is used to execute the interpretable machine learning method for optimizing the interfacial thermal conductivity of self-assembled monolayers.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] (1) The present invention provides an interpretable machine learning method, system, and medium for predicting and optimizing the interfacial thermal conductivity of self-assembled monolayers. In view of the limited existing experimental and computational data, the present invention uses molecular dynamics simulation to obtain relevant interfacial thermal transport data. To address the problem of a small number of interfacial thermal transport data samples, interpretable machine learning training is carried out through interpretable physical feature engineering, and independent and unrelated physical features are fused through a symbolic regression algorithm to create a new interpretable physical screening index for the reliable thermal transport design of self-assembled monolayers.

[0050] (2) Through the interpretable machine learning method of the present invention, it is possible to screen for high thermal conductivity of self-assembled monolayers at the interface, assisting scientific researchers in conducting data-driven research such as machine learning on self-assembled monolayers under complex structures, filling this research gap and providing theoretical support and experimental basis for related applications.

[0051] (3) The present invention provides an interpretable machine learning method, system, and medium for predicting and optimizing the interfacial thermal conductivity of self-assembled monolayers, generating a series of simple and efficient physical indices for screening. This method reveals the interfacial heat transport regulation mechanism based on the design of self-assembled monolayers from both a physical and data-driven perspective, and has guiding significance for the design and screening of interfacial thermal conductivity properties of self-assembled monolayers in the field of materials genetic engineering.

[0052] (4) The method provided by the present invention is highly applicable. The present invention can obtain a machine learning interpretable model related to the interface heat transport physics by changing the relevant framework settings such as model type, training parameters, training times and training process involved in the machine learning training process in accordance with common sense training. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 A schematic diagram of the process of the interpretable machine learning method for optimizing the interfacial thermal conductivity of self-assembled monolayers of the present invention;

[0054] Figure 2 This is a schematic diagram of the feature filtering process in step 1) of the present invention;

[0055] Figure 3 This is a schematic diagram of the training effect of the machine learning model of the present invention;

[0056] Figure 4 This is a schematic diagram of the SHAP analysis of the machine learning model with the best fitting performance of the present invention;

[0057] Figure 5 This is a schematic diagram of the average SHAP statistical analysis of the top 25% of the machine learning models of the present invention;

[0058] Figure 6 This is a schematic diagram of physical screening indicators identified and screened through Pareto frontier in the present invention;

[0059] Figure 7 Schematic diagram of the screening comparison between the new physical screening index generated by the present invention and a single physical screening index. DETAILED DESCRIPTION

[0060] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. The embodiments are based on the technical solutions of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments. Any features such as component models, material names, connection structures, control methods, algorithms, etc. that are not explicitly described in this technical solution are considered common technical features disclosed in the prior art.

[0061] The present invention provides an interpretable machine learning method for optimizing the interfacial thermal conductance of self-assembled monolayers. The method comprises the following steps: obtaining an initial machine learning training feature dataset, performing feature engineering processing based on the interfacial thermal conductance of the self-assembled monolayer to obtain key physical features that are conducive to explaining the physical mechanism, and using them as the machine learning model training input set; constructing and training an interfacial thermal conductance machine learning model based on the interfacial thermal conductance of the self-assembled monolayer in combination with the filtered physical features; performing SHAP feature interpretability analysis on the trained interfacial thermal conductance machine learning model to determine a set of symbolic regression variables; and further obtaining an interpretable physical screening index. Compared with the prior art, the present invention performs interpretable machine learning through feature engineering with physical meaning, and fuses independent and unrelated physical features through a symbolic regression algorithm to create a new interpretable physical screening index for reliable thermal transport design of self-assembled monolayers.

[0062] Furthermore, the method specifically includes the following steps:

[0063] 1) Conduct feature engineering for the training of machine learning models for thermal conductivity of self-assembled monolayer interfaces while retaining the original physical meaning of the features;

[0064] 1-1) Use low variance features for dimensionality reduction;

[0065] 1-2) Comprehensively filter the input physical feature set using three major correlations

[0066] 2) Develop a machine learning model for the interfacial thermal conductivity of self-assembled monolayers, combining the physical features obtained through feature engineering filtering.

[0067] 3) Conduct a detailed SHAP feature interpretability analysis on the machine learning model trained on the interfacial thermal conductivity of self-assembled monolayers to determine the set of symbolic regression variables;

[0068] 4) Conduct interpretable machine learning on the interfacial thermal conductivity of self-assembled monolayers;

[0069] 4-1) Conduct symbolic regression gridding formula search for the interfacial thermal conductivity of self-assembled monolayers;

[0070] 4-2) Identify interpretable physical screening indicators with better fit and simpler formulas through the Pareto frontier;

[0071] 4-3) Compare the screening results of the explainable physical screening indicator with those of a single physical indicator to confirm the screening effect of the explainable physical screening indicator.

[0072] Furthermore, the present invention provides an interpretable machine learning method for optimizing the interfacial thermal conductivity of a self-assembled monolayer, the method comprising the following steps:

[0073] 1) Obtain the physical correlation features related to thermal transport at the interface of self-assembled monolayers and the physical and chemical descriptor features of organic molecules, perform preliminary feature engineering processing for the training of the machine learning model of thermal conductivity at the interface of self-assembled monolayers, filter the features to retain the original physical meaning of the features, and obtain key physical features as the input set for subsequent interpretable machine learning training, including the following process:

[0074] 1-1) Obtaining physical correlation features related to thermal transport at the interface of self-assembled monolayers and physical and chemical descriptor features of organic molecules as an initial machine learning training feature dataset, performing preliminary feature engineering processing for training a machine learning model of thermal conductivity at the interface of self-assembled monolayers, and performing feature dimensionality reduction on the initial machine learning training feature dataset using low-variance filtering to obtain a low-variance filtered input training feature set;

[0075] 1-2) Using comprehensive correlation screening to achieve feature dimensionality reduction of the input training feature set after low variance filtering, to obtain a set of key physical features that are used for machine learning model training and retain the original physical meaning of the features;

[0076] 2) Targeting the interfacial thermal conductivity of self-assembled monolayers, we build and train an interfacial thermal conductivity machine learning model based on the key physical features obtained through feature engineering filtering.

[0077] 3) Perform SHAP feature interpretability analysis on the trained interface thermal conductivity machine learning model to determine the set of symbolic regression variables;

[0078] 4) Based on the set of symbolic regression variables, obtain interpretable physical screening indicators, including the following process:

[0079] 4-1) Based on the symbolic regression variable set, perform symbolic regression grid formula search to generate a set of candidate interpretable physical indicators;

[0080] 4-2) Using the Pareto frontier to identify interpretable physical equations with better fit and simpler formulas as interpretable physical screening indicators;

[0081] 4-3) Compare the final determined interpretable physical screening indicator with the screening results of a single physical indicator to confirm the screening effect of the interpretable physical screening indicator.

[0082] Example 1:

[0083] This embodiment provides an interpretable machine learning method for predicting and optimizing the thermal conductivity of the interface of a self-assembled monolayer. Figure 1 ), including the following steps:

[0084] 1) Obtain physical correlation features related to thermal transport at the interface of self-assembled monolayers and physical and chemical descriptor features of organic molecules, perform preliminary feature engineering for the training of machine learning models for the thermal conductivity of self-assembled monolayer interfaces, filter features to retain their original physical meaning, and obtain key physical features as the input set for subsequent interpretable machine learning training. In this case, interpretable machine learning work was carried out on the thermal conductivity characteristics of the solid-liquid interface of self-assembled monolayers with 300 different end group structures. For feature engineering of machine learning models for the thermal conductivity of self-assembled monolayer interfaces, this downward filtering method effectively avoids the problem of ignoring the inherent physical meaning of variables in dimensionality reduction techniques such as principal component analysis;

[0085] 1-1) Low-variance feature dimensionality reduction was adopted. Referring to formula (1), a total of 343 descriptors from the MD feature set (dynamic training feature dataset) and the Molecular feature set (static training feature dataset) were subjected to feature screening. Specifically, the calculated physical correlation features of the self-assembled monolayer, such as the interface interaction energy / force and its components, the energy and component information of the simulated system, the vibration spectrum information of the self-assembled monolayer, such as the peak value, the coupling strength of the vibration spectrum of the self-assembled monolayer (the ratio of the vibration spectrum overlap area), and the thickness of the self-assembled monolayer (dynamic chain length), were used as the input of the dynamic training feature dataset, and the physicochemical descriptor features obtained by the open source software RDKit were used as the input of the static training feature dataset. Descriptors with a variance less than 0.001 were deleted, leaving 288 descriptors.

[0086] Formula (1) is as follows:

[0087]

[0088] Among them S 2 The variance of the descriptor is set, and the cleaning threshold is set. The default value is 0.01. Descriptors below the cleaning threshold are excluded. D represents the physical feature set, j represents the j-th type of one-dimensional feature data, and i represents the i-th data of the one-dimensional feature data of this type.

[0089] 1-2) The three major correlations are used to filter the input physical feature set; the three statistical correlation indicators of linearity (Pearson), monotonicity (Spearman), and nonlinearity (Distance) are used to carry out comprehensive feature filtering. The three data correlation formulas are as follows: formulas (2) to (4). Specifically, the selection criteria for linearity and monotonicity are that the significance p value is less than 10 -5, and the nonlinear threshold is a coefficient greater than 0.33. In terms of screening requirements, descriptors that do not meet any of the three selection criteria are not considered. In order to avoid multicollinearity, the present invention classifies the descriptors according to their physical association in the screening results. Finally, 15 physical features were selected for the subsequent model interpretability analysis. The feature screening process is shown in Figure 2 .

[0090] Formulas (2) to (4) are as follows:

[0091]

[0092]

[0093] Among them, R pearson 、R spearman 、R dist They represent the correlation coefficients of linearity, monotonicity, and nonlinearity respectively, D represents the set of physical features after low-variance feature filtering, Y represents the interface thermal conductivity, m represents the mth type of one-dimensional feature data, i represents the i-th data of this type of one-dimensional feature data, and n represents the amount of data of each type of one-dimensional data. The above filtering method can effectively avoid the loss of physical information caused by feature dimensionality reduction and retain the original physical meaning of the features.

[0094] 2) Aiming at the interfacial thermal conductivity of self-assembled monolayers, combined with the physical features obtained by feature engineering filtering, an interfacial thermal conductivity machine learning model was built; specifically, after feature screening, 15 physical features were used as training input sets for interpretable machine learning. A total of three types of machine learning models were deployed, namely random forest (RF), extreme gradient boosting (XGB) and gradient boosting (GB) regression, and 10-fold cross-validation was performed. Each training uses the global optimization tool Bayesian optimization package to adjust the hyperparameters of all machine learning models to improve prediction accuracy. During the hyperparameter optimization process, the Gaussian process and acquisition function were initially trained with 20 pairs of random parameters, and the ideal parameters of each independent machine learning model were determined after 100 optimization iterations. The R-square values ​​of these best models were 0.844, 0.879 and 0.873, respectively. See the model training effect diagram. Figure 3 .

[0095] 3) Carry out a detailed SHAP feature interpretability analysis on the machine learning model trained on the interface thermal conductivity of self-assembled monolayers to determine the set of symbolic regression variables; specifically, select the machine learning model with the best performance (see Figure 4 ) for subsequent SHAP analysis, and also statistically analyzed the average SHAP values ​​of the top 25% models, such as Figure 5Finally, a single screening index was determined: the average interfacial interaction energy E between the self-assembled monolayer and water, the average chain length L of the self-assembled monolayer, and the vibration spectrum overlap area ratio C between the self-assembled monolayer and water molecules in the bending spectrum region. b , the overlapping area ratio of the vibration spectrum of the self-assembled monolayer and water molecules in the stretching spectrum region C s Used for subsequent symbolic regression formula search.

[0096] 4) Conduct interpretable machine learning on the interfacial thermal conductivity of self-assembled monolayers, and obtain interpretable physical screening indicators based on a set of symbolic regression variables;

[0097] 4-1) A symbolic regression grid-based formula search was conducted for the interfacial thermal conductivity of self-assembled monolayers. Specifically, a symbolic regression formula construction strategy was incorporated into a simple screening descriptor creation process and implemented in gplearn software to generate candidate interpretable physical indices. The Pearson coefficient was used as the fitness function for the symbolic regression of the interfacial thermal conductivity data, generating new descriptors with higher linear correlation as screening criteria.

[0098] 4-2) Based on the formula complexity (formula length) of the interpretable physical index and the Pearson coefficient (fit) of its linear correlation with the interface thermal conductivity, the density distribution method is finally used to identify multiple interpretable physical screening index formulas with higher fit and simpler formulas (shorter formulas) on the Pareto front. Figure 6 , the selected formulas are all located on the global optimal Pareto frontier of formula length and fit, and the formula length of the interpretable physical screening index formulas finally determined in this embodiment is less than 13, and the linear correlation coefficient is greater than 0.79; the specific results can be referred to formulas (5) to (10), as follows:

[0099]

[0100] ln(1.02-E)-L(7)

[0101]

[0102] where E is the average interfacial interaction energy between the self-assembled monolayer and water, and L is the average chain length.

[0103] 4-3) Compare the screening results of the explainable physical screening indicators with those of the single physical indicators to confirm the screening effect of the explainable physical screening indicators. Figure 7 , compared with single screening indicators (E, L, C b 、C s), even E showed inconsistent performance under different screening conditions. In contrast, the newly proposed strongly correlated physical metric (an interpretable physical screening metric) demonstrated much greater screening stability, particularly when screening the top 20% of self-assembled monolayers, achieving a pass rate exceeding 60%. Under these conditions, the recognition rate for the top 5% of highly thermally conductive self-assembled monolayers reached over 93%.

[0104] Traditional material development models can require extremely high experimental preparation and characterization costs, and the lack of strongly correlated physical screening indicators often leads to extremely poor reliability in the design of self-assembled monolayers with small sample sizes. The above-described method overcomes these shortcomings of traditional material development methods and enables interpretable machine learning of the interfacial thermal conductivity properties of self-assembled monolayers, specifically the exploration of the heat transport regulation mechanism. This significantly improves the interpretability of machine learning models for interfacial heat transport in self-assembled monolayers, saving both cost and time.

[0105] Example 2

[0106] This embodiment provides a system for optimizing the thermal conductivity of a self-assembled monolayer interface, comprising:

[0107] A memory, a processor, and computer instructions stored in the memory and running on the processor, wherein when the computer instructions are run by the processor, the interpretable machine learning method for optimizing the thermal conductivity of the self-assembled monolayer interface described in Example 1 is completed.

[0108] This embodiment further provides a storage medium comprising computer-executable instructions, which, when executed by a computer processor, is used to perform the interpretable machine learning method for optimizing the interfacial thermal conductivity of a self-assembled monolayer as described in Example 1.

[0109] Storage media can be electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems or propagation media. Storage media can also include semiconductor or solid-state memory, magnetic tape, removable computer disks, random access memory (RAM), read-only memory (ROM), hard disks, and optical disks. Optical disks can include compact disk-read only memory (CD-ROM), compact disk-read-write (CD-RW), and DVD.

[0110] As used herein, the term "computer" or "computing-based device" refers to any device with processing capabilities so that it can execute instructions. Those skilled in the art will appreciate that such processing capabilities are incorporated into many different devices, and thus the terms "computer" and "computing-based device" each include personal computers, servers, mobile phones (including smartphones), tablets, set-top boxes, media players, game consoles, personal digital assistants, and many other devices.

[0111] The above describes the embodiments of the method of the present invention in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments. Various changes can be made according to the purpose of the invention of the present invention. Any parameter changes or calculation simplifications made according to the principles of the technical solution of the present invention, as long as they comply with the purpose of the invention of the present invention and do not deviate from the principles and concepts of the method of the present invention, fall within the scope of protection of the present invention.

[0112] The above description of the embodiments is intended to facilitate understanding and use of the invention by those skilled in the art. It will be apparent that those skilled in the art can readily make various modifications to these embodiments and apply the general principles described herein to other embodiments without requiring inventive effort. Therefore, the present invention is not limited to the above-described embodiments. Improvements and modifications made by those skilled in the art based on the disclosure of the present invention, without departing from the scope of the present invention, should be within the scope of protection of the present invention.

Claims

1. An interpretable machine learning method for optimizing interfacial thermal conductivity of self-assembled monolayers, characterized in that: The method comprises the following steps: 1) Obtain the physical correlation features related to thermal transport at the interface of self-assembled monolayers and the physical and chemical descriptor features of organic molecules, perform preliminary feature engineering processing for the training of the machine learning model of thermal conductivity at the interface of self-assembled monolayers, filter the features to retain the original physical meaning of the features, and obtain key physical features as the input set for subsequent interpretable machine learning training; 2) Targeting the interfacial thermal conductivity of self-assembled monolayers, we build and train an interfacial thermal conductivity machine learning model based on the key physical features obtained through feature engineering filtering. 3) Perform SHAP feature interpretability analysis on the trained interface thermal conductivity machine learning model to determine the set of symbolic regression variables; 4) Based on the set of symbolic regression variables, obtain interpretable physical screening indicators, including the following process: 4-1) Based on the symbolic regression variable set, perform symbolic regression grid formula search to generate a set of candidate interpretable physical indicators; 4-2) The set of interpretable physical equations is screened through the Pareto frontier to obtain the interpretable physical screening index.

2. The interpretable machine learning method for optimizing the interfacial thermal conductivity of self-assembled monolayers according to claim 1, characterized in that: Step 1) includes the following process: 1-1) Obtaining physical correlation features related to thermal transport at the interface of self-assembled monolayers and physical and chemical descriptor features of organic molecules as an initial machine learning training feature dataset, performing preliminary feature engineering processing for training a machine learning model of thermal conductivity at the interface of self-assembled monolayers, and performing feature dimensionality reduction on the initial machine learning training feature dataset using low-variance filtering to obtain a low-variance filtered input training feature set; 1-2) Comprehensive correlation screening is used to achieve feature dimensionality reduction of the input training feature set after low variance filtering, and a set of key physical features is obtained for machine learning model training while retaining the original physical meaning of the features.

3. The interpretable machine learning method for optimizing the interfacial thermal conductivity of self-assembled monolayers according to claim 2, characterized in that: In step 1), the calculated thermal conductivity of the self-assembled monolayer interface is regarded as the objective function Y, the calculated physical correlation characteristics related to the thermal transport of the self-assembled monolayer interface are used as the input dynamic training feature dataset, and the physicochemical descriptor features obtained through the open source software RDKit are used as the input static training feature dataset. The input dynamic training feature dataset and the input static training feature dataset are used as the initial machine learning training feature dataset; The dynamic training feature data set includes one or more of interface interaction energy / force and its components, energy and component information of the simulation system, vibration spectrum information of the self-assembled monolayer such as peak value, vibration spectrum coupling strength between the self-assembled monolayer and the interface material, and thickness of the self-assembled monolayer.

4. The interpretable machine learning method for optimizing interfacial thermal conductivity of self-assembled monolayers according to claim 2, characterized in that: In step 1-1), low variance features are removed from the input training features by setting the variance threshold. The reference formula is as follows (1): Among them S 2 The variance of the descriptor is set, and the cleaning threshold is set. The default value is 0.

01. Descriptors below the cleaning threshold are excluded. D represents the physical feature set, j represents the j-th type of one-dimensional feature data, and i represents the i-th data of the one-dimensional feature data of this type. In step 1-2), the process of implementing comprehensive correlation screening to reduce the dimension of the input training feature set after low variance filtering specifically includes the following steps: Comprehensive feature filtering is performed by using three data statistical correlation indicators: linear, monotonic, and nonlinear. The three data correlation formulas are as follows: (2) to (4): where R pearson 、R spearman 、R dist They represent the correlation coefficients of linearity, monotonicity, and nonlinearity respectively, D represents the set of physical features after low-variance feature filtering, Y represents the interface thermal conductivity, m represents the mth type of one-dimensional feature data, i represents the i-th data of this type of one-dimensional feature data, and n represents the amount of data of each type of one-dimensional data.

5. The interpretable machine learning method for optimizing interfacial thermal conductivity of self-assembled monolayers according to claim 1, characterized in that: In step 2), during the process of building the interface thermal conductivity machine learning model, the deployed machine learning models include the random forest regression model, the extreme gradient boosting regression model, and the gradient boosting regression model, and 10-fold cross validation is performed; In step 2), during the process of building the interface thermal conductivity machine learning model, the global optimization tool Bayesian optimization package is used to adjust the hyperparameters of all machine learning models in each training to improve the prediction accuracy.

6. The interpretable machine learning method for optimizing interfacial thermal conductivity of self-assembled monolayers according to claim 1, characterized in that: In step 3), for the trained interface thermal conductivity machine learning model, the SHAP toolkit is used to explain the relationship between the key physical feature set obtained after step 1) and the interface thermal conductivity, and the feature importance is evaluated based on the machine learning models ranked in the top 25% of the overall training performance. The SHAP value matrix of this type of trained interface thermal conductivity machine learning model is used for the interpretable work of machine learning, and finally the set of symbolic regression variables is determined.

7. The interpretable machine learning method for optimizing interfacial thermal conductivity of self-assembled monolayers according to claim 1, characterized in that: In step 4-1), based on the symbolic regression variable set, the symbolic regression formula construction strategy is incorporated into the simple screening descriptor creation process, and a symbolic regression grid formula search is performed. This is implemented in the gplearn software, where the Pearson coefficient is used as the fitness function for the symbolic regression of the interface thermal conductivity data, and new descriptors with higher linear correlation are generated as screening criteria, finally generating a set of candidate interpretable physical indicators; In step 4-2), based on the formula complexity of the interpretable physical indicator and the Pearson coefficient of the linear correlation between the interpretable physical indicator and the interface thermal conductivity, the interpretable physical screening indicator formula is finally determined, and the multiple interpretable physical screening indicator formulas determined are all located on the global optimal Pareto front of the formula complexity and the Pearson coefficient of the linear correlation; In step 4-2), the determined interpretable physical screening index formulas include formulas (5) to (10), as follows: ln(1.02-E)-L(7) where E is the average interfacial interaction energy between the self-assembled monolayer and water, and L is the average chain length.

8. The interpretable machine learning method for optimizing interfacial thermal conductivity of self-assembled monolayers according to claim 1, characterized in that: After step 4-2), perform the following steps: 4-3) Compare the final determined interpretable physical screening indicator with the screening results of a single physical indicator to confirm the screening effect of the interpretable physical screening indicator.

9. A system for optimizing thermal conductivity of a self-assembled monolayer interface, characterized in that: include: A memory, a processor, and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the interpretable machine learning method for optimizing the interfacial thermal conductivity of a self-assembled monolayer according to any one of claims 1 to 8 is completed.

10. A storage medium containing computer-executable instructions, characterized in that: When the storage medium of the computer executable instructions is executed by a computer processor, it is used to perform the interpretable machine learning method for optimizing the interfacial thermal conductivity of a self-assembled monolayer according to any one of claims 1 to 8.

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