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Research Article  |  Open Access  |  16 Jun 2024

Thermal stability prediction of copolymerized polyimides via an interpretable transfer learning model

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J Mater Inf 2024;4:8.
10.20517/jmi.2024.13 |  © The Author(s) 2024.
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To address the issues with molecular representation of copolymerized polyimides (PIs) and the mini dataset of PI powders. We constructed an interpretable machine learning (ML) model for PI films using the weighted-additive Morgan Fingerprints with Frequency descriptors and developed an interpretable transfer learning model for PI powders. To enhance Thermal Stability (Temperature at 5% weight loss) of PI films and powders, it is recommended to add conjugated functional groups to diamines, control phenyl ring side chains, and reduce pyridine and hydroxyl groups; select copolyimides (co-PIs); ensure that anhydride is directly connected to the benzene ring in dianhydrides, avoiding aliphatic cycles. It is noteworthy that the close alignment between experimental results and model predictions serves to confirm the model is a reliable prediction tool. It is hoped that this polymer informatics approach will provide further implementation for practical applications of other functional materials.


Transfer learning models, copolymerized polyimides, thermal stability


The dream of chemists is to create substances to advance human knowledge and benefit society[1]. Traditionally, chemists have used experiments to achieve these goals. However, this approach is labor-intensive. As we stand on the cliff edge of artificial general intelligence, the collaborative potential between machine learning (ML) and chemistry is vast and promising[2-4].

Accurate and effective property prediction is crucial for polymer design in various applications, including polymer electrolytes[5,6], energy storage[7,8], organic optoelectronics[9,10], and many other applications[11,12]. The demand in these fields for enhanced thermally stable polymers that preserve their useful properties at high temperatures has been significantly increased[13-16]. Polyimides (PIs) are a class of high-performance polymers widely used in the aerospace industries and microelectronics[17-20]. Thermal distortion temperature, good chemical resistance and high mechanical strength are brought about by rigid aromatic heterocyclic structure and strong chain-chain interaction[21-26]. Temperature at 5% weight loss (T5%) refers to the temperature at which a material’s mass decreases by 5% during heating, a key indicator of suitability of PIs for high-temperature applications. Therefore, studying the T5% not only aids in optimizing the formulations of existing materials but may also drive the development of new high-performance PIs. Different dianhydrides and diamines are selected to tailor the properties of PIs. For example, diacid anhydride and m-phenylene diamine yield polyetherimide with excellent toughness and rigidity[27]; pyromellitic dianhydride and 4,4’-oxy-dianiline can be used to produce KaptonTM[28] with high thermal resistance and mechanical strength. Experimental studies on the reactions between dianhydrides and diamines have already produced a range of multifunctional PIs that meet diverse requirements. However, it is not feasible for experimenters to exhaust all possible two-component reactions for material design and the discovery of novel PIs[29].

Polymer informatics[30-32] is advancing research on high-performance polymers, particularly in building correlations between the chemical structure and properties of polymers[33-35]. Researchers[36,37] have proposed a theoretical relationship between the chemical structure of polymers and their glass transition temperature (Tg). These empirical methods assume that the chemical groups within the repeating units of the polymer chain influence Tg through additive effects with varying weighting factors. For the Quantitative Structure-Property Relationship (QSPR) approach, a large array of molecular descriptors is extracted from the repeating units of polymers, applicable to any chemical structure[38]. For instance, Katritzky et al. have extracted over 400 constitutional, geometrical, topological, and quantum chemical descriptors for the repeating units of polymers[38]. Subsequently, multi-step linear regression analysis is employed to train these descriptors, resulting in a strong match between predicted and experimental for 88 homopolymers. However, quantum chemical descriptors require time-consuming density functional theory calculations, and other molecular descriptors can generate many parameters difficult to physically interpret, such as Kier shape indices and topological bond connectivity[36]. Rationally representing polymer maps in a continuous vector space is crucial for applying ML tools in polymer performance prediction. Fingerprints have been proven effective in molecular ML models and have been introduced for polymer-related tasks[39]. Tao et al. employed the Morgan fingerprint to represent the simplified molecular-input line-entry system (SMILES) of PI repeating units, counting the occurrence frequency of each substructure[29]. This method engendered a vector containing 121 prominent substructures, effectively reflecting the structural characteristics of the polymers. They established a comprehensive library of PIs based on dianhydrides and diamines/diisocyanates, covering eight million hypothetical PIs. The entire hypothetical dataset was screened, and molecular dynamics validation was conducted. Using graphs as input for molecular representation learning[36] has been proven to be a viable option. Volgin et al. developed a graph convolutional neural network to estimate the Tg of PI with a mean absolute error of approximately 20 K[40]. However, the effect of graph representation learning on small data sets and the translation of implicit “machine language”[41] into chemical knowledge with clear physicochemical meaning related to target properties still need to be explored. Huang et al. proposed a high-throughput screening framework for polymer chains with thermal conductivity (TC) via physical feature engineering[42]. They reduced 320 initial physical descriptors to 20, enabling ML models to achieve an R2 over 0.80, outperforming traditional graph descriptors. Many efforts have begun to apply Transformer to predict the properties of small organic molecules[43-45]. Due to its complex self-attention mechanism, the model has limited interpretability[46], requires substantial training data, and demands high computational resources. According to Occam’s Razor principle[47], ML should employ simple methods as much as possible to solve complex problems.

Currently, Zhang et al. proposed a materials genome approach to design and screen silicon-containing acetylene resins with excellent processing properties and heat resistance, but there are a few studies using ML methods to predict T5%[48]. Using only repeating units as research objects may result in missing structural information[49]; synthetic monomers, as substitutes, can solve this problem to a certain extent. Additionally, the issue of copolymerization rates in copolyimides (co-PIs) needs attention, which is often overlooked when using repeating units alone, and no ML studies have yet addressed it. ML studies on PIs often do not specify material types due to limited data, especially for PI powders. The “transfer learning” approach has been extensively tested in research dedicated to predicting the properties of small molecules[50-53]. Wu et al. implemented a transfer learning scheme to mitigate the small dataset issue for TC and developed an alternative model based solely on 28 experimental data[54]. Similarly, training on a large dataset of film materials and then fine-tuning for the powder model could be an effective strategy to improve the accuracy of the powder model.

This study aims to explore and develop ML methods for PI powders, enhancing material performance prediction accuracy and efficiency through improved molecular representation techniques and transfer learning models. Additionally, it focuses on enhancing model interpretability to provide actionable insights for materials scientists and engineers. We propose the flowchart of Figure 1: (1) A new method of weighted-additive Morgan Frequency Fingerprints (MFF) for both homopolyimides (homo-PIs) and co-PIs, using the copolymerization rates of dianhydrides and diamines as weights, and the MFF is added to form new descriptors; (2) Training a ML model on PI films and transferring it to the PI powder model to solve the problem of small data sets; (3) Utilizing expert knowledge and the SHapley Additive exPlanations (SHAP) method to interpret the structural characteristics related to performance in both films and powders; (4) The prediction results are highly consistent with the experimental values, and the model has good practical value. This research not only demonstrates the transformative potential of ML in chemical research but also provides new avenues for accelerating scientific discovery and interdisciplinary collaboration.

Thermal stability prediction of copolymerized polyimides via an interpretable transfer learning model

Figure 1. The workflow of our work. MFF: Morgan Frequency Fingerprint.


Raw molecular dataset and data cleaning

A dataset comprising 270 entries on the T5% T5% (N2 atmosphere) of experimentally synthesized PI films, involving various combinations of dianhydrides and diamines, was compiled[25,55-97]. The data are presented in Supplementary Table 1 and illustrated in Supplementary Figures 1 and 2. Experimental procedures are prone to errors, potentially affecting the collected data and making it susceptible to noise. Handling outliers is crucial for ensuring data quality and consistency in model training. Supplementary Figure 3 shows that an outlier is identified when applying the 1.5 * interquartile range (IQR) rule to draw box plots of T5%. In addition, the outcomes of utilizing the method of mean ± 3 standard deviations to pinpoint the outlier are uniform. After removing the outlier, the histogram in Figure 2A reveals that T5% ranges from 325 to 600 °C, predominantly clustering between 425 and 575 °C.

Thermal stability prediction of copolymerized polyimides via an interpretable transfer learning model

Figure 2. Distribution histogram of the experimental values of T5% of (A) 269 PI films (outliers deleted) and (C) 42 PI powders. (B) Weighted-additive co-PI MFF molecular representation learning method. PI: Polyimide; MFF: Morgan Frequency Fingerprint.

Descriptor factory

A total of 22 dianhydrides and 67 diamines molecular structures generated 327 and 897 MFFs, respectively. More details on MFFs can be found in Supplementary Material and Supplementary Figure 4. The MFFs[98] were “weighted-additive”, as shown in Figure 2B, where the copolymerization rates of diamines were used as weights and then summed to form a new MFF, which was overlaid with the diamines. Similarly, diamines can be integrated with the “weighted-additive” MFF of two dianhydrides. It is important to note that the MFF of the diamines should precede that of the dianhydrides in the combination. Considering the differences between copolymers and homopolymers, an additional “copolymer” descriptor was added. “Copolymer” is one-hot encoded, with co-PIs represented as “1” and homo-PIs as “0”. Redundancy may increase the difficulty of data processing. During data cleaning, incomplete features, such as zero values (which do not contain structural characteristics), can be removed. Additionally, 1,225 descriptors were preprocessed, and those with a Pearson correlation coefficient greater than 0.90 were eliminated. The descriptors were subsequently normalized through min-max scaling to confine them within standard ranges[99]. Randomly allocate 85% of the data for the training set and the remaining 15% for the test set.

ML process

These data were input into our ML framework. For the 161 descriptors remaining after preprocessing, nested recursive feature elimination with Ridge, Random Forest, XGBoost, and CatBoost models (RFE-Ridge, RFE-RF, RFE-XGBoost, and RFE-CatBoost) was used to determine the optimal feature subset. The construction of Model-A adheres to the best model for feature selection, which is CatBoost. Individual descriptors from model-A were transferred and combined with model-C individualized descriptors to construct a predictive model for PI powder T5% (model-D). Model parameters were fine-tuned. One of the critical challenges is opening the black box of ML. The SHAP method is used to nest the above models, providing feedback on descriptor contributions and their positive or negative impacts. The meaning of the filtered descriptors is also discussed. All the above code is executed in Python.

Experimental synthesis and validation

PI powder was prepared using two-step and thermo-imide methods. Some N,N-dimethylacetamide (DMAc) was added to the reactor under N2 protection. Then, dianhydride and diamine in a certain proportion were added and stirred well. The reaction feeding ratio was shown in Supplementary Table 2 and Table 1. The reaction temperature was controlled, and the viscous precursor polyamide-acid (PAA) was obtained by stirring for 3 h at room temperature. A certain amount of xylene was continued to be added to the reaction system, and the temperature was raised to the reflux temperature and kept for 3 h, and PI powders were obtained using a thermo-imide approach. Materials and test methods are found in the Experimental section of the supporting information. The histogram in Figure 2C shows that T5% ranges from 580 to 615 °C. Supplementary Figures 5 and 6 are the synthetic routes of PI-a and PI-b, respectively. Experimental section in support information can be viewed.

Table 1

Structures of co-PI powders at different molar ratios, along with the T5% values predicted by model-B and validated experimentally



Feature engineering

The optimal subset is carefully selected to reduce the dimensionality of the data. This subset contains a minimal number of descriptors while maintaining a close relationship to the required material properties[100,101]. The 1,225 descriptors declined to 161 after removing the redundancy with the Pearson correlation coefficient of less than 0.90. Four nesting methods, RFE-Ridge, RFE-RF, RFE-XGBoost, and RFE-CatBoost were used to compare and determine the optimal descriptor sets. The average R2 and root mean square error (RMSE) of five-fold cross-validation (5-fold-CV) were determined as the metrics to evaluate the model performance. For the RFE-Ridge method, Supplementary Figure 7A indicates no inflection points. This observation suggests that nonlinear algorithms might not be ideal for handling high-dimensional datasets. Considering the selections from the four models, further increasing the number of descriptors to achieve better model results will not be pursued. An effective descriptor must be simpler to obtain than the target property and be as low-dimensional as possible[102]. A subset of 18 selected descriptors was identified as the optimal solution. The other three methods selected optimal feature subsets of 18, 12, and nine descriptors, respectively [Supplementary Table 3, Supplementary Figure 7B and C, Figure 3A]. Guided by the “Occam Shaver” principle[47], the smallest number of descriptors necessary for sufficient accuracy is selected. The RFE-CatBoost model, which offers the best performance with the fewest descriptors, achieves optimal values of 28.84 for RMSE and 0.75 for R2. Among the subsets selected by RFE-CatBoost [Supplementary Table 3], the descriptors selected twice by the other three were the most. The same preprocessing and feature engineering were applied to the PI powder dataset, reducing 643 descriptors to 11, and ultimately determining an optimal subset of six descriptors based on Supplementary Figure 8A[Supplementary Table 4]. The heat map in Supplementary Figure 9 indicates that the correlation coefficients between descriptors are generally low across both datasets, suggesting a “global” representation.

Thermal stability prediction of copolymerized polyimides via an interpretable transfer learning model

Figure 3. Descriptor sniping and optimal models. (A) The changes in R2 and RMSE for model-A (5-fold-CV), built using RFE nested CatBoost with different numbers of descriptors, were accurately described. Scatter plots of the best model to predict the T5% values versus their experimental values for the train and test sets for (B) model-A and (C) model-D. RMSE: Root mean square error; 5-fold-CV: five-fold cross-validation; RFE: recursive feature elimination.

Performance of the four models

The CatBoost algorithm was selected for modeling, with hyperparameters optimized using the grid search method [Supplementary Table 5]. Figure 3B shows the plots of the experimental T5% values that match the predicted T5% values. The R2 and the RMSE of the CatBoost model (model-A) are 0.86 and 21.78, respectively. For the independent test set, the R2 and the RMSE of Model-A are 0.79 and 23.50. The dataset was randomly split 20 times to ensure the reliability of the ensemble model. As shown in Supplementary Table 6, the average R2 and RMSE for the training set are 0.86 and 21.60, respectively, while the test set achieved an average R2 of 0.74 and RMSE of 28.40. The results of the existing model predicting the external test set[103] are shown in Supplementary Table 7. Zhang et al. constructed an artificial neural network model based on molecular descriptors to predict the T5% of silicon-containing aromatic acetylene resins[48]. The R2 values of their training and test sets were 0.66 and 0.65, respectively. Model-A was described as robust, stable, capable of good generalization and accurate.

In order to address the issue with the small dataset (powders), all descriptors and model parameters from model-A were transferred to model-B. In Supplementary Figure 8B, model-B achieved an R2 of 0.88 and an RMSE of 2.97 on the training set, and an R2 of 0.77 and an RMSE of 3.13 on the test set. In contrast to powders, the film formation process undergoes heat treatment, which affects the degree of cross-linking[104] and the d-space[105] between polymer chains, thereby influencing its thermal stability and performance characteristics. For the different effects caused by film and powder morphology, descriptors were ranked in model-A [Supplementary Table 8]. These descriptors were then transferred to a separately built powder, model-C [Supplementary Figure 8C], resulting in model-D. The optimal model parameters are shown in Supplementary Table 6. Model-D demonstrated outstanding performance with an R2 of 0.999 and an RMSE of 0.06 on the training data. When evaluated on the independent test set, it achieved an R2 of 0.954 and an RMSE of 1.39. These results are shown as a scatter plot in Figure 3C. As shown in Supplementary Table 9, the data set was randomly divided six times, resulting in an average R2 and RMSE of 0.99 and 0.07, respectively, for the training sets and 0.88 and 2.44, respectively, for the test sets. Due to the insufficient size of the dataset, generalizability was somewhat affected, yet the results remain commendable. Zhang et al. constructed an artificial neural network model based on molecular descriptors to predict the T5%, with training and test set R2 values of 0.66 and 0.65[48]. The transferred model, model-D, is more robust and stable.

To improve the model’s user-friendliness, an interactive online prediction tool was developed. As illustrated in Figure 4, researchers can effortlessly leverage this toolkit by entering descriptor values and clicking on “Predict”. This straightforward prediction tool allows researchers to quickly predict the T5% of a candidate PI, whether in film or powder form (

Thermal stability prediction of copolymerized polyimides via an interpretable transfer learning model

Figure 4. A prediction toolkit for predicting T5% of PI films and PI powders from descriptor values. PI: Polyimide.

Model interpretation and structure mapping

To further understand the implications of structural descriptors of PI monomers in T5% and offer guidance for experimental synthesis, SHAP and expert knowledge were leveraged to interpret the meaning of descriptors. Figure 5 illustrates that eigenvalues colored blue correspond to lower model output values, while red ones indicate higher output values. A3975295864, copolymer, and A864662311 have obvious positive effects on T5%, A3431531268, G2976033787, and A4216335232 have a negative correlation with T5%. A951226070 and G994485099 have a positive correlation trend, while A3217380708 has a negative correlation trend in Figure 5A. In Figure 5B, A951226070, A2041434490, A4216335232, A2084364935, A2720313463, and G3692055567 demonstrate a negative effect on T5% of PI powders, while G3276511768 is shown to positively influence. In it, A951226070 appears in both forms of PI. Figure 5 shows the importance of each filter descriptor for T5%. The larger the SHAP value, the greater the impact of the feature on the model’s objectives, warranting more focus on it. The effect of amines on T5% is more acute than that of anhydrides. The SHAP method facilitated the establishment of a link between T5% and descriptors, creating a bridge from descriptors to molecular structure, which then directly correlated with T5% [Figure 1].

Thermal stability prediction of copolymerized polyimides via an interpretable transfer learning model

Figure 5. SHAP value of the output of the best descriptors of the SHAP nested CatBoost algorithm for (A) model-A and (B) model-D. On the left, the importance ranking of the best-chosen subset of the SHAP nested CatBoost algorithm. On the right, blue color for negative correlation and red color for positive correlation. SHAP: SHapley Additive exPlanations.

A3975295864 represents a benzene ring connected to an amino group. Supplementary Figure 10 shows the diamine molecule with the A3975295864 structure highlighted. Figure 6A demonstrates that A3975295864 exhibits a clear positive correlation, with SHAP values increasing as it increases. This is consistent with practical applications. For diamines, enhancing the π-π interactions between molecules by increasing the rigid naphthalene rings and reducing the flexible ether bonds in the structure, as seen in 4,4’-(2,6-naphthalenediyl)bis[benzenamine]) (NADA)[58], can lead to a denser stacking of the molecular chains. This orderly and dense arrangement helps to enhance the thermal stability of the polymer, as the more rigid molecular chains reduce internal rotation, thereby strengthening the overall structural stability. A64 and A21 have similar structures, but A64 contains two A3975295864 units while A21 does not. Correspondingly, the T5% values for PI-190 containing A64 in Supplementary Table 1 are lower than those for the PI containing A21. Similarly, A23 and A24 are compared, and the T5% values for PI-6 (which also contains two A3975295864 units) are higher than those for the PI featuring A24. Increasing rigid structures, such as benzene and naphthalene rings, can indeed benefit the enhancement of T5% values of polymers, improving their ability to maintain structural integrity during heating. Therefore, it is advisable to directly attach amino groups to benzene rings in diamines.

Thermal stability prediction of copolymerized polyimides via an interpretable transfer learning model

Figure 6. The relationship between the descriptor values and the SHAP values output by the SHAP nested CatBoost algorithm for the four best descriptors of model A (A) A3975295864 (B) A3431531268 (C) copolymer (D) G2976033787 and the two best descriptors of model-B (E) A951226070 (f) A2041434490. SHAP: SHapley Additive exPlanations.

A3431531268 represents a carbon-oxygen single bond [Figure 5]. In Supplementary Figure 10, the highlighted sections of the selected dianhydride fragments are all ether bonds. Comparing Supplementary Figure 2, it is observed that only the ether bonds adjacent to pyridine are highlighted, such as in A17 and A41. Therefore, the influence of pyridine requires more attention. The region selected within the blue box in Figure 6B displays that as A3431531268 approaches zero, the SHAP value increases, indicating a more favorable effect on T5%. Introducing pyridine into diamines with biphenyl structures for synthesizing PIs can effectively improve their solubility[79]. However, incorporating these structures might compromise the material’s thermal stability[106], as the increased flexibility and larger steric hindrance could reduce the tight packing of the molecules, thereby affecting the material’s performance at high temperatures. The A26, A41 and A43 fragments can reflect the regularity. A41 and A43 both feature two ether bonds linked to pyridine, with an A3431531268 value of 2, whereas A26, which lacks these, has a value of 0. This is corroborated in Supplementary Table 1 entries PI-66, 141, and 215, where the anhydrides are the same, and PIs containing A26 exhibit higher T5% values than those containing A41 and A43. To reduce the A3431531268 value, diamines should minimize the occurrence of ether bonds linked to pyridine as much as possible.

The influence of copolymer on T5% is positively correlated [Figures 5 and 6C]. The “1” for copolymer represents co-PI, and “0” denotes homo-PI. The SHAP values for co-PIs are positive, while those for homo-PIs are negative. Researchers predominantly use co-PIs to improve various material properties[75,80,93,94], yet their effectiveness varies depending on the specific property. Co-PIs may be favored in future work involving T5%.

In Figures 5 and 6D, when the G2976033787 value is 0, the SHAP values are positive, and the T5% is higher. G2976033787 indicates the number of branches in aliphatic rings, which are highlighted in Supplementary Figure 11. Although a higher number of branches tends to increase the SHAP values, in this case, all the SHAP values are negative, suggesting that the best performance is observed when there are no aliphatic rings. Compared to aliphatic compounds, aromatic compounds show superior effectiveness in enhancing the thermal stability of PIs[64,74,83]. G9 has two more side chains than G4, as seen in Supplementary Table 1 entries PI-59 and 58, with 59 having a higher T5% value. Comparing G1 and G14, G1 is linked to an aromatic benzene ring, while G14 is linked to an aliphatic four-membered ring [Supplementary Figure 3]. The T5% values for PIs with the G14 structure, such as entries PI-155 and 156 in Supplementary Table 1, are significantly lower than those containing the G1 structure, such as entries PI-20, 21, and 22. It is aromatic rings that should be used in dianhydrides rather than aliphatic rings, for better T5%. Supporting information in Supplementary Figure 12 discusses the remaining five descriptors, their relationship with structure, and their impact on performance.

A951226070 is a descriptor that establishes a certain correlation between films and powders, representing the number of unsubstituted hydrogens (vacancies) on the benzene ring [Supplementary Figure 13]. Figure 6E shows that A951226070 values between 4-5 result in positive SHAP values, which benefit T5%. Excessive substitution of hydrogen atoms on the benzene ring increases side chains and disrupts molecular chain regularity. This spatial hindrance reduces the packing density of the molecular chains, thereby decreasing the thermal stability of the PI[58]. In Supplementary Table 2, with the same dianhydride G1, as the amount of diamine A1 (A951226070 = 8) increases, the T5% values for PI-2 to PI-4 gradually decrease. Therefore, it is necessary to control the frequency of side chains on the benzene ring in the diamine structure. Likewise, the impact of A951226070 on the T5% of PI films can be seen in Supplementary Figure 12.

Once the structure A2041434490 [Supplementary Figure 13] appears, it leads to a decrease in T5%, as demonstrated in Figure 6F. This is attributed to the nitrogen atom in the main chain. The localized lone pair of electrons on the sp2 orbit of the nitrogen atom[74] reduces the thermal stability of PI when nitrogen is added to its main chain. This point is confirmed in Supplementary Table 2, where PI-9 to PI-11, all using the same dianhydride G1, show a gradual decline in T5% as the concentration of diamine A71 (A2041434490 = 1) rises. Consequently, nitrogen atoms should not be present in the main chain of diamines. The remaining four descriptors are discussed in the supporting information Supplementary Figure 14.

Experimental verification results

Based on the known structures, diamines A70 and A71, which exhibit more negative structural effects, are excluded, while any dianhydride with minimal impact on performance is considered suitable. Different ratios of selected dianhydrides and diamines are chosen to form PI powders for experimental validation. The thermogravimetric and Fourier transform infrared (FTIR) spectra of the prepared PI-a and PI-b powders were shown in Supplementary Figures 15 and 16. The statistical data of 5%, 10% thermogravimetric temperature and 1,000 °C residual amount of PI powder was shown in Supplementary Table 10. The PI powder can maintain good thermal stability before 500 °C. The thermal decomposition temperatures of PI-a at 5% and 10% in nitrogen are 600 and 620 °C, respectively. Those of PI-b at 5% and 10% in nitrogen are 606 and 623 °C, respectively, showing good thermal stability. Table 1 lists different ratios of dianhydride and diamine codes, along with model predictions and experimental values. The experimental and predicted RMSE values for PI-a and PI-b are 8.9. A low RMSE is a positive indicator, suggesting that the predictions made by model-B are accurate.


We have implemented an effective strategy using a novel MFF approach to address the co-PI molecular expression method, transferring from the PI film model to the PI powder model. This allows for the prediction of the T5% for PI powders and reveals the relationship between structure and performance across different material forms. The enhanced MFF, which weights according to molar ratios and aggregates for co-PIs, has constructed a robust PI-film model (model-A). Descriptors and the model were transferred to develop a superior PI-powder model (model-D). Model-A exhibits excellent robustness and generalizability, achieving an R2 of 0.86 for the training set and 0.79 for the test set. Model-D is more outstanding, with R2 values of 0.999 for the training set and 0.954 for the test set. The link between structure and performance is bridged by descriptors, highlighting the structural characteristics associated with each descriptor. Overall, to improve the T5% of PI film materials: (1) Add more conjugated functional groups to diamines but control the number of side chains on benzene rings, reducing pyridine and hydroxyl groups; (2) Co-PI is a good choice; (3) In dianhydrides, there are no aliphatic rings and anhydrides are directly connected to benzene rings. In parallel, for enhancing the T5% of PI powder materials: (1) Control the number of side chains on benzene rings in diamines, reducing the presence of nitrogen atoms in the main chain; (2) Ensure anhydrides are directly connected to benzene rings. More importantly, the results predicted by model-B align with the experimental outcomes (RMSE value of 8.9), demonstrating the reliability of the model as a prediction tool. Structure, descriptors, and performance are interconnected. Additionally, it is encouraging that the online prediction platform ( assists researchers in the field with rapid predictions.

It is acknowledged that attempting to postulate unknown chemical structures and property relationships through models presents challenges. This endeavor requires innovative data and new experimental results to train the models, enabling them to capture new scientific laws and insights. Additionally, the influence of experimental parameters is a critical factor that cannot be ignored. Continued efforts will be made to conduct in-depth studies exploring the adaptability of different experimental conditions within the model, aiming to provide valuable guidance for designing a wider range of functional materials.


Authors’ contributions

Conceived the idea and designed the project: Zhang Y, Ding P, Xu T

Performed data analysis and interpretation: Zhang Y, Li X, Xu T

Supervised the project: Ding P, Li M, Xu G, Lv W

Drafted the manuscript: Zhang Y, Fang Y, Li L, Xu T, Peng F

Revised and finalized the manuscript: Zhang Y, Ding P, Li M

All authors read and approved the final manuscript.

Availability of data and materials

Supplementary Materials are available from the Journal of Materials Informatics or the authors. The dataset for polyimide films and the predicted dataset are provided with this article.

Financial support and sponsorship

This work was supported by the National Key Research and Development Program of China (2022YFB3707800) and the Key Program of Science and Technology of Yunnan Province (No. 202302AB080022).

Conflicts of interest

Ding P is the guest editor of the Special Issue. Xu G and Lv W are affiliated with Shanghai Plastics Research Institute Co., Ltd, while the other authors have declared that they have no conflicts of interest.

Ethical approval and consent to participate

Not applicable.

Consent for publication

Not applicable.


© The Author(s) 2024.

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Zhang Y, Fang Y, Li L, Xu T, Peng F, Li X, Xu G, Lv W, Li M, Ding P. Thermal stability prediction of copolymerized polyimides via an interpretable transfer learning model. J Mater Inf 2024;4:8.

AMA Style

Zhang Y, Fang Y, Li L, Xu T, Peng F, Li X, Xu G, Lv W, Li M, Ding P. Thermal stability prediction of copolymerized polyimides via an interpretable transfer learning model. Journal of Materials Informatics. 2024; 4(2): 8.

Chicago/Turabian Style

Yu Zhang, Yating Fang, Ling Li, Tongle Xu, Fang Peng, Xiong Li, Guangrui Xu, Wei Lv, Minjie Li, Peng Ding. 2024. "Thermal stability prediction of copolymerized polyimides via an interpretable transfer learning model" Journal of Materials Informatics. 4, no.2: 8.

ACS Style

Zhang, Y.; Fang Y.; Li L.; Xu T.; Peng F.; Li X.; Xu G.; Lv W.; Li M.; Ding P. Thermal stability prediction of copolymerized polyimides via an interpretable transfer learning model. J. Mater. Inf. 2024, 4, 8.

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