Machine intelligence accelerated design of conductive MXene aerogels with programmable properties

Tuning mechanical and electrical properties of conductive aerogels through varying multiple fabrication parameters

As shown in the TEM images in Supplementary Fig. 3a, b, Ti₃C₂T_x MXene nanosheets showed average lateral dimensions of 1.4 × 1.1 µm², and CNFs exhibited an average diameter of 15 nm and an average length of 1 µm. Supplementary Fig. 4a reveals that CNF and MXene dispersions exhibited average zeta potentials of less than –40 mV. As shown in Supplementary Fig. 4a, b, the zeta potentials of MXene and CNF dispersions were monitored before and after 2-week of storage. Their zeta potentials remained consistent, with no signs of oxidation or aggregation detected. Supplementary Fig. 4c indicates that the MXene/CNF/gelatin/GA mixtures, across various ratios and mixture loadings, retained high dispersity. After undergoing a freeze-drying process at –80 °C and 0.3 Pa, these MXene/CNF/gelatin/GA mixtures at different ratios and mixture loadings produced various conductive aerogels. By modifying the MXene/CNF/gelatin/GA ratios and altering the mixture loadings, Supplementary Fig. 5a reveals a non-linear variation in the mechanical properties of conductive aerogels. Similarly, Supplementary Fig. 5b depicts the non-linear shifts in the electrical properties of conductive aerogels, such as electrical resistance, in response to changes in the fabrication parameters.

To establish a comprehensive database linking the fabrication parameters with the end properties of conductive aerogels, over 5300 data points are required, given a step size of 2.0 wt% and four mixture loadings (see our estimation in Supplementary Note 2 and Supplementary Fig. 6). However, building such a dataset is impractical due to time and resource constraints. To overcome this challenge, an integrated platform that leveraged collaborative robotics and AI/ML predictions was developed to acquire high-quality data points and construct a high-accuracy prediction model. By harnessing the model’s prediction capabilities, the development of conductive aerogels with user-designated mechanical and electrical properties was facilitated.

Defining a feasible parameter space through automated pipetting robot and support-vector machine (SVM) classifier

To construct a high-accuracy prediction model, an AI/ML framework was developed and had three critical phases: (1) establishing a feasible parameter space, (2) implementing active learning loops, and (3) synthesizing virtual data points. The rationale of each phase is detailed in Supplementary Note 3. Supplementary Table 1 summarized the descriptors (i.e., labels) used in the prediction model. Supplementary Fig. 7 compares the prediction accuracy of models using different labels to represent the mechanical properties of conductive aerogels.

As illustrated in Fig. 1a, the first phase aimed to define a feasible parameter space using an OT-2 robot and an SVM classifier. The OT-2 robot was commanded to prepare a library of aqueous mixtures with different MXene/CNF/gelatin ratios and mixture loadings (from 2.5 to 10.0 mg mL^–1). Supplementary Movie 1 showcases the OT-2 robot’s efficiency to prepare 264 mixtures in 6 h, with an interval of 10 wt.% for four mixture loadings. Once prepared, these mixtures were vortexed, cast into silicone molds, and then subjected to a freeze-drying process. Afterward, the 264 freeze-dried samples were obtained and then categorized based on their structural integrity and monolithic nature (classification standards in Supplementary Note 4). As shown in the inset of Fig. 1a, classification varied from (1) sizable, intact samples (A-grade), (2) smaller fragmented samples (B-grade), to (3) extensively altered forms with inconsistent pieces (C-grade). As detailed in Fig. 1b and Supplementary Table 2, the collection consisted of 201 A-grade, 49 B-grade, and 14 C-grade samples. Two blind tests were performed by different researchers to maintain unbiased evaluations.

Afterward, these discrete grades served as training data points for a SVM classifier, the goal of which was to distinguish the hyperplanes with maximal margins between the data points at different grades (see Supplementary Note 5). Given a specific MXene/CNF/gelatin ratio, the trained SVM classifier was able to predict the possibility of obtaining an A-grade aerogel at a high accuracy of 95% (examined by a set of testing data points not previously introduced to the SVM classifier, Supplementary Table 3). As shown in Fig. 1c, the SVM classifier produced four heatmaps (one for each mixture loading), illustrating the possibilities of obtaining A-grade aerogels across the entire parameter space. By setting the A-grade possibility threshold at 65%, a feasible parameter space was defined in Supplementary Fig. 8a. Supplementary Fig. 8b shows that the area of the feasible parameter space shrank from 83.7% to 48.6%, as the mixture loading decreased from 10.0 to 2.5 mg mL^–1, respectively. Supplementary Fig. 9 illustrates similar data distribution plots using the MXene and gelatin loadings as the axes. Within the AI/ML framework, the SVM classifier acted as an important filtering unit for the prediction model, and only the MXene/CNF/gelatin ratios that led to A-grade aerogel production were suggested. The SVM classifier effectively eliminated the need of exploring of the unfeasible regions that led to fragile conductive aerogels with scale-up difficulties.

During the robot-assisted mixture preparation, an optional step is to incorporate GA as a crosslinking agent into the MXene/CNF/gelatin mixtures. GA is widely acknowledged as a chemical crosslinker for CNFs⁶⁸, gelatin⁶⁹, and MXene nanosheets^30,36. To investigate possible covalent bonds formed between CNFs and/or MXene nanosheets, two kinds of MXene/CNF aerogels (at the 80/20 ratio and at 10 mg mL^–1) were produced: one incorporated with GA (denoted as “+”) and the other without GA (as “–”). Afterward, X-ray photoelectron spectroscopy (XPS) was adopted to characterize the chemical bonds in two MXene/CNF aerogels. As shown in Fig. 1d, the C 1 s spectrum of the GA-crosslinked aerogel demonstrated the increased intensities of both C–C (at 285 eV) and C = O bonds (at 288 eV), suggesting that the covalent bonds were majorly formed amongst CNFs. Moreover, the Ti 2p XPS spectra provided in Supplementary Fig. 10 reveal that the characteristic Ti–C bonds indicative of MXene integrity are preserved, as there is no evidence of new Ti–C bond formation. This suggests that the MXene nanosheets maintain their structural integrity throughout the aerogel fabrication process, even with the GA introduction. The XPS finding confirms that the intrinsic properties of the MXene nanosheets remained intact after the aerogel fabrication processes.

Constructing a prediction model via active learning loops, data augmentation, and collaborative robots

Within the feasible parameter space, active learning loops and in silico data augmentation were employed to gather representative data points, and a high-accuracy prediction model for conductive aerogels was progressively constructed. During the active learning loops, two collaborative robots, including an OT-2 robot and a UR5e-automated compression tester, were implemented to reduce the workload on human operators and enhance the data acquisition rates.

As illustrated in Fig. 2a, the active learning loops were initiated by commanding the OT-2 robot to prepare 20 aqueous mixtures at random MXene/CNF/gelatin/GA ratios and mixture loadings. Once vortexed, cast in silicone molds, and freeze-dried, the aqueous mixtures yielded the first batch of conductive aerogels. The MXene/CNF/gelatin/GA ratios of these conductive aerogels were recorded as the “composition” labels, while their mixture loadings served as the “loading” labels. Subsequently, the mechanical and electrical properties of these conductive aerogels were characterized. As shown in Fig. 2b, to increase the data acquisition rates, a UR5e robotic arm was integrated with an Instron compression tester to achieve an autonomous testing platform. As demonstrated in Supplementary Movie 2, the UR5e arm was programmed to transfer conductive aerogels continuously from the sample station to the testing station. Once the UR5e arm completed placing a conductive aerogel at the testing station, an audio signal prompted the Instron tester to begin the compression test. After the test was finished, the Instron tester signaled the UR5e arm to remove the conductive aerogel and then position a new one. During the active learning loops, >400 conductive aerogels (3–4 replicates for each data point) were evaluated using the autonomous testing platform, and the total operation time was estimated to be 81 h, averaging about 12 min to test one aerogel sample.

From the stress–strain curve of each conductive aerogel, the compressive stress at 30% strain (abbreviated as \({\sigma }_{30}\)) was characterized, and the average \({\sigma }_{30}\) value from 3–4 aerogel replicates was designated as the “mechanical” label. Next, by using a two-electrode system (with a 1-cm gap between electrodes), the initial electrical resistance of each conductive aerogel (abbreviated as \({R}_{0}\)) was measured, and the average \({R}_{0}\) value from 3–4 aerogel replicates was recorded as the “electrical” label. In short, each kind of conductive aerogel resulted in one data point, which included four “composition” labels, one “loading” label, one “mechanical” label, and one “electrical” label (see Supplementary Table 1). For one active learning loop, 20 new kinds of conductive aerogels were produced, therefore adding 20 data points to the database.

To improve model training efficiency and counteract potential overfitting, the User Input Principle (UIP) method was adopted to synthesize virtual data points (refer to Supplementary Note 6 for detailed description). The creation of virtual data points took place in the vicinity of collected real data points. For instance, Supplementary Fig. 11a, b demonstrate that, with slight variations in the MXene/CNF/gelatin/GA ratios (e.g., 64/24/12/+ vs. 62/26/12/+) led to the conductive aerogels with similar \({\sigma }_{30}\) (10.58 kPa vs. 10.63 kPa) and \({R}_{0}\) values (8.9 Ω vs. 10.1 Ω). Meanwhile, when the replicates of conductive aerogels were characterized, Supplementary Fig. 11c indicates that there were slight measurement variations in \({\sigma }_{30}\) and \({R}_{0}\). To synthesize virtual data points, Gaussian noises were introduced in the proximity of the composition, mechanical, and electrical labels based on our experimental observations. Afterward, both real and virtual data points were utilized as training data points for an ANN-based model using 4-fold cross-validation⁷⁰.

To collect more data points in the next active learning loop, the ANN model assessed the unfamiliarity level of each data point within the feasible parameter space using a hybrid acquisition function termed A Score, represented by Eq. (1)⁷¹,

where \(\hat{L}\) denotes the Euclidean distance between in-model and model-targeted data points and \(\hat{\sigma }\) denotes the ANN model’s prediction variance (as detailed in Supplementary Note 7). The data points with the highest A Scores were the least familiar to the model and pinpointed for experimental validation in the next loop. By extracting the composition and loading labels of pinpointed data points, the OT-2 robot was activated to prepare a new set of MXene/CNF/gelatin/GA mixtures. Once vortexed, cast, and freeze-dried, a new batch of conductive aerogels was produced. Similarly, the \({\sigma }_{30}\) and \({R}_{0}\) values of these conductive aerogels were characterized via the autonomous testing platform and the two-electrode system, respectively. Based on these real data points, virtual data points were synthesized using the UIP method. Upon inputting the real and virtual data points, the ANN model was retrained, re-assessed A Scores, and suggested another set of fabrication parameters for the next active learning cycle.

With the operation of two collaborative robots, the active learning loops were largely facilitated. Each loop took an average of 2.5 days: 2 h dedicated to OT-2 pipetting, 48 h for freeze-drying, 4 h allocated to autonomous testing, and another 4 h for model training. In total, 8 active learning loops were carried out, and 162 kinds of conductive aerogels were stagewise produced (refer to Supplementary Table 4). In this work, we collected 162 real data points during 8 active learning loops. Afterwards, to improve model training efficiency and counteract potential overfitting, the UIP method was adopted to synthesize virtual data points in a 1-to-1000 ratio, thus leading to the generation of ~160,000 virtual data points. Afterward, both real and virtual data points were utilized as training data points for constructing the ANN model using 4-fold cross-validation.

During the active learning loops, the ANN model continued to evolve and was evaluated from two perspectives: (1) the distribution of collected data points and (2) the accuracy of multi-property predictions. First, as shown in Fig. 2c, d and Supplementary Figs. 12, 2D Voronoi tessellation diagrams were plotted to visualize how data points were sequentially collected and distributed within the feasible parameter space. During active learning loops, the ANN model efficiently explored the feasible parameter space and guided experiments towards the unfamiliar regions, effectively mitigating the rise of redundant data clusters.

Second, the accuracy of multi-property predictions was assessed using a set of testing data points, which were never input into the model (see Supplementary Table 5). For each testing data point, the ANN model provided the predicted \({\sigma }_{30}\) and \({R}_{0}\) values based on the “composition” and “loading” labels. Then, the model-predicted \({\sigma }_{30}\) and \({R}_{0}\) values were compared with the actual \({\sigma }_{30}\) and \({R}_{0}\) values of the testing data point. The deviation between model-predicted and actual \({\sigma }_{30}\) values was evaluated using the mean absolute error (MAE), as detailed in Eq. (2),

where N is the cumulative number of testing data points, \({{{{{\rm{predicted}}}}}}\,{\sigma }_{30}^{i}\) is the model-predicted \({\sigma }_{30}\) value based on a testing data point (i), \({\sigma }_{30}^{i}\) is the actual \({\sigma }_{30}\) value of a testing data point (i). On the other hand, the deviation between model-predicted and actual \({R}_{0}\) values were assessed using the mean relative error (MRE), as detailed in Eq. (3),

where N is the cumulative number of testing data points, \({{{{{\rm{predicted}}}}}}\,{R}_{0}^{i}\) is the model-predicted \({R}_{0}\) value based on a testing data point (i), \({R}_{0}^{i}\) is the actual \({R}_{0}\) value of a testing data point (i). Smaller MAE and MRE values indicated higher prediction accuracy, while larger values indicated lower accuracy. By evaluating MAEs and MREs, we were able to assess the model’s prediction accuracy in predicting the mechanical and electrical properties of conductive aerogels from their fabrication parameters.

Throughout 8 active learning loops, the MAE (that assessed the accuracy of \({\sigma }_{30}\) prediction) continually decreased from 2.5 to 1.5 kPa (Fig. 2e, top), and the MRE (that assessed the accuracy of \({R}_{0}\) prediction) decreased from 49.0% to 18.4% (Fig. 2e, bottom). Towards the end of active learning loops, both MAE and MRE values were stabilized and gradually approached toward the measurement variations of \({\sigma }_{30}\) (~1.1 kPa) and \({R}_{0}\) (~10.1%). Among other models based on linear regression, decision tree, gradient-boosted decision tree, random forest algorithms, the ANN model demonstrated the lowest MAE and MRE values (Fig. 2e). Furthermore, without conducting data augmentation, the ANN model presented a higher MAE of >1.9 kPa (for \({\sigma }_{30}\) prediction) and a higher MRE of >37% (for \({R}_{0}\) prediction), due to the model overfitting upon the use of a small database (Fig. 2f). As the virtual-to-real data ratio increased to 100 and 1000, the MAE values decreased to 1.8 kPa and 1.5 kPa, and the MRE values decreased to 21.5% and 18.4%, respectively. In this work, the optimal virtual-to-real data ratio was set to be 1000, which enabled high learning efficiency and still kept the model training time below 4 h. On the other hand, when the virtual-to-real data ratio increased to 5000 and 10,000, the model training time increased to >1 and >2 days, respectively. Finally, the ANN model that demonstrated the lowest MAE and MRE values was selected as “the champion model”, which was deployed the next to automate the design of conductive aerogels with programmable mechanical and electrical properties.

In addition, the selection of a suitable sampling method is important for the construction of an accurate prediction model. Comparative analyses of different sampling methods were conducted: random sampling, Latin hypercube sampling, and active learning sampling (as demonstrated in our study). Supplementary Fig. 13 and Supplementary Table 6 provide details on the three sampling cycles for each method, with five separate physical experiments carried out in each cycle. As shown in Supplementary Fig. 14a, the active learning sampling method outperformed the others, achieving a success rate of >95% in recommending the MXene/CNF/gelatin/GA ratios that resulted in the production of A-grade aerogels. In comparison, random sampling and Latin hypercube sampling yielded lower success rates of 80% and 67%, respectively. After the three sampling cycles, we applied the UIP method to the real data points collected from the different sampling methods and synthesized virtual data points at a ratio of 1-to-1000. Using these real and virtual data points, we trained multiple ANN-based prediction models. As shown in Supplementary Fig. 14b, among all the sampling methods, the prediction model trained on data points from the active learning sampling exhibited superior learning efficacy and enhanced prediction accuracy, achieving the lowest recorded MAE values of 1.1 kPa. Whereas the MAEs from random sampling and Latin hypercube sampling were 5.8 kPa and 5.0 kPa, respectively, after completing three cycles.

Predicting compressive strengths and electrical resistances of conductive aerogels

By leveraging the champion model’s prediction capabilities, two-way design tasks were successfully demonstrated, involving (1) predicting the \({\sigma }_{30}\) and \({R}_{0}\) values of a conductive aerogel from its fabrication parameters and (2) suggesting an ideal set of MXene/CNF/gelatin/GA ratio and mixture loading to produce a conductive aerogel with user-designated characteristics.

First, by selecting different sets of fabrication parameters, various conductive aerogels were fabricated and characterized (recipes #1–#8 in Supplementary Table 7). As evidenced in Fig. 3a, b, the champion model predicted the \({\sigma }_{30}\) and \({R}_{0}\) values of these conductive aerogels accurately based on their “composition” and “loading” labels, and the predicted values were close to the experimentally characterized results. Second, the inverse design of conductive aerogels was automated by the champion model, without the need for iterative optimization experiments. As illustrated in Fig. 3c, two conductive aerogels were targeted with specific property requirements, including (1) high-strength aerogels (\({\sigma }_{30}\) > 10 kPa) and (2) high-strength, conductive aerogels (\({\sigma }_{30}\) > 10 kPa and \({R}_{0}\) < 10 Ω). By inputting these design requests, the champion model performed clustering analyses to pinpoint the most suitable sets of fabrication parameters. By following the model-suggested fabrication parameters, two kinds of conductive aerogels were produced. As demonstrated in Fig. 3d, for the design request #1, the champion model suggested two aerogels (recipes #9–#10 in Supplementary Table 8), both of which demonstrated the \({\sigma }_{30}\) values that were higher than the input requirement of 10 kPa. For the design request #2, the champion model suggested four aerogels (recipes #11–#14 in Supplementary Table 8), showing the average \({\sigma }_{30}\) and \({R}_{0}\) values > 10 kPa and <10 Ω, respectively. The inset of Fig. 3c and Supplementary Fig. 15 show the SEM images of the model-suggested aerogels (recipes #9 and #14). As displayed in the violin plots (Fig. 3e), the achievable \({\sigma }_{30}\) and \({R}_{0}\) values of conductive aerogels spanned widely between 0.1 < \({\sigma }_{30}\) < 16.0 kPa and 10⁰ < \({R}_{0}\) < 10¹⁰ Ω, through navigating the DOFs of MXene/CNF/gelatin/GA ratios and mixture loadings.

SHAP model interpretation and FE simulations to uncover complex fabrication–structure–property correlations

To address the “black box” nature of the champion model, the SHAP model interpretation method was applied to 162 data points collected during active learning loops. SHAP relies on a game theoretic approach and contains a permutation explainer program to explain the output of any AI/ML model⁷². By iterating over complete permutations of the features, the SHAP values are calculated to approximate the contribution of each fabrication parameter to a specific property. A positive SHAP value indicates a positive correlation, and vice versa (see Supplementary Note 8 and Supplementary Fig. 16 for further details). In this study, the SHAP values of MXene, CNF, gelatin, GA loadings, and mixture loading on the \({\sigma }_{30}\) and \({R}_{0}\) values of conductive aerogels were calculated. Figure 4a shows that the SHAP value of mixture loading on \({\sigma }_{30}\) ranged the widest from –1.00 to +0.97 among the others (e.g., MXene loading from –0.28 to +0.28, CNF loading from –0.41 to +0.32, gelatin loading from –0.71 to +0.56, and GA loading from –0.23 to +0.19). The above SHAP results suggest that the mixture loading of aqueous mixture (that affected the density of a conductive aerogel) presented the most significant impact on the mechanical properties.

On the other hand, Supplementary Fig. 17 shows that the SHAP values for MXene loading on \({R}_{0}\) ranged from –0.94 to +0.97, demonstrating the most substantial variability and pronounced impact compared to other factors: CNF loading (–0.41 to +0.65), gelatin loading (–0.83 to +0.94), GA loading (–0.24 to +0.36), and mixture loading (–0.35 to +1.00). These SHAP results highlight that increasing the MXene loading significantly lowered the \({R}_{0}\) of conductive aerogels, marking it as the most influential factor. As detailed in Supplementary Fig. 18, the mixture loading notably correlated positively with the aerogel density. Similarly, increasing the mixture loading, which corresponds to increased aerogel density, had a similar effect on lowering the \({R}_{0}\) of conductive aerogels. However, the influence of mixture loading (or aerogel density) was statistically less significant than that of MXene loading, and it showed a high degree of correlation with the MXene/CNF/gelatin/GA ratio.

To validate the SHAP-identified correlations, additional experiments were conducted in Supplementary Fig. 19. With the MXene/CNF/gelatin/GA ratio fixed at 11/77/12/+, conductive aerogels consistently exhibited high \({R}_{0}\) values with minimal variations across different mixture loadings (ranging from 10.0 to 2.5 mg mL^–1) as demonstrated in Supplementary Fig. 19a. The corresponding SEM images are provided in Supplementary Fig. 19b. Conversely, when the MXene/CNF/gelatin/GA ratio was set to 61/28/11/–, conductive aerogels displayed a significant decrease in their \({R}_{0}\) values but followed a similar trend across different mixture loadings with values ranging from 2.1 to 17.3 Ω (Supplementary Fig. 19a). The corresponding SEM images are provided in Supplementary Fig. 19c. In contrast, the conductive aerogels prepared from the MXene/CNF/gelatin/GA ratio of 43/42/15/–, showed pronounced variations in \({R}_{0}\) values spanning from 7.5 to 228.4 Ω at different mixture loadings (Supplementary Fig. 19a). The corresponding SEM images are provided in Supplementary Fig. 19d. These results show that the MXene loading exhibited a higher impact on the \({R}_{0}\) of conductive aerogels than the mixture loading.

Next, to investigate strong correlations between mixture loading and \({\sigma }_{30}\) value, four conductive aerogels were fabricated at the same MXene/CNF/gelatin/GA ratio of 80/20/0/– but at different mixture loadings (from 2.5 to 10.0 mg mL^–1). As shown in Fig. 4b, as the mixture loadings increased, the \({\sigma }_{30}\) values of conductive aerogels rose significantly from 0.2 kPa to 5.9 kPa. Four other conductive aerogels were produced at the same mixture loading of 10.0 mg mL^–1 but with various MXene/CNF/gelatin/GA ratios (from 80/20/0/– to 20/80/0/–). Despite the difference in aerogel composition, the \({\sigma }_{30}\) values exhibited only a minor shift to 7.5 kPa from 5.9 kPa. Supported by SHAP analyses and experimental results, it was determined that adjusting the mixture loading level was a more effective method for tuning the compression resilience of a conductive aerogel (e.g., \({\sigma }_{30}\)).

To delve deeper into the mechanistic effects of mixture loadings on the mechanical properties of conductive aerogels, three FE models were constructed. These FE models represented the conductive aerogels at the same MXene/CNF/gelatin/GA ratio (80.0/20.0/0.0/–) yet at different mixture loadings (10.0, 7.5, 5.0 mg mL^–1). These FE models were named as high-, medium-, and low-density aerogel models. Extracted from the SEM images in Fig. 4c and summarized in Supplementary Table 9, several structural features of conductive aerogels, such as pore dimensions, wall thicknesses, and fracture densities, were input to construct these FE models using a commercial package of ABAQUS/CAE 2020. In the FE simulations, the microstructures of conductive aerogels were represented as the 4 × 4 supercells containing two-dimensional staggered lattices using second-order plane strain elements, and the periodic boundary conditions were imposed. Then, wall discontinuities were randomly introduced into the FE models to account for the structural imperfections of conductive aerogels. Supplementary Note 9, Supplementary Fig. 20, and 21 provide further details regarding the construction of FE models. Next, by exerting a vertical compressive strain of 30%, the \({\sigma }_{30}\) values of three FE models were simulated in Fig. 4b, showing good agreement with the experimentally characterized \({\sigma }_{30}\) values. Figure 4d showcases the FE models of conductive aerogels under 30% compression to provide insights regarding internal displacements and localized stress distributions. As compared in Fig. 4e, the FE models under 30% compression cohered with the SEM observations of conductive aerogels at their compressed states.

The high-density aerogel exhibited small, closely packed pores (with the average size of 18.2 × 6.4 µm²) and thus allowed for uniform stress distributions upon compression, largely suppressing internal displacements of compartments. In the high-density aerogel, the localized stress tended to concentrate at the corners of each compartment, while the MXene-based walls were robust enough (with Young’s modulus at 3.4 GPa) to prevent significant deformation toward cracking. On the other hand, as the mixture loading decreased, the medium- and low-density aerogels had larger and wider pores (28.3 × 17.8 and 39.1 × 19.0 µm²), which were less efficient to transmit vertical stresses to neighboring compartments. As a result, the pores were likely to deform and distort upon the localized stress, resulting in significant internal displacements of compartments. Through the combined use of SHAP analyses, experimental validation, and FE simulations, we provided a promising solution to the “black box” challenges often associated with AI/ML predictions, enhancing the champion model’s interpretability.

Machine intelligence accelerated discovery of strain-insensitive conductive aerogels for wearable thermal management

Conductive aerogels offer promising applications in personal thermal management, owing to their lightweight feature, high electrical conductivity, and thermal insulation properties¹⁴. Fig. 5a outlines the machine intelligence accelerated design process to fabricate a strain-insensitive conductive aerogel suitable for wearable heating applications. First, two property requirements were considered: (1) compatible compressive strength with current filling materials (\({\sigma }_{30}\) ~ 4–8 kPa) and (2) high electrical conductivity for efficient Joule heating (\({R}_{0}\) < 20 Ω). Upon inputting these design requests, the champion model was able to suggest multiple sets of fabrication parameters, and various conductive aerogels that met two property requirements were fabricated (see Supplementary Table 10).

Next, an additional criterion of low pressure sensitivity was set to discover a strain-insensitive conductive aerogel, ensuring strain-stable Joule heating performance under repetitive compression. The definition of pressure sensitivity is provided in Eq. (4),

As demonstrated in the \({R}_{0}\)–sensitivity profiles (Fig. 5b), the conductive aerogel based on recipe #16 was selected (at the MXene/CNF/gelatin/GA ratio of 78/13/9/– and at the mixture loading of 7.5 mg mL^–1). The model-suggested conductive aerogel exhibited a \({\sigma }_{30}\) value of 4.0 kPa, a low \({R}_{0}\) value of 1.7, and an ultralow pressure sensitivity of 0.02 kPa^–1. Figure 5c demonstrates that the relative resistance changes of the strain-insensitive conductive aerogel was only 0.9% under 100 cycles of 20% compression. Next, the Joule heating performance of the strain-insensitive conductive aerogel was investigated by applying various voltages, as evidenced in the measured temperature–time profiles (Fig. 5d). At the applied voltages of 0.5, 1.0, 1.5, and 2.0 V, the strain-insensitive conductive aerogel demonstrated sharp temperature increases up to 29, 37, 51, and 70 °C, respectively, within 300 s. As shown in Supplementary Fig. 22, the strain-insensitive conductive aerogel displayed a linear relationship between the maximum temperature and the square of the applied voltage, well adhering to Joule’s law.

To further assess the Joule heating performance under compression, the strain-insensitive conductive aerogel at both relaxed and 20% compressed states was subject to 100 heating cycles at 1.0 and 1.5 V. As shown in Fig. 5e, the conductive aerogels demonstrated strain-unresponsive heating/cooling profiles, with stable average temperature variations for 100 heating cycles. Such efficient and strain-stable Joule heating performance was well-suited for wearable heating applications. Additionally, we conducted thermal conductivity measurements to assess the thermal insulation properties of the strain-insensitive conductive aerogel. The density and thermal insulation performance of the strain-insensitive conductive aerogel were characterized as 10.1 mg cm^–3 and 0.034 W mK^–1, respectively. Compared with other thermal insulation materials in Supplementary Fig. 23, the strain-insensitive conductive aerogel offered lightweight features, competitive thermal insulation properties, and efficient Joule heating performance. To demonstrate its practical exploitation, multiple strain-insensitive conductive aerogels with the dimensions of 5.0 × 5.0 × 1.0 cm³ were inserted into a commercial jacket. Powered by a portable battery system (at 1.5 V), the aerogel-incorporated jacket was heated on demand to warm the subregion of a volunteer (thermal images in Fig. 5f).

Compared with the state-of-the-art works of conductive aerogels, our robotics/ML-integrated workflow demonstrates multiple advancements, as summarized in Supplementary Table 11^73,74,75, 12^{2,8,19,20,29,33,76,77,78,79,80,81,82,83,84,85}, and 13^{8,19,20,29,33,76,77,78,79,80,81,82}. The first advancement is to construct a prediction model with high accuracy across the entire parameter space. As detailed in Supplementary Table 11, the state-of-the-art works typically focus on pinpointing an optimal set of fabrication parameters to maximize device performance or identifying precise conditions necessary for successful chemical reactions. While some of these works also utilize high-throughput robotic platforms to navigate a parameter space with multiple degrees of freedom (DOFs), they do not intend to examine data points that stray from the primary objectives, such as determining the most effective parameter combination or sequence of reaction steps. Consequently, if the design requirements shift—for instance, the synthesis of a new chemical compound—new round(s) of optimization experiments would be necessary. This requirement for additional experimentation may not align well with demands for rapid customization. In contrast to traditional methods, our integrated workflow that combines collaborative robotics with SVM classification, active learning loops, and data augmentation, resulted in a prediction model that consistently delivers high accuracy across the entire parameter space. Consequently, to respond to diverse design requests for customization, our prediction model can automatically identify the optimal fabrication parameters, eliminating the need for repeated optimization experiments.

The second advancement is to automate the design of conductive aerogels with programmable properties. Through the robotics/ML-integrated workflow, the prediction model can perform two-way design tasks: (1) predicting the physicochemical properties of conductive aerogels based on their fabrication parameters and (2) automating the inverse design of conductive aerogels to align with specific property requirements. The prediction model is well-suited for crafting conductive aerogels with customizable mechanical and electrical properties. Given the laborious nature of self-assembly and the absence of robotic systems available for fully automating freeze drying processes, our prediction model can directly identify viable and optimal fabrication parameters, without the need for iterative optimization experiments. Compared with the state-of-the-art works of conductive aerogels (see Supplementary Table 12), our automatic design method demonstrates superior efficiency in discovering conductive aerogels with programmable properties.

The third advancement is to elucidate data-driven design principles in complex material systems. Supplementary Table 13 presents a comparison of our work with multiple studies focusing on MXene-based aerogels, including MXene/CNT, MXene/rGO, MXene/ANF, and MXene/CNF. Traditionally, these state-of-the-art works explore the intricate correlations between fabrication parameters and aerogel properties through the one-factor-at-a-time (OFAT) design of experiment (DoE) method. The OFAT DoE method has yielded diverse design insights across different MXene-based aerogel systems. For example, Zeng et al., Xu et al., Jiang et al., and Wang et al. groups discovered that increasing the MXene loading decreased the compressive strength and electrical resistance of conductive aerogels^33,76,80,81. In contrast, our research harnesses the synergy of collaborative robotics and advanced AI/ML predictive analytics. By constructing a robust prediction model followed by model interpretation (e.g., SHAP), we can investigate several component–property correlations and generalize design principles with statistical significance, offering a more systematic understanding of complex material systems.